Continuous-discontinuous fiber-reinforced polymers: an integrated engineering approach 9781569906927, 9781569906934, 1569906920

Table of contents :
Cover......Page 1
Continuous–Discontinuous Fiber-Reinforced Polymers:An Integrated Engineering Approach......Page 4
© Carl Hanser Verlag, Munich 2019......Page 5
Progress in Polymer Processing (PPP) Series......Page 6
Foreword......Page 8
Acknowledgments......Page 10
Preface......Page 12
List of Contributors......Page 14
List of Symbols......Page 20
List of Acronyms......Page 22
Contents......Page 24
1 Introduction toContinuous–DiscontinuousFiber-Reinforced PolymerComposites......Page 30
2 Manufacturingof CoDiCoFRP......Page 40
3 Characterizationof CoDiCoFRP......Page 130
4 Simulation of SheetMolding Compound (SMC)and Long Fiber-ReinforcedThermoplastics (LFTP)......Page 179
5 Designing CoDiCoFRPStructures......Page 277
6 Compression Moldingof the DemonstratorStructure......Page 325
Index......Page 343

Citation preview

Thomas Böhlke · Frank Henning Andrew Hrymak · Luise Kärger Kay A. Weidenmann · Jeffrey T. Wood (Eds.) Musa R. Kamal (Series Editor)

Continuous – Discontinuous Fiber-Reinforced Polymers An Integrated Engineering Approach

Design Simulation

Characterization

Technology

POLYMER PROCESSING SOCIETY

Böhlke / Henning / Hrymak / Kärger / Weidenmann / Wood (Eds.) Continuous–Discontinuous Fiber-Reinforced Polymers

Thomas Böhlke (Ed.) Frank Henning (Ed.) Andrew Hrymak (Ed.) Luise Kärger (Ed.) Kay A. Weidenmann (Ed.) Jeffrey T. Wood (Ed.)

Continuous–Discontinuous Fiber-Reinforced Polymers An Integrated Engineering Approach

With Contributions by: A. Albers, W. Altenhof, F. Ballier, T. Böhlke, D. Bücheler, V. Butenko, C. Denniston, P. Elsner, B. Fengler, J. Fleischer, J. Görthofer, P. Gumbsch, A. Helfrich, F. Henning, M. Hohberg, J. Hohe, A. Hrymak, S. Ilinzeer, L. Kärger, L. Kehrer, T. Kuboki, D. Kupzik, G. Lanza, J. Lienhard, N. Meyer, B. Nestler, T. D. Pallicity, C. B. Park, P. Pinter, A. Rizvi, M. Schäferling, M. Schemmann, D. Schneider, M. Schober, L. Schöttl, L. Schulenberg, V. Schulze, F. K. Schwab, T. Seelig, M. Spadinger, M. Thompson, A. Trauth, K. A. Weidenmann, J. T. Wood, F. Zanger

Hanser Publishers, Munich

Hanser Publications, Cincinnati

The Editors: Thomas Böhlke, Institute for Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Frank Henning, Fraunhofer Institute for Chemical Technology (ICT), Pfinztal, Germany; Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Andrew Hrymak, Department of Chemical and Biochemical Engineering, University of Western Ontario, Canada Luise Kärger, Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Kay A. Weidenmann, Institute for Applied Materials – Materials Science and Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Jeffrey T. Wood, Department of Mechanical and Materials Engineering, University of Western Ontario, Canada

Distributed in the Americas by: Hanser Publications 414 Walnut Street, Cincinnati, OH 45202 USA Phone: (800) 950-8977 www.hanserpublications.com Distributed in all other countries by: Carl Hanser Verlag Postfach 86 04 20, 81631 Munich, Germany Fax: +49 (89) 98 48 09 www.hanser-fachbuch.de The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. The final determination of the suitability of any information for the use contemplated for a given application remains the sole responsibility of the user. Library of Congress Control Number: 2019947698 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, without permission in writing from the publisher. © Carl Hanser Verlag, Munich 2019 Editor: Dr. Julia Diaz-Luque Production Management: Jörg Strohbach Coverconcept: Marc Müller-Bremer, www.rebranding.de, Munich Coverdesign: Max Kostopoulos Typesetting: le-tex publishing services GmbH, Leipzig Printed and bound by Druckerei Hubert & Co GmbH und Co KG BuchPartner, Göttingen Printed in Germany ISBN: 978-1-56990-692-7 E-Book ISBN: 978-1-56990-693-4

Progress in Polymer Processing (PPP) Series Musa R. Kamal, Series Editor McGill University, Canada

Editorial Advisory Board

Jean-FranÇois Agassant CEMEF, École des Mines France

José Covas University of Minho Portugal

M. Cengiz Altan University of Oklahoma U.S.A.

Furong Gao Hong Kong University of Science & Technology Hong Kong

Patrick Anderson Eindhoven University of Technology Netherlands Satinath Bhattacharya RMIT University Australia Mosto Bousmina Hassan II Academy of Science and ­Technology Morocco Philippe Cassagneau Université Claude Bernard France Shia-Shih Chen Chung Yuan Christian University Taiwan Phil Coates University of Bradford United Kingdom

Frank Henning Fraunhofer-Institut für Chemische ­Technologie (ICT) Germany Andrew Hrymak Western University Canada Sadhan Jana University of Akron U.S.A. Dilhan Kalyon Stevens Institute of Technology U.S.A. Samuel Kenig Shenkar College Israel Takeshi Kikutani Tokyo Institute of Technology Japan

Ica Manas-Zloczower Case Western Reserve University U.S.A.

Mark Smith Carl Hanser Verlag GmbH & Co. KG Germany

Masami Okamoto Toyota Technological Institute Japan

Giuseppe Titomanlio Università degli Studi di Salerno Italy

Chul B. Park University of Toronto Canada

Lih-Sheng (Tom) Turng University of Wisconsin U.S.A.

Luiz A. Pessan Universidade Federal de São Carlos Brazil

John Vlachopoulos McMaster University Canada

Changyu Shen Dalian University of Technology China

Foreword

The editors are deeply grateful to Dr. Tarkes Dora Pallicity for his exceptional commitment to this collective work and for the very effectively organized coordination in gathering and arranging all information for the potential audience. Dr. Tarkes Dora Pallicity has played one of the key roles in this book by coordinating and unifying all the contributions made by the authors from Germany and Canada within the International Research Training Group (IRTG) consortium. He is currently a post-doctoral employee within the IRTG at the Institute of Engineering Mechanics (ITM), Karlsruhe Institute of Technology (KIT), Karlsruhe.  He received his doctoral degree from Indian Institute of Technology Madras (2017), postgraduate degree from the National Institute of Technology, Trichy (2011), and undergraduate degree in Mechanical Engineering from the Biju Patnaik University of Technology (2009), Rourkela, India. His research interests are in the area of multi-physics and multi-scale simulations. He is currently working in the area of multi-scale simulations of residual stress in fiber-reinforced composites during composite processing. His doctoral research work was in the area of the measurement and simulation of residual stress in an optical glass lens manufactured by a precision glass molding process.

Acknowledgments

This volume summarizes the research of the first generation of doctoral researchers of the International Research Training Group “Integrated engineering of continuous–discontinuous long fiber-reinforced polymer structures” (GRK2078) from April 2015 to March 2018. This research was fully funded by the German Research Foundation (DFG). This financial support is gratefully acknowledged. The editors of the book sincerely thank Prof. Musa R. Kamal (Editor of Progress in Polymer Processing (PPP) series) for the opportunity to publish this book as part of the PPP series. We are also thankful to Hanser Publishers and Dr. Mark Smith (Editorial Office, Hanser Publishers) for their constant and efficient support. Finally, all authors gratefully acknowledge the infrastructural support by Fraunhofer Institute of Chemical Technology (ICT) within the research activities of the research training group. Thomas Böhlke Frank Henning Andrew Hrymak Luise Kärger Kay A. Weidenmann Jeffrey T. Wood

Preface

Hybrid materials, i.e., composites made or joined from several materials, including fiber-reinforced composites with different fiber architectures, play an increasingly important role in industrial applications. The general aim of a hybrid lightweight design is the mass reduction of lightweight structures and simultaneously the increase of performance of the construction, which is reflected in a higher strength, stiffness, or in an improved fatigue strength. Nevertheless, the combination of different materials in hybrid composites results in the evolution of a process-related, hierarchical microstructure, which defines the composite’s performance. Hence, designing high performance hybrid materials needs a holistic approach in the interaction between product design, processing technologies, material science, and engineering mechanics. The relevance of hybrid materials in lightweight structures in industry has increased during the last years. The BMW electric car concept featuring a CFRPbased life module and the use of composites in the aircraft industry are prominent examples for the enhanced used of high-performance composites in vehicle structures. Composite use in aircraft cumulates today in the design of the Boeing 787 featuring a composite-based fuselage concept. Nevertheless, such designs mainly based on the use of continuous carbon fibers are expensive in comparison to metalbased solutions and the design freedom is also limited. Consequently, hybrids based on a combination of cost-efficient long fiber-reinforced plastics and highperformance continuous fiber-reinforced plastics – so-called continuous–discontinuous fiber-reinforced polymers (CoDiCoFRP) – can help to overcome disadvantages and enables an economical lightweight design approach. In this book, the editors present the results of a transatlantic research cooperation under the leadership of Karlsruhe Institute of Technology (KIT), Germany, and University of Western Ontario, Canada, directly focusing on the new material class of CoDiCoFRP bringing together scientists from production science and development, lightweight technology, mechanics, and material science. This International Research Training Group, “Integrated engineering of continuous-discontinuous long fiber-reinforced polymer structures” (GRK2078), has been fully funded by the German Research Foundation (DFG).

XII

Preface

Divided between thematic chapters on technology (Chapter  2), characterization (Chapter 3), simulation (Chapter 4), and design (Chapter 5), the results from the first generation of doctoral researchers at KIT are presented. Especially, Chapter 6, on establishing the process chain for a demonstrator product, clearly shows the benefit of very strong interactions between all disciplines involved to realize a holistic approach. Thomas Böhlke Frank Henning Andrew Hrymak Luise Kärger Kay A. Weidenmann Jeffrey T. Wood

List of Contributors

Albert Albers Institute for Product Engineering, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany William Altenhof Mechanical, Automotive and Materials Engineering, University of Windsor, Canada Fabian Ballier wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Thomas Böhlke Institute for Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karls­ruhe, Germany David Bücheler Fraunhofer Institute for Chemical Technology, Pfinztal, Germany Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Viktoriia Butenko Institute of Product Engineering, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Colin Denniston Department of Applied Mathematics and Department of Physics and Astronomy, University of Western Ontario, Canada Peter Elsner Fraunhofer Institute for Chemical Technology, Pfinztal, Germany Institute for Applied Materials – Materials Science and Engineering, Karlsruhe In­ stitute of Technology (KIT), Karlsruhe, Germany

XIV

List of Contributors

Benedikt Fengler Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Jürgen Fleischer wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Johannes Görthofer Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Peter Gumbsch Fraunhofer Institute for Mechanics of Materials IWM, Germany Institute for Applied Materials – Computational Materials Science, Karlsruhe Insti­ tute of Technology (KIT), Karlsruhe, Germany Anton Helfrich wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Frank Henning Fraunhofer Institute for Chemical Technology, Pfinztal, Germany Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Martin Hohberg Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Jörg Hohe Fraunhofer Institute for Mechanics of Materials IWM, Germany Andrew Hrymak Deptartment of Chemical and Biochemical Engineering, University of Western On­ tario, Canada Sergej Ilinzeer Fraunhofer Institute for Chemical Technology, Pfinztal, Germany Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Luise Kärger Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

List of Contributors

Loredana Kehrer Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Takashi Kuboki Department of Mechanical and Materials Engineering, University of Western On­ tario, Canada Daniel Kupzik wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Gisela Lanza wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Jörg Lienhard Fraunhofer Institute for Mechanics of Materials IWM, Germany Nils Meyer Institute of Vehicle System Technology, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Britta Nestler Institute for Applied Materials – Computational Materials Science, Karlsruhe Insti­ tute of Technology (KIT), Karlsruhe, Germany Tarkes Dora Pallicity Institute for Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karls­ruhe, Germany Chul B. Park Department of Mechanical and Industrial Engineering, University of Toronto, Canada Pascal Pinter Institute for Applied Materials – Materials Science and Engineering, Karlsruhe In­ stitute of Technology (KIT), Karlsruhe, Germany Ali Rizvi Department of Mechanical and Industrial Engineering, University of Toronto, Canada Marielouise Schäferling wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany

XV

XVI

List of Contributors

Malte Schemmann Institute for Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karls­ruhe, Germany Daniel Schneider Institute for Applied Materials – Computational Materials Science, Karlsruhe Insti­ tute of Technology (KIT), Karlsruhe, Germany Michael Schober Fraunhofer Institute for Mechanics of Materials IWM, Germany Institute for Applied Materials – Computational Materials Science, Karlsruhe Insti­ tute of Technology (KIT), Karlsruhe, Germany Ludwig Schöttl Institute for Applied Materials – Materials Science and Engineering, Karlsruhe In­ stitute of Technology (KIT), Karlsruhe, Germany Lukas Schulenberg Fraunhofer Institute for Mechanics of Materials IWM, Germany Institute of Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Ger­ many Volker Schulze wbk Institute of Production Science and Institute for Applied Materials – Materials Science and Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Ger­ many Felix K. Schwab Institute for Applied Materials – Computational Materials Science, Karlsruhe Insti­ tute of Technology (KIT), Karlsruhe, Germany Thomas Seelig Institute of Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Ger­ many Markus Spadinger Institute of Product Engineering, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany Michael Thompson McMaster Manufacturing Research Institute (MMRI), Department of Chemical En­ gineering, McMaster University, Canada

List of Contributors

Anna Trauth Institute for Applied Materials – Materials Science and Engineering, Karlsruhe In­ stitute of Technology (KIT), Karlsruhe, Germany Kay A. Weidenmann Institute for Applied Materials – Materials Science and Engineering, Karlsruhe In­ stitute of Technology (KIT), Karlsruhe, Germany Jeffrey T. Wood Department of Mechanical and Materials Engineering, University of Western On­ tario, Canada Frederik Zanger wbk Institute of Production Science, Karlsruhe Institute of Technology (KIT), Karls­ ruhe, Germany

XVII

List of Symbols

Symbol

Definition

Symbol

Definition

α

Coefficient of thermal expansion

d

Scalar damage variable

β

Coefficient of chemical shrinkage

Ef

Elastic modulus of the fiber

"

Infinitesimal strain tensor

Em

Elastic modulus of the matrix

‌ "

Infinitesimal effective strain tensor

f(n)

"cu

Curing strain tensor

Fiber orientation distribution function

"e

Elastic strain tensor

n

Fiber orientation

"th

Thermal strain tensor

N

"v

Viscous strain tensor

Fiber orientation tensor of second order

θ

Absolute temperature

ℕ

Fiber orientation tensor of fourth order

θg

Glass transition temperature

νf

Poisson’s ratio of the fiber

ℙ1

First isotropic projector tensor

νm

Poisson’s ratio of the matrix

ℙ2

Second isotropic projector tensor

σ – σ

Cauchy stress tensor

ρ

Mass density

τ

Relaxation time

a, b, A, B…

Scalar quantities

a, b, c, …

First-order tensors

A, B, C, …

Second-order tensors

, , ,…

Fourth-order tensors



Strain localization tensor



Stress localization tensor

cf

Fiber volume fraction

cm

Matrix volume fraction



Stiffness tensor

f

Stiffness tensor for fiber

m – 

Stiffness tensor for matrix

Effective Cauchy stress tensor

Effective stiffness tensor

I

Second-order identity tensor



Fourth-order identity tensor

q q⋅

Degree of cure

R

Universal gas constant

t

Time

u

Displacement vector



Viscosity tensor

Curing rate

List of Acronyms

Acronym

Expanded form

Acronym

Expanded form

2D

Two-dimensional

IAM-WK

3D

Three-dimensional

Institute for Applied Materials – Materials Science and Engineering

CT

Computed tomography

IAM-CMS

CoFRP

Continuous fiber-reinforced polymer

Institute for Applied Materials – Computational Materials Science

ICT

CoDiCoFRP

Discontinuous fiber-reinforced polymer with continuous fiber

Fraunhofer Institute for Chemical Technology

IFM

Institute of Mechanics

CoDiCoFRTP

Discontinuous fiber-reinforced thermoplastic with continuous fiber

IPEK

Institute of Product Engineering

ITM

Institute of Engineering Mechanics

CoDiCoFRTS

Discontinuous fiber-reinforced thermoset with continuous fiber

IWM

Fraunhofer Institute for Mechanics of Materials IWM

CoFRTP

Continuous fiber-reinforced thermoplastic

KIT

Karlsruhe Institute of Technology

LFTP

CoFRTS

Continuous fiber-reinforced thermoset

Long fiber-reinforced thermoplastic

PA6

Polyamide-6

Discontinuous fiber-reinforced polymer

RVE

Representative volume element

SMC

Sheet molding compound Thermoplastic material

DiCoFRP DiCoFRTS

Discontinuous fiber-reinforced thermoset

TP TS

Thermoset material

DiCoFRTP

Discontinuous fiber-reinforced thermoplastic

UPPH

Unsaturated polyester polyurethane hybrid

FAST

Institute of Vehicle System Technology

FEM

Finite element method

FFT

Fast Fourier transformation

FODF

Fiber orientation distribution function

FOD

Fiber orientation distribution at material point

FPC

Fraunhofer Project Center

GF

Glass fiber

UoW

University of Windsor

UT

University of Toronto

UWO

University of Western Ontario

wbk

Institute of Production Science

Contents

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

VII IX XI XIII XIX XXI

Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Thomas Böhlke, Andrew Hrymak, Luise Kärger, Tarkes Dora Pallicity, Kay A. Weidenmann, Jeffrey T. Wood

1.1 Fiber-Reinforced Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 About IRTG GRK2078 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Compression Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Constituent Materials of CoDiCoFRTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.1 Thermoset Matrix Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4.2 Fiber Reinforcements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Demonstrator Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Manufacturing of CoDiCoFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 David Bücheler, Frank Henning, Andrew Hrymak 2.1.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

XXIV Contents

2.2 Processing of CoDiCo Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 David Bücheler 2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Material and Process Development . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.3 Characterization and Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Automated Integrated Handling and Preforming . . . . . . . . . . . . . . . . . . . 25 Daniel Kupzik, Fabian Ballier, Jürgen Fleischer 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.2 Grippers in Composite Production . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.3 Automated Placement of Grippers in Handling Systems . . . . . . . 28 2.3.4 Prepreg-Specific Handling Tasks in Gripper Design . . . . . . . . . . . 31 2.3.5 Demonstrator Units for Integrated Handling and Preforming . . . 42 2.3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC . . . . 45 Marielouise Schäferling, Gisela Lanza, Michael Thompson 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.4.2 Defects in SMC and Unidirectional Prepregs . . . . . . . . . . . . . . . . . 46 2.4.3 Classification of Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.4 Measuring Methods and Testing Techniques . . . . . . . . . . . . . . . . . 48 2.4.5 Multi-Sensor System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4.6 Data Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.4.7 Evaluation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4.8 Effects of Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5 Machining of CoDiCoFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Anton Helfrich, Frederik Zanger, Volker Schulze 2.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.5.2 Experimental Study of the Machining of CoDiCoFRP . . . . . . . . . . 65 2.5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.6 Foaming of Microfibrillar Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Ali Rizvi, Chul B. Park 2.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.6.2 Fibril Formation during Blending . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2.6.3 Uniaxial Extensional Flow Response of Fibrillar Blends . . . . . . . . 83 2.6.4 Linear Viscoelastic Shear Response of Fibrillar Blends . . . . . . . . 86 2.6.5 Effect of Fibers on the Crystallization of Polymers . . . . . . . . . . . . 87 2.6.6 Role of Crystallization in Foaming . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.6.7 Foaming of Fibrillated Blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 2.6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Contents

3 Characterization of CoDiCoFRP . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Kay A. Weidenmann 3.1.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.1.2 Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.2 Interlaminar Fracture Analysis of Consolidated GF-PA6-Tapes . . . . . . . . 104 Michael Schober, Jörg Hohe, Peter Gumbsch, Takashi Kuboki 3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.2.2 Sample Manufacturing and Testing . . . . . . . . . . . . . . . . . . . . . . . . 105 3.2.3 Results of the Fracture Toughness Experiments . . . . . . . . . . . . . . 109 3.2.4 Analysis of the Microstructure and Crack-Initiating Factors . . . . 112 3.2.5 Assessment of the Physical Experiments by Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 3.3 Microstructure Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Pascal Pinter, Kay A. Weidenmann, Peter Elsner 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.3.2 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 3.3.3 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3.3.4 Orientation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 3.3.5 Fiber Volume Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 3.3.6 Fiber Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 3.3.7 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 3.4 Mechanical Characterization of HybridContinuous–Discontinuous Glass/­Carbon Fiber Sheet Molding Compound Composites . . . . . . . . . . 134 Anna Trauth, William Altenhof, Kay A. Weidenmann 3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 3.4.2 Material Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 3.4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4 Simulation of Sheet Molding Compound (SMC) and Long Fiber-­Reinforced Thermoplastics (LFTP) . . . . . . . . . . . . . . . . . . 151 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Thomas Seelig, Thomas Böhlke 4.1.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.1.2 Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

XXV

XXVI Contents

4.2 Rheological Characterization and Process Simulation of SMC . . . . . . . . 153 Martin Hohberg, Luise Kärger, Frank Henning, Andrew Hrymak 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.2.2 Rheological Measurements and Models . . . . . . . . . . . . . . . . . . . . . 158 4.2.3 3D Process Simulation of SMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.3 Phase-Field Modeling of the Curing Process in Fiber-Reinforced Thermosets on a Microscale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Felix K. Schwab, Daniel Schneider, Colin Denniston, Britta Nestler 4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.3.2 Microscale Simulation on the Basis of the Phase-Field Method . . 169 4.3.3 Modeling the Curing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 4.3.4 Simulating the Curing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 4.4 Multiscale Finite Element Simulation of Residual Stress in Laminates during Cure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Tarkes Dora Pallicity, Thomas Böhlke 4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.4.2 Thermo-Chemo-Mechanical Modeling of CoFRTS Laminates . . . . 185 4.4.3 Implementation in Finite Element Simulation . . . . . . . . . . . . . . . . 187 4.4.4 Validation of Evolution of Residual Stress in Laminates at the Macroscale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 4.4.5 Microscale Simulation of Residual Stress in Laminates . . . . . . . . 191 4.4.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 4.4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 4.5 Micromechanical Material Modeling and Experimental Characterization of DiCo SMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Loredana Kehrer, Jeffrey T. Wood, Thomas Böhlke 4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 4.5.2 Characterization of DiCo UPPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 4.5.3 Prediction of Thermo-Elastic Material Behavior . . . . . . . . . . . . . . 202 4.5.4 Comparison of Simulation Results and Experimental Data . . . . . 205 4.5.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 4.6 Mean-Field Damage Modeling of DiCoFRTS . . . . . . . . . . . . . . . . . . . . . . . 209 Malte Schemmann, Johannes Görthofer, Thomas Seelig, Andrew Hrymak, Thomas Böhlke 4.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 4.6.2 Continuum Mechanical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 4.6.3 Parameter Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 4.6.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 4.6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Contents

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic . . . . . . . . . . 224 Lukas Schulenberg, Thomas Seelig, Jörg Lienhard 4.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4.7.2 Material and Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 4.7.3 Material Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 4.7.4 Parameter Identification and Model Verification . . . . . . . . . . . . . . 231 4.7.5 Quasi-Static Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 4.7.5.1 Simulations of Dynamic Tests . . . . . . . . . . . . . . . . . . . . . . 234 4.7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

5 Designing CoDiCoFRP Structures . . . . . . . . . . . . . . . . . . . . . . . . 249 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Luise Kärger 5.1.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 5.1.2 Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 5.2 Production-Oriented Dimensioning of Local Patches under Consideration of Distortion and Manufacturing Constraints . . . . 252 Benedikt Fengler, Luise Kärger, Frank Henning, Andrew Hrymak 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.2.2 Draping Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 5.2.3 Curing and Warpage Simulation Method . . . . . . . . . . . . . . . . . . . . 256 5.2.4 Multi-Objective Patch Optimization Algorithm with Embedded Draping and Curing Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 5.2.5 Application Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 5.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 5.3 A Process-Related Topology Optimization Method to Design DiCoFRP Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Markus Spadinger, Albert Albers 5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 5.3.2 State of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 5.3.3 Influence of Material Orientations on Topology Optimization Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 5.3.4 Coupled Optimization Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 5.3.5 Application Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 5.3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 5.4 CoDiCo-FiberFox – Decision-Support Systemin Early Phases of Product Development with Fiber-Reinforced Composites . . . . . . . . . . . . . . . . . . . 276 Viktoriia Butenko, Albert Albers 5.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 5.4.2 Design Guidelines for FRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 5.4.3 Demand for Topics and Content in Design Guidelines for FRP . . 281

XXVII

XXVIII Contents

5.4.4 Development of a Reference Design Guideline . . . . . . . . . . . . . . . 283 5.4.5 CoDiCo-FiberFox – Decision-Support System . . . . . . . . . . . . . . . . . 287 5.4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

6 Compression Molding of the Demonstrator Structure . . . . . . . 297 Johannes Görthofer, Nils Meyer, Ludwig Schöttl, Anna Trauth, Malte Schemmann, Pascal Pinter, Benedikt Fengler, Sergej Ilinzeer, Martin Hohberg, Tarkes Dora Pallicity, Luise Kärger, Kay A. Weidenmann, Peter Elsner, Frank Henning, Andrew Hrymak, Thomas Böhlke

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 6.2 Design and Manufacturing Technology of the Demonstrator . . . . . . . . . 299 6.3 Compression Molding Simulation, Experimental Validation and Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 6.3.1 Flow Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 6.3.2 Mapping of Flow Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 303 6.3.3 Microstructure Characterization Using µCT Volume Images . . . . 304 6.3.4 Mapping of Orientation Tensor N . . . . . . . . . . . . . . . . . . . . . . . . . . 305 6.3.5 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 6.4 Structural Simulation and Its Experimental Validation . . . . . . . . . . . . . 307 6.4.1 Structural Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 6.4.2 Experimental Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 6.4.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

1

Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites Thomas Böhlke, Andrew Hrymak, Luise Kärger, Tarkes Dora Pallicity, Kay A. Weidenmann, Jeffrey T. Wood

„„1.1 Fiber-Reinforced Composite Materials Composite materials have ushered in a new era in materials science and engineering, allowing the design of engineered materials with superior mass-specific mechanical properties. Current demand in the transportation and energy sectors to reduce carbon dioxide emissions has motivated designs with such materials, a trend expected to increase in the coming years. Fiber-reinforced plastics (FRP) are an important class of such materials that have gained increasing attention due to their characteristics of light weight, high strength, and stiffness [1, 2]. These materials are made of two constituents – fiber and matrix – that differ in their mechanical properties. The role of the matrix is primarily to bind the fibers together, transfer loads, and protect fibers from abrasion and the environment. The matrix material is usually either a thermoset (TS) or thermoplastic (TP). The fibers primarily carry the load transferred from the matrix and hence provide macroscopic stiffness and strength to the structure. Glass fiber and carbon fiber are the two most widely used reinforcements in FRP composites. FRP materials can be broadly categorized as discontinuous FRP (DiCoFRP) and continuous FRP (CoFRP), based on the length of the fibers. Further, these can be either the TS or TP type, based on the matrix material used in the composite. CoFRP consists of aligned fibers similar in length to the dimensions of the structural component. The alignment of fibers along the loading direction results in high stiffness and strength. However, continuous fibers limit the design freedom and result in high production costs. Fabricating components from DiCoFRP is easier, as this material has better formability (i.e., the natural ability to conform to curved surfaces) and flow ability than CoFRP, thus making it easier to form complex geometries, such as ribs. The mechanical properties of DiCoFRP, such as strength and stiffness, are lower, but DiCoFRP provides increased design freedom and economical production costs. Figure 1.1 schematically shows the advantages and disadvan-

2

1 Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites

tages of CoFRP and DiCoFRP, considering all the material and process design factors. A new class of composite materials, so-called discontinuous fiber-reinforced polymers with local continuous fiber reinforcements (CoDiCoFRP), is considered in the consortium of the International Research Training Group (IRTG). It is a German research foundation (Deutsche Forschungsgemeinschaft (DFG))-funded GRK2078 project. Figure 1.2(a) shows an automotive back seat made of DiCoFRP with a steel frame reinforcement. Figure  1.2(b) shows the same structure in which the steel frame is replaced by FRP featuring a local reinforcement of CoFRP, thus leading to weight saving. The goal in considering this new material class is to optimally combine the advantages of CoFRP and DiCoFRP, as shown schematically in Figure 1.1. DiCoFRP allows fabrication of structural components with complex geometries, whereas the position and alignment of the CoFRP determines the structural in­ tegrity of the component. This class of materials has a significant potential for energy savings, due to the high specific stiffness and strength and the variety of design options in diverse engineering applications, including vehicle design. In contrast to continuous fiber-reinforced composites of non-crimp or woven fabrics, which are used in the aircraft industry, there is still a lack of integrated and experimentally proven concepts for the manufacturing, modeling, and dimensioning of combinations of discontinuously and continuously reinforced polymer structures.

Figure 1.1 Schematic illustrating advantages and disadvantages of CoFRP, DiCoFRP, and CoDiCoFRP

1.2 About IRTG GRK2078

Figure 1.2 Automotive back seat made of (a) DiCoFRP with steel frame (b) DiCoFRP with local CoFRP reinforcement [3]

„„1.2 About IRTG GRK2078 The main objective of the IRTG is to promote the efficiently structured education of doctoral candidates in this strategically important, but not yet fully developed, field of continuous–discontinuous fiber-reinforced polymer structures by taking advantage of the complementary competencies of the research groups from Germany and Canada. The complementary research expertise of the participating institutions is strongly linked to the national industries and research structures of Germany and Canada. This helps ensure a comprehensive education and, in the medium term, a transfer of research results to industrial applications. The focus of the research training group is to gain a fundamental understanding of the material, the processing, and the structural behavior of CoDiCoFRP. It also includes optimizing processing routes and developing design strategies that would ultimately enable many new applications of lightweight materials, especially in the context of 3D load-bearing components. This can be attained on the basis of an integrated collaborative approach in which predictive computational engineering tools are coupled with methods of characterization, process optimization, and product development. Tools for integrating computational materials engineering and the related characterization techniques in materials science are now sufficiently mature that they can offer significant benefits in the product development process. Integrating the various research areas of CoDiCoFRP thus requires coordinated research and the training of engineers and scientists from Germany and Canada. Consequently, the research program is implemented in four interacting research areas (RAs): characterization (C), which includes methods of materials science; simulation (S), which includes mechanics and computational science; technology (T), which includes processing technologies, strategies, and quality control; and design (D), which includes design and optimization methods.

3

4

1 Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites

Figure 1.3 schematically shows different RAs and several participating institutions in the IRTG framework for the product development process. The main objectives within the simulation RA are to connect the results of fluid-type and solid-type simulations and to generate a robust, mechanism-based process and structural simulation of the whole processing route, up to the final product performance. In the characterization RA, experimental characterization of the composites on both the macroscopic and microscopic levels helps elucidate the relationships between the microstructure and the resulting structural properties of DiCoFRP and CoDiCoFRP. This further serves to specify and validate the computational models. The main objectives within the technology RA are to understand the integrative process chain and further develop the handling, manufacturing, and quality assurance strategies for CoDiCoFRP. The design RA aims at virtual optimization strategies for the integrated process and structural performance of CoDiCoFRP components. Here, robust design rules and a research-based knowledge management system will also be established.

Figure 1.3 Institutes in various research areas for the integrated approach to product development of CoDiCoFRP in the International Research Training Group (expanded forms of institute names are available in the list of acronyms)

Investigation of the classes of material are planned over a decade, which is divided into three generations of investigators (three years per generation). Important observations and findings from the first generation of IRTG on thermoset-based FRP are summarized in this book.

1.3 Compression Molding Process

„„1.3 Compression Molding Process Choice of the manufacturing route for fabricating DiCoFRTS-based structural components is usually based on the fiber’s aspect ratio (i.e., ratio of fiber length to fiber diameter) and architecture for CoFRTS [4]. The primary objective is to locally reinforce with CoFRTS, while fabricating the DiCoFRTS composite structure. Consequently, the compression molding process is a suitable choice for fabricating such structures. Here, the process cycle time is low – which allows high-volume production at low cost – and the surface finish of the products is of a high quality. In the compression molding process, ready-to-mold DiCoFRTS prepregs are initially fabricated in a sheet mold compound (SMC) production line, as shown schematically in Figure 1.4. In this production line, resin and additives are mixed and transferred to two doctor boxes. The doctor boxes are used to evenly apply the resin onto a film. The film is conveyed through the system and the mixture is distributed onto it. Chopped fibers fall randomly onto the film. A second film is fed through the system, and the thermoset mixture is distributed onto it. This second film is joined with the fiber-coated first film, thus creating a sandwich of thermoset and fiber. The SMC is rolled onto a coil for transportation and storage at a specific temperature and time for maturing. The SMC is then unrolled and cut, and the film is removed for processing. The SMC with the CoFRTS is placed in the press on the hot molds, as shown in Figure 1.5. The compression molding process forms the part, bonds the DiCoFRTS with the CoFRTS, and cures the thermoset. The part is then removed from the press and allowed to cool down to room temperature for final finishing or post-processing.

Figure 1.4 Schematic of fabricating a SMC for the compression molding process

5

6

1 Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites

In further discussions, the term SMC is used as a shorthand descriptor for compression molded SMC composite.

Figure 1.5 Schematic of co-molding of CoDiCoFRTS. (a) Placement of DiCoFRTS SMC charge on the hot molds with CoFRTS, (b) flow of SMC charge by pressing it against the molds, (c) curing, and (d) release of the fabricated structural part

„„1.4 Constituent Materials of CoDiCoFRTS 1.4.1 Thermoset Matrix Material Thermosetting polymers are irreversibly cured polymers made from a viscous liquid. The most commonly used thermosets in compression molding are based on unsaturated polyester, vinyl ester, polyurethane [5], and epoxy resin [6]. Thermoset polymers usually undergo three stages during material processing: A-stage, Bstage, and C-stage. In the A-stage, the resin is fusible and soluble. In the B-stage, the thermosets are partially cured, almost insoluble, and can remain molten for only short durations, since the temperatures promoting flow cause cross-linking or curing. In the C-stage, the cross-linking reaction is completed in the presence of controlled heat and pressure. To be suitable for use in compression molding of

1.5 Demonstrator Product

CoDiCoFRTS, the thermoset in CoFRP must be chemically stable and highly viscous in the B-stage. It must have a long shelf life (with no degradation of its properties) and the initial SMC must be easy to cut, when desirable. These characteristics are important for reliable co-molding of CoFRP with DiCoFRP. In view of such desirable characteristics, a new resin, an unsaturated polyester–polyurethane hybrid (UPPH) is used for fabricating CoDiCoFRTS structures.

1.4.2 Fiber Reinforcements Fiber reinforcements are the key components of FRP, since they impart high strength and stiffness to the matrix material. The most suitable choice of reinforcement used in the CoFRP parts is carbon fibers, whereas both glass and carbon fibers are suitable for DiCoFRP parts. This combination of fibers in CoFRP and DiCoFRP parts would theoretically offer the highest potential to achieve the various optimization goals, including a light weight, high strength, low warpage, a long lifetime, and acceptable costs. However, in view of the experiments to be conducted, glass fibers are advantageous for DiCoFRP parts due to their good flow ability, better wettability, and increased detectability in tomography. Establishing robust experimental validation methods is also easier when glass fibers are used, and hence, combinations of glass fibers in DiCoFRP are considered for all analyses reported in this book.

„„1.5 Demonstrator Product Generally, any part used for structural applications consists of geometrical features, such as curved surfaces, ribbed structures, through holes, etc. The need to fabricate such parts with available manufacturing facilities and apply experimental characterization techniques limits the dimensionality of the structure. A demonstrator must therefore be carefully selected to include the necessary geometrical features and take advantage of the experimental capabilities of different RAs. Figure 1.6(a) shows the geometrical model of a demonstrator structure consisting of the geometrical features of curved surfaces, ribbed structures, and a machined trapezoidalshaped hole. However, tackling such a complex geometrical specimen is quite challenging both computationally and experimentally. Hence, a simplified version of the demonstrator part without the ribs (Figure 1.6(b)) is also used in IRTG to address the complex problem. Figure 1.6(c) shows the dimensional details of the structure. Figure 1.6(d) and (e) show the DiCoFRTS demonstrator part fabricated without and with CoFRTS patches co-molded by a compression molding process.

7

8

1 Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites

Figure 1.6 Top view of the CAD geometry of (a) a demonstrator structure and (b) a simplified demonstrator structure. (c) Dimensional details of the demonstrator structure. (d) Molded DiCoFRTS structure and (e) DiCoFRTS structure with a CoFRTS patch comolded

„„1.6 Organization of the Book Designing a 3D load-bearing component based on CoDiCoFRP required integrating engineering approaches in the research fields of technology, characterization, simulation, and design. All the findings of the first generation of research are presented in this book and are organized into six chapters. Chapter 1 (current chapter) introduces the basic idea of CoDiCoFRP, along with the materials and manufacturing methods used to fabricate such new classes of materials. The research work carried out in the IRTG consortium is introduced to describe the collaborations established to handle the integrated engineering of CoDiCoFRP structures. Chapter 2 addresses the technology for material processing and fabricating CoDiCo materials using UPPH. Various machining technologies for the secondary finishing processes of the fabricated component are discussed. The quality of the semi-finished and finished components is assessed by a multi-sensor technology. This chapter also covers polymer foaming technology for fabricating micro-fibrillar composites. Chapter 3 characterizes the process–structure–property relationship of the composite materials at different length scales. Strategies to characterize the micro-

1.6 Organization of the Book

structure of the DiCoFRTS at the end of the molding process using CT scanning are established. The interaction mechanisms of inhomogeneity of the composite materials at different scales (i.e., fiber–matrix interaction and interaction between CoFRTS and DiCoFRTS) are experimentally and numerically investigated. Experimental characterization of the mechanical behavior of the individual components and the overall composite from the coupon sample to the component level is reported. Chapter 4 presents simulation tools and material models for simulating the process chain and the effect of structural loadings. Rheological material models and phase field modeling approaches are developed to simulate the flow and curing behavior of SMC during compression molding, respectively. A multiscale simulation is developed in a finite element framework to simulate the residual stress during cure. Homogenization approaches are used to evaluate macroscopic properties for DiCoFRTS at different application temperature ranges and this work is verified experimentally. An anisotropic damage model that accounts for local damage mechanisms in DiCoFRTS is proposed and verified with experiments. Later in this chapter, anisotropic material modeling, damage evolution, and failure in injectionmolded, long-fiber-reinforced thermoplastics are also explored. Chapter 5 covers design issues specifically with CoFRTS patch optimization, DiCoFRTS topology optimization, and CoDiCoFRP knowledge management. A multi-objective optimization method that includes a kinematic forming simulation is used to compute the final CoFRTS patch position and orientation. Process-dependent topology optimization is addressed for DiCoFRTS structures. The development of a dynamic knowledge management system is also discussed to summarize the CoDiCoFRP research achievements that can be used by design engineers in the earliest phases of CoDiCoFRP product development. Chapter 6 presents an integrated engineering approach for the design and analysis of compression molding of the demonstrator (Figure 1.6(b)). Evolution of the demonstrator’s design and the position and shape of the CoFRTS patches based on optimization techniques is explained. The manufacturing technology for fabricating the optimized design of the demonstrator made of DiCoFRTS with locally reinforced CoFRTS is demonstrated. Later, this technology is used for fabricating the simplified demonstrator without CoFRTS patches or ribs (Figure 1.6(b)), for characterizing the microstructure, and for structural analysis. Process simulation of the compression molding of SMC material captures the evolution of fiber orientation for the simplified demonstrator. The fiber orientations obtained from flow simulations are validated with the characterized microstructure. Material anisotropy in the structural simulations are included by importing the orientation data from the process simulation. Four-point bending tests are carried out on the simplified demonstrator to validate the structural simulations.

9

10

1 Introduction to Continuous–Discontinuous Fiber-Reinforced Polymer Composites

References [1]

Witten, E., Sauer, M., Kuehnel, M., Composites Market Report 2017: Market developments, trends, outlook and challenges

[2]

Growth Opportunities in the Global Advanced Composites Market [Internet] (2017) Lucintel, available from: https://www.lucintel.com/advanced-composites-market-2017.aspx

[3]

Henning, F., Moeller, E., Handbuch Leichtbau (2011) Hanser, Munich

[4]

Advani, S.G., Sozer, E.M., Process modeling in composites manufacturing (2011) CRC Press

[5]

Mallick, P.K., Processing of Polymer Matrix Composites: Processing and Applications (2017) CRC Press

[6]

Akiyama, K., Development of PCM Technology. 11th-Annual Automot. Compos. Conf. Exhib. (2011), p. 37

2

Manufacturing of CoDiCoFRP

„„2.1 Introduction David Bücheler, Frank Henning, Andrew Hrymak 2.1.1 Challenges Chopped glass and carbon fiber sheet molding compounds (GF-SMC and CF-SMC) offer excellent characteristics concerning complex part geometry, functional integration, material utilization, and productivity at reasonable costs. However, limited fiber length and insufficient process control over fiber orientation restrict mechanical strength and stiffness. The characteristics of continuous fiber reinforced prepreg materials show the opposite behavior. That is, they offer superior mechanical properties at very limited freedom of design, and exhibit high costs for the material and sometimes even the process. Co-molding of prepreg material with SMC allows for fast and cost-effective manufacturing of complex, load-bearing composites. While the flowability of SMC is adequate to realize complex geometries (e.g., ribs) and integrate inserts, the continuous fiber reinforcement creates the structural backbone of the component. However, the combination of CoFRP with DiCoFRP also introduces several challenges along all of the FRP production chain. For instance, the position and alignment of the continuous fibers inside a component determine its structural integrity. Retaining the alignment of the CoFRP during co-molding with DiCoFRP may prove difficult due to heavy displacement or distortion of the CoFRP during material flow of the SMC, which in turn may negatively impact the structural integrity of a part. A novel approach concerning both material and process development is needed to target this issue. Further, automation of simultaneous CoFRP preforming and handling is required in order to achieve a reliable and robust process chain with short cycle times. Additional challenges are faced in machining of CoDiCoFRP, as different failure modes, e.g., delamination or fiber pull-out, may arise, especially in the interface between Co and DiCoFRP.

12

2 Manufacturing of CoDiCoFRP

2.1.2 Approach In this chapter, the scientific investigations of the manufacturing related challenges concerning CoDiCoFRP structures are addressed. This involves fabricating the semi-finished materials, preforming the continuous fiber reinforcements, comolding both material classes, and milling the resulting molded parts. Furthermore, process related defects are investigated by non-destructive testing to yield structures having desirable and reproducible mechanical properties. An exemplary build-up of such a CoDiCoFRP structure is shown in Figure 2.1 using a section from an automotive subfloor.

Figure 2.1 Exemplary build-up of a complex CoDiCoFRP structure [1]

The manufacturing route to realize such CoDiCo structures is shown in Figure 2.2 and was explored within this project (see Section 2.2). The fabrication of the semifinished materials is done with the help of a flat conveyor plant (a, b). The DiCo material is then matured for a minimum of 72 hours, whereas the Co material is matured directly on the line in less than five minutes. This is made possible by a customized formulation and additional heating. However, in both cases, the maturation is performed to raise the viscosity of the resins and thus enable the subsequent handling and cutting operations. After cutting, the desired fiber architecture is built up by stacking the individual CoFRP layers. Here, the removal of the carrier films (previously needed for impregnation of the fibers with the low viscous resin) is a challenging task and is more closely investigated. In the next step, the Co material is draped to near its net shape via a preforming device (c). For this key technology, four different methods, namely manual draping, sequential stamp draping, draping by magnetic fields, and a robot-based method using grippers are investigated. The position and orientation of the reinforcement fibers can be controlled by laser triangulation or thermography (d). Afterwards, the two materials are co-molded (e). Here, the flow behavior of the DiCo material inside the mold is of special interest. The DiCo material must fill complex shapes, such as ribs, without deforming or displacing the Co reinforcement structure. Furthermore, the flow de-

2.2 Processing of CoDiCo Material

termines the local orientation of the discontinuous fibers and therefore the mechanical performance of the part. Molding duration depends on part thickness. After demolding, the part is deburred by milling (f). During milling, the abrupt change of material properties in the interfacial area between CoFRP and DiCoFRP requires tailored machining strategies. Otherwise, pull-out of fibers or local cracks can occur. This may harm the structural integrity of the part and must be avoided.

Figure 2.2 CoDiCo structures’ manufacturing route [1]

„„2.2 Processing of CoDiCo Material David Bücheler 2.2.1 Introduction Chopped glass and carbon fiber reinforced plastics offer excellent characteristics for complex part geometry, function integration, material utilization, productivity, and economical production. However, limited fiber length and insufficient process control over fiber orientation lead to limited mechanical strength and stiffness. Continuously fiber reinforced materials, in contrast, exhibit the opposite behavior. That is, they offer superior mechanical properties, but with limited design freedom and high costs. Co-molding a continuously reinforced material (CoFRP) with a discontinuously reinforced material (DiCoFRP) permits the rapid and cost-effective manufacturing of complex structural composites (CoDiCoFRP). The flowability of DiCoFRP is used to

13

14

2 Manufacturing of CoDiCoFRP

form complex geometries such as ribs and to integrate inserts, whereas the position and alignment of the continuous fiber material determines the structural integrity of the component. The research presented in the following subsections is a summary from the doctoral thesis Locally Continuous-fiber Reinforced Sheet Molding Compound [2]. Current State of the Science State of the art, continuously fiber reinforced thermoset material CoFRTS resin systems are based on unsaturated polyester (UP), vinyl ester (VE), or epoxy (EP) matrices. All these resins lack the ability to create a chemically stable, highly viscous B-stage. The viscosity of UP and VE CoFRTS thickened with alkaline earth metal oxides or hydroxides drops dramatically when molded under process conditions at 150 °C. Thus, the CoFRTS cannot withstand the forces applied by the flowing, co-molding material. This behavior is illustrated in Figure  2.3 and also reported in the literature [3, 4]. The B-staging of EP resins leads to higher viscosity levels under compression molding conditions, but the material shows a narrow process window for preforming and a short shelf life [5, 6]. For state-of-the-art resin systems, it is clear that a reinforcing effect can only be achieved by eliminating flow inside the mold. Because DiCoFRP (especially sheet molding compound (SMC)) is known for its superior design freedom and suitability for function integration, this limitation is not acceptable. Thus, material and process development is needed to fix the continuous fiber position and alignment while co-molding.

Figure 2.3 (a) Tensile strength as a function of layup and flow. (b) Crack path of CoDiCoFRTS 0° type 2 specimen after flow [2]

2.2 Processing of CoDiCo Material

Process Chain The process chain developed here is schematically shown in Figure 2.4. The semifinished DiCo material (chopped glass or carbon fiber SMC) is produced with the help of a state-of-the-art flat conveyor plant (1a), matured, cut, and combined into a stack (1b). The Co material is manufactured accordingly on a modified and heatable flat conveyer plant (2a). The Co matrix is based on an unsaturated polyester– polyurethane hybrid resin (UPPH) and is combined with a 50 k carbon fiber noncrimp fabric (NCF). The UPPH resin offers an alternative thickening technology that leads to a stable, highly viscous B-stage. This B-stage is reached in less than five minutes at 80 °C. Thus, the material is viscous enough to enable direct cutting to dimensions of the final reinforcements (2b) without requiring maturation. The Co matrix also contains ferri-magnetic particles, which permits draping of the reinforcement by one solid mold-half (2c). After a second heating step on the draping device (2d), stiff, B-stage reinforcements (2e) are obtained, which can be stored or processed further. The final part (4) is generated by compression molding (3). Here, magnetic fields are used to fix the local reinforcements inside the mold during co-molding with DiCo material.

Figure 2.4 Processing CoDiCo material [2]

15

16

2 Manufacturing of CoDiCoFRP

2.2.2 Material and Process Development For reliable co-molding of Co with DiCo material at high flow rates, it is postulated that the following two framework conditions must be fulfilled: the Co matrix must provide a stable, high viscosity B-stage to achieve a stiff and stable reinforcement under molding conditions. The CoFRTS must be fixed inside the mold to prevent displacement due to the forces applied by the flowing DiCoFRTS. These framework conditions can be achieved by process and material development [7, 8]. Material To achieve a chemically stable, high viscosity B-stage, an alternative thickening chemistry was applied, offered by an alternative resin system. The two-step curing resin is an unsaturated polyester–polyurethane hybrid (UPPH). The resin is made of two main components, A and B, which in turn consist of various chemicals: Component A: ƒƒResin: polyester polyol dissolved in styrene (Daron AQR 9001, by Aliancys) ƒƒMold release agent: BYK-P 9085, by BYK ƒƒInhibitor: 10% poly-benzoquinone (pBQ) dissolved in methyl methacrylate (MMA) ƒƒAccelerator: metal carboxylate (Borchi Kat 0243, by Borchers) Component B: ƒƒChain extender: diisocyanate (MDI) (Lupranat M 20 R, by BASF) ƒƒInitiator: organic peroxide (Trigonox 117, by AkzoNobel or Peroxan BEC, by Pergan) Mixing component A with component B results in a low viscosity liquid, whose first reaction step will proceed immediately (see Figure 2.5). Only by using a heatstable initiator can the two reaction steps be separated. Otherwise, both reaction steps would occur in parallel. The first reaction step involves the MDI and hydroxyl functional groups of the resins’ backbone. The result is a chain extension by urethane linkage showing a rubber-like B-stage. This material is about one order of magnitude higher in viscosity than MgO-thickened resins and permits production of semi-finished CoFRTS with high stiffness. The reaction time can be shortened by introducing an accelerator and elevating the temperature. The second reaction is initiated by the organic peroxide at even higher temperatures (90 °C to 110 °C). Here, the extended chains are crosslinked with styrene. This radical polymerization results in a rigid, three-dimensionally crosslinked thermoset.

2.2 Processing of CoDiCo Material

Figure 2.5 Hybrid-resin-curing mechanics [2]

Since magnetic fields are used to manipulate the material behavior of the CoFRP during draping and co-molding, ferromagnetic particles are added to the thermoset matrix. Fe3O4 was chosen, since this magnetite delivers a high specific magnetic permeability and good processability. It is available with an average grain size of 200 nm, and so Brownian diffusion overcomes the effect of sedimentation induced by gravity. This behavior was also validated by experiments (see [2] for detailed results). Processing To evaluate both the co-molding process concept and the materials used, samples of varying complexity must be produced. The basic mechanical properties of the DiCoFRTS and the CoFRTS are determined with specimens taken from flat plates. The basic mechanisms of co-molding are also investigated by locally continuous fiber reinforced DiCoFRTS plates. To validate the co-molding mechanisms for more complex parts, a section of an automotive subfloor is used (see [2] for results). Production of Semi-Finished Materials The individual components for the matrix are mixed under vacuum conditions with a dissolver. Then, the compound is produced with an industrial flat conveyor plant (see Figure 2.6). Here, the reinforcement fibers are cut to a length of 25.4 mm for the DiCo materials by a chopper. During production of the Co material, the NCF is fed directly. Five heating zones and one cooling zone allow for direct processing and improve fiber impregnation. Finally, the material is coiled up and, after an optional maturation phase, it is ready for cutting, stacking, and draping.

17

18

2 Manufacturing of CoDiCoFRP

Figure 2.6 Modified flat conveyor plant used for compounding [2]

Molding Hydraulic presses are used to compression mold plates and structures. To mold the plates, two different shear edge molds are used. Due to the shear edge, the plate/ structure thickness is the result of weight and the density of the inserted material, and therefore variable. A simple square mold manufactures plates of 456 mm edge length. For producing rectangular plates, process characterization, and small structural parts, the mold shown in Figure 2.7 is used. The steel mold comes with a flash face of 70 mm height, seven pressure sensors, and the possibility to change the geometry by inlays. These inlays are also used to integrate permanent magnets (PMs) to enable a fixation of CoFRTS containing magnetite by magnetic fields during co-molding. The PMs are mounted on the backs of the inlays, so they are not visible in the mold cavity, have no contact with the material, and leave no visible marks on the final product. To maximize the fixation force acting on the CoFRTS reinforcement, finite element simulation software was used to optimize the magnetic fields and structural design. Parts of more complex geometry are molded with a generic subfloor mold. This mold is supplied by the publicly funded project MAI qfast [9]. The projected size of the subfloor is 600 mm  400 mm  110 mm. Part thickness is variable.

2.2 Processing of CoDiCo Material

Figure 2.7 Terminology and technical structure of the rectangular plate mold [2]

2.2.3 Characterization and Modeling The previous sections established the materials, formulations, manufacturing, and processing conditions for generating parts made of CoDiCoFRP. In this section, the CoFRTS is characterized, with the objective of describing the effects and mechanisms during co-molding. Mechanics of Local CoFRTS during Co-Molding Figure  2.8 illustrates a two-dimensional cross section of a simplified, planar comolding trial with respect to the forces on the CoFRTS material. The normal force FN is applied by the hydraulic press. The magnetic force FM is applied by the magnetic field. The proportions of these forces acting in the molding direction are beneficial for the fixation. However, friction is needed to transfer these forces to the direction of the displacement. For a conservative and fail-safe design, the dynamic friction coefficient must be used. Forces perpendicular to the molding direction will result in a displacement force acting on the reinforcement, unless they are balanced or compensated by the fixation forces.

Figure 2.8 Forces acting on CoFRTS during co-molding, schematic

19

20

2 Manufacturing of CoDiCoFRP

Characterization of Friction Besides gravity, there are two other forces fixating the CoFRP during co-molding. One is the hydrostatic pressure, which is applied by the press, but transferred by the DiCoFRP material. The other is the attraction force applied by the optional magnets. Neither of these forces acts directly against the direction of the displacement force applied by the flowing DiCo material. Instead, friction is needed to transfer the force. Thus, the friction between the CoFRTS and mold must be investigated in detail. There are several parameters that affect the friction coefficients of static friction St and dynamic friction Dy of CoFRTS materials at the surface of a mold: temperature, resin system, fiber content, fiber orientation, and composition of fillers (e.g., magnetite). To investigate these relationships, a heatable friction measuring apparatus is used. The set-up is shown in Figure 2.9, along with exemplary measurement results. The dark line represents the average of the measurements. The bright area around it displays the standard deviation. In summary, the frictional properties show strong dependencies on the resin system and temperature. The influence of fiber orientation is small, or even negligible. The influence of magnetite content ' is significant.

Figure 2.9 Friction measurement set-up and exemplary results [2]

2.2 Processing of CoDiCo Material

Magnetic Characterization and Modeling As the general basis for predicting the magnetic fixation force, the CoFRTS must be characterized regarding its magnetite content and temperature. Toward this end, measurements with a vibrating sample magnetometer (VSM) are performed, as shown schematically in Figure 2.10. Besides the new magnetization curve of the FRP, the influence of magnetite content ', process temperature T, and residual magnetization caused by previous process steps are of interest. Thus, measurements of the magnetic hysteresis are performed at a magnetic field strength, H, of ±1200 kA/m at three selected temperatures that occur in the handling, draping, or molding operations. In summary, the saturation polarization of CoFRTS without any magnetite is positive, but negligibly small. The remaining magnetization is negligible for all conditions. The saturation polarization increases with rising magnetite content and decreases with rising temperature. Furthermore, the polarization can be expressed by an empirical model (with C1 H 0.31401 T, C2 H 14.14078 T−1, C3 H −0.04492 T, and C4 H 3.4979  10−4 C−1):

  Jemp .T; '; H/ D ' .C1  .C3 C C4 T// 1  e.C2 0 H/ 

(2.1)

The measured values and the model are shown in Figure 2.10. Starting with an external field strength of 300 kA/m, the model shows a relative error of less than 5% for each temperature–magnetite combination. The average relative error over the total measurement range is 3.6%.

Figure 2.10 Schemata of a vibrating sample magnetometer and polarization measurements of CoFRTS at different temperatures and magnetite content

21

22

2 Manufacturing of CoDiCoFRP

Using Eq. (2.1) and finite element simulation software, the magnetic fixation force acting on the CoFRTS during co-molding can be calculated in relation to the stamp distance. For one stripe of CoFRTS containing 8.21 vol% of magnetite, there is an initial fixation force of 4.5 N (open mold) and forces between 5.2 N and 4.0 N during co-molding. Deformation and Displacement of Local CoFRTS during Co-Molding with DiCoFRTS The hypothesis that the fundamental requirement for a reliable co-molding is a stiff, stationary reinforcement is examined in this section. Molding trials were performed to either verify or refute the hypothesis [7]. First, CoFRTS materials from two different resin systems, with and without magnetite, are produced. As resin systems, a state-of-the-art MgO-thickening UP resin and the UPPH resin are used. The powder Bayferrox 318 m is used as a ferrimagnetic filler for half of the materials to permit magnetic fixation. After maturation, the prepreg is cut via computerized numerical control (CNC) into patches of 220 mm  220 mm. The molding is performed by a hydraulic press and the 800 mm  250 mm-sized rectangular mold. The mold is heated by oil to ≈145 °C and is equipped with the permanent magnets. For molding, one patch of CoFRTS is placed in the cavity exactly over the PMs. Then, a stack of glass fiber reinforced DiCoFRTS is placed in the mold. The initial position of the patch is kept constant for all trials, but the DiCoFRTS position and mold coverage is varied (compare Figure 2.11).

Figure 2.11 DiCoFRTS mold coverage and patch position during co-molding

2.2 Processing of CoDiCo Material

After positioning the materials, the compression molding is started. The closing speed of the press is set to 1 mm/s. A final pressure of 50 bar is used as a standard, although some plates are molded at 75 and 100 bar, according to an experimental plan generated using a design of experiments (DoE) software. The cure time is 120 s and the parallelism control of the press is activated. After de-molding, the lower side of each plate is photographed perpendicular to its surface. To measure the position and geometry of a CoFRTS in reference to its initial position, image analysis software is used. Here, a “rolling ball” algorithm subtracts the smooth change in brightness over the total length of the CoDiCoFRTS plate. Furthermore, the colors of the image are converted into grey values. Next, the dark carbon fiber reinforced Co material can be separated from the light glass fiber reinforced DiCo material using a threshold for the grey value. Now, the centroid of the CoFRTS and a bounding rectangle drawn around it are measured within the coordinate system of the plate. This makes it possible to calculate key values for the two main failure mechanisms of the CoFRTS during co-molding: displacement and deformation (compare Figure 2.12). The displacement is expressed as a vectorial shift d in mm of the CoFRTS’s centroid and as a rotation ˇ in degrees of the bounding rectangle. The deformation is described by a change in width ∆w and length ∆l (both in %) of the bounding rectangle in relation to the initial shape of the CoFRTS.

Figure 2.12 Position measurement and failure mechanisms of CoFRTS patch [2]

23

24

2 Manufacturing of CoDiCoFRP

Visual inspection of the plates and image processing show a clear dependency of the molding result on the molding conditions, resin system, and magnetic fixation. Figure 2.13 displays exemplary pictures of the plates after molding and the key values for the M33 molding condition.

Figure 2.13 Co-molding result and key values for the M33 molding condition [2]

In summary, both parts of the hypothesis were confirmed. For unfavorable process conditions, such as (S33), both fixation and a stiff reinforcement are essential to limit displacement and deformation. The difference in the viscosity drop of UP resin to UPPH resin when placed in the hot mold is reflected by a wash out of magnetic particles for the conventionally thickened resin system. If the displacement forces mostly compensate each other, as for the (M33) conditions, one of these improvements may be sufficient. For all experiments, the molding conditions, placement of the DiCoFRTS charge, and the mold coverage had the highest impact on the outcome. On the material side, the magnetic fixation had the highest impact.

2.3 Automated Integrated Handling and Preforming

2.2.4 Conclusions The research postulates of the introduction are confirmed. The use of modern draping techniques, new resin systems, and new fixation concepts significantly improves the performance and reliability of CoDiCoFRTS components. The material formulations, the materials models, the characterizations, and the simulation techniques described here represent a major step toward industrialization of this process.

„„2.3 Automated Integrated Handling and Preforming Daniel Kupzik, Fabian Ballier, Jürgen Fleischer 2.3.1 Introduction An important step forward to the automated production of combined continuously and discontinuously reinforced parts is the integration of handling and preforming. Integrating further auxiliary processes into handling will improve the price competitiveness of CoDiCo by reducing the number of separate process steps. The steps in the production chain for CoDiCo parts are presented in Figure 2.14, with an emphasis on handling and other auxiliary processes. Here, the boxes show the main process steps, and auxiliary steps are listed as bullet points. To reduce the number of separate process steps, it is desired to integrate all the steps leading up to press loading (Figure 2.14) into one combined handling and preforming device. Combining value adding process steps (e.g., preforming) with non-value adding steps (e.g., handling) avoids steps without added customer value. In the approach selected here, the auxiliary steps needed for preforming will be automated first, and then a way of integrating preforming into a handling device will be developed. The manual aspects of the process, which will be integrated into one device, are structured as follows: the SMC and UD raw materials are unrolled on the cutting table and cut to size. The pre-cuts must be grabbed and stacked. Suitable grippers for the handling system must be selected. For cost and resource efficient handling, it is necessary to use as few grippers as possible, while still meeting boundary conditions, such as lay down precision and maximum raw material deflection. Therefore, grippers must be positioned at the right place in the

25

26

2 Manufacturing of CoDiCoFRP

handling device. While moving the pre-cuts from the cutting table to the stack, backing foils must be removed. This step is strongly dependent on the properties of the resin, and different strategies are therefore needed for different materials and at different stages along the process chain. The varying tack of the resin along the process chain is also a challenge for the release of material from grippers. Thus, methods to separate the prepreg from gripping devices are also presented. The implemented handling units for demonstrating the results of the examinations are presented.

Figure 2.14 Auxiliary processes in CoDiCo production

2.3.2 Grippers in Composite Production Types of Grippers The handling of raw materials introduces forces into the material. At the interface between part and handling device, standard gripper units are often used. These are usually equipped with a mechanical coupling to the handling device’s frame, supply system connections (e.g., electricity, compressed air, vacuum, or information), and a contact surface to the part. Björnsson described the particularities of handling pre-impregnated (prepreg) material [10]. A detailed overview of the characteristics and usability of various grippers for textile sheets was given by Förster [11]. In the following sections, different gripper types from [11] will be discussed, along with their suitability for prepreg handling. Vacuum Grippers Vacuum grippers use ambient air pressure to induce a dis-equilibrium between the normal forces on the surface of the gripped specimen inside the suction cup and the force on the opposite surface. The lateral forces are influenced by the fric-

2.3 Automated Integrated Handling and Preforming

tion coefficient between suction cup and part and a reduction of the gripper force by external means. Generally, a low volume flow at a high pressure difference is generated by a nozzle ejector for vacuum gripping. The vacuum is maintained by an airtight suction cup. The low volume flow makes vacuum grippers inappropriate for highly permeable materials, such as textiles, whereas pressure can indeed be maintained in prepreg handling. Using a larger ejector nozzle to maintain pressure with permeable materials leads to high compressed air consumption. The use of vacuum grippers is limited by part deformation caused by the strong suction and by the need for free surfaces within the cup. Low Vacuum Grippers Low vacuum grippers deploy the same principles as vacuum grippers, but the process is optimized to a moderate negative pressure at a high volume flow. Coanda ejectors are often used to produce an appropriate flow. Their functional principle was described by Lien and Davis [12]. The higher volume flow increases design freedom for the suction cup, since an airtight seal between gripper and part is no longer necessary. Parts are also less prone to damage by the lower vacuum with adapted suction cups. Fleischer, Ochs, and Förster showed that sufficient process reliability can be reached even with the lower negative pressure [13]. Bernoulli Grippers Bernoulli grippers deploy Bernoulli’s principle to generate a zone with low static pressure. Here, a flat film of streaming air is blown between gripper and workpiece. In theory, there is no contact between gripper and workpiece and therefore only normal forces can be applied. To apply lateral forces, many commercially available grippers have pins that interact with the workpiece. Needle Grippers Needle grippers push needles through the workpiece to create a shape-fitting connection. The movement of the needles can be adjusted to lift a given number of layers from a stack. Disadvantages with this system are damage to the material, inability to slide along the workpiece, and obstruction of shear deformation if the workpiece is to be preformed during the handling operation. Clamp Grippers Clamp grippers use two or more jaws to mechanically clamp the workpiece [14]. When handling raw materials for composite production, the clamping of the workpiece between two jaws implies that one jaw must be below the mat. This makes it difficult to grip or lay down sheets on flat surfaces [15]. In summary, clamp grippers offer good efficiency and large gripping forces combined with limited usability, since both sides of the material must be accessible.

27

28

2 Manufacturing of CoDiCoFRP

Gripper Characteristics and Selection Low vacuum and Bernoulli grippers have been chosen for this study, since they offer flexible handling without damaging the prepreg. The normal and lateral forces for both grippers have been characterized. These grippers can be combined for preforming, since low vacuum grippers transmit normal and lateral forces in a similar manner, while Bernoulli grippers hardly transmit lateral forces (Figure  2.15). Therefore, areas of the prepreg that need to glide along the gripper should be held by Bernoulli grippers.

Figure 2.15 Lateral forces on low vacuum (SCG) and Bernoulli (SBS) grippers

2.3.3 Automated Placement of Grippers in Handling Systems There are different strategies for handling flat parts. Along with the question of what gripper to use, the arrangement of the grippers on the part is also important [16]. Because of the low rigidity of semi-finished materials for lightweight parts, the material can easily be deformed during handling. Such deformations may cause collisions of the handled parts with other objects in the environment or lead to inaccuracies when the part is laid down on the target position. The textile might even fall off the handling system if not enough grippers are used to hold it [17, 18]. This problem can be solved in different ways. Applying a full body gripping principle or numerous individual gripper elements close together, the handling system is most likely over-dimensioned and none of these problems will occur [19]. However, the more grippers being used, the heavier the handling system becomes and the more energy is needed to drive it. It is important to know that most of the energy (between 61% and 95%) is consumed by the robot itself [20, 21]. The weight

2.3 Automated Integrated Handling and Preforming

of the handling system directly influences the power consumption of the robot [22, 23]. In general, it is a good idea to minimize the number of gripper elements, so as to reduce the weight of the handling system itself. It is also good to minimize the number of grippers that need power, so as to save energy in the handling process overall. The use of fewer grippers increases the importance of their positioning. Since the shape of a flat semi-finished part depends greatly on the shape of the finished product, a positioning method must be very flexible. Different lightweight production processes also have different requirements regarding handling accuracy. For example, the resin transfer molding (RTM) process needs accuracies below ±5 mm [20, 21, 24]. If sheet molding compound (SMC) is used, the handling accuracy is less important, due to the flowability of the material. The accuracies are also influenced by the deflection of the material during the handling process. To solve this problem, a method to find a gripper positioning system is discussed in the next subsections. Gripper Positioning Based on the Shape Information of the Flat Part The positioning of grippers on a surface is often performed by humans [20]. This is because the task has a quite creative element and is based on human intuition. The field of neural networks (NN) offers new solutions for such problems. A category of NN is the so-called self-organizing map (SOM), which was introduced by Kohonen [25]. With this method, a set of neurons N is matched to an input data set. Static SOMs have a pre-defined number of neurons and structure [26], but there are also approaches with a flexible number and structure of neurons, such as the growing neural gas (GNG) [27]. The basic idea here is to find a suitable gripper arrangement for the shape of the part by using GNG. For this, the neurons represent the gripper elements N and the input data are points x that define the shape of the part. Figure 2.16 shows the result of such an adapted GNG algorithm.

Figure 2.16 Gripper arrangement based on part shape

29

30

2 Manufacturing of CoDiCoFRP

According to Eq. (2.2) and the concepts of SOM, each point x selects the closest neuron N at the position ws1 and drags the neuron towards its own position. The factors b and n are normally significantly smaller than one, so the neuron will not land on the point x. Furthermore, all neighbors of the neuron that are connected to it also move from their position wn in the direction of point x (Eq. (2.3)).

w s1 D b : .x  w s1 /

(2.2)

w n D n : .x  w n /

(2.3)

Neurons become neighbors if they are the closest to one point x. This principle is also called competitive Hebbian learning (CHL). In addition to these functions [28], a line-of-sight condition between the neurons is also implemented. This condition deletes connections between neurons if the line-of-sight is blocked by the shape of the part. Consequently, a neuron that moves outside the part’s perimeter will lose all its connections to other neurons and be deleted. Adjustment of the Gripper Arrangement Based on Simulation Data If a gripper arrangement is found by considering only the shape of the part, a simulation process can be started to calculate the expected deflection during handling. Using the simulation results, the deflection of the part can now be taken into account for the adjustment of the neuron positions. This is implemented by supplementing Eq. (2.2) and Eq. (2.3) with a function depending on the deflection uZ(x).

w s1 D b  .x  w s1 /  f .uZ .x//

(2.4)

w n D n  .x  w n /  f .uZ .x//

(2.5)

Such a function needs a target value tV. This target value represents the maximum absolute permissible deflection during handling. The following definition for f(uZ(x)) was used to adjust a gripper arrangement.

f .D.x// D



0 for uZ .x/  tV 3 .uZ .x// for uZ .x/ > tV 

(2.6)

By adding this weighting to the formula, the neurons will move to points with a deflection larger than the target value tV. If the deflection of a point is smaller than this target value, the point will have no effect on the neurons. Normally, the GNG is executed until an error value reaches a user defined value. The execution may thus contain several iteration loops. However, re-positioning the grippers (or neurons)

2.3 Automated Integrated Handling and Preforming

also changes the deflection of the part. Therefore, each iteration of the GNG is interrupted by FEM simulation to update the deflection. An example of such an adjustment of the gripper arrangement is shown in Figure 2.17.

Figure 2.17 (a) Initial gripper arrangement and (b) adjusted gripper arrangement

Figure 2.17(a) shows the deflection occurring with the initial gripper arrangement (section on Gripper Positioning Based on the Shape Information of the Flat Part). The neurons try to minimize the mean deflection over the whole part via Eq. (2.4) and Eq. (2.5). In doing so, the mean deflection of the part shrinks from 1.453 mm to 0.889 mm in 28 iteration steps. Despite this improvement in mean deflection, it is not possible for the algorithm to reach the target value for this experiment of tV H 2 mm with only three grippers. Regardless of where the grippers move, there remain points on the part with unacceptable deflection. Thus, a new neuron/gripper is added, based on the rules of GNG to the problem, and the whole process is repeated. In summary, this method allows one to generate gripper configurations for the transport of flat SMC cuts.

2.3.4 Prepreg-Specific Handling Tasks in Gripper Design Although handling solutions already exist for different raw composite materials, there are specific challenges to deal with when processing pre-impregnated materials. Two such challenges addressed by Björnsson [10] for other types of prepreg are also addressed in this work. The first is that many grippers were designed for handling dry, non-sticky materials and are therefore unsuitable for the release of the tacky prepregs. The importance of this problem grows if preforming is integrated into handling, due to the higher necessary contact forces. The second is that prepreg is usually supplied with a backing paper or foil, which must be removed

31

32

2 Manufacturing of CoDiCoFRP

during processing. This can be done as the first step after unrolling, in a later process step after cutting, or after preforming. In large-scale production, the first solution is usually chosen, since the backing paper can then be rolled up in one big piece for disposal. For the process described in Figure 2.14, however, the backing paper must remain on the part during cutting, preforming, and B-staging to prevent the evaporation of chemicals needed during curing. Thus, the foil must be removed at the end of the integrated handling step, and special solutions for removing backing paper from small surfaces are necessary. Release of Tacky Prepreg Standard gripping devices are usually designed to release the gripped object solely by deactivating the gripping mechanism and using separation forces acting from the outside, such as gravity. This also applies to the grippers used in textile and part handling in various process chains, such as RTM or liquid composite molding (LCM). When using low-pressure vacuum composite grippers for experimentation, some prepregs could not be released from the grippers using solely ambient forces. The release behavior depends on many factors specific to one task in part production. Examples include the surface properties of the prepreg (which influence the adhesion between prepreg and gripper) and the part size and thickness (which influence the gravitational forces). To permit reliable automation of handling processes with integrated preforming, a mechanism to release tacky prepreg from gripping devices has to be found. State of the Art The handling of prepreg can be divided into automated tape laying (ATL) with subsequent cutting of continuous tapes and the handling/placement of pre-cut tapes or tape layups. In ATL, one end of the tape is pressed to the mold/target area to achieve adherence to it. When the tape laying head moves on, new tape is unreeled and pressed onto the mold [29]. The release from the handling device is secured by the adherence of the tape to the mold. The cohesion to the mold exceeds the cohesion to the handling unit and simple measures such as applying a non-stick coating to the pressure roller are sufficient [29]. ATL is a process used industrially in the aviation sector [30]. When placing small patches, it is unacceptably complex to place the prepreg beginning at one end and then proceeding to the other end, since a handling unit adapted to the workpiece will be necessary. Instead, the whole patch should be placed in one operation. In the processes illustrated in Figure 2.18, it is necessary to handle small UD-patches. Critical steps for the separation from the gripper occur after the handling steps for stacking the layup, preforming, and B-staging. The handling of the SMC used in this project seems less critical due to the larger mass of the pre-cuts and lower tack of the material. Therefore, solu-

2.3 Automated Integrated Handling and Preforming

tions for the release of the prepreg from the gripper without strong adhesion to the target area are required. Björnsson [31] described two gripping devices, named “single manipulator demonstrator” and “dual arm demonstrator”. The “single manipulator demonstrator” can handle and stack different pre-cuts into one larger layup. It consists of suction areas that can be combined to form different rigid gripping areas. The gripper handles the prepreg on the side covered with backing paper, while having to pull the paper off the cutting table. Here, a slow lift-off helps the release due to the time-dependency of tack. The dual arm demonstrator grips the prepreg at both ends and lifts it from the cutting table. With its help, a peeling motion helps release the prepreg from the table. These solutions have disadvantages in process time and the complexity of the robotics. To implement small patches into SMC parts, it would be desirable to have a gripping system that can reliably lay down those patches. The systems presented in this chapter are not particularly suited for this task, since they are either not applicable to small pre-cuts or they are very complex. Experimental Set-Up In the experiments, a 40 mm  40 mm 0°-90°-0° UD-layup of Hexcel HexPly® M77/42%/UD90/CHS is gripped from a non-stick paper and placed on an aluminum target area. The experiments are conducted with a 2 s or 30 s handling time and the prepregs are released when they are in contact with or close to the aluminum plate. For gripping, a low-vacuum gripper is combined with either a round 40 mm suction pad of polyoxymethylene or a 3D-printed angular suction pad of PA3200 (Figure 2.18). The vacuum is switched on from the point of lift-off from the non-stick paper until the prepreg is positioned on or above the aluminum plate. The suction is then deactivated and, if applicable, the release mechanism is activated. The various release mechanisms are ranked according to which mechanism was able to release the prepreg after which handling process. For example, the longer handling time led to stronger adhesion between prepreg and gripper, and release was therefore more difficult.

Figure 2.18 Angular and round suction pads

33

34

2 Manufacturing of CoDiCoFRP

Experimental Results for the Various Methods Four main influencing factors for the gripper release have been identified: ƒƒEffectiveness of the release mechanism ƒƒAdhesion to the suction pad ƒƒAdhesion to the target area ƒƒStickiness of the raw material Only those variables that can be changed independently from the process were examined further. The surface properties of the tool can often not be changed, since they have a great influence on the surface quality of the finished product. Therefore, the adjustment of the adhesive properties of the target area is not examined. The properties of the prepreg depend on many different factors (e.g., humidity, temperature [32]). The resulting material behavior can only be influenced by changing the chemical composition of the matrix material or the production process. Since both the process environment and the matrix material are usually fixed, the experimentation is conducted in constant environmental conditions to avoid the influence of ambient conditions. This way, the results will have a wide applicability. The remaining influencing factors to be examined are thus the mechanical separation by means of compressed air or ejector pins and the surface properties of the suction pad. Mechanical Separation Ejector pins are examined using the angular suction plate. A plate with 24 ejector pins on one side and one stud for manual movement on the other side is integrated into the gripper (Figure 2.19). In contrast to all other separation mechanisms, no separation air is blown between gripper and prepreg. The results of the depositing tests showed that a reliable lay-down is possible in all situations. A significant force is necessary to manually push out the ejector pins. In comparison to the other concepts, integration into the existing gripping systems is relatively difficult. After the initial series of trials, a release demonstrator using three solenoids was built (Figure 2.19). The adhesion between gripper and material (fused deposition modeling (FDM) printed polylactic acid (PLA)) proved to be strong enough to block the solenoid’s movement in some cases. In most experiments, however, the solenoids separated the prepreg and release was possible. Since each solenoid pushed on only one point of the prepreg, minor deformation occurred.

2.3 Automated Integrated Handling and Preforming

Figure 2.19 Mechanical ejector pins and solenoid ejectors for removing prepreg from the gripper

Improved Blow-Off Mechanism The composite grippers feature an integrated blow-off mechanism in which a sharp jet of air is directed against the inner side of the suction plate at one position. In experiments with the round suction plate, this led to no release or an asymmetrical release, since the prepreg still adhered to the suction plate after activation of the release mechanism. The release improved by positioning a pneumatic hose with an open end in the outlet of the ejector chamber of the vacuum generator contrary to the usual flow direction. The amount of air blown between the vacuum generator and suction plate could be varied. The prepreg release improved, but some one-sided, incomplete separations still occurred, since the air distribution was uneven. The results with the increased airflow showed differences between the two suction pads. Releases from the angular suction pad were mostly successful, despite the larger surface, whereas releases from the round suction pad were only improved slightly. By combining the improved blow-off mechanism with other concepts, reliable release could be ensured. An effect that must be taken into account is Bernoulli’s principle. In some cases (e.g., with different gripper geometries employing strong blow-off air), the effect is reversed, and the blow-off air sucks the prepreg to the gripper, although there is no longer direct contact. This reversed effect is, in fact, used in the Bernoulli grippers. Coating the Suction Pad Reducing adhesion between prepreg and gripper is the second point of attack for improving the lay-down of prepreg. To do so, the angular suction pad was covered with either siliconized paper or a PTFE foil. The coatings were fixed at the edges of the gripping surface and pulled tight. A self-adhesive PTFE foil was also tested, which was glued to the gripping surface. Different hole patterns were pierced into the coatings. Either all the holes of the suction pad below were pierced, or only five holes were pierced near the center of the gripping surface. Reduced ad-

35

36

2 Manufacturing of CoDiCoFRP

hesion was expected for all coatings, since the siliconized paper is used as a release agent between the layers on the stock roll, and PTFE is a widely used nonstick coating. The non-self-adhesive coatings led to consistently successful results in depositing the material when used in conjunction with the blow-off mechanism, although the PTFE foil had a small advantage. In some cases, it was even possible to separate prepreg and gripper by pressing and adhering the prepreg to the aluminum plate before lifting the gripper up without using the blow-off mechanism. When using self-adhesive foil, adhesion between the prepreg and the adhesive layer of the foil at cutting edges or holes must be prevented. An additional detaching effect occurs when slack, non-self-adhesive foil is used in combination with blow-off air. The foil is then deformed in a convex way, which leads to a peeling movement at the edges of the adherence zone. Peeling-off was described as advantageous by Björnsson [31]. Influence of Suction Pad Roughness The surface roughness of the suction pads was analyzed, after they showed different behavior in the experiments with the improved blow-off mechanism. Both suction pads were measured in stock condition and after grinding with either 400-grit or 40-grit abrasive paper. The 400-grit paper smoothens the surface minimally, while 40-grit abrasive paper leads to a noticeably rougher surface. The angular gripper has a much higher stock roughness than the round gripper and the influence of grinding is therefore much stronger on the round gripper (Figure 2.20). Experiments showed that the release of prepreg works better from rough surfaces than from smooth surfaces. Whereas the release of prepreg from the angular gripper plate in stock condition worked reliably with maximum blow-off airflow, problems occurred when it was sanded with 400-grit paper. After sanding the angular plate with 40-grit paper, the separation improved in detail. When sanded with 40grit paper, the round suction pad showed similar results to the angular plate after 40-grit grinding. In the other cases (stock, 400-grit sanding), reliable lay down was not possible with the round suction pad. In conclusion, a very smooth surface was disadvantageous for the separation.

2.3 Automated Integrated Handling and Preforming

Figure 2.20 Roughness measurements of an angular suction pad (top, 50 μm scale) and round suction pad in stock condition (bottom, 5 μm scale)

Design Guidelines for the Release of Tacky Prepreg Handling devices must be adapted to the challenges of handling tacky material. The release should be made as easy as possible by using suitable material, such as PTFE, or rough materials for the gripping surface. Blow-off air is a suitable measure to improve a gripper that does not work reliably. It must be ensured that no contamination is caused through the use of compressed air, however. Ejector pins work well if they are evenly distributed and actuated with sufficient force. Single ejector pins might cause deformations of prepreg with strong tack. Removal of the Backing Paper/Foil UD-prepreg is often delivered with backing foil or paper to separate the layers on the spool. The backing must be removed before consolidation of the layers and pressing of the part. Alternative process chains are to remove the backing either before or after cutting the patches. If the foil is removed on the upstream side of the cutting table, it can be pulled off in one large piece. Backing Foil/Paper in the Production of Small Patches In the production process, backing foil and paper are used to enable the production of the raw material and to protect the resin from evaporative styrene losses. The following sections describe foils for SMC and for UD. SMC is produced with a layer of styrene-tight plastic foil on each side. The foil remains on the material for the layer-wise cutting process and is removed just before stacking. The pull-off of the foil from SMC is performed manually in most

37

38

2 Manufacturing of CoDiCoFRP

trials. This is of medium difficulty, since a starting point for stripping the foil could not always be found on the first attempt. The foil is only torn apart when being stripped from the more complex pre-cut geometries. The SMC is laid into the press as two stacks before and after the UD reinforcement patches. UD-material is produced with the same type of foil as SMC on one side and a layer of siliconized paper on the other side. The paper is necessary because of its tensile strength at the increased temperatures used during the first pre-curing step in continuous raw-material production. The tape is cut into large patches and stacked after raw material production. Before stacking, the siliconized paper is pulled off, which is relatively easy to perform manually. Although it was hard to find a starting point for stripping in some cases, the paper’s good tensile strength prevented tearing. The foil remains on the material to retain the styrene. The foil must be removed from some layers when stacks with more than two layers are produced. In contrast to the SMC, the UD-resin has not been matured at that time, so that the resin is very sticky. A repeating problem was that single fibers stuck to the foil, so that the prepreg was damaged locally. The gloves also had to be changed regularly, as they became sticky from resin. After cutting the small patches out of the stack, they are formed and B-staged. The foil remains on the surface until just before molding. Manually stripping the foil from the B-staged patches proved difficult due to the strong adhesion to the partly-cured resin and the small cuts in the foil at part corners. It was very difficult to find a starting point to grasp the foil, which often tore, so that another starting point had to be found. After the experience in the manual process, foil removal from SMC and from Bstaged UD-tape were chosen for experimentation. The removal was split into two steps because the main difficulty was very different between the steps. In the first step, a small gap between material and foil has to be generated, which demands very precise work. In the second step, the foil must be pulled off the material across the whole surface, which calls for a firm grip on the foil, which is easier to obtain if the foil is accessible from both sides. The probability of tearing the foil is also higher in the second step. Separation Concepts Vacuum Grippers Vacuum grippers are examined for suitability in both removal steps. According to Björnsson [33], vacuum grippers can only be used to pull off backing paper from completely uncured prepreg if an initial separation has already been established. Since foil is often more difficult to strip than siliconized paper, no better results are expected. Experiments show that no initial lift up is possible with flexible, flat, or bellow suction cups, since the suction forces cannot be transferred onto the edge of the foil.

2.3 Automated Integrated Handling and Preforming

When the vacuum grippers are used on a large separated corner of the foil, the initial separation can be enlarged. However, as soon as the separation line between SMC and foil grows, the small gripper begins to slide. When using larger grippers, the foil is partly sucked into the gripper and then begins to slide. Using a mechanical clamp on the vacuum gripper improves the pull-off step, although no large forces can be applied due to the low stiffness of the suction cup material. The adhesion between B-staged UD and foil is too strong for foil removal with vacuum grippers. Brushes Since the introduction of the pull-off force for a large area cannot release the foil, another concept is to introduce the force locally. This is to be accomplished by a small pin, which would touch the edge of the foil and pull it off in a small area. Since, in practice, it would be hard to hit the edge of a very thin foil, brushes with bristles are used. Experimentation is done with steel, brass, and nylon brushes having different bristle diameters. The brushes are either rotating or standing still. Medium bristle stiffness and sharp edges proved useful. Therefore, 0.1 mm steel bristles and 0.2 mm brass bristles are more successful than 0.2 mm steel or 0.1 mm brass and especially 0.15 mm nylon bristles. The peeling of the foil is improved when using rotating brushes (Figure 2.21). The method of using brushes to create an initial separation is very successful when treating SMC. When removing backing foils from B-staged UD-material, the foil generally separated from the part, but a lot of damage occurred to the foil. Removal of the whole foil from a rectangular piece of pre-cured UD using a clamping gripper succeeded in only 94% of the trials. The disadvantages of this procedure are thus the possible foil damage resulting in an unsuccessful removal and relatively large lateral forces on the material, which make the handling more difficult.

Figure 2.21 Rotating brushes can be used to create an initial separation

39

40

2 Manufacturing of CoDiCoFRP

Friction to Rubber As a way to prevent foil damage, the concept of using rubber instead of brushes to induce forces into the foil via friction is selected. When treating SMC, a very small initial separation from the preceding cutting process is necessary to allow for successful separation. Therefore, the reliable peeling of the backing foil from perfectly cut SMC is not possible. Peeling the foil from B-staged UD is not possible with friction via a rubber element. Additionally, rubber wear debris contaminates the raw material and the workplace. In summary, the removal of the foil with rubber is worse than in concepts using brushes and holding forces for the raw material are also larger, so that the disadvantages outweigh the advantage of less foil damage. Thus, concepts using rubber are no longer examined. Air Injection Björnsson [33] proposed blowing air between backing paper and material through a needle to create an initial separation. This procedure is tested on foil, since removing foil is expected to be more difficult than removing paper. Injecting air between B-staged UD and foil is not possible, since the resin is too hard to be pierced by the tip of the needle and the air is mostly released above the foil. When processing SMC, a bubble below the foil can be generated (Figure 2.22). The general direction of the bubble can be controlled by using a guide for the airflow. The development of the bubble works best with the largest available needle diameter (0.9 mm). However, the enlargement of the bubble stops as soon as the first opening to the environment arises due to differences in properties between paper and foil. Therefore, it is not possible to reliably detach a corner of the foil for subsequent gripping.

Figure 2.22 Injecting air below the foil with a needle

A different concept is to blow compressed air against the cut edge of the raw material to generate a positive pressure between foil and material. This positive pressure should then create a small initial separation, which would be sufficiently enlarged by the airstream to create a graspable corner. Different nozzle

2.3 Automated Integrated Handling and Preforming

diameters are tested, ranging from 0.4 mm to approx. 3 mm. The nozzle is either held at a constant position or moved along the normal direction of the material. The moving nozzle increases the probability of separating the foil, as many positions are treated. The progress of the separation can only be controlled by clamping the foil and material at a certain position. If clamping is not desired, the process for pulling off the whole foil must tolerate variations in separation. One problem that may occur is that the impact pressure separates the whole material from the gripper, unless measures are taken to prevent the air stream from hitting the gap between gripper and material. In summary, the separation by blowing compressed air against the cut edge worked well for SMC, but often failed for B-staged UD. Adhesive Tape Adhesive tape is used to remove backing foils in several patents [34–36]. The adaptability of the proposed procedure of pressing the tape against the foil is tested in manual experiments. Experimental parameters are the type of tape (paperbacked rubber adhesive tape, box-sealing tape) and the procedure of pressing the tape on the workpiece (with bare hands, a plastic roller, or the edge of a piece of sheet metal). Initial separation from both SMC and B-staged UD material can be generated reliably. For the separation from UD, the paper-backed rubber adhesive tape must be used and firmly pressed against the raw material with a force of 25 N via the sheet metal. Both the creation of an initial separation and the stripping of the whole foil is possible with adhesive tape. Advantages of the procedure are the probabilities of less damage to the material and the relatively low lateral forces, since separation forces are directly transferred onto the foil. A disadvantage is the high engineering complexity for unrolling and positioning new tape and for removing the old tape with the backing foils. Combined Clamping Gripper A gripping device to completely strip foil at an initial separation is desired. Instead of the usual approach to combine a vacuum gripper with a clamping device, a clamping gripper with a suction function is designed, as shown in Figure  2.23. Requirements are a sufficient gripping force and the ability to grip a foil that is lying flat on the raw material, but not adhered to it. An encapsulated clamp gripper is built, into which the foil could be sucked. For SMC sheets, success occurs in all cases in which the initial separation is large enough to grasp the foil. When stripping from B-staged UD, the mechanical stress on the foil sometimes becomes large enough to tear it. Here, gripping the foil, pulling off a bit more, and then re-gripping the larger initial separation can be advantageous. The combined suction clamp gripper can be used to strip initially separated foil.

41

42

2 Manufacturing of CoDiCoFRP

Figure 2.23 Combined clamping gripper: the foil is sucked into the gripping gap, which can then be closed by the pneumatic cylinder

Design Guidelines for the Removal of Backing Foil An important insight gained from the research on foil removal is that this process step needs to be considered in both process and product design. For ease of production, it would be desirable to remove the foils in one large piece before cutting. If the foil is required for later process steps, it should be removed at a time when the tack is low, if possible. During manual part production, it also becomes apparent that different backings separate differently. For example, siliconized paper releases by gravity in most process steps, while the foil shows high tack. Therefore, the stripping step also needs to be regarded in the selection of raw material backing. If stripping a difficult backing is necessary due to process restrictions, the pre-cuts should be designed so that only one initial separation needs to be created and the whole foil can be pulled off in one piece. Toward this end, two things should be avoided: sharp edges where the foil might rip and, in particular, damage to the foil caused by the cutting knife. Afterwards, methods for stripping the backing can be selected depending on the remaining degree of difficulty.

2.3.5 Demonstrator Units for Integrated Handling and Preforming Two devices are built to demonstrate the integration of preforming into handling. The first is based on a deformation of the suction cup and can be used for relatively easy geometries of UD patches or SMC sheets. The second device drapes the prepreg using a positive and a negative mold and can be used for more complex geometries. Further steps, such as B-staging and separation, are integrated into the second device. Complete integration of all steps into one device cannot be demonstrated yet, since there are still two production lines necessary for SMC and UD. The deformable draping gripper principle can be used for SMC stacking and preforming if enhanced with an air nozzle and a combined clamping gripper

2.3 Automated Integrated Handling and Preforming

for foil removal. The stamp-draping device can be used to produce UD patches and integrate them into the SMC stack. The foils must be removed as a whole before cutting. This is possible, since the stamp draping demonstrator can be used for B-staging without foil, in as much as the aluminum of the mold is tight to prevent evaporation of chemicals. Deformable Draping Gripper A demonstrator unit is built to perform a simple gripper-based 2.5 D bending on patches placed on a specific side of the reference structure. For the gripping force in this unit, low vacuum suction is used. The gripper is a hollow shell design consisting of two box-shaped ends connected with a pipe. The pipe is shaped in a way that keeps the vacuum within the shell, while moving the two gripper parts relative to each other. All three parts have small holes on the underside through which the vacuum sucks the prepreg against the gripper. Therefore, the prepreg will be pulled against the gripper across its whole surface. The unused gripping surface should be taped shut to keep a higher level of vacuum when small patches are processed. After gripping the patch, the gripper is deformed so that the patch follows the new, step shaped, gripper surface. The formed patch can then be placed on a mold. An alternative process route would be to first press the large end of the gripper on the mold and then deform the gripper. This way, the prepreg cannot peel off from the large end and larger deformation forces are available. The deformed gripper is shown in Figure 2.24.

Figure 2.24 Deformable draping gripper adjusted to fit the mold: the two shells (left and right) can perform a circular movement around the connecting piece in order to drape the prepreg

Stamp Draping Gripper A demonstrator unit has been developed for the automated handling and preforming of the reinforcement patches in the reference structure. It preforms the patch

43

44

2 Manufacturing of CoDiCoFRP

using a female mold into which the gripper pushes the pre-cut. Integrated functionalities are the handling, forming, and heating of the UD-tape. Knowledge gained from research on the separation of the sticky material is incorporated into the design of the stamp draping gripper. The stamp draping gripper consists of a male mold (dynamic) and a female mold (static), which are derived from the reference structures’ molds (Figure 2.25). Both molds are made of aluminum and can be heated with embedded heating elements. The gripping forces are introduced by vacuum, which is guided through holes in the male mold. The release of the part is accomplished by ejector pins. The female mold is in a static position, while the male mold, with its built-in gripping functionality, is mounted to an industrial robot. The preforming process is structured as follows: ƒƒGripping: the heated male mold is positioned directly above the patch on the supply area. The vacuum ejector is activated and the patch is sucked against the mold. ƒƒHandling: the robot moves the mold with the patch directly above the heated female mold. ƒƒForming: the robot slowly lowers the male mold into the female mold. The patch is held in place by the gripping suction. The vacuum ejector is deactivated to save energy once the final position is reached. The robot holds this position for the B-staging time. ƒƒPalletizing: the vacuum ejector is reactivated to securely grip the part. The ejector pins in the female mold are activated and the robot hand moves upwards. The robot places the male mold above the storage area (or an SMC stack), switches off the vacuum ejector, and lays the B-staged patch down by activating the ejector pins in the male mold. Later, all the ejector pins are deactivated and the next patch is produced. The stamp draping gripper as it is mounted on the robot is shown in Figure 2.25.

Figure 2.25 The stamp draping unit mounted on an industrial robot. The patches are gripped from the cutting area, preformed in the female mold, and positioned in the target area

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

2.3.6 Conclusions In the area of process automation, the process optimization for co-molding thermoset UD and SMC was investigated. This research focuses on the automated placement of grippers in handling systems and the integration of further process steps into handling, so as to avoid non-value-adding steps. For handling processes without preforming, a model is developed for the deflection of SMC sheets gripped at discrete points. With the help of this model, an integrated engineering solution for the automatic placement of grippers on a handling device is developed that complies with process limitations on part deflection and maximum force per gripper. A flexibly reconfigurable gripping system is constructed for the validation of the optimization process. To develop a handling system with preforming capabilities, different grippers are compared and the necessary degree of preforming is determined. The gripping force of the most suitable types of grippers (low-pressure suction grippers and Bernoulli grippers) is characterized in the normal and lateral directions. After demonstrating the necessity of preforming and identifying gripper performance, two prepreg specific challenges had to be solved for the preforming and handling of CoDiCo parts. The first is to reliably separate gripper and prepreg after handling, in spite of the tack of the resin in the prepreg. The second is to remove backing foils from pre-cut patches of SMC or UD-tapes. To integrate preforming into handling, a concept for a gripper with integrated stamp draping functionality is developed and set up in a demonstrator unit. Preforming by a deformable gripper surface is examined. To show the combination of different steps, such as gripperbased preforming, separation from the gripper, foil removal, and the placement of grippers for the handling of prepreg, a process demonstrator unit is implemented.

„„2.4 Quality Assurance of Continuous– Discontinuous Glass-Fiber SMC Marielouise Schäferling, Gisela Lanza, Michael Thompson 2.4.1 Introduction Systems for quality assurance are well known and widely used. Originally, quality meant simply that the product was undamaged and fulfilled the functional and structural requirements of the customer. Over time, the understanding of quality has been extended to refer to the expected performance after a certain period of usage [37]. From an external perspective, the customer’s satisfaction is a key tar-

45

46

2 Manufacturing of CoDiCoFRP

get to be met. Therefore, knowing and ensuring the quality of the elements that impact production is important for success and for the customer’s satisfaction. The ability to guarantee a specific level of quality also creates a unique selling point in the competition with alternative products. Moreover, identifying defective parts as soon as possible in the production process prevents unnecessary manufacturing steps and, therefore, unnecessary costs [38]. This suggests that a detailed evaluation is required of what technology should be used for testing quality in the various production steps. From the manufacturer’s point of view, there are other important reasons for quality assurance: tracking a product’s quality forms the basis for continuously improving the entire production process. Understanding the determinants of the production process and those steps that are critical for maintaining quality means understanding the core know-how. This leads to improved planning decisions on a strategic and functional level. With this information, a more efficient and resource effective process can be realized [39]. And finally, risks can be minimized before they occur [38], for example, by ensuring that every part of a system meets the quality level required for it to interact reliably with every other part of the system. In some cases, extrinsic reasons may also demand the implementation of an appropriate quality management system, such as governmental and other normative regulations existing in particular branches. Well-established standards are also mandatory for the acquisition of new customer projects, for example the ISO 9000 series [39]. These arguments for quality assurance are offered from the production and development perspective. The quality assurance of resources and the semi-finished goods required for production is also part of this perspective. Thus, the quality assurance of both semi-finished and finished parts is examined in this chapter.

2.4.2 Defects in SMC and Unidirectional Prepregs SMC is known for its good surface quality and, therefore, is frequently used in the automotive industry for visible components. However, there is the possibility that air inclusions and delamination may occur in SMC parts, which impair the mechanical properties and can lead to unsightly surfaces, especially during painting. Porosity of one or more small cavities or open pores in the surface usually occurs when trapped gases escape during the molding process. Porosity promotes the formation of cracks and reduces the maximum theoretical strength of the component [40]. Delamination is the separation of two adjoining layers within the laminate. In many cases, this defect is not visible from the outside, but can sometimes be identified by the presence of a milky clouding of the surface. Delamination de-

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

creases compressive strength and can lead to a total failure of the component due to progressive growth [41]. In addition to preventing porosity and delamination, it is important to avoid accumulations of resin, dry areas of fibers without resin, and folds. These problems can lead to an inhomogeneity of the fiber matrix ratio and thus to a local weakening of the components. To improve the mechanical properties of discontinuous SMC components, they are reinforced with continuous carbon fiber prepregs to strengthen them locally. Here, costs can also be reduced by using smaller quantities of more expensive carbon fiber material. Since this is a unidirectional material, further defects must be protected against, such as the wrong fiber orientation or gaps. If the cured unidirectional tape has a different position or orientation than planned, the strengthening of the reinforced component to suit the load is no longer possible. The defects described represent some of those frequently found in this material. There are others, such as diesel effects [40] or staining, which are not examined in detail in the next section.

2.4.3 Classification of Defects The defects listed in 2.4.2 can be classified into two groups: internal and external. Figure 2.26 gives an overview of both of these groups.

Figure 2.26 External and internal defects in a continuous–discontinuous sheet molding compound

All these defects influence the mechanical properties of the components in ways that are not yet known. Thus, these influences must be investigated to better quantify the effect of a given defect.

47

48

2 Manufacturing of CoDiCoFRP

2.4.4 Measuring Methods and Testing Techniques This section shows which measuring and testing methods are appropriate for the quality assurance of continuous–discontinuous sheet molding compounds. Here, ancillary conditions, such as the measurement time and the size of the components to be examined, are also taken into account. Measurement and Testing Technology Requirements In analyzing the requirements for measurement and testing technology, a distinction must be made between two different types: those imposed by the component and the material, and those arising from the boundary conditions of the process. Since complete quality assurance should be carried out at an early stage of the process, the semi-finished products used as inputs must also be examined. Here, defects such as impurities can occur. Therefore, different degrees of curing of the material, semi-finished material, and cured parts, have to be investigated. Due to the sticky consistency of the semi-finished products, the inspection process must be contactless. Furthermore, it should be able to examine the 3D geometry and detect internal and external defects. Since quality assurance takes place during production, it must be inline-compatible. The measurement time must fit within the production cycle, which makes speed a priority. Since components vary in size, the process must be able to handle different dimensions. Moreover, it must be easy to use and not pose any danger to human workers. The wide variety of possible measurement methods is illustrated in Figure 2.27. Among these, tactile measurement methods are excluded, since the examination must be non-contact.

Figure 2.27 Overview of measurement methods for contactless measurements according to [42]

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

Selection of Possible Measurement Methods As described in the previous chapter, there are a number of methods that can work contactless. However, not all of these are suitable. The material for the eddy current process, for example, must be conductive. However, this stipulation holds only for the carbon fiber material, but not the glass fiber SMC [42]. Strip light projection and image processing methods are well suited for capturing external defects, but they have clear disadvantages in terms of measurement time and investigable component size. Computed tomography (CT) can detect both external and internal defects, but is slow and not an option for inline use. The ultrasonic method also has clear disadvantages in terms of component size and measurement time. Laser light sectioning is a method with which external defects can be detected adequately and reproduced in the form of a 3D point cloud. The auxiliary requirements concerning measuring time, component size, and inline capability are also partially fulfilled. Thermography is well suited for internal defects and, here too, some of the auxiliary constraints have also been met to a large extent. The properties of the methods described are summarized in Figure 2.28, which also provides an overview of the suitability of the methods. A completely filled circle means that the boundary conditions are completely fulfilled and that this method is suitable. If only three quarters of the circle is filled, the conditions are almost completely fulfilled, but a few points are not reached and, in this case, improvements are required. The degree of fulfillment decreases with decreasing circle.

Figure 2.28 Selection of the measurement and testing method

49

50

2 Manufacturing of CoDiCoFRP

To evaluate which method is suitable for examining the material being studied here, tests were carried out with thermography and ultrasound. In this case, thermography proved to be more suitable, since it could also be applied to semi-finished products [43]. The two selected methods, laser light section and thermography, are explained in more detail in the next section. Laser Light Section Method The laser light section method is based on the triangulation principle. Distance is measured by detecting diffusely reflected laser light. A matrix camera calculates the line shape and distance by analyzing the intensity profile of the laser line. To obtain 3D data, the laser line is traversed over the component and generates a cloud of points representing the surface with x, y, and z coordinates. This principle is shown in Figure 2.29.

Figure 2.29 Principle of the laser light section system according to [44]

A laser light section system configuration has been developed at the wbk Institute of Production Science. This configuration has the special feature that two laser light section systems interact with each other. This is necessary to completely detect complex geometries with undercuts or edges [45]. The structure of

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

this system, which is used for the quality assurance of the SMC components, is shown in Figure 2.30.

Figure 2.30 Laser light sectioning system at the wbk Institute of Production Science

Thermography Active thermography is already an established method for investigating fiber reinforced plastics. There are different procedures, such as pulse thermography, lock in thermography, and pulse phase thermography. Pulse phase thermography is used for this work. In pulse phase thermography, shown schematically in Figure 2.31, the component is excited thermally with the help of a flash light. The thermal course of the excitation can be recorded and detected with an infrared camera [46]. If there are flaws in the interior of the component, such as delaminations, the image appears warmer at these points, since the heat accumulates there. Thus, the infrared camera records warm and cold areas and displays them in images. By means of a subsequent fast Fourier transformation, it is possible to obtain phase and amplitude images that are less sensitive to noise and can provide information about the defect depth [47].

51

52

2 Manufacturing of CoDiCoFRP

Figure 2.31 Principle of active thermography

2.4.5 Multi-Sensor System The two methods, laser light section and thermography, offer the possibility to detect both internal and external defects. To be able to carry out quality assurance within the specified timeframe, both procedures must be integrated into one system. This multi-sensor system is explained in more detail in the next section. Design of the Multi-Sensor System First, a feasibility study was carried out to check whether it is even possible to integrate thermography into the existing laser light sectioning system and, if so, which type of thermography is most suitable [48]. To integrate thermography into the existing laser light section system, four boundary conditions must be considered: Since the tool center point of the portal is designed for a maximum of 40 kg, the thermography system must not exceed approx. 15 kg. The cables of both systems must be insulated from each other to avoid electromagnetic coupling. There is only limited space for thermography, since complete mobility in all three spatial directions and a rotation around the z-axis is desirable. The infrared camera must be rotatable. The design implementation of these conditions is shown in Figure 2.32.

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

Figure 2.32 Design of the multi-sensor system with laser light section and active thermography [49]

Implementation of the Multi-Sensor System The implementation of the design is realized in cooperation with edevis, a company that specializes in thermography systems for measurement applications. It was possible to attach all components at the tool center point and still ensure mobility. Thus, the system works with the same coordinate system as the portal and allows evaluation by MATLAB®. The examination of the components is carried out sequentially, that is, the geometry is first recorded by means of the laser light section system and then internal defects are detected with several thermographic images. The implementation of this multi-sensor system is shown in Figure 2.33.

Figure 2.33 Implementation of the multi-sensor system

53

54

2 Manufacturing of CoDiCoFRP

2.4.6 Data Fusion A data fusion approach is used to merge data obtained by the two measuring methods in the multi-sensor system. Data fusion allows new or more precise knowledge about physical quantities to be gained by using different sources of information. This is often done in less time and with lower costs. The output data can be raw signals from sensors, but also mathematical or verbal descriptions of object properties [50]. A concise definition describes data fusion as “the act or process of combining two or more pieces of data or information regarding one or more entities in order to improve one’s capability (or provide a new capability) for detection, identification, or characterization of that entity” [51]. The focus of data fusion, therefore, is on the enhancement of perception (detection) and the discovery of characteristic properties (characterization) and features that are not possible with single-sensor measurements. Over the years, merger models have been developed to generate a common understanding of the process [52]. A general data fusion model is shown in Figure 2.34.

Figure 2.34 General model of data fusion [52]

This fusion model combines all objects for which information is available into a world model. In addition, there are relevant status parameters, such as position or orientation. The world model is updated iteratively or on demand in order to record changes. By knowing the state of the sensors and utilizing sensor models, statements about the world model are derived [52]. There is also the JDL model developed by the joint directors of laboratories data fusion working group and the omnibus model [53].

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

The principles of the data fusion process are illustrated in Figure 2.35. After data acquisition, the data must be preprocessed. To carry out data fusion, it is necessary to register and synchronize the data according to space. Then the fusion can take place. In the last step, the fusion is evaluated and a detection is performed.

Figure 2.35 Processing steps of data fusion [50]

Application of Data Fusion In recent years, the field of data fusion has received increasing attention in both military and non-military fields of application (e.g., in the material testing of wind turbine blades [54]) and has developed rapidly. Depending on the application area, different types of data are fused. Sensor integration can be accomplished according to three concepts, as shown in Figure 2.36. The concept used in this research is cooperative integration. Here, two different sensors are used, each of which can only add value by using the other sensor. Since two different sensors are used, only this type of integration can be selected. The implementation of the merger is explained in more detail in the following chapter.

Figure 2.36 Concepts for sensor integration [50]

55

56

2 Manufacturing of CoDiCoFRP

Implementation The procedure for merging laser light section data and thermographic images of continuous discontinuous glass fiber SMC is shown in Figure 2.37. First, the 3D geometry is recorded with the laser light section system. After calibration of the thermographic camera, 2D images are taken using thermography. In both cases, registration bodies are included. By recording the registry bodies, it is possible to map the images together. This is the basic requirement for data fusion, which is described in more detail in the following chapter.

Figure 2.37 Data fusion procedure of laser light section and thermography [55]

2.4.7 Evaluation and Results This section introduces the results of the data fusion of laser light section and thermography and explains the procedure in more detail. Suitable registration bodies must first be selected for the data fusion of the laser light section and thermography. Toward this end, cylinders are used, which are detected by laser light section and thermography (see Figure  2.38). In the laser light section method, the upper surfaces of the cylinders are extracted and measured to align them with the upper surfaces of the thermographic images. The surface area is 22.35 mm in diameter.

Figure 2.38 Detection of reference bodies by (a) a laser light section system and (b) thermography [55]

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

The laser light section system generates a cloud of points, which is shown in Figure 2.39.

Figure 2.39 Cloud of points generated by the laser light section system [55]

Figure 2.40 Data fusion result of laser light section and thermography [55]

57

58

2 Manufacturing of CoDiCoFRP

Subsequently, individual thermographic images of the component are taken and mapped to the cloud of points, as shown in Figure 2.40. This makes it possible to generate a 3D image from 2D thermograms, which facilitates defect identification in relation to the component. This data fusion approach makes it possible to quickly detect defects in the examined material. The laser light section method makes it possible to detect external defects of discontinuous glass fiber SMC and continuous carbon fiber SMC. Thermography is suitable for use with both materials to locate internal defects and detect fiber displacements. Mapping permits the internal defects to be localized more clearly. It also makes it possible to determine the distance between internal and external defects. Figure 2.40 shows the carbon prepreg on the surface and the orientation of the prepreg.

2.4.8 Effects of Defects To ensure function-oriented quality assurance, it is necessary to know the effect of a defect so as to assess whether the component is still acceptable or must be sorted out. The investigation of these effects of defects are discussed. The knowledge of the effect of a defect makes it possible to give the user an initial guideline value for the component quality. In a next step, this knowledge must be incorporated into the data base. To be able to evaluate defects, they must be introduced into components in a defined way. Plates with defects are produced for this purpose. The defects fold, resin accumulation, and angular deviation (of 5°, 10°, and 15°) of the fibers are examined. In the fold defect, the unidirectional carbon fiber material is crimped. In the resin accumulation defect, pure resin is applied in the middle of the samples. Then tensile specimens are cut from the plates. These have a size of 20 mm  210 mm. Figure 2.41 shows an example of the cutting plan of a plate with 15° specimens.

Figure 2.41 Cutting plan of a plate with 15° specimens

2.4 Quality Assurance of Continuous–Discontinuous Glass-Fiber SMC

The samples are then used for tensile tests with a Zmart.Pro universal testing machine by Zwick Roell with a load cell capacity of 200 kN. The tests were carried out in cooperation with the project partner IAM-WK, which provided the tensile tester. The specimens were pre-stressed up to 100 N and then strained with a nominal load capacity of 2  mm/min up to fracture. The longitudinal strain was recorded with a tactile extensometer and an initial measurement length of L0 H 60 mm. Table 2.1 provides an overview of the results of the tensile tests. Table 2.1  Results of Tensile Test Specimens Number of samples broken in the middle of the specimen

Number of specimens that failed in the measurement region

Reference

22

9

Fold

13

9

Resin accumulation

9

8

Angle 5°

13

3

Angle 10°

16

4

Angle 15°

10

4

Total

83

37

The Young’s modulus is calculated with all samples taken in Table 2.1. The results of the good parts are given as a reference. The tensile strength is only calculated for the components that are broken in the measuring region in the middle of the specimens. The Young’s modulus of the reference samples varies from 24.2  GPa to 28.8  GPa (arithmetic mean value: 26.7  GPa, standard deviation: 1.28 GPa). The large standard deviation can be attributed to the inhomogeneous material properties. The mean value of the tensile strength is 422.3 MPa, with a standard deviation of 25.7 MPa. The Young’s modulus and tensile strength are plotted with their mean values and standard deviations. To evaluate the defective samples, their values are compared with the values of the reference components (see Figure  2.42 and Figure 2.43). It is shown that the fold and the resin build-up reduce the Young’s modulus by 4.77% and 13.5%, respectively. An angle deviation of 5° results in a reduction of only 3.28%, whereas a 15° angle deviation leads to a significant reduction of 21.79%. The same trend holds for tensile strength, with the fold causing a more pronounced reduction here (23.15%) than for the Young’s modulus. An angular deviation of 5° also leads to a decrease of 17.83%. These results provide an initial overview of the influence of the defects and offer a guideline as to which defects lead to which reductions. Thus, the user has an opportunity to evaluate the components.

59

60

2 Manufacturing of CoDiCoFRP

Figure 2.42 Young’s modulus of test specimens

Figure 2.43 Tensile strength of test specimens

2.4.9 Conclusion In this section, it is implied that complete quality assurance is necessary to guarantee faultless production and current research verifies this assertion. Combining continuous and discontinuous material extends the number of defects that must be detected. It is not possible to do so with a single-sensor system within an acceptably short time, which is why a multi-sensor system was developed. Combining different types of data makes it possible to convert 2D thermographic images into 3D images. This enables a better determination of the defect position, since the defect now includes the location information derived from a laser light section system. In a further step, it is necessary to determine the measurement uncertainty of the individual sensors and the data fusion results to assess the quality of the multi-

2.5 Machining of CoDiCoFRP

sensor system. This would be a future project. Furthermore, an analysis of the phase images of the thermography can be used to estimate the defect depth. This can be integrated into the data fusion to obtain depth information. The results of the data fusion also provide a basis for evaluating the effects of defects. It is shown that the Young’s modulus decreases due to resin accumulations and increasing angular deviations. With increasing angular deviation, the Young’s modulus and the tensile strength also decrease. This is also clearly evident in its tensile strength. The fold has a more pronounced negative effect on the tensile strength than it does on the Young’s modulus. The results provide an initial indication of how defects can affect the mechanical properties. Thus, a system is created in this research work that contributes to holistic quality assurance of continuous– discontinuous sheet molding compounding materials.

„„2.5 Machining of CoDiCoFRP Anton Helfrich, Frederik Zanger, Volker Schulze 2.5.1 Introduction The manufacturing costs for fiber reinforced polymers (FRP) are one of the main challenges in regard to increasing the production capacity [56]. The finishing processes range from introducing holes and pockets for subsequent joining operations to trimming edges to obtain the final contour to separating parts after the molding process. For all these machining processes, the anisotropic properties and layered structure represent key challenges. Characteristic damage types resulting from machining are delamination, fiber pull-out, fraying, and spalling [57]. This chapter presents an overview of the machining processes with the current state of the research, followed by results from experiments conducted in this study with the newly proposed CoDiCoFRP. Overview Although fiber reinforced polymers are often manufactured near net shape, further processing steps are required to ensure their complete functionality or to prepare for the remaining production steps of a part. The main machining processes used are drilling and milling. Machining, in general, is based on the same principle as shown in Figure 2.44 for orthogonal cutting. The cutting edge penetrates the workpiece material at a certain depth h, thereby forming a chip, which is removed from the new surface by the rake face of the cutting wedge. The tool material and pro-

61

62

2 Manufacturing of CoDiCoFRP

cess parameters must be adjusted to the workpiece material, otherwise high tool wear and low-quality machining will result.

Figure 2.44 Orthogonal cutting process

Drilling – the most effective way to produce holes in parts – is a process with a circular cutting motion at the tip of the tool. The feed motion (vf) is parallel to the rotation axis, as shown in Figure 2.45 on the left side. The machining force F is composed of the cutting force Fc, the feed force Ff, and the passive force Fp. Fc and Ff can be combined to the so-called active force Fa. Fc is always directed in cutting direction, meaning that the orientation is rotating with the tool. The rotating orientation is also found for Fp, which is always perpendicular to the active force Fa. The forces mentioned are significantly involved in the resulting quality of the machined workpieces. The magnitude of the total machining force F is influenced by the adjustable process parameters, i.e., cutting speed vc and feed rate vf. The feed rate is adjusted as the feed per tooth fz in mm, which is the distance that the tool is moved forward before the next cutting edge reaches the same angular position. Additionally, the material used as reinforcement (e.g., glass or carbon fibers) is crucial for the magnitude of F, as well as for the machining quality and wear behavior. The main cutting edges are engaged for the whole drilling process.

Figure 2.45 Effective forces during drilling and milling operations adapted from [58]

2.5 Machining of CoDiCoFRP

The process of milling enables many different tasks. Since FRP parts are produced to near net shape, the most frequently applied task is trimming. Milling also allows one to produce holes, grooves, and pockets. The composition of the total machining force is the same as for drilling. Unlike drilling, however, the feed direction is perpendicular to the rotation axis and the cutting-edge engagement is not permanent. The cutting edges are engaged and disengaged during every rotation, as shown in Figure 2.46. This is called interrupted cutting.

Figure 2.46 Milling modes depending on the feed direction, adapted from [59]

Therefore, the resulting machining force fluctuates with every engagement and disengagement of the cutting edges. The frequency and severity of the change in direction depends on the mode of milling and the set parameters. Figure  2.46 shows two basic modes that depend on the feed direction of the workpiece. Since the cutting conditions differ for each mode, the mode must be chosen carefully. These modes are combined with cutting modes that depend on the orientation of the tool-turning axis relative to the workpiece surface (see Figure 2.47). When machining high strength materials like FRP, the results vary vastly, depending on the chosen mode.

Figure 2.47 Milling modes depending on the tool, adapted from [59]

The main challenge of machining of FRP results from its inherent structure. Most importantly, its brittle fracture behavior leads to difficulties in machining. In Fig-

63

64

2 Manufacturing of CoDiCoFRP

ure 2.48(a), the correlation between the fiber cutting angle and cutting modes is shown. At H 0°, the fibers to be cut are compressed and lifted up, which leads to a fiber fracture occurring at some distance in front of the tool. At the same time, this lifting causes an inter-laminar crack to propagate into the material, which in turn can lead to delamination. At H 90°, the fibers break when the cutting edge goes through them. Since the fibers possess a high cutting resistance, some fibers will break later. They will be compressed, which leads to inter-laminar cracking perpendicular to the cutting direction. This cracking leads to greater damages, as shown in Figure  2.48(b). The inter-laminar cracks can lead to delamination and spalling. Fraying or fuzzing occurs when the fibers are not cut completely and can bend out of the cutting plane. Delamination and spalling are the exclusion criteria for most FRP parts.

Figure 2.48 (a) Interdependence of cutting modes and fiber cutting angle, adapted from [60] and (b) possible damage types resulting from machining [61]

State of the Art for FRP Processing Although FRP machining has been investigated since the 1980s, many researchers are still studying drilling and milling processes, since they vary greatly depending on the layer arrangement of the material. Since the CoDiCo reinforcement is a new type of reinforcement structure, most of the existing investigations regard these operations for different configurations of glass fiber reinforced plastics (GFRP) or carbon fiber reinforced plastics (CFRP). Drilling CoFRP often results in delamination, spalling, and fraying [62]. The severity of these failure modes was found to depend not only on the drilling parameters, cutting speed, and feed rate [62], but also on the clamping situation [63], the tool (micro)geometry [64], the processing strategy [65], and the wear state of the tool [63, 66]. The clamping situation has a profound influence on the resulting process forces, which, in turn, influence the resulting failure modes [63]. By choosing the machining parameters carefully, the resulting failure of CoFRP can be reduced or

2.5 Machining of CoDiCoFRP

completely avoided [63, 64]. Even for worn tools, the resulting damages can be reduced using adapted machining parameters [66]. By developing new drilling strategies like wobble milling, it is possible to direct the resulting forces into the material. This way the best damage reduction can be achieved. With this process strategy, it is even possible to use a tool beyond its normal tool life, since the higher force is directed in a more favorable direction [65]. Through finely tuned process control, the high tool wear caused by the fibers can be compensated to get the same machining results with the same tool, thereby even exceeding its estimated tool life [67]. Investigations of the milling process show similar results as for drilling. The resulting failure modes also depend on the machining parameters, cutting speed, and feed rate. The feed rate was found to have a greater influence than the cutting speed [67, 68]. The influence of the clamping situation on workpiece damage in the milling of FRPs has received little attention. In [69], no influence on damage was recognized, but the resulting forces changed when the clamping situation was changed. As for drilling, the tool wear state has a significant influence on the quality of the machined area. For sharp cutting edges, damages were rarely seen. Medium to heavily worn tools lead to significant damage with the same process parameters [70]. The influence of the fiber orientation has been investigated most thoroughly, since this is the most defining property of FRP. As mentioned in the Overview section, the machining of FRP often takes place within a certain fiber cutting angle range. The size of the fiber cutting angle strongly determines the machining quality [70, 71]. In woven fabric FRP, the weave structure also alters the damage behavior of the material [72]. In a direct comparison between CFRP and GFRP, the machining forces measured were always smaller for glass fibers than for carbon fibers [68].

2.5.2 Experimental Study of the Machining of CoDiCoFRP In the present work, a mixed material/reinforcement combination is examined regarding its milling properties. This combination is called CoDiCoFRP. The discontinuous fibers are represented by short glass or carbon fiber reinforced thermosets in the form of sheet molding compounds (SMC); the continuous fibers are represented by carbon-fiber-reinforced thermosets in the form of unidirectional fiber prepregs. This new combination holds great potential for extending the use of FRP in commercial applications. Since glass fibers are cheaper than carbon fibers, the basic structure of a part can be made of SMC, while defined load paths can be reinforced locally by continuous fibers. This could lead to cheaper FRP structures if glass fibers are used for less loaded areas, while keeping the structural stability through intelligent placement of the high-priced carbon prepregs. A comparison to

65

66

2 Manufacturing of CoDiCoFRP

those effects seen for uniform material is important in order to understand how the structure changes the resulting defects and forces and to improve analysis strategies for upcoming investigations. Based on the literature reviewed in the State of the Art for FRP Processing section, experiments were designed to assess the machinability of the CoDiCoFRP. In the following, the approach, execution and results of these investigations will be presented. They are based on previously published work by the authors [73, 74]. Challenges Due to the Nature of the Combination In all the presented studies, the machining of either CFRP or GFRP is under investigation. The combinations of the different fiber reinforcement materials have been investigated before as hybrid materials by a few researchers. Hardaker and Richardson pointed out [137] that the hybrid effects can be used to lower the price, adjust the laminate properties, allow for unique hybrid material effects, and insert pre-catastrophic damage indicators. Since that time, various research groups have investigated the mechanical properties and manufacturing of hybrid composites. However, the investigation of machinability for hybrid fiber reinforced composites such as CoDiCo has attracted little attention. Since, as shown in previous chapters, the combination of long fibers and continuous fibers and the combination of glass and carbon fibers both alter the properties of the laminate, it is also expected to change the machining properties. It is not only the force distribution and magnitude that will change, but also the machining qualities that depend on the material fractions and layer set-up. Experimental Set-Ups To investigate machinability, various specimens and experimental set-ups were used. The order of the experiments discussed is the sequence in which these experiments were performed. In this chapter, the experimental set-ups of the investigation are presented according to the object of investigation. Investigating the Influence of Thickness, Layer Structure, Machining Parameters, and Milling Modes Figure 2.49 shows the layer structure of the specimens with their respective layer set-up and thickness. The names of the specimens were chosen to represent the structure of the laminate. The material carbon is represented by “c” and glass is represented by “g”. The letters “u” and “s” refer to the layers UD layer and SMC, respectively. The numbers in the name describe the number of layers of the same type and material. The name “g_2s” thus means that there are two glass fiber SMC layers. The combined layers are named like this: “gc_s6us”. The order of “g” and “c” shows which material comes first in the structure and is subsequently bound to the layer type. This name thus means that the “s” layer is made of glass fibers and the “u” layer is

2.5 Machining of CoDiCoFRP

made of carbon fibers. Here “s6us” represents one glass fiber layer above and below six carbon fiber layers, as illustrated in Figure 2.49. This nomenclature was chosen to keep the structure of the different specimens in mind. With these layer set-ups, the influence of several variables on the machining force and quality could be identified. For this investigation, the specimens were cut from the pressed plates into smaller plates, as shown in Figure 2.50. The orientation of all UD-tapes and layers is always perpendicular to the milling direction (y-axis) in these experiments. The set-up, as shown in Figure 2.50, was chosen to analyze the effects of climb milling and conventional milling in conjunction with the same machining parameters. The laminates g_2s and g_4s have the same material and differ only in thickness, thereby enabling one to interpret the influence of the thickness. Comparison of the laminates cg_u2su and cg_u4su allows one to see the influence of additional CF-layers on the machining forces and quality. Because the laminates gc_s6us and cg_3u2s3u consist of the same layers in a different order, the influence of the layer set-up can be made apparent. To perform the experiments, a HELLER MC16 machining center was used. The resulting forces were captured by a rotating dynamometer of the type 9125A11 on the spindle and a three-component force measuring platform of the type 9255SP by KISTLER. The measuring platform was oriented so that the z-axis of both measuring systems and the coordinate systems of the specimens line up. A custom made clamping system was used to minimize the distance between the machined area and the clamping area, as in [69].

Figure 2.49 Layer structure and thickness of the investigated specimens. The coordinate system shows the orientation of the specimen in the machining set-up

In Figure 2.50(a), the schematic arrangement of the clamping system can be seen, as well as the position of the tool during the milling process.

67

68

2 Manufacturing of CoDiCoFRP

Figure 2.50 Experimental set-up for the investigation and the specimen coordinate system (see Figure 2.49) during the machining process

The tool used for milling the slots was an uncoated, cemented, carbide end mill by Walter AG with a diameter of 6 mm, which complies with DIN 6527 L. The end mill has two flutes and a helix angle of 30°. The cutting edge of the unused tool was measured with a confocal measurement device of the type surf custom by nanofocus. The cutting edge had a radius of about 6 m. Since tool wear was not being investigated, its impact was minimized by changing the tools after two meters of milling, at the latest, which corresponds to one tool per specimen. The order of the experiments was also randomized to further minimize the impact of tool wear on one particular parameter set. A full factorial design of experiments was used with four repetitions for every set of parameters, as shown in Table 2.2. Table 2.2  Parameters Varied in the Experiments Cutting speeds vc in m/min

Feed per tooth fz in mm

Cutting width Cutting depth ae in mm (tool diameter) ap in mm

100, 200, 300

0.01, 0.03, 0.05

6

2 to 4

Investigating the Influence of Helix Angle and Feed Rate In the further investigations, carbon fiber SMC was used. The specimens used are shown in Figure 2.51. The names of the laminates follow the same system as for the previous specimens, with the exception that when all layers are made of carbon only one “c” is written. As in the previous part of the investigations, here too, the influences on the total machining force and the machining quality were analyzed. In this experimental set-up, the influence of the layer set-up has been further investigated. The specimens were cut into strips of 4 mm  20 mm, which were clamped on one side to allow a down milling process at the edge. The main aspects of the machine set-up are similar to those in the previous investigations shown in Figure 2.50. The main parameter being observed was the influence of the helix angle of the tools.

2.5 Machining of CoDiCoFRP

Figure 2.51 Layer structure and thickness of the investigated specimens. The coordinate systems show the orientation of the specimen in the machining set-up

The workpiece alignment and tools used in these experiments are shown in Figure 2.52. Tool (b) is the same tool as used in the previous experiments. The other tools are also uncoated, cemented carbide tools, but these were manufactured by Hufschmied GmbH. Tool (c) has a helix angle of 14° and tool (d) has an angle of 0°. All tool diameters are 6 mm. Here, a comparison of the machining performance of these three mills was made to find the ideal helix angle. The cutting speed is set at 300  m/min and the feed per tooth is varied as before between 0.01  mm and 0.05 mm. The cutting depth also corresponds to the laminate thickness and the cutting width is 4 mm.

Figure 2.52 (a) Scheme of the investigated edge-trimming process and the milling tools with helix angles of (b) 30°, (c) 14°, and (d) 0° used for the investigation

Investigating Complex Tool Geometries and Temperature Development In this investigation, more complex tool geometries were investigated. The laminates investigated for these experiments are shown in Figure 2.53. Laminates gc_ s6us and cg_3u2s3u are the same as in the previous investigations, with one distinction: the UD-tapes are now oriented parallel to the machining direction. The other laminates are taken from the baseplate of the reference structure, which were partly reinforced with one UD-tape at one surface. The taped surface was always oriented according to the coordinate system in Figure 2.50 and Figure 2.53. The tools that were used are shown in Figure 2.54. The tool shown in Figure 2.54(a)

69

70

2 Manufacturing of CoDiCoFRP

is the same as used in the previous experiments, enabling a direct comparison with the forces and qualities of the other investigations. The other three tools are designed by Hufschmied GmbH especially for machining FRP. The tool shown in Figure 2.54(b) has a helix angle of −14°, with an additional tooth-like structure on the cutting edges that facilitates the cutting of the fibers. The tool shown in Figure 2.54(c) is a poly-crystalline diamond (PCD) tool with no helix angle. PCD is often recommended as the ideal cutting tool material for machining CFRP, since it resists wear longer than cemented carbide tools. The tool shown in Figure 2.54(d) has a helix angle of −2°, along with four flutes, each with a smaller trailing cutting edge, which should produce a better cutting result.

Figure 2.53 Layer structure and thickness of the investigated specimens. The coordinate systems show the orientation of the specimen in the machining set-up

The experimental set-up is similar to the previous experiments. An edge-trimming operation was performed as in Figure 2.52(a). However, the cutting width was set to 2 mm. The cutting depth, as before, was equal to the laminate thickness. For all experiments in this part, the performance of the different tools is the focus. Simultaneously, the influence of a single ply on the forces might possibly be seen. Another investigated issue was heat development during the milling process. The experiments were performed with the conventional end mill and the laminates c_4s, c_u4s, and gc_s6us. The temperature was recorded by a thermography camera of the type ImageIR 3300 MCT. For all laminates, the parameters were the same as before (vc H 200 m/min, fz H 0.05 mm). In the case of c_u4s and gc_s6us, half of the feed per tooth was also investigated. The reason for the small sample and parameter set was the absence of thermal damage in all comparable experiments. Nevertheless, the resulting temperature was still of interest for future investigations.

2.5 Machining of CoDiCoFRP

Figure 2.54  T ools used to investigate complex tool geometries: (a) conventional end mill, helix angle 30°, diameter 6 mm (SF30), (b) “hexacut” end mill, helix angle −8°, diameter 8 mm (HEX8), (c) polycrystalline diamond end mill, helix angle 0°, diameter 8 mm (PCD) (d) “carb star twister” end mill, helix angle −2°, diameter 6 mm (HEX6)

Force Measurements The forces in all three parts of the paper were measured via a force-measuring platform separately in the three directions (Fx, Fy, Fz). The total machining force (F) is equivalent to the modulus of the vector sum of the separately measured forces. Since the machining force F is a superposition of the feed force, the cutting force, and the passive force (see Figure  2.45), the applied measurement system does not allow a separation. The force oscillates during one experiment, because the engagement of the cutting edges changes during each rotation. To get a comparable result, the peaks of this oscillating signal were identified and an arithmetical average was calculated with the corresponding standard deviation. For every experiment with the same conditions, a weighted average was calculated subsequently. The resulting quantity can then be compared.

2.5.3 Results and Discussion In this chapter, the results of the various experiments are presented in the context of the parameters influencing the machining quality or forces. The results of the three investigations described in the previous section are combined to show the cumulative effect. Layer Structure To analyze the influence of layer structure on the machining forces and quality, various laminates machined with the same parameters can be compared. Aspects of the layer structure that can be considered are: ƒƒthe difference due to added layers: increase for added continuous (CF) layers or change in thickness and ƒƒthe difference due to a different stacking order of the same layers.

71

72

2 Manufacturing of CoDiCoFRP

Figure 2.56 shows the process forces based on the material thickness. The change of force due to thickness can be shown for the glass laminates g_2s and g_4s. These laminates were milled by circumferential milling. Comparing the forces for all parameters, a mean value increase of 19% is found for the doubled thickness, while the differences range between +43% and −12%. This increase can be explained, since the chipping width increases with laminate thickness. The reduced machining force for the thicker material might be traceable to inconsistencies in the material production, especially for laminates thicker than 3 mm. Nonetheless, the mean increase of 19% shows that the thickness influences the forces. In the experiments conducted, no quantitative dependence between the resulting machining forces and layer thickness could be observed. In the qualitative evaluation, the addition of a single unidirectional carbon fiber layer was not detectable. The resulting forces stay at about the same level for all investigated tools and in some cases even show tendencies to decrease. Since one layer of a laminate only accounts for a small fraction of the whole laminate thickness, the theoretical increase in the force of this additional layer is lost in the oscillating force signal and cannot be singled out. The stacking order of the laminate determines how the loads and stresses are distributed. Since the laminate is often designed to sustain certain loads, the amount of carbon fiber layers may be fixed. The addition of glass fiber SMC or carbon fiber SMC can then be made to achieve a certain thickness without the costly continuous carbon fiber prepregs. While increasing thickness by adding layers contributes to the total machining force, no influence of stacking order can be detected. The influence of stacking order on the damage, however, was more serious. With UD layers at the top, the fraying and delamination occurred more often and were more distinct. With SMC layers on top, single fibers or fiber groups stood out in some cases, but placing an SMC layer on top generally resulted in better machining quality. Figure 2.55 shows the difference between UD and SMC layers on top.

Figure 2.55  Different failure appearance for machined laminates with vc H 200 mm/min and fz H 0.03 mm

2.5 Machining of CoDiCoFRP

Process Parameters The adjustments that must be considered for every machining process are the cutting speed vc and the feed per tooth fz. These two parameters are the most influential on the machining forces after deciding on a certain machining set-up. Varying the cutting speed and the feed per tooth can then influence the machining forces. Figure 2.56 shows that the machining forces rise with rising process parameters, and the increase is more pronounced when the feed per tooth is changed than when the cutting speed is changed.

Figure 2.56 Influence of cutting speed and feed rate on the maximum machining forces for different laminate stacks and thicknesses

The reason for the higher influence of the feed rate as compared to the cutting speed is the changing chipping volume. The feed rate per tooth coincides with the maximum chip thickness. This, in turn, requires a higher cutting force. The cutting speed, on the other hand, does not change the chipping volume. Instead, it changes the frequency at which the cutting edges plunge into the material. The higher speed equates to a higher kinetic energy of the tool, which can explain the higher machining force. However, the choice of the machining parameters depends strongly on the choice of the machining tool and the machined material. Tool Geometry Figure 2.57 shows the influence of process parameters on the resulting machining forces as well as the resulting delamination area. The examined process parameters are tool geometry and feed per tooth. With an increased feed rate, the resulting machining forces increase for all investigated tool geometries. The highest resulting machining forces are observed for a feed rate of fz H 0.05  mm, while the lowest machining forces are observed for fz H 0.01 mm. In this context, an increased feed rate does not result in a quantitative increase in delamination area.

73

74

2 Manufacturing of CoDiCoFRP

Further evaluations of the experiments conducted show no direct correlation between the feed rate and the damaged area. However, influences on the reproducibility could be observed. Helix angles of 0° and 30° and a feed rate of 0.05 mm results in high standard derivations. This leads to reduced process reliability. This correlation can also be observed at a helix angle of 14° and a feed rate of 0.03 mm. The highest feed rate led to a reproducible damaged area. This is indicated by a moderate standard deviation. Depending on the tool used, an increase in feed rate can cause an increase in delamination area and a decrease in process reproducibility. This can be explained by the filling of the chip chamber flutes of the different tool geometries. The chip removal influences the chip formation and therefore the resulting component quality. In conclusion, for the investigated process parameters, the influence of machining parameters on the resulting delamination area depends on the tool geometry. Therefore, an individual adjustment of the process parameters depending on the tool used is necessary to achieve optimum machining results. In Figure 2.58, the resulting maximum machining forces depending on the laminates and different tool geometries are shown. A comparison of the tools with the adjusted geometry (Figure 2.54) showed that, although the standard end mill with the 30° helix angle showed the lowest machining forces, it also produced the most damage. The least damage and therefore best machining qualities were achieved with the PCD end mill, followed by the third mill with four main cutting edges and four smaller trimming edges. The mill with the toothed cutting edge showed the highest machining force with the third lowest damage level.

Figure 2.57 Influence of tool geometries on delamination and machining force: (a) helix angle 0°, (b) helix angle 14°, and (c) helix angle 30°. Laminate: c_2u3s2u

2.5 Machining of CoDiCoFRP

Figure 2.58 Influence of adjusted tool geometries on the maximum machining forces

Temperature Development The temperature has to rise in the machining area due to the massive mechanical energy present during this process. Figure 2.59 shows a cumulated difference image of the measurement. The temperature rise outside the specimen results from pulverized matrix material and fibers. The reference for the difference image is a frame shortly before the machining starts. The experiments showed a temperature difference of around 90  K for various materials as well as thicknesses and feed rates. For the 4 mm specimen gc_s6us, the temperature was constant for both parameter sets. One explanation for this behavior might be that the temperature decrease due to the slower feed rate is canceled out by the increased friction of thicker specimens. Either way, the temperature difference measured in this short-term examination is not high enough to thermally induce damage to the matrix of the FRP. The observation that the temperature remains constant at least for a given feed rate and thickness is very positive for future investigations. It means that thermal damage is unlikely. Since observations were only made for the standard 30° helix end mill, the temperature rise could be higher for different tools, especially since they require higher machining forces. Moreover, compared to the temperatures for machining metals, the temperatures observed in these studies are considerably lower.

Figure 2.59 Cumulated difference picture of the thermography recording. The maximum temperatures were used as the base for the differences

75

76

2 Manufacturing of CoDiCoFRP

2.5.4 Conclusions The investigations performed here confirmed various effects that were observed for pure CFRP and GFRP laminates. The following conclusions for machining CoDiCoFRP can be drawn from the results: ƒƒThe machining forces rise with higher ratios of CF-layers, whether UD or SMC, since they possess a higher machining resistance. The thickness is clearly seen to have an effect on the machining forces. The influence of adding a single layer to a laminate, however, is undetectable. ƒƒThe order of the layers has an effect on both machining and damage behavior. Glass-fiber SMC layers on the outside seem to reduce the damage associated with certain machining parameters. Having a UD layer on the outside has a negative effect on the quality. The influence on the machining forces could not be seen in any investigations. ƒƒThe machining force is influenced by the machining parameters. The feed per tooth has a higher influence on the total machining force than the cutting speed. Furthermore, the machining parameters also influence the machining quality. It was shown that an increase in feed per tooth increases damage more than an increase in cutting speed. ƒƒThe tool geometry has an effect on the damage resulting from the machining process and also on the force distribution into the material. The results show that the helix angle of a tool has an influence on the machining forces as well as on the resulting damage. Adjusting the tool geometry even more can lead to significantly better machining quality, at the expense of slightly increased machining forces. ƒƒThe temperature rises by around 90 K, which is not high enough to induce thermal damage to the thermoset matrix. The temperature decreased slightly as feed per tooth and cutting speed were reduced, but the temperature generally remains within the same range.

„„2.6 Foaming of Microfibrillar Composites Ali Rizvi, Chul B. Park 2.6.1 Introduction Polymer foams are commercially and technologically important materials characterized by a light weight, excellent strength/weight ratio, thermal and sound insula-

2.6 Foaming of Microfibrillar Composites

tion, and energy absorption [75]. These properties make foams suitable for various applications in the construction, packaging, automotive, and medical industries. The foaming of polymers typically involves the following steps: (1) dissolution of a gas (blowing agent) into a polymer; (2)  generation of bubbles or cells by phase separation of the blowing agent from the polymer; and (3) stabilization of the porous or cellular structure. The primary mode of deformation during cell growth in polymer foaming is extensional. Consequently, the viscoelastic properties of polymer melts and their ability to crystallize are important in foaming. During the foaming process, the melt viscosity must increase either by cooling the melt, crystallization, or through strain hardening in extension until it reaches a degree suitable for stabilizing the growing cells and preventing them from rupturing. The use of semi-crystalline polymers for foaming applications is restricted, since these polymers generally exhibit inadequate rheological properties at processing temperatures. Unlike amorphous polymers, semi-crystalline polymers show a rapid reduction in viscosity and melt strength around the melting temperature. Therefore, it is a challenge to achieve the processing temperature range required for generating stable foams, where the polymer is stiff enough to prevent cell rupture but soft enough to deform under relatively small stresses during bubble growth [76]. Various methods have been proposed to broaden the foam processing window of semi-crystalline polymers. Crosslinking semi-crystalline polymers is an effective strategy for increasing their melt strength and strain hardening response in extensional flows. Unfortunately, however, it renders the polymer unrecyclable [77, 78]. Furthermore, the degree of crosslinking must be carefully controlled, since excessive crosslinking can restrict cell growth. Long-chain branching is also effective in increasing the melt strength and strain hardening behavior of the semicrystalline polymers. Here, however, the cost of such resins is significantly higher than their linear counterparts. For example, long-chain branched polypropylene (PP) effectively produces low density PP foams, but commercially available high melt strength PP costs twice as much as linear PP [79–81]. Melt viscosity modification in semi-crystalline polymers, such as polylactic acid (PLA), has been accomplished using chain extenders. Here, however, there is a danger of gel formation, which dramatically reduces the material’s flowability characteristics [82]. Exfoliation of nanoparticles, such as organically modified, layered nanoclay, carbon nanofibers, and carbon nanotubes, in semi-crystalline polymers has been shown to improve the melt viscosity and elasticity [83–85]. The drawback here is that exposure to such nanoparticles poses a significant health hazard. Exfoliation of nanoparticles in polymers is also technically challenging and requires fine tuning of the nanoparticle surface chemistry, as well as their synthesis and processing conditions [86–88].

77

78

2 Manufacturing of CoDiCoFRP

Despite the existence of several methods to compensate for the poor melt strength and weak strain hardening in the extension of semi-crystalline polymers, improving their rheological properties for foam processing applications remains a challenge. The deficiencies of these existing methods point toward a need to develop strategies to improve the foaming ability of semi-crystalline polymers in an environmentally sustainable, inexpensive, and completely scalable way. Blending immiscible polymers has emerged as an effective tool to control the rheological and crystallization properties of polymers. The behavior of a polymer matrix is critically dependent on the morphology of the dispersed phase [89], and divergence in the performance of seemingly identical blend compositions is often attributed to morphological differences. Therefore, morphological control is a critical parameter, when optimizing the performance of a polymer matrix. The morphological characteristics of the dispersed phase domains in immiscible polymer blends are governed by: (a) the complexity of the thermal and hydrodynamic flow fields experienced by the blend during physical blending, (b) the competition between droplet break up and coalescence of the dispersed phase domains, and (c) the viscoelastic properties of the phases [90]. The fibrillar morphology where the dispersed phase deforms into extended submicron filamentous structures in a polymeric host is of particular importance. The fibrils can bend substantially in response to inter-fibrillar interactions during flow, due to their high aspect ratio [91]. This bending causes the formation of a disordered physical network characterized by superior mechanical and rheological properties at a concentration greater than the random close-packing of fibers [92– 95]. The presence of a fibrillar network defined by topological (entangled) interactions is expected to create additional, large contributions to the viscoelasticity of the polymer matrix. A disordered physical fibril network forms within the matrix beyond the rheological percolation threshold and imparts such desirable properties to the matrix as improved melt strength, strain hardening in extensional flow, and increased melt elasticity. For the fibrillar network, the mechanism of strain hardening in extensional flow is analogous to that of long-chain branched polymers, that is, strain hardening originates from restricted stretching of the backbone between branch points [96]. Modifying the crystallization and rheological characteristics of a host polymer by controlling the microstructure of the dispersed phase can have substantial effects on the foam processing of the matrix. In this work, the relationship between polymer blend morphology and foam processability of semi-crystalline polymers is presented, with specific focus on the fibrillar morphology. The aim is to better understand the role of fibrillar domains on the viscoelastic properties and crystallization kinetics of the matrix polymer, so that superior polymer formulations can be developed for large-scale foam processing.

2.6 Foaming of Microfibrillar Composites

2.6.2 Fibril Formation during Blending The deformation of an immiscible liquid droplet in a surrounding liquid matrix is governed by the rheological and interfacial properties of both components and by the dynamic equilibrium between two counteracting stresses: (1) the hydrodynamic stress , which deforms the droplet into elongated, filamentous structures and (2) the interfacial stress dc ∕ R (where dc is the interfacial tension and R is the unperturbed droplet radius), which minimizes the interfacial energy by retaining the spherical shape of the dispersed phase [90]. The ratio between these two competing stresses is known as the capillary number Ca. The second dimensionless number controlling droplet deformation is the viscosity ratio  D d =c , where d is the viscosity of the dispersed phase and c is the viscosity of the surrounding continuous phase. There is also a critical capillary number Cacrit, above which the deformation and disintegration of the droplet occurs. Cacrit depends on the viscosity ratio and the type of flow (shear or extensional) [97]. The interfacial stress overrides the hydrodynamic stress when the magnitude of Ca is lower than Cacrit. Here, droplets do not break, but undergo only slight deformation from their equilibrium shape. The hydrodynamic stress dominates the interfacial stress when the Ca > Cacrit. Here, droplets continue to stretch until they break, due to growing disturbances at the interface [98]. Ultimately, the interfacial stress becomes negligible with respect to the hydrodynamic stress when Ca >  Cacrit, where  is about 2 for simple shear flow and 5 for elongational flow [99]. Here, droplets undergo affine deformation with respect to the applied macroscopic strain, that is, they act as a material element and are stretched into an extended fibrillar structure. Upon flow cessation, the fibrillar structure of the droplet recoils back into a spherical shape by interfacial tension in the molten state. However, a prompt solidification process prohibits this deformation upon flow cessation and results in a dispersed fibrillar system [90, 100]. The blend can be subjected to cold drawing to further extend the dispersed phase domains [101–103]. The quenched, metastable, fibrillar structure of the dispersed domains ultimately influences the viscoelastic and crystallization properties. Small-Scale Production of Fibrillar Blends Figure 2.60(a)–(d) shows the SEM micrographs of PE/PP (95/5 wt%) [103] and PP/ PET (95/5 wt%) [94] before and after fibrillation using the aforementioned strategy in a laboratory-scale, co-rotating, twin-screw micro-compounder. The dispersed phase exists as spherical domains prior to the fibrillation process, with an average diameter of about 3 m. The dispersed phase domains exist as fibrils with an aspect ratio of about 200 after the fibrillation process. Fibrillation of the dispersed phase domains is believed to occur when the temperature of the twin-screw microcompounder is reduced from above the melting point of both components of each blend to a temperature between their melting points. The capillary number and

79

80

2 Manufacturing of CoDiCoFRP

viscosity ratio change dynamically during this cooling process. Eventually, a temperature window is reached where the aforementioned criteria (i.e., Ca >  Cacrit) is fulfilled and the dispersed phase domains can undergo affine deformation. The elongated dispersed phase domains continue to solidify as the PE/PP or PP/PET system cools, until their morphology is no longer deformable, thus yielding a dispersed fibrillar system. Subsequent heating of the fibrillar blend above the melting temperature of the fibrils leads to the recoiling of the fibrils into spherical domains distributed randomly in the matrix.

Figure 2.60 SEM images of (a) PE/spherical-PP (95/5 wt%) [103]; (b) PE/fibrillated-PP (95/5 wt%) [103]; (c) PP/spherical-PET (95/5 wt%) [94]; (d) PP/fibrillated-PET (95/5 wt%) [94]

Large-Scale Production of Fibrillar Blends Laboratory-scale, twin-screw compounding is effective for research and development to rapidly study polymeric systems and optimize material formulations. However, it does not scale up to larger-volume twin-screw extruders, since the equipment design attributes and processing parameters are fundamentally different. Factors that may differ include screw size and configuration, material residence time, flow rate, heat transfer rate, and heat distribution [104]. Consequently, there is considerable technological and scientific interest in the feasibility of producing fibrillar blends in a pilot-scale system that can be scaled up to industrial scale with relatively little process modification. Unfortunately, the expense of equipment and mass of raw material required for conducting the appropriate experiments limit such research.

2.6 Foaming of Microfibrillar Composites

Recently, a fully scalable fiber spinning process was developed to fibrillate immiscible polymer blends [93]. Macroscopic extensional flows applied during fiber spinning cause both the matrix and the dispersed-phase domains to stretch and orient in the flow direction. The macroscopic extensional flow applied during fiber spinning represents a promising high throughput route for the in-situ generation of fibrils in immiscible polymer blends. The degree of fibrillation in the dispersed phase is governed by parameters such as the speed of the draw rolls, the dimensions of the spinneret, the spinning temperature, and the rate of cooling of the spun material [105]. Effect of Draw Ratio on Fibrillar Blend Morphology Figure 2.61(a) shows the morphology of twin-screw extruded PP/PET before fiber spinning. The PET exhibits no evidence of fibrillation and exists as well dispersed, isolated domains in the PP matrix. Figure 2.61(b) shows the morphology of PP/PET after pumping the blend through the spinneret of the fiber-spinning equipment without drawing. Some degree of fibrillation is captured in the electron micrograph. We attribute this fibrillation of PET to the extensional flow that occurs in the spinneret die, where the blend experiences transverse contraction and longitudinal elongation. Figure 2.61(c) shows the morphology of fiber-spun PP/PET after drawing at a draw ratio of 10.2:1. A larger degree of fibrillation is seen, a change attributable to two factors: (1) the transverse contraction and longitudinal elongation in the die and (2) the extension caused by cold-drawing performed using the godet. A distinctive morphology of the PET domains can be observed in Figure 2.61(c), consisting of a bead-in-a-thread type structure. Such morphology has also been observed in other studies and may correspond to a transient intermediate state during the morphological transition of the dispersed phase from an isolated spherical domain to a completely fibrillated one [106, 107]. Figure 2.61(d) reveals that when the draw ratio is increased to 20.4:1, the PET domains are fibrillated to a larger degree. The average fibril diameter is 210 nm, and the average fibril length is 38 m. Thus, the aspect ratio is about 181. High aspect ratio fibrils are known to contribute substantially towards the mechanical and rheological properties of polymers. In the case of semi-crystalline polymers, the high aspect ratio fibrils also influence the crystallization properties of the matrix. Thus, the scalable production of such fibrillar morphologies is scientifically and technologically interesting.

81

82

2 Manufacturing of CoDiCoFRP

Figure 2.61 Effect of draw ratio on the morphology of fiber-spun PP/PET (95/5 wt%) (a) meltblended PP/PET in a twin-screw extruder; (b) undrawn PP/PET where the PP/ PET blend in (a) is pumped through the spinneret of the fiber spinning equipment without drawing; (c) fiber-spun PP/PET drawn at a draw ratio of 10.2:1; (d) fiberspun PP/PET drawn at a draw ratio of 20.4:1 [93]

Fibrillation of PTFE in Polymers Although polymeric dispersed phases must usually be molten to undergo fibrillation during blending, PTFE has a tendency to undergo plastic deformation even as a solid upon application of a flow field. The fibrillation mechanism of solid PTFE during blending with polymers has been described previously [108]. Above 19 °C, crystalline PTFE exists in a hexagonal polymorph characterized by weak cohesive forces, and even slight shear forces can cause the PTFE macromolecules packed in the crystals to unwind, a phenomenon that increases at higher temperatures [108]. The degree of fibrillation and the morphological characteristics of the fibrils depend on properties that influence the stress transfer from the matrix to the PTFE, such as the viscosity of the matrix, the interfacial tension, PTFE deformability at the blending temperature, the shear rate, and the duration of blending [109]. Figure 2.62 shows the morphology of fibrillated PTFE in the PP matrix after blending at a temperature of 200 °C, where PP is molten, but PTFE is solid. The micrograph in Figure 2.62(a) is obtained after solvent vapor etching of a fractured surface of the PP/PTFE blend. The micrograph in Figure  2.62(b) is obtained after dissolving PP in xylene and observing the PTFE residue. Figure 2.62 confirms that PTFE undergoes fibrillation and deforms into fibrillar structures of large aspect ratios (fibril diameters are less than 500 nm and lengths evidently exceed 100 m). The fibrillar morphology adopted by PTFE is a consequence of its low yield strength for undergoing plastic deformation, particularly at elevated temperatures. The fibrillar morphology can be maintained in the matrix as long as the blending tem-

2.6 Foaming of Microfibrillar Composites

perature is not increased above the melting point of PTFE, since the PTFE molecules are prevented from undergoing molecular relaxation and recoiling back into spherical domains. Thus, the mechanism of PTFE fibrillation differs from most polymers, which need to be molten to fibrillate: PTFE can fibrillate even as a solid, due to its loosely packed crystals, which can unwind readily upon experiencing a deformation stress such as those typically found during twin-screw extrusion. This characteristic also gives rise to the properties of PTFE, such as high ultimate strain and low yield stress for plastic elongation [92, 108].

Figure 2.62 SEM micrographs of the morphology of PTFE fibrils in PP/PTFE (97/3 wt%): (a) obtained after solvent-vapor etching; (b) obtained after removal of PP using xylene [110]

2.6.3 Uniaxial Extensional Flow Response of Fibrillar Blends The growth of nucleated bubbles exerts a biaxial extension on the matrix when polymers are foamed. The matrix cannot withstand this extensional force if it exhibits weak strain hardening and the bubbles rupture, which leads to the diffusion of gas out of the polymer and, ultimately, the collapse of the foam. Consequently, strain hardening plays a critical role in facilitating gas retention by preventing bubble rupture and gas escape. While biaxial extension is the primary mode of deformation during foam processing, uniaxial extensional measurements are more readily available and are often used to measure the strain hardening behavior of polymers. Figure  2.63(a)–(d) shows the uniaxial extensional viscosity C P/ at various E .t; " constant extensional strain rates "P for fibrillated PE/PP (95/5 wt%), fibrillated PP/ PTFE (97/3 wt%), fibrillated PP/PET (97/3 wt%) obtained via micro-compounding, and fibrillated PP/PET (95/5 wt%) obtained via fiber spinning. For PE/PP and PP/ PET, the fibrillar blend is compared with the regular blend with spherical dispersed phase domains. Such a comparison could not be made for PP/PTFE due to the tendency of PTFE to elongate during compounding even in the solid state. Thus, the extensional viscosity of PP/PTFE is compared against that of neat PP. The solid line in the figures represents the linear viscoelastic prediction of extensional vis-

83

84

2 Manufacturing of CoDiCoFRP

cosity 3+(t), where +(t) is the growth curve of shear viscosity in the linear viscoelastic region obtained from startup shear experiments at a strain rate of 0.001 s−1. The uniaxial extensional flow behavior of PE/spherical-PP and PP/spherical-PET is similar to that of linear PP [111]. There is no upward deviation from the linear viscoelastic prediction of the extensional viscosity 3+(t) within the strain-rate scale studied, and the extensional viscosity curves obtained at different strain rates superimpose. The uniaxial extensional viscosity for the blends with spherical P/ Š 3+(t) domains has a tendency to follow the Trouton relationship: C E .t; " [112], in the limit of steady state (t → ∞). On the other hand, the uniaxial extension viscosity of the fibrillated blends exhibits upward deviation, often called “strain hardening”. The magnitude of strain hardening can be defined by

D

C E 3C .t/ (2.7)

where  is the strain-hardening factor of the extensional flow and 3+(t) is the three-fold linear viscoelasticity. The divergence in extensional viscosity of the fibrillar blends relative to the spherical blends is thought to result from the formation of a network superstructure through physical entanglements of flexible fibers [91, 92, 113]. The origins of strain hardening in extensional flow for the fibrillar network is analogous to that of long-chain branched polymers, where strain hardening is generally related to the inability of the macromolecules to disentangle quickly enough and follow the deformation [95, 114]. Other proposed mechanisms for the origins of strain hardening during uniaxial extension include the elastic response to bending deformation and frictional forces between the fibrils [91, 92]. The degree of fibrillation influences the strain-hardening factor. For example, the fiber-spun PP/PET fibrillar blend exhibits a higher magnitude of strain hardening in uniaxial extension than the micro-compounded PP/PET fibrillar blend. This divergence occurs for two reasons: (1) PET fibril content is higher in the fiber-spun PP/PET, so a denser fibrillar network develops and (2) the PET domains are able to reach a higher degree of fibrillation in fiber-spun PP/PET due to the higher achievable draw ratio of 20.4:1, compared to 6.3:1 in micro-compounded PP/PET [93]. The higher draw ratio in the fiber-spinning process is achieved through a more efficient cross ventilation cooling system, which reduces fracture from instabilities (e.g., draw resonance, localized necking) in the drawn extrudate. Thus, PET domains can undergo a higher degree of extensional deformation in the fiber-spinning process before the morphology quenches. The development of a rheologically percolated network of high aspect ratio fibrils in the matrix is essential to create the strain-hardening response in extensional flows. For example, when the fibril content in PP/PET fibrillar blends is reduced from 5  wt% to 1  wt%, the strain-hardening response in uniaxial extension is no

2.6 Foaming of Microfibrillar Composites

longer observed [93]. The disappearance of the strain-hardening response at a fibril content ≤1 wt% is believed to result from an insufficiently developed physical network of PET fibrils in the PP matrix. Since the origin of strain hardening in uniaxial extension is related to the generation of physical entanglement of the fibrils, the linear viscoelastic behavior of the fibrillar blends is subsequently investigated to gain further understanding of the network structure.

Figure 2.63 Uniaxial extensional viscosity of fibrillated blends. The fibrils remain in the solid state during measurements: (a) PE/PP (95/5 wt%), where the PP domains are spherical or fibrillated [103], (b) PP/PTFE (97/3 wt%), where the PTFE domains are fibrillated [110], (c) PP/PET (97/3 wt%), where the PET domains are spherical or fibrillated and the fibrillation is conducted on a laboratory scale with a twin-screw micro-compounder [94], (d) PP/PET (95/5 wt%), where the PET domains are spherical or fibrillated and the fibrillation is conducted on a scalable fiber-spinning system [93]

85

86

2 Manufacturing of CoDiCoFRP

2.6.4 Linear Viscoelastic Shear Response of Fibrillar Blends The presence of a percolated fibrillar network defined by topological entanglements can be detected by characterizing the storage G'(!) and loss G″(!) moduli as a function of frequency (!). Interconnected microstructures assumed by anisotropic fillers, such as high aspect ratio fibrils, affect the frequency behavior of the elastic G'(!) and viscous G″(!) moduli. When the fibril content is high enough, the system may exhibit the characteristics of a pseudo-solid or gel, with a three-dimensionally percolated network of fibrils extending throughout the sample volume [91].

Figure 2.64  R  heological behavior of PP/PET fibrillar blends at 165 °C for five samples with different PET fibril content. PET remains in the solid state during this investigation; (a) frequency dependence of elastic modulus G'(ω); (b) frequency dependence of viscous modulus G″(ω); (c) frequency dependence of loss tangent tan δ; (d) tan δ as a function of fibril content. Different lines represent different frequencies ranging from 0.1 to 100 rad/s. The lines intersect at the gel point content cg. The direction of the arrow indicates increasing frequency [94]

2.6 Foaming of Microfibrillar Composites

Figure 2.64(a)–(b) illustrates G'(!) and G″(!) as a function of frequency for PP/ PET at different PET fibril contents ranging from 0 to 7 wt% [94]. Increasing the fibril content leads to a gradual increase in both G'(!) and G″(!), but the increase in G'(!) is more pronounced. Furthermore, the slope of the double logarithmic plot of G'(!) and G″(!) progressively decreases with the increase in the fibril content. The observation that G'(!) and G″(!) become increasingly independent of ! as the fibril content is increased, indicates that the viscoelastic response is changing from “liquid-like” to “gel-like”. Figure  2.64(c) plots the loss tangent tan ı D G 00 .!/=G 0 .!/ as a function of frequency using the data in Figure 2.64(a)– (b). The tan ı values decrease with an increase in the fibril content. This can be explained by a lower viscous/elastic ratio when the fibril content is increased. At a fibril content of 3  wt%, tan ı seems to exhibit frequency independence. The physical meaning of this result is that the critical fibril concentration required to trigger a transition in the behavior of the PP matrix from liquid-like to solid-like is estimated to be 3 wt%, since the frequency independence of tan ı occurs in the vicinity of the gel point [115, 116]. A multi-frequency plot of tan ı versus the fibril content reveals an intersection that precisely marks the gel point. The data in Figure 2.64(c) can be re-expressed to prepare such a plot, which is presented in Figure 2.64(d). The common point in Figure 2.64(d) occurs at a fibril content of 3 wt%. Thus, the gel point concentration is accurately identified to be 3 wt% for the PP/fibrillated PET. A similar analysis for PE/fibrillated PP yields a percolation threshold of 4.5 wt% [103].

2.6.5 Effect of Fibers on the Crystallization of Polymers

Figure 2.65 SEM micrograph of a permanganate-etched sample of PP/PTFE (99.9/0.1 wt%) isothermally crystallized for a period of (a) 0 s; (b) 1550 s; and (c) 2100 s at a temperature of 137 °C [117]

The enhancement of desirable properties and processing characteristics of polymers results not only from the dispersed phase morphology but also from the interfacial binding between the two phases, both of which enable efficient stress transfer from the matrix to the fibrils. The formation of an oriented crystalline structure around fibrils dispersed in a semi-crystalline polymer occurs under the

87

88

2 Manufacturing of CoDiCoFRP

appropriate temperature and pressure conditions [118]. The fibrils promote alignment of the matrix polymer chains and preferentially nucleate crystals around the fibrils when the melt containing solid-state fibrils is cooled, thus improving the stress transfer from the matrix to the fibrils. A transcrystalline layer develops around the fibrils in a quiescent state in the absence of a flow field. Figure  2.65 shows the development of a transcrystalline layer of PP around a PTFE fibril at various time intervals [117]. However, during industrial processes such as fiber spinning or extrusion, in which the fibrillar blend is subjected to rapid cooling under strong extensional flow, a shish-kebab-type morphology develops around the fibrils, instead of a transcrystalline layer. Rizvi et al. [117] and Li et al. [119] successfully visualized the formation of shish-kebab structures of PP around PTFE and PET fibrils, respectively, after subjecting the fibrillar blends to hot stretching followed by rapid quenching processes. Figure  2.66 shows a typical example of a shish-kebab morphology observed for PP/PTFE fibrillar blends [117].

Figure 2.66 SEM micrograph of a permanganate-etched [120] sample of PP/PTFE after extrusion [117]

Furthermore, the large surface-to-volume ratio of high-aspect-ratio fibrils with submicrometer diameters increases the crystallization rate of the polymer matrix due to the heterogeneous crystal nucleation effect of the fibrils. Thus, increasing the fibril content in a polymer matrix leads to a concurrent increase in the kinetics of crystallization. However, it is noteworthy that the kinetics of crystallization will differ in polymer foaming, where a blowing agent such as CO2 is dissolved in a polymer matrix. The dissolution of CO2 in a melt influences polymer chain mobility, and consequently, the crystallization behavior [121].

2.6.6 Role of Crystallization in Foaming The ability of semi-crystalline polymers to crystallize provides an effective means to overcome the challenges associated with foaming semi-crystalline polymers.

2.6 Foaming of Microfibrillar Composites

Unlike most additives and fillers, crystallites are unique in that they are coupled to the molten phase by chains extending from the crystallites. If these chains are not too short, and if the crystalline fraction is not too small, a substantial degree of tie chains develop, which connect different crystallites. Thus, a physical network of lamellae is generated that enhances melt strength and the strain-hardening response in extensional flows [122]. This physical network can suppress cell deterioration mechanisms and prevent gas loss, thus allowing semi-crystalline polymer foams to expand and stabilize. It should be noted that a large crystalline fraction will suppress foam expansion due to excessive stiffness. This prevents bubble expansion and also limits gas dissolution in the polymer, since gas dissolution occurs in the amorphous fraction. Crystals can influence the bubble nucleation rate in polymer melts with a dissolved foam blowing agent through two mechanisms: (1) rigid crystals can induce local stress variations in the melt, thus decreasing the activation energy for cell nucleation according to the cell nucleation theory [123, 124] and (2) crystal growth results in the expulsion of the blowing agent to the adjoining interface of the crystal and the melt, thus increasing the local concentration of the blowing agent at the interface. Upon depressurization, cell nucleation is enhanced at the interface of the crystals and the melt [125]. More recently, crystallites in a partially crystallized polymer have been shown to generate open cell foams by creating a structurally heterogeneous melt [126] with well dispersed arrays of rigid crystalline segments in a soft matrix [117]. Open cell foams are technologically very interesting due to their cushioning and mass transport properties [127, 128]. The rigid crystalline segments form points of stress concentration in the cell wall membranes during bubble expansion, thus inducing cell opening. While the crystallization of polymers can occur in the absence of any filler, the thermodynamics and kinetics of crystallization in the presence of fillers such as high-aspect-ratio fibrils are higher [117]. Foams with open cell content above 97.7% can be achieved in polymer fibrillar blends when the crystalline fraction is not too small and the crystalline regions are well dispersed throughout the matrix [127].

89

90

2 Manufacturing of CoDiCoFRP

2.6.7 Foaming of Fibrillated Blends

Figure 2.67 Comparison of foam morphologies of neat PP, PP/spherical-PET (95/5 wt%), and PP/fibrillated-PET (95/5 wt%) obtained using the method described in [93]. (a) SEM micrographs of foams obtained after the continuous foam extrusion process of (i) PP, (ii) PP/spherical-PET, and (iii) PP/fibrillated-PET at a temperature of 150 °C; (b) cell density as a function of die temperature for the three samples; (c) foam volume expansion ratio as a function of die temperature for the three samples [93]

The foaming of fibrillated polymer blends must be conducted at a temperature below the melting temperature of the fibrils, so that the fibrils remain in the solid state. The fibrils will relax and recoil back into spherical domains if the processing is conducted around or above the melting temperature of the fibrils, thereby altering the rheological and crystallization characteristics of the fibrillar blend. In Figure 2.67, PP/PET (95/5 wt%) is used as a model polymer blend to compare the extruded foam morphology of a neat polymer, a polymer blend with spherical domains, and a fibrillated polymer blend [93]. It can be seen from Figure 2.67(a) that the presence of a spherical-PET second phase results in a decrease in cell size. However, the most significant decrease in cell size is seen when the PET domains are fibrillated. The cell density and expansion ratio shown in Figure  2.67(b)–(c) also seems to follow the same trend, in which the fibrils tend to result in the most

2.6 Foaming of Microfibrillar Composites

pronounced increase in cell density and expansion ratio compared to the neat polymer. The classical nucleation theory [129] describes the nucleation efficiency of bubbles, where gas bubbles larger than a critical radius Rcr continue to grow spontaneously, while smaller ones tend to collapse. Assuming that the polymer/gas solution prior to bubble nucleation is dilute, the expressions for the free energy needed for bubble nucleation (G) and Rcr are given by [129–132]:

G D

Rcr D

16lg3 F .c /  2  3 HC  Psys C Plocal 

2lg  HC  Psys C Plocal 

(2.8)

(2.9)

where lg is the surface tension at the polymer/gas interface, F(c) is a geometric factor that equals the ratio of the volume of a heterogeneously nucleated bubble to that of a spherical bubble having the same radius of curvature, H is the Henry’s Law constant, C is the gas concentration, Psys is the system pressure, and Plocal is the local pressure variation. Equations (2.8) and (2.9) indicate that an increase in the gas concentration C is expected to reduce the free energy barrier for bubble nucleation and the critical radius. In such a case, a larger bubble density will be obtained. The gas concentration in a melt can be increased by increasing the gas saturation pressure during foaming [103] by injecting a larger amount of gas in extrusion foaming, or by incorporating secondary components in the matrix that exhibit a stronger thermodynamic affinity for the gas [110]. Fluoroalkyl functional groups are known to exhibit a strong thermodynamic affinity for CO2. Thus, when PP is foamed with 3 wt% CO2-philic PTFE fibrils using CO2 as the foam blowing gas, more gas is localized in the PP and the resultant foams exhibits cell densities three orders of magnitude higher than neat PP [110]. The cell density also increases by three orders of magnitude when the saturation pressure for foaming PE containing 5  wt% PP fibrils is increased from 4.1  MPa to 17.3 MPa [103]. Localization of a larger concentration of the foam blowing gas allows the matrix to reach a higher degree of super-saturation during depressurization, thus leading to the formation of more cell nuclei [133]. Cell nucleation is also influenced by microscopic stress variations within the melt that affect the magnitude of Plocal in Eq. (2.8) and (2.9). The entanglements of fibrils create topological constraints that prevent fibrils from flowing along with the melt during bubble growth. Consequently, the network of fibrils undergoes a mac-

91

92

2 Manufacturing of CoDiCoFRP

roscopic strain, which creates a complex and locally varying superposition of shear, compressive, and extensional stresses within the melt. In regions where a tensile stress is created, that is, where Plocal  3 mm. (b): Fibers longer than 4 mm with a bending radius of 0:5 mm  r  1:5 mm:

Figure 3.26 Mass-weighted bending radius histogram: the LFT material (a) shows a smaller average bending radius than the SMC material (b)

3.3.8 Summary ƒƒFiber orientation of glass and carbon fiber reinforced polymers using volumetric images can be determined by an algorithm based on the structure tensor. Images of glass and carbon fiber reinforced SMC and LFT material are evaluated. It is possible to derive the orientation of the fibers in each voxel. Glass fibers can be easily separated from matrix material due to the high material contrast. However, this is not possible for carbon fiber reinforced polymers. Nevertheless, the orientation data examined from carbon fiber reinforced material systems is quite reliable.

133

134

3 Characterization of CoDiCoFRP

ƒƒDeterminations of the fiber volume fraction using different approaches show that there are some promising techniques that lead to good results. The Moments method leads to the best results for both material systems. ƒƒFiber tracking methods offer good results for smaller specimens with an edge length of up to 5 mm. The spatial curves derived from the volumetric images match the fibers in the initial image very well and can be used to derive the fiber length or curvature. Investigations on scans of LFT and SMC material show that the mean fiber bending radius of LFT material is much smaller than that of SMC material.

„„3.4 Mechanical Characterization of Hybrid Continuous–Discontinuous Glass/­ Carbon Fiber Sheet Molding Compound Composites Anna Trauth, William Altenhof, Kay A. Weidenmann 3.4.1 Introduction Hybrid composites featuring a combination of different fiber types and reinforcement architectures enable one to obtain a material compound with properties tailored to the specific requirements of a given component. As a result, however, the mechanical material properties may become significantly more complicated. To successfully combine continuous and discontinuous SMC for structural applications, robust experimental and analytical tools are needed to understand and describe mechanical material and structural properties. Strategies must be developed to characterize hybrid composites in a reliable way with experimental techniques and approaches adapted to this innovative material class. Experimental characterization aims to provide validation data for processing and related optimization and numerical simulation efforts. The structure– property relationships of glass fiber (GF) and carbon fiber (CF) reinforced SMC are of great interest, especially for the automotive industry, which seeks to successfully implement advanced SMC in new vehicle concepts [23–25]. Unfortunately, the mechanical performance of chopped discontinuous fiber reinforced SMC materials is limited. In this regard, different hybridization concepts of SMC composites have already been presented. Discontinuous SMC composites have been combined with both dry textile preforms [26] and pre-impregnated fabrics [27, 28] in a one-shot process to

3.4 Mechanical Characterization of Hybrid CoDiCo 3.4 Mechanical Glass/Carbon Characterization Fiber SMC Composites of Hybrid

obtain hybrid continuous–discontinuous SMC. These two approaches improved the mechanical properties of the resulting hybrid material for quasi-static tensile and bending loads. For impact loads, the absorbed energy was increased by introducing woven fabrics or multidirectional non-crimp fabrics as reinforcing elements. A crucial factor for the effectiveness of reinforcement with dry textile is the impregnation quality of the textile preforms [26]. Fiber misalignment of the continuous component resulting from resin cross-flow during molding also has a decisive effect on resulting material properties [28, 29]. As presented in [30], continuous carbon fiber reinforced SMC materials can be efficiently manufactured on a modified conveyor belt. Thus, the hybrid material characterized in this chapter offers two distinct advantages: the pre-impregnated non-crimp fabric introduced in the mold reduces the impact of insufficient impregnation. Furthermore, this technique enhances the possibility of achieving and controlling the B-stage of the continuous material. Consequently, the misalignment of the fibers is also reduced significantly. Combining a two-step curing resin system with an adapted manufacturing process makes it possible to manufacture both components of hybrid continuous–discontinuous SMC composites on a conventional SMC conveyor belt. In the following discussion, an interlayer hybridization [31] is considered for manufacturing hybrid continuous–discontinuous SMC composites, based on two different semi-finished materials. To support the manufacturing and design of hybrid SMC materials, a profound understanding of the process-induced microstructure, structure–property relationships, and mechanical material properties of hybrid continuous–discontinuous SMC is required. Since SMC components are frequently considered for automobile body components prone to crash damage, impact properties are also important. Characterization methods to deduce mechanical material, structural, and component properties are presented in the next section. The focus is on investigating hybridization effects in terms of material behavior.

3.4.2 Material Manufacturing The continuous carbon and discontinuous glass or carbon fiber semi-finished SMC sheets were manufactured on a flat conveyor plant of the type Schmidt & Heinzmann HM-LB-800 at the Fraunhofer ICT in Pfinztal, Germany. The set-up was slightly modified to be able to ensure appropriate heating and cooling cycles during the manufacture of the continuous carbon fiber SMC. The resin system for both components contained no fillers, so as to optimize mechanical performance. The discontinuous SMC composites were reinforced by 25.4 mm long glass fibers with a nominal fiber content of 41 wt%. The continuous carbon fiber semi-finished sheets were based on a non-crimp fabric having a unidirectional lay-up, which was fed into the

135

136

3 Characterization of CoDiCoFRP

conveyor belt. The continuously reinforced semi-finished sheets had a nominal fiber content of 60 wt%. After maturation of the discontinuous semi-finished material, the sheets were cut into plies and the stack was placed in the middle of a rectangular mold having a cross section of 250 mm  800 mm. The initial mold coverage of the discontinuous semi-finished sheets was set at approximately 35% to ensure sufficient flow during molding (Figure 3.27).

Figure 3.27 Manufacturing of hybrid continuous–discontinuous (CoDiCo) SMC plaques: stacking of semi-finished SMC sheets with two continuous carbon fiber reinforced sheets at the top and bottom and discontinuous glass fiber reinforced sheets in the middle. The stack is placed inside the rectangular mold and compression molded to plaques with the flow of the discontinuous component

To characterize a hybridization effect, CoFRP based on carbon fiber SMC, DiCoFRP based on glass fibers, and hybrid CoDiCo sheets with a discontinuous core and continuously reinforced shell layers were manufactured. The pure continuouslyreinforced sheets did not flow during molding. Specimens were extracted by water-jet cutting (Figure  3.28) and stored at room temperature (23 °C) for several days before mechanical testing.

Figure 3.28 Example of investigated materials. Top: hybrid continuous–discontinuous glass/ carbon fiber SMC (CoDiCo SMC), middle: continuous carbon fiber SMC (Co CF SMC), and bottom: discontinuous glass fiber SMC (DiCo GF SMC)

3.4.3 Methods Computed Tomography To investigate the microstructure of CoDiCo SMC materials, a specimen was scanned in an Yxlon-CT precision computed tomography system (Yxlon International CT GmbH, Hattingen, Germany) containing an open micro-focus X-ray transmission tube with tungsten target and a 2048 pixel  2048 pixel flat panel detector

3.4 Mechanical Characterization of Hybrid CoDiCo 3.4 Mechanical Glass/Carbon Characterization Fiber SMC Composites of Hybrid

from Perkin Elmer (Waltham, MA, USA). The acceleration voltage was 100 kV and the tube current 0.05 mA. The scans were acquired with a focus object distance of 31.3 mm and a focus detector distance of 750 mm, leading to a voxel size of approximately 8 m. Tensile Testing at the Coupon Scale Tensile testing was carried out on a ZwickRoell Zmart Pro Universal testing machine with a load cell capacity of 200 kN in a conditioned laboratory at 23 °C. The rectangular specimens (200 mm  15 mm) were hydraulically clamped with a clamping distance of 100 mm and mechanically loaded at a nominal crosshead speed of 1.8 mm·min−1 until fracture. A stereo digital image correlation system (GOM ARAMIS with 4MP Teledyne Dalsa cameras and 50 mm Schneider Kreuz­ nach objectives) measured the resulting displacement fields at a frame rate of 5  Hz. The tensile modulus of elasticity was determined in the strain range of 0.05% to 0.25% with a least squares method, taking into account the arithmetic mean value of calculated strains in a measurement section of approximately 70 mm  10 mm. A specimen was only evaluated if failure occurred within the considered measurement section and the regression coefficient (r2) was greater than 0.9. Compression Testing at the Coupon Scale Compression testing was carried out on a ZwickRoell Zmart Pro universal testing machine with a load cell capacity of 100 kN in a conditioned laboratory at 23 °C. The rectangular specimens (100 mm  15 mm) were hydraulically clamped with a clamping distance of 15  mm and mechanically loaded at a nominal crosshead speed of 0.8 mm·min−1 until fracture. Displacement was measured with a tactile clip-on extensometer on two sides of the specimen to control for bending. Compressive modulus of elasticity was determined in the strain range of 0.05% to 0.25% with a least squares method, taking the arithmetic mean value of the measured strains at both sides of the specimen with an initial gauge length of 10  mm. A specimen was only evaluated if failure occurred within the considered measurement section and the regression coefficient r2 was greater than 0.9. Flexural Testing at the Coupon Scale Three-point bending testing was carried out on a ZwickRoell Zmart Pro universal testing machine with a load cell capacity of 20 kN in a conditioned laboratory at 23  °C. The rectangular specimens featured a length of 100  mm and a width of 15 mm. The span to thickness ratio was 1:32. Specimens were mechanically loaded with a crosshead speed of 5  mm·min−1 until fracture. Deflection was measured with a laser measurement system (type: opto NCDT 2300 by MICRO-EPSILON) below the specimen. Flexural modulus of elasticity was determined in the strain range of 0.05% to 0.25% with a least squares method.

137

138

3 Characterization of CoDiCoFRP

Puncture Testing at the Structural Scale Quasi-static puncture testing was carried out with rectangular specimens featuring a section of 140 mm  140 mm, which were mechanically clamped under a metallic plate to provide a circular puncture area with a diameter of 100 mm (Figure 3.29). The specimen was punctured at its center perpendicular to the surface with a hemispherical striker having a diameter of 20  mm, on an MTS Criterion Model 45 electromechanical load frame (load cell capacity of 150 kN) and a nominally uniform velocity of 2.6 mm·min−1. Clamping of the specimen led to a complex 2D stress state, which combined multi-axial tension and bending. In addition, the contact of the striker led to a localized 3D stress state.

Figure 3.29 Test set-up of quasi-static puncture test with fully clamped specimen

Dynamic (low velocity) puncture tests were carried out according to ISO 6603-2 instrumented impact testing. The impacting unit, which consisted of the crosshead, the shaft including the load cell and a hemispherical tip having a diameter of 20 mm, was released and punctured the mechanically clamped specimen (same boundary condition as for quasi-static puncture testing) perpendicular at its center. The release height was defined such that the impacting unit obtained a nominal velocity of 4.4 ˙ 0.2 m·s−1.

The quasi-static force–deflection data was not filtered. The raw force signal captured during dynamic loading was filtered with a four pole Butterworth filter. Characterization of puncture properties at different loading rates was based on evaluation of maximum force and the absorbed energy until puncture deflection (referred to as puncture energy). As proposed in [32], the puncture deflection refers to the deflection at which the measured load is half of the preceded maximum force occurring during the puncture of the specimen. From this point, energy is mostly absorbed due to friction between the specimen and the striker.

3.4 Mechanical Characterization of Hybrid CoDiCo 3.4 Mechanical Glass/Carbon Characterization Fiber SMC Composites of Hybrid

Four-Point Bending Testing at the Component Scale Component tests were carried out on the demonstrator part. For this purpose, tests were performed on a ZwickRoell Zmart Pro universal testing machine with a load cell capacity of 500 kN. The components were loaded in a four-point bending condition, as depicted in Figure 3.30(a). The lower supports were mounted on an aluminum cage to permit measurement of the deflection directly below the specimen with a tactile transducer. Displacement controlled four-point bending tests were conducted by means of several loading–unloading cycles (Figure  3.30(b)) with a nominal crosshead velocity of 2 mm·min−1. Each test started by loading the component with a defined preload of 100 N. After reaching the maximum deflection at the beginning of each cycle, which increased from 0.5 mm to 5 mm within eight cycles, three loading–unloading cycles in the range of 30–70% of the maximum preceded deflection were realized. At the end of each cycle, the component was unloaded to 100 N. This load was maintained for 90 s before starting the next cycle. The global stiffness of the component was evaluated by calculating the slope of three subsequent descending paths in the 30–70% of the maximum preceded deflection that occurred. Maximum load corresponds to the load sustained by the specimen at the beginning of each cycle and the maximum observed deflection.

Figure 3.30 Test set-up of component testing (a) and testing procedure (b) to realize fourpoint bending tests with several loading and unloading cycles in the range of 30–70% of the preceded maximum deflection. In the end, the component was loaded up to final failure

3.4.4 Results Microstructural Observation Figure 3.31 illustrates the color-coded fiber orientation of a DiCo GF SMC specimen obtained from computer tomography. The slices correspond to the shell layer (a) and the core (b). Material flow during compression molding corresponds to the y-axis.

139

140

3 Characterization of CoDiCoFRP

Figure 3.31 Computer tomographic observation showing fiber orientation of DiCo GF SMC in a representative specimen. Fiber bundles are spread in the shell layer (a) and oriented in the core (b)

In general, one-dimensional material flow led to an orientation of the fiber bundles parallel to the flow direction. Within the shell layer, fiber bundles were sheared in the manufacturing process and the characteristic SMC bundle structure was no longer present. Individual fibers or agglomerations of a small number of fibers became visible. The fibers were also characterized by a distinct curvature in the shell layer. Within the core, fiber bundles most preferably aligned in the flow direction define the microstructure of the investigated DiCo GF SMC. Due to the unidirectional flow of the discontinuous semi-finished sheets during manufacturing, discontinuous glass fiber SMC materials show anisotropic material properties with an anisotropy ratio of 1.4 and 2 for tensile stiffness and strength, respectively. Figure 3.32 depicts the microstructure of hybrid CoDiCo SMC specimens with a global thickness of approximately 3 mm. The hybrid CoDiCo SMC features a transition zone between the continuously and discontinuously reinforced layers. Due to the flow of the discontinuous SMC, the continuous carbon fiber bundles were pushed apart at z approximately equal to 0.192 mm and 0.352 mm. The interface between the two materials is not sharp, but was characterized by a gradual transition. The discontinuous component shows again spread fiber bundles and curved agglomerations of fibers within the transition zone (up to z approximately equal to 0.7 to 0.8 mm). Within the core, the discontinuous component (DiCo) featured the characteristic SMC microstructure, defined by oriented fiber bundles.

3.4 Mechanical Characterization of Hybrid CoDiCo 3.4 Mechanical Glass/Carbon Characterization Fiber SMC Composites of Hybrid

Figure 3.32 Computer tomographic observation showing the microstructure of a hybrid CoDiCo SMC. Glass fiber bundles are spread and pushed apart in the transition zone between the continuous and discontinuous component

141

142

3 Characterization of CoDiCoFRP

Mechanical Properties at the Coupon Scale Figure 3.33 depicts the modulus of elasticity and strength resulting from (a) uniaxial tensile, (b) compressive, and (c) flexural loading of DiCo glass fiber SMC, Co carbon fiber SMC, and hybrid CoDiCo glass/carbon fiber SMC in the fiber direction of the continuous reinforcement, which corresponds to the flow direction of the discontinuous material. A continuous reinforcement of discontinuous glass fiber SMC leads to a significant increase of stiffness (+170%) and strength (+190%) for uniaxial tensile loading. In terms of compressive loading, hybridization did not influence the compressive strength. The compressive modulus of elasticity increased significantly (+140%).

Figure 3.33 Mechanical properties in terms of stiffness and strength of DiCo GF SMC, Co CF SMC, and CoDiCo SMC: (a) tensile, (b) compressive, and (c) flexural

The hybridization effect resulting from stacking the laminate with continuously reinforced face layers was most important for flexural loadings and the flexural modulus of elasticity and flexural strength both increased significantly (+370% and +120%). The final stiffness of the hybrid CoDiCo SMC can be estimated by a rule of hybrid mixtures [31]. To analytically predict flexural stiffness, classical laminate theory is a valuable tool to analytically approach flexural stiffness (Figure 3.34). However, the tension–compression anisotropy of Co CF SMC must be considered, and an asymmetrical lay-up of the laminate results in the most accurate estimation.

3.4 Mechanical Characterization of Hybrid CoDiCo 3.4 Mechanical Glass/Carbon Characterization Fiber SMC Composites of Hybrid

Figure 3.34 Analytical prediction of stiffness of hybrid CoDiCo SMC laminate with the rule of hybrid mixtures (tension and compression) and classical laminate theory (bending)

In addition to enhancing mechanical properties, the hybridization also increased the tensile failure strain of the CoDiCo SMC by approximately 0.3% over that of the Co CF SMC. This effect is often referred to as pseudo-ductility [31]. Mechanical Properties at the Structural Scale Figure 3.35 shows the structural properties, namely, the maximum force and puncture energy resulting from quasi-static and dynamic puncture. Continuous reinforcement of discontinuous glass fiber SMC significantly increased the maximum force (+36%) and puncture energy (+35%) for specimens punctured in a quasi-static manner. The purely discontinuous glass fiber SMC showed positive rate dependence for maximum force (+60%) and puncture energy (+50%) in the investigated loading rate range. Furthermore, the continuous–discontinuous glass/carbon fiber SMC specimens also showed positive rate dependence for maximum force (+33%) and puncture energy (+18%) when loaded in a dynamic manner. Hence, the dynamic properties were governed by the discontinuous component of the hybrid CoDiCo SMC.

Figure 3.35 Puncture properties in terms of puncture energy and maximum load of DiCo GF SMC, Co CF SMC, and CoDiCo SMC, which were exposed to quasi-static (a) or dynamic (b) puncture

143

144

3 Characterization of CoDiCoFRP

Figure 3.36 shows representative force–deflection and energy–deflection responses resulting from quasi-static and dynamic puncture of discontinuous glass and hybrid continuous–discontinuous SMC. The force–deflection evolution of both SMC composites started with an ascending part when punctured in a quasi-static manner. This initial force increase was marked by a stiffness decrease resulting from partial failure of the specimen, once failure initiated due to crack formation at the lower surface. Cracks increased in number and size, forming a cross-shaped crack network for the DiCo SMC. Hybrid CoDiCo SMC was characterized by inter-fiber fractures in the fiber direction of the continuous material to absorb energy resulting from puncture of the specimen. After reaching the maximum force, specimens could no longer maintain any load and the striker pushed through the failed material, bending it outwards. As soon as the specimen was fully penetrated, the force reached a plateau. From this point, any further energy dissipation resulted due to frictional sliding between the specimen and the shaft of the striker. For the dynamic puncture tests of discontinuous glass fiber SMC, slight force reductions were observed during displacements of approximately 1.5  mm. These fluctuations resulted from testing set-up, vibratory response, and wave reflections and do not reflect actual material behavior or failure. Nevertheless, the slope of the force–deflection response slightly increased compared to the case of quasi-static puncture loading.

Figure 3.36 Force–deflection curves of DiCo GF SMC (a) and CoDiCo SMC (b) resulting from quasi-static or dynamic puncture

Unlike the purely discontinuous SMC, the hybrid materials failed partially with progressive failure of the three different layers, regardless of the loading rate. The evolution of absorbed energy could generally be divided into three sections. At the beginning of the puncture, at very low deflections d, the absorbed energy slightly increased (≈ 0 mm < d < 3 mm), but was still negligible compared to the final absorbed energy value (elastic deformation). As soon as the first cracks appeared at the lower surface of the specimen, the slope of energy absorption response decreased significantly (yield point, ≈ 3 mm < d < 12 mm). Crack formation and growth are the most important failure mechanisms of SMC materials when absorbing energy from mechanical loading [33]. In the last part of the puncture

3.4 Mechanical Characterization of Hybrid CoDiCo 3.4 Mechanical Glass/Carbon Characterization Fiber SMC Composites of Hybrid

event, the absorbed energy was defined by frictional effects between the striker and the punctured specimen and connected with a significant decrease of absorbed energy as deflection increased. The deflection at maximum force and puncture deflection were not affected by hybridization. Thus, for this loading case, the effect of pseudo-plasticity is not present. Mechanical Properties at the Component Scale To investigate component properties, demonstrator parts made from DiCo GF SMC (Figure 3.37(a)) and locally reinforced components (Figure 3.37(b)) were mechanically loaded by means of four-point bending, as described in the section on FourPoint Bending Testing at the Component Scale.

Figure 3.37 (a) Demonstrator parts made of DiCo GF SMC and (b) locally reinforced CoDiCo SMC

Figure 3.38 Component properties of DiCo GF SMC and CoDiCo SMC resulting from fourpoint bending with several loading and unloading steps. Stiffness evolution (a) and load–deflection evolution (b) of demonstrator parts

Figure 3.38(a) compares the resulting stiffness from four-point bending loading– unloading cycles of the pure discontinuous glass fiber SMC component with the locally reinforced part. Clearly, the stiffness was significantly increased (approxi-

145

146

3 Characterization of CoDiCoFRP

mately 250 to 300 N·mm−1) by the local reinforcement for every cycle. Initial stiffness significantly increased, but hybrid components showed a certain scatter in the initial value of the stiffness in comparison to pure discontinuous SMC parts. This may be a process-induced difference based on a misalignment of the local reinforcement. Stiffness evolution and thus damage of the component did not show any significant difference. Hence, the damage evolution was comparable for both component types. During the final loading stage, specimens with continuous carbon fiber reinforcements carried an average load surplus of 946 N, corresponding to an increase in strength of 32%. The average fracture strength of hybrid components was 739 N higher due to the local reinforcements (+17%, Figure 3.38(b)). Discussion The mechanical testing of discontinuous glass or carbon SMC at the coupon and structural scales was characterized by an important scatter of resulting mechanical material properties. Due to one-dimensional flow of the semi-finished materials during molding, the chopped fiber bundles tended to orient in the flow direction and this process-induced fiber orientation led to significantly different material properties in the flow and perpendicular directions. The macroscopic material properties of SMC are strongly influenced by the microstructure of the materials. The microstructure of the glass fiber SMC can be characterized by 25.4-mm-long glass fiber bundles with a diameter ranging between 0.5 mm and 1 mm [34]. The bundles are randomly distributed and oriented in the x–y plane. The scatter of material properties for the hybrid materials is also caused by the misalignment of the carbon fibers and the shearing of the individual carbon fiber bundles within the non-crimp fabric during flow of the discontinuous phase. Hybridization of DiCo GF SMC enhanced material performance. Tensile, compressive, and flexural stiffness can be predicted by a rule of hybrid mixtures. In contrast, tensile and flexural strength outperform the analytically predicted values. The hybrid SMC is, in these cases, more than the sum of its individual components, which underscores the effect of hybridization and the possibilities of achieving superior material performance with hybrid composites. The discontinuous glass fiber SMC showed a positive rate dependence for the considered loading rate and test set-up. This is mainly the result of the increase in tensile strength of the glass fibers [35, 36]. The increasing ability of discontinuous glass fiber SMC to absorb energy when loaded at higher rates can be explained by a change in the failure mechanism. Instead of individual fiber–matrix interface failure, interface failure of entire fiber bundles (pseudo-bundle delamination) was observed, which is linked to large matrix cracks [37]. Large matrix cracks and interface failure between the matrix and complete fiber bundles (pseudo-delamination) also enhance energy absorption capabilities. Thus, matrix and interface properties play an important role in damage evolution.

References

3.4.5 Conclusion It was possible to manufacture continuous–discontinuous glass/carbon SMC in a one-shot process using two individual semi-finished SMC materials. Material flow during molding led to anisotropic material properties at the coupon scale. The hybridization effect was evident for tensile, compressive, and flexural stiffnesses. Compressive strength could not be increased due to the low compressive strength of the Co CF SMC. The material stiffness resulting from uniaxial loadings could be predicted by a rule of mixtures. To estimate the stiffness resulting from out-ofplane loadings (flexural), the most promising approach was classical laminate theory under consideration of asymmetric laminates. Due to the non-rate-dependence of carbon fibers and the low puncture resistance at higher loading rates of continuous carbon fiber SMC, hybridization of puncture specimens reduced the rate dependent increase of maximum force and puncture energy for discontinuous glass fiber SMC. As a result of the local reinforcement of discontinuous glass fiber SMC leading to enhanced stiffness of three-dimensional components, such an approach to composite materials engineering presents a promising scheme to implement SMC in structural components in the form of lightweight, locally reinforced composite structures. The mechanical testing of discontinuous (long) fiber reinforced polymers is challenging, especially in terms of specimen geometry. The definition of an appropriate specimen type becomes even more complicated for hybrid composites. To understand the intrinsic failure mechanisms and mechanics of hybrid continuous–discontinuous SMC materials, it is necessary to establish appropriate testing and damage-monitoring strategies, e.g., acoustic emission testing. References [1]

Joppich, T., Doerr, D., van der Meulen, L., Link, T., Hangs, B., Henning, F., Layup and process dependent wrinkling behavior of PPS/CF UD tape-laminates during non-isothermal press forming into a complex component. AIP Conf. Proc. (2016) AIP Publishing LLC, p. 170012

[2]

Graf, M., Verfahrenskombination für verschnittarmes UD-Tapelegen. Light. Des. (2016) 9, pp. 34–39

[3]

Chen, J.H., Schulz, E., Bohse, J., Hinrichsen, G., Effect of fibre content on the interlaminar fracture toughness of unidirectional glass-fibre/polyamide composite. Compos. Part A Appl. Sci. Manuf. (1999) 30, pp. 747–755

[4]

Davies, P., Moore, D.R., Glass/nylon-6.6 composites: Delamination resistance testing. Compos. Sci. Technol. (1990) 38, pp. 211–227

[5] Gross, D., Seelig, T., Bruchmechanik (2016) Springer Berlin, Heidelberg [6] Hardenacke, V., Hohe, J., Assessment of space division strategies for generation of adequate computational models for solid foams. Int. J. Mech. Sci. (2010) 52, pp. 1772–1782 [7]

Hardenacke, V., Hohe, J., Local stochastic analysis of the effective material response of disordered two-dimensional model foams. Magnetohydrodynamics (2009) 4080002, pp. 511–518

147

148

3 Characterization of CoDiCoFRP

[8] Kachanov, M., Shafiro, B., Tsukrov, I., Handbook of Elasticity Solutions (2003) Springer Netherlands, Dordrecht [9] Robb, K., Wirjadi, O., Schladitz, K., Fiber Orientation Estimation from 3D Image Data: Practical Algorithms, Visualization, and Interpretation. 7th Int. Conf. Hybrid Intell. Syst. (HIS 2007) (2007) IEEE, pp. 320–325 [10] Daniels, F., ter Haar Romeny, B.M., Rubbens, M., van Assen, H., Quantification of Collagen Orientation in 3D Engineered Tissue. IFMBE Proc. B. Ser. (2007), pp. 282–286 [11] Krause, M., Hausherr, J.M., Burgeth, B., Herrmann, C., Determination of the fibre orientation in composites using the structure tensor and local X-ray transform. J. Mater. Sci. (2010) 45, pp. 888–896 [12] Pinter, P., Dietrich, S., Bertram, B., Kehrer, L., Elsner, P., Weidenmann, K.A., Comparison and error estimation of 3D fibre orientation analysis of computed tomography image data for fibre reinforced composites. NDT E Int. (2018) 95, pp. 26–35 [13] Advani, S.G., Tucker, C.L., The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites. J. Rheol. (N. Y. N. Y.) (1987) 31, pp. 751–784 [14] Leopardi, P., A partition of the unit sphere S Ì R into regions of equal measure and small diameter. Electron. Trans. Numer. Anal. (2006) 25, pp. 309–327 [15] Sabiston, T., Pinter, P., Lévesque, J., Inal, K., Evaluating the number of fibre orientations required in homogenization schemes to predict the elastic response of long fibre sheet moulding compound composites from X-ray computed tomography measured fibre orientation distributions. Compos. Part A Appl. Sci. Manuf. (2018) 114, pp. 278–294 [16] Fu, S.-Y., Effects of fiber length and fiber orientation distributions on the tensile strength of shortfiber-reinforced polymers. Compos. Sci. Technol. (1996) 56, pp. 1179–1190 [17] Jähne, B., Digitale Bildverarbeitung (2005) Springer-Verlag, Berlin/Heidelberg [18] Glasbey, C.A., An Analysis of Histogram-Based Thresholding Algorithms. Graph. Model. Image Process. (1993) 55, pp. 532–537 [19] Otsu, N., A Threshold Selection Method from Gray-Level Histograms. IEEE Trans. Syst. Man. Cybern. (1979) 9, pp. 62–66 [20] Kapur, J.N., Sahoo, P.K., Wong, A.K.C., A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vision, Graph. Image Process. (1985) 29, pp. 273–285 [21] Yoo, T.S., Ackerman, M.J., Lorensen, W.E., Schroeder, W., Chalana, V., Aylward, S., Metaxas, D., Whitaker, R., Engineering and algorithm design for an image processing API: A technical report on ITK – The Insight Toolkit (2002), pp. 586–592 [22] Paik, D.S., Beaulieu, C.F., Rubin, G.D., Acar, B., Jeffrey, R.B. Jr., Yee, J., Dey, J., Napel, S., Surface normal overlap: A computer-aided detection algorithm with application to colonic polyps and lung nodules in helical CT. IEEE Trans. Med. Imaging (2004) 23, pp. 661–675 [23] Bruderick, M., Denton, D., Shinedling, M., Application of Carbon Fiber SMC for the Dodge Viper [Internet]. Available from: http://www.quantumcomposites.com/pdf/papers/Viper-SPE-Paper.pdf [24] Lamanna, G., Ceparano, A., Sartore, L., Reliability of sheet moulding composites (SMC) for the automotive industry. AIP Conf. Proc. (2014) American Institute of Physics, pp. 338–341 [25] Gardiner, G., Is the BMW 7 Series the future of autocomposites? [Internet]. Available from: https://www.compositesworld.com/articles/is-the-bmw-7-series-the-future-of-autocomposites [26] Gortner, F., Medina, L., Mitschang, P., Influence of Textile Reinforcement on Bending Properties and Impact Strength of SMC-components. KMUTNB Int. J. Appl. Sci. Technol. (2015) 8, pp. 1–11 [27] Wulfsberg, J., Herrmann, A., Ziegmann, G., Lonsdorfer, G., Stöß, N., Fette, M., Combination of Carbon Fibre Sheet Moulding Compound and Prepreg Compression Moulding in Aerospace Industry. Procedia Eng. (2014) 81, pp. 1601–1607

References

[28] Corbridge, D.M., Harper, L.T., De Focatiis, D.S.A., Warrior, N.A., Compression moulding of composites with hybrid fibre architectures. Compos. Part A Appl. Sci. Manuf. (2017) 95, pp. 87–99 [29] Mallick, P.K., Effect of fiber misorientation on the tensile strength of compression molded continuous fiber composites. Polym. Compos. (1986) 7, pp. 14–18 [30] Bücheler, D., Locally Continuous-fiber Reinforced Sheet Molding Compound (2018) Institute of Vehicle System Technology (FAST), Department of Mechanical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Doctoral Thesis [31] Swolfs, Y., Gorbatikh, L., Verpoest, I., Fibre hybridisation in polymer composites: A review. Compos. Part A Appl. Sci. Manuf. (2014) 67, pp. 181–200 [32] ISO 6603-2:2000 Plastics – Determination of puncture impact behaviour of rigid plastics. Part 2: Instrumented impact testing [Internet]. International Organization for Standardization (2000), p. 23. Available from: https://www.iso.org/standard/25172.html. [33] Derrien, K., Fitoussi, J., Guo, G., Baptiste, D., Prediction of the effective damage properties and failure properties of nonlinear anisotropic discontinuous reinforced composites. Comput. Methods Appl. Mech. Eng. (2000) 185, pp. 93–107 [34] Dumont, P., Orgéas, L., Favier, D., Pizette, P., Compression moulding of SMC: In situ experiments, modelling and simulation. Compos. Part A Appl. Sci. Manuf. (2007) 38, pp. 353–368 [35] Arao, Y., Taniguchi, N., Nishiwaki, T., Kawada, H., Strain-rate dependence of the tensile strength of glass fibers. J. Mater. Sci. (2012) 47, pp. 4895–4903 [36] Shirinbayan, M., Fitoussi, J., Meraghni, F., Surowiec, B., Bocquet, M., Tcharkhtchi, A., High strain rate visco-damageable behavior of Advanced Sheet Molding Compound (A-SMC) under tension. Compos. Part B Eng. (2015) 82, pp. 30–41 [37] Trauth, A., Bondy, M., Weidenmann, K.A., Altenhof, W., Mechanical properties and damage evolution of a structural sheet molding compound based on a novel two step curing resin system. Mater. Des. (2018) 143, pp. 224–237

149

4

Simulation of Sheet Molding Compound (SMC) and Long Fiber-­Reinforced Thermoplastics (LFTP)

„„4.1 Introduction Thomas Seelig, Thomas Böhlke 4.1.1 Challenges Despite extensive research during recent decades, theoretical and computational modeling of fiber-reinforced polymer materials still poses many open issues and challenges. This is not surprising, since new material systems are steadily being developed, including hybrids containing phases with continuous and discontinuous fiber reinforcement. Much effort is also currently being invested in the holistic, simulative description of the entire process chain, including manufacturing, flow-induced material microstructure, and the final performance of technical components under complex thermo-mechanical loading. With regard to the SMC and LFTP materials considered in the IRTG, specific difficulties arise from the fact that the discontinuous fibers are rather long and prevail at high volume fractions. This significantly affects flow behavior during processing in terms of strong interactions among the fibers and with the mold boundaries. Long fibers and high fiber-volume fractions, however, violate the assumptions underlying state-of-the-art models for mold flow simulations, which have been established only for short-fiber materials and weak fiber interactions. Enhanced computational models must therefore be developed to properly account for the effective flow behavior during the mold-filling process and to predict the spatial variation of fiber content and fiber orientation distribution throughout a component. During the solidification stage, with its strong temperature gradients, fiber-reinforced polymers undergo a complex interplay of shrinkage, viscosity changes, and – for SMC – temperature- and pressure-dependent curing of the thermoset matrix. This gives rise to eigenstresses, which may result in component warpage or even cause damage during manufacturing, which must then be accounted for in subsequent solid-state loading analyses. Constitutive models that incorporate both the complex che-

152

Simulation of SMC and LFTP

mo-physics of the solidification stage and the resulting chemo-thermo-mechanical effects, such as residual stresses and initial damage in the solid state, are thus needed for the predictive computational modeling of fiber-reinforced polymers. Constitutive modeling of SMC and LFTP in the solid state is further complicated by the typically large fiber-volume fractions and the fact that fiber lengths are comparable to the characteristic dimensions of technical components. While a strict micro–macro scale separation, which is required for homogenization, does not exist, homogenized models are indispensable for the macroscopic numerical analysis of components. Hence, the applicability and predictive capabilities of mean-field models must be carefully investigated. Due to recent increases in computer power, the comparison with full-field analyses has become one way to do so. Another challenge for computational modeling of SMC and LFTP arises from the statistically non-uniform microstructure, which leads to a significant macro-heterogeneity and significant scatter in the effective properties. To numerically assess the ultimate performance of technical components, the various micro-scale damage mechanisms in SMC and LFTP (e.g., fiber–matrix de-bonding, fiber breakage, and matrix cracking) must be taken into account along with the local fiber orientation distribution. Their incorporation in homogenized (e.g., mean-field) models, however, requires severe simplifications, the effects of which need to be understood. For example, predictive material models must describe the evolving macroscopic anisotropy that arises from the damage-induced changing of the orientation distribution of load-carrying fibers.

4.1.2 Approaches Within the holistic approach pursued by the IRTG, modeling and simulation activities consider the entire product development chain. This consists of component design and manufacturing, the load-carrying capabilities of final components, including component damage and failure behavior. Issues arising on various length scales are also addressed, so as to gain a deeper understanding of the particular material systems and to develop theoretical–numerical models with enhanced predictive capabilities. The present chapter, consisting of five articles organized according to the process chain (i.e., from fluid to solid), provides an overview of activities in the research area “Simulation” during the first doctoral generation. Several of the challenges mentioned are addressed in these works. Section 4.2 (Hohberg et al.) deals with the rheological characterization, rheological modeling, and process simulation of SMC materials, including the development of a novel experimental technique to investigate the effective flow behavior. Section  4.3 (Schwab et al.) is devoted to modeling the curing process in SMC for the prediction of residual stresses on the

4.2 Rheological Characterization and Process Simulation of SMC

microscale, for which a phase-field modeling approach is used. In Section 4.4 (Pallicity et al.), a methodology is established in a finite element framework to simulate residual stress at different length scales and this is demonstrated for laminates. The experimental characterization and modeling of the fiber-orientation-dependent macroscopic elastic and visco-elastic properties of SMC and the assessment of the predictive capabilities of mean-field vs. full-field models via comparison with the experimental results is covered in the Section 4.5 (Kehrer et al.). Section 4.6 (Schemmann et al.) presents a novel constitutive model for damage processes in SMC materials – based on a mean-field Mori–Tanaka homogenization scheme and accounting for both fiber–matrix de-bonding via a probabilistic Weibull strength criterion and matrix damage. Section 4.7 (Schulenberg et al.) deals with LFTP materials, and proposes an efficient computational model for their fiber-orientation-dependent elastic-plastic behavior, including damage and ultimate failure.

„„4.2 Rheological Characterization and Process Simulation of SMC Martin Hohberg, Luise Kärger, Frank Henning, Andrew Hrymak 4.2.1 Introduction The correct prediction of SMC flow behavior and the resulting fiber orientation distribution at the end of the molding process is crucial for holistic virtual part design [1–3]. Therefore, a 3D process simulation approach is developed to predict the complex flow of SMC. This flow is dominated by the resin-rich lubrication layer at the mold surface and the extensional viscosity in the core region. Since simulation models are only as good as the material parameters on which they are based, a new rheological tool is also designed. Using this rheological tool, the compressibility of a semi-structural SMC formulation is shown and considered in the rheological models. As a short introduction, the first section briefly describes the current state of research. In the next section, the rheological measurements of three different SMC material formulations are described and the rheological model is developed. Based on these rheological results, the effect of material formulations on the rheological properties is given. In the third section, the development and implementation of the SMC-specific 3D process simulation is given. Finally, the IRTG reference structure is simulated, including the local unidirectional (UD) reinforcements.

153

154

Simulation of SMC and LFTP

Modeling the SMC Flow Process The modeling of SMC is necessary to evaluate the experimental results and simulate the flow behavior. The same approaches should be used in both cases for consistent material characterization. It can be assumed that no curing reaction occurs during the compression molding process due to the relatively slow reaction kinetics of typical SMC resins. Therefore, reaction kinetics and viscosity changes due to the reactivity need not be modeled. This was proven by experiments of Marker and Ford [4] and Barone and Caulk [5]. Consequently, the flow can be described using (thermo-) mechanical models. These can be classified into groups, depending on their level of detail. The first group considers fibers and matrix separately. This leads to detailed simulations with the need to account for the individual fiber–fiber and fiber–matrix interactions, since the fibers are resolved individually [6]. Fiber– matrix separations can be predicted using such an approach, which is important in T-shaped parts [7] and ribs [8, 9]. Two-phase approaches based on a modified Darcy’s law were developed [10] due to high computational effort. Additional equilibrium and constitutive equations are required to model these two phases and their separation. Such models are used solely for quantitative numerical studies, due to their high characterization effort. The models in the second group describe fiber and matrix as one phase and are widely used. Here, SMC is described as a continuum fluid with the same velocity for fibers and matrix, so that no fiber–matrix separation can occur. Most of these models are based on a generalized Hele–Shaw approach, due to the shell-like shape of most SMC parts and a relatively low thickness compared to the in-plane dimensions. Various models have been developed [11–14] based on this approach using a Newtonian fluid model and a no-slip condition between the contacting surfaces of the SMC and the mold. Barone and Caulk [15] showed the existence of a thin lubrication layer at the mold surface and a plug-flow of the core region. They investigated different friction formulations in a generalized Hele–Shaw model [16]. Here, the hydrodynamic friction approach based on the relative velocity at the mold surface gave the best description of their experimental observations. Considering the uniform in-plane shear, extensional deformation [17, 18], and exclusively out-of-plane shear in the lubrication layer [19], new combinations of SMC flow models have also been developed [18, 20–22]. The basic idea of all these models is the superposition of the hydrostatic fluid pressure p, the viscous stress of the core region rheo, and the friction stress from the lubrication layer fric:

 D pI C  rheo C  fric :(4.1) Since the lubrication layer is relatively thin compared to the core region or possible thickness discretization, a hydrodynamic friction approach based on a power–

4.2 Rheological Characterization and Process Simulation of SMC

law model becomes state of the art for SMC [18, 22]. This hydrodynamic friction is applied as a boundary condition and is denoted as

 fric D 



kvk v0

m1

v N s  kvk ksk

(4.2)

with the reference velocity v0, the hydrodynamic friction coefficient , the power– law coefficient m, the surface normal s and the velocity at the mold surface plane v, which is perpendicular to the surface normal. As for the friction, a power–law approach fits best with the experiments for the viscous stress rheo [18]. It is denoted as

 rheo D ps



kDk D0

n1

D

(4.3)

with the extensional viscosity for a pure strain load case ps, the strain rate tensor D, a reference strain rate D0, and the viscous stress power–law coefficient n. All these models give good filling predictions for flat shapes without ribs, provided no local reinforcements or load introduction elements are considered. Since this is one of the experimental challenges within the project, these 2.5D approaches need to be extended towards a full 3D simulation. In these one-phase approaches, a separate fiber orientation model is required to predict the fiber orientation. Jeffery [23] developed the first model for a rigid ellipsoidal particle in a Newtonian fluid, a linear velocity field far away from the fiber, and no buoyancy or inertia effects. The fiber movement for these conditions could be analytically described with a unit vector n for the orientation as

dn D W  n C  .D  n  Œn  D  n n/ ;(4.4) dt with the vorticity tensor 2W H rv − (rv)T, the strain rate tensor 2D H rv C (rv)T, and the particle shape , which is defined as

D

r2  1 (4.5) r2 C 1

where r is the aspect ratio of a fiber with length l and diameter d, defined as r H l/d. Therefore, the following particle shape definitions apply:  H −1: disc,  H 0: sphere,  H 1: ellipsoid with l >> d.

Since this model is only valid for single fibers, further models were developed to better capture the observed fiber orientations. By adding a phenomenological term modeling fiber interaction to Jeffery’s equation, Folgar and Tucker [24] developed a model for concentrated fiber suspensions. Wang et al. [25] developed the reduced

155

156

Simulation of SMC and LFTP

strain closure (RSC) model to increase the prediction accuracy across the thickness. Since all these models over-predict the reorientation of long fibers, Phelps and Tucker [26] developed the anisotropic rotary diffusion (ARD) model to add a fiber-orientation-dependent interaction coefficient to the RSC model. Therefore, the Folgar–Tucker model with the ARD-RSC extension can be expressed as:

NP D .W  N  N  W / C  .D  N C N  D  2 ŒN C .1  / .L  M W N/ W D/  C P 2 ŒC  .1   / M W C  2  tr .C/ N   (4.6)  5 .C  N C N  C/ C 10 ŒN C .1  / .L  M W N/ W C

A detailed discussion of the model would go beyond the scope of this section, but can be found in the original publications. In the subsequent modeling chapters, this ARD-RSC model is used without modifications, since it is the state of the art for long-fiber-reinforced materials and the fiber reorientation models are not the focus of this work. Rheological Characterization of SMC In the context of process simulation, the rheological characterization is needed to provide the necessary material data. Two approaches may be employed for the rheological characterization of SMC: shear or rotational rheometers and in-line rheometers. Shear or rotational rheometers are common for rheological polymer characterization. Nevertheless, this approach has two disadvantages: the rheometer applies a high shear rate to a relatively small sample, which leads to different flow behavior than for the plug-flow in a compression molding tool. This effect is also amplified, since a shear or rotational rheometer cannot apply hydrostatic pressure, as exists in the real process. Besides the process conditions, the sample size leads to problems. The typical sample size is in the range of standard chopped glass fibers in SMC and is not representative for the material. This can be attributed to the impact of fiber length and fiber orientation on material properties [18, 27]. For these reasons, the in-line approach is used more frequently. Most in-line rheometers are based on in-situ measurements, such as press sensors or transparent molds, in which the flow front can be detected. The first in-line rheometers [17, 28, 29] used the squeeze flow method, which is schematically shown in Figure 4.1(a) Here, the material can be characterized over a large strain rate range by varying the closing speed. While recording the pressure force, a generalized Hele–Shaw model can be used to determine the material parameters. Since only the press force is used for the pressure computation, no friction models can be used and therefore, a no-slip condition is crucial for these experiments. Therefore, the flow kinetics in the sample are neither homogeneous through the thickness, nor along the flow radius. This leads to a characterization method, in which

4.2 Rheological Characterization and Process Simulation of SMC

the flow models need to be inversed and solved iteratively, a process that leads to inaccuracies if complex models are used. To overcome this disadvantage, simple compression in-line rheometers were developed [18, 30] (cf. Figure 4.1(b)). These rheometers enforce a slip condition between the material and the mold surface by applying a lubricating film onto the mold surface. Furthermore, the sample size is modified to yield a higher length to height ratio. This leads to more homogeneous flow, which in turn simplifies the determination of material parameters. Once again, no friction parameters can be determined with such a set-up, which includes the lubricating film. This extra layer also leads to a different flow compared to the original compression molding process. Reducing the flow from 2D to 1D and adding pressure sensors resulted in the plane strain rheometer (cf. Figure 4.1(c)) [18, 31]. Here, characterizations are performed with and without an extra lubrication film. In each case, this leads to a homogeneous flow kinetic without gradients, since the correct process boundary condition, especially the mold temperature, can be used. Due to the extra information from the pressure sensors, more complex generalized Hele–Shaw models can be used, which consider both the plug flow and the SMC lubrication layer.

Figure 4.1 (a) Schematic illustration of a squeeze flow rheometer [28], (b) a simple compression rheometer [18], and (c) a plane strain rheometer [18]

Multiple measurements are necessary for one characterization experiment with all the currently available rheological in-line tools. This leads to errors due to the local inhomogeneity of the SMC material. Furthermore, no characterization regarding the compressibility of the material can be performed. These two disadvantages should be avoided with any newly developed rheological tool.

157

158

Simulation of SMC and LFTP

4.2.2 Rheological Measurements and Models In this section, the newly developed rheological in-line tool is presented and characterization experiments with three different SMCs are performed. Based on these experiments, the compressibility of one SMC class is proven and considered in the rheological models. After determining the material parameters for the different SMCs, a correlation between the parameters and the material composition is developed. Rheological Tool and Experimental Set-Up The new rheological tool design is based on the plane strain in-line rheometer (cf. section on Rheological Characterization of SMC). To counteract the disadvantages described earlier, this tool must have a long flow length, a high strain rate range, and a locally high pressure resolution along the flow. Such a tool with a rectangular cavity of 800  mm  250  mm was designed at the Fraunhofer Institute for Chemical Technology (ICT), in Pfinztal, in which samples with a final thickness between 1 mm and 5 mm can be produced. To measure the pressure over the flow length, seven pressure sensors are integrated along the flow direction (see Figure 4.2). Due to the long possible flow length, different flow behaviors can be observed by varying the initial charge coverage between 20% and 80%. To log the pressure distribution from the pressure sensors simultaneously with the press data (e.g., current press force and the position of the moving mold side), both systems are linked to one recording system. Since the rheological tool is on an industrial scale, the experiments were performed at the Fraunhofer ICT on two industrial hydraulic presses from Dieffenbacher (COMPRESS PLUS DCP-G 3600/3200 AS and Dieffenbacher DYL 630/500).

Figure 4.2 Dimensions of the new in-line rheometer and the position of the seven pressure sensors [32]

Three different SMC formulations have been investigated. The first one is an unsaturated polyester (UP)-based low-density (LD) Class-A SMC that was developed for exterior automotive parts by the Fraunhofer ICT [33]. To reduce the density, micro hollow glass spheres were added as part of the filler. The composition of the resin is given in Table 4.1. The second SMC is a semi-structural SMC, which has more

4.2 Rheological Characterization and Process Simulation of SMC

fibers and no fillers. A vinyl ester (VE) resin is used for this formulation (for composition, see Table 4.2). The third formulation is a semi-structural SMC with carbon fibers. Due to the co-molding process with local unidirectional reinforcements (cf. Section  2.2), the B-stage unsaturated polyester polyurethane hybrid (UPPH) resin is used (for composition, see Table  4.3). All these SMC formulations use chopped fibers with a length of 1 inch (approx. 25 mm). The fiber fractions and the fibers used are given in Table 4.4. In this context, the term “semi-structural” indicates material properties of fiber-reinforced polymers between those of surface parts as Class-A SMC and continuous reinforced polymers. Table 4.1  Composition of the Paste of the LD Class-A SMC [32, 33] Component

Trade name

Quantity

UP resin

Palapreg Premium G22-01 LE

100 parts

Adherent and flow aids

BYK W9010

3 parts

Styrol

–

7 parts

Peroxide

Palapreg Premium G21-01LE Cure

1 part

L&V 50%MgO

Luvatol® MK35

2.77 parts

Filler: calcium carbonate

Omya Millicarb

105 parts

Filler: micro hollow glass spheres

3M VS5500

28 parts

Table 4.2  Composition of the Paste of the Semi-Structural VE SMC [34] Component

Trade name

Quantity

VE resin

Atlac XP810X

100 parts

Adherent and flow aids

BYK 9085

2 parts

Peroxide

Trigonox 117

1 part

L&V 50%MgO

Luvatol EK 100KM

4.2 parts

Table 4.3  Composition of the Paste of the Semi-Structural UPPH Carbon Fiber SMC [34] Component

Trade name

Quantity

UPPH resin

Daron ZW 14142

100 parts

Adherent and flow aids

BYK 9085

2 parts

Impregnation aid

BYK 9076

3 parts

Deaeration aid

BYK A-530

0.5 parts

Inhibitor

pBQ

0.03 parts

Peroxide

Trigonox 117

1 part

Isocyanate

Lupranat M20R

24.2 parts

159

160

Simulation of SMC and LFTP

Table 4.4  Fiber Type, Fiber Volume, and Length of the SMC Formulations [34] LD Class-A SMC

VE SMC

Fiber type

Glass fiber

Glass fiber

Trade name

JM MultiStar 272

JM MultiStar 272

Zoltek PX 35

Fiber roving bundles

4800 tex/12K

4800 tex/12K

2700tex/50K

Fiber diameter

13.5 µm

13.5 µm

7.2 µm

Fiber length

25 mm (1 inch)

25 mm (1 inch)

25 mm (1 inch)

Fiber fraction

38 wt% (20 vol%)

41 wt% (22.7 vol%)

55 wt% (42 vol%)

®

UPPH C-SMC Carbon fiber ®

Rheological Measurements of Different SMC Formulations Slightly different process settings and initial charge (IC) coverings are necessary due to the different resin systems used for the SMC formulations. These are given in Table 4.5. All materials are molded with a constant closing speed of 1 mm s−1 for direct comparison. Furthermore, tests with other constant closing speeds and strain rates are performed to characterize the different SMC formulations. Here, the nominal strain rate D is defined as the ratio of the current closing speed h(t) and the gap height h(t):

ˇ ˇ ˇPh.t/ˇ D.t/ D  h.t/

(4.7)

Table 4.5  Process Settings for the Different Material Molding Trials LD Class-A SMC

VE SMC

UPPH C-SMC

Tool temperature

Upper: 150 °C Lower: 160 °C

Upper: 150 °C Lower: 160 °C

Upper: 140 °C Lower: 145 °C

Max press pressure

2000 kN

1600 kN

3000 kN

IC coverage

36.25% (290 mm)

20% (160 mm)

20% (160 mm)

IC av. height

9.0 mm (4 layer)

10.1 mm (8 layer)

18.0 mm (16 layer)

IC av. weight

890 g

648 g

970 g

Part av. height

3.2 mm

2.2 mm

3.2 mm

Three exemplary pressure distributions of the different material compositions for a constant closing speed of 1 mm s−1 are given in Figure 4.3, Figure 4.4, and Figure  4.5. These diagrams are plotted over the relative gap height, defined as the difference between the current gap height h(t) and the final gap height hf. This makes it easier to compare the different process settings. When comparing these pressure distributions, the same pattern in different characteristic features can be observed. At the beginning of the molding process, the sensors covered by the initial charge show an increase up to a threshold. During this short phase, the mate-

4.2 Rheological Characterization and Process Simulation of SMC

rial is compressed and trapped air is released. After this transversal compression, the flow of SMC starts. During this flow phase, the pressure is increasing continuously due to the increased friction stress. For the semi-structural VE-SMC, this increase is lower, since the strain rate is increasing and therefore the rheological stress is decreasing (cf. Eq. (4.1) and (4.2)). This already implies a higher extensional viscosity compared to the other material formulations. For the two semi-structural SMC formulations, the pressure of sensor 1 decreases during this phase. This is due to a small defect of the short pegboard, which causes some material to flow through the gap between the tool sides. After the material in this gap is cured, the pressure is restored. Just before the final plate thickness is reached, the maximum pressure can be observed. This is the switching point, where the maximum compression force is reached and the press switches to the pressure controlled closing speed.

Figure 4.3  Pressure distribution for the LD Class-A SMC for a closing speed of 1 mm s−1 [32]

Figure 4.4  P  ressure distribution for the semi-structural VE SMC for a closing speed of 1 mm s−1 [32]

161

162

Simulation of SMC and LFTP

Figure 4.5  P  ressure distribution for the semi-structural UPPH carbon fiber SMC for a closing speed of 1 mm s−1 [32]

The flow front can be tracked during the molding process with the new rheological tool design. Therefore, the volume can be calculated every time the flow front reaches a pressure sensor. By using this information, a material-dependent relative volume change ˇ can be determined, which is defined as

ˇ.t/ D

1 V



@V @t





V .t/  V0 lSi h.t/  l0 h0 D  V0 t l0 h0 .t  t0 /

(4.8)

where l0 and h0 represent the initial charge length and height. The variables lSi and h(t) represent the position of the sensor that has just been reached and the current gap height, respectively. The moment at which the press touches the SMC initial charge for the first time is denoted as t0. These distributions are given for the three SMC formulations in Figure 4.6. The LD Class-A SMC exhibits incompressible behavior (ˇ H 0), since a high percentage of filler is used in the formulation. The VE-SMC formulation shows an increased relative volume change, which could be attributed to the foaming behavior of the VE resin. For other process conditions with higher closing speeds, a compressibility of VE SMC can also be observed [34]. The UPPH carbon fiber SMC shows a decrease in volume, which was also observed for glass fiber SMC materials by Guiraud et al. [35] and Hohberg et al. [32]. Therefore, the compressibility needs to be considered in the rheological model, at least for semi-structural SMCs.

4.2 Rheological Characterization and Process Simulation of SMC

Figure 4.6  R  elative volume change β for the three different SMCs at the current flow fronts at different times during the molding process [32]

Compressible Rheological 2D Shell Model To model the pressure distributions within the rheological tool, the generalized Hele–Shaw approach is used. Therefore, some basic assumptions are necessary to model the flow: ƒƒThe SMC is a one-phase continuum material, so that the matrix and the fibers have the same velocity and no separation occurs. ƒƒThe material is practically isothermal [5], except for the thin resin layer near the mold. ƒƒDue to the short compression time (below 15 s) and the resins used, no curing occurs in the flow phase [22]. ƒƒNo external or acceleration forces need to be considered, since they are small compared to the viscous forces. This leads to the first momentum balance equation, which is written as:  div. / D 0

(4.9)

ƒƒBased on the observed compressibility behavior, it is assumed to be spatially constant and isotropic [35]. Using these assumptions and the coordinate system introduced in Figure  4.2, a compressible rheological model can be developed based on the model introduced by Dumont et al. [36]. Therefore, the 1D flow in the rheological tool is used to build a simple stress model based on the axial stress component. This model uses a power–law approach for the hydrodynamic friction stresses (cf. Eq. (4.2)) and the

163

164

Simulation of SMC and LFTP

rheological stress (cf. Eq. (4.3)). The compressible model was developed by Hohberg et al. [34] and uses empirical fitting for the relative volume change ˇ. To characterize the rheological and lubrication layer properties, the model is written in a volumetric-averaged axial stress form , to use geometrical simplifications:

ˇ ˇn1 ˇ ˇ !m1  mC1   P ˇ hP ˇ ˇPhˇ lo ho 2 h hP ˇ ˇ .t ˇ.t/ C 1/ C h¢33 i D ps n1 ˇ ˇ m C 2 hmC1 v0 h h D0 ˇ h ˇ ˇ ˇn1 ˇ ˇ !m1   P mC1  ˇ hP ˇ ˇPhˇ 2 lo ho hP h ˇ ˇ  (4.10) .t ˇ.t/ C 1/ C ˇ ˇ ˇhˇ h m C 2 hmC1 v0 h 1

h¢33 i D ps

1 D0n1

and a local axial-thickness-averaged stress form 33, which is defined at the mold h surface ( x3 D ˙ ): 2 ˇ ˇn1 ˇ ˇ !m1 "   P  ˇPhˇ 1 ˇˇ hP ˇˇ 2 h lo ho hP mC1 .t ˇ .t/ C 1/ †33 .x1 / D ps n1 ˇ ˇ   x 1 mC1  mC1 h v0 h h D0 ˇ h ˇ ˇ ˇn1 ˇ ˇ !m1 "   P  mC1 # ˇPhˇ 1 ˇˇ hP ˇˇ 2 l h hP h o o  .t ˇ .t/ C 1/ †33 .x1 / D ps n1 ˇ ˇ  x1mC1  h m C 1 hmC1 v0 h D0 ˇ h ˇ (4.11)

In both equations, ps represents the extensional viscosity under plane strain for the reference strain rate D0 with the corresponding power–law coefficient n. Furthermore,  represents the hydrodynamic friction coefficient with the reference closing speed v0 and the corresponding power–law coefficient m, while x1 represents the current interpretation point position in the flow direction. The characterization is done in two steps. First, the hydrodynamic friction coefficient  and its power–law coefficient m are determined by using Eq. (4.11). By determining the difference between two pressure sensors,  can be calculated using experiments with a constant closing speed as:

mC1 D 2

ˇ ˇ !mC1 ˇPhˇ hmC1 33 .xII /  33 .xI /  mC1  : v0 xII  xImC1 hP

(4.12)

Here, xI and xII refer to the positions of two consecutive pressure sensors. Second, the plane strain extensional viscosity ps is fitted to the pressure sensor results with various strain rates by using Eq. (4.11). Effects of the Material Formulation on the Rheological Properties By using the model from the section on the Compressible Rheological 2D Shell Model, the three SMC formulations introduced in the section on the Rheological

4.2 Rheological Characterization and Process Simulation of SMC

Tool and Experimental have been characterized. The detailed steps of the characterization are given in Hohberg et al. [32]. The results for the three material compositions are given in Table  4.6. The UPPH carbon fiber SMC exhibits a special behavior. A difference of the material parameter between the initial charge area and the flow area was observed [37] due to the carbon fibers and the resulting temperature distribution. For the LD Class-A SMC formulation, experiments with the pure paste were also made and added to the results. ⋅ Table 4.6  Summary of the Rheological Material Properties for a Closing Speed of h H 1 mm s−1 [32] Extensional viscosity ηPS in MPa s at D H 1 s−1

n

Hydrodynamic friction coefficient λ in MN s m−3 ⋅ at h H 1 mm s−1

m

LD Class-A SMC

4.10

0.44

LD Class-A resin

0.75

2.00

0.6

0.58

0.85

0.6

VE SMC UPPH C-SMC

12.00

0.27

0.80

0.6

3.65 (IC area)

0.27

1.23 (IC area)

0.6

2.75 (flow area)

0.60 (flow area)

Comparing these results with those from Dumont et al. [18], one observes an accordance regarding the power–law coefficients for the standard SMC (LD Class-A SMC) and its paste. A correlation between the power–law coefficients m and n and the material composition is observed, when the results from Hohberg et al. [32, 38] are also taken into account. Regardless of the material formulation or type of resin, the hydrodynamic friction power–law coefficient m is a constant parameter with a value of 0.6. The power–law coefficient of the extensional viscosity is assumed to be n H 0.58 for the paste without fibers, n H 0.44 for standard SMCs with fillers, and n H 0.27 for semi-structural SMCs without fillers and a higher fiber volume content.

4.2.3 3D Process Simulation of SMC To date, only SMC-specific 2D or insufficient 3D models have been developed for SMC process simulations [38, 39]. New approaches are necessary to predict the correct flow and fiber orientation in complex 3D structures. Therefore, a new method is developed and implemented here. SMC-Specific Material Model The extensional-rate-dominated core region and the shear-rate-dependent lubrication layer must be modeled to correctly predict the SMC material behavior during the compression molding process. Since the lubrication layer is significantly thinner than the core region or the designated element thickness, the friction model from the section on Modeling the SMC Flow Process (Eq. (4.2)) is used. Therefore, friction

165

166

Simulation of SMC and LFTP

and viscous stresses are superposed where the SMC is in contact with the mold surface. The friction stress becomes part of the material stress, since no user-defined friction model is available within ABAQUS CEL. For the core region, the deformation-rate-dependent approach from the rheological model is used again. Therefore, the model is based on the same basic equations (Eq. (4.1)–(4.6)) as the shell model for the rheological characterization, but extended towards a 3D approach. Implementation of the Material Models The coupled-Eulerian–Lagrangian (CEL) method within ABAQUS is used [40] to implement the models described previously. With this CEL method, large deformations can be modeled with the Eulerian flow of the material. Furthermore, a fluid– structure interaction is intrinsically included in the Lagrangian contact formulation. This permits one to model the SMC–tool interaction and to consider local unidirectional reinforcements in the process simulation.

Figure 4.7 Schematic illustration of the order and interaction of scripts, subroutines, and internal information for the SMC process simulation [39]

Calculating the stresses due to the current strain rate is implemented within the user-defined material subroutine (VUMAT). Here, the pressure due to compressibility, the rheological stresses based on extensional and shear viscosity, and the friction stresses of the lubrication layer are computed. Besides the material behavior, the fiber orientation is also computed in this VUMAT. Therefore, the Folgar– Tucker model with the ARD-RSC extension (cf. Eq. (4.6)) is implemented and the IBOF closure approximation is used [41]. A script-based plug-in is available in the implementation to initialize the fiber orientation within the initial charge. A set of

4.2 Rheological Characterization and Process Simulation of SMC

subroutines and scripts is developed to gather all the information there (cf. Figure 4.7), since not all parameters needed to localize the lubrication layer are available within this VUMAT. In a first step, the geometrical information is passed to the state variables (SDV). In the user-defined amplitude subroutine (VUAMP), the current closing speed is defined and passed to the user-defined state and field variable subroutine (VUSDFLD). Within this subroutine, the lubrication layer is identified and passed to the VUMAT to activate the extra friction stress calculation at designated integration points. The external database subroutine (VUEXTERNALDB) is used to secure the thread safety during the simulation. Detailed information on the implementation of material models can be found in Hohberg [38]. Hybrid Process Simulation of the IRTG Reference Structure The IRTG reference structure without ribs and with tapes (cf. Section 4.2.2) is used to demonstrate the capabilities of the process simulation. The complete tool with dimensions of 800 mm  250 mm is modeled, with the reference structure in the center. The positions of the local unidirectional reinforcements (UD-tapes) are optimized according to Section  4.2.2 and adapted by the processing (cf. Section  2.2 and 2.3) for the prototype manufacturing. The initial charge is placed under the tapes as illustrated in Figure 4.8. The material is then molded and flows in both directions. A homogeneous linear-elastic material is used for the reinforcements. During the molding process, the increased pressure of the SMC leads to a better adaption of the reinforcement’s shape towards the mold surface. In principle, this forming of the reinforcement could also be predicted with this hybrid process simulation. The results, such as the fiber orientation distribution, can then be exported and used in the structural simulation. Therefore, a plug-in has been developed that can map the results from the process simulation mesh to the structural mesh. In a second step, the orientation information is clustered and used for a homogenization of stiffness and thermal properties [38].

Figure 4.8 Initial configuration for the process simulation of the hybrid IRTG reference structure with the SMC-specific material model

167

168

Simulation of SMC and LFTP

4.2.4 Conclusion In this section, it is shown that a precise understanding of the SMC material behavior during the compression molding process is crucial for rheological characterization, rheological modeling, and process simulation. By developing a new inline rheological tool, the compressibility of semi-structural SMC formulation has been proven and considered in the model. Based on this new model, different SMC material formulations have been characterized and compared. Based on these material parameters, a new 3D SMC-specific process simulation method is developed. This method considers both the thin lubrication layer at the mold surface and the core region, which is dominated by the extensional viscosity. In the context of the IRTG reference structure, this approach is used for a simplified prediction of the patch displacement during the molding process and for providing fiber orientation data to the structural simulation projects.

„„4.3 Phase-Field Modeling of the Curing Process in Fiber-Reinforced Thermosets on a Microscale Felix K. Schwab, Daniel Schneider, Colin Denniston, Britta Nestler 4.3.1 Introduction The curing process of thermoset-based fiber-reinforced polymers highly influences the resulting material properties, the behavior, and the shape of manufactured parts. Eigenstresses are induced by temperature- and cure-driven strain gradients, as well as by non-uniform thermo-chemo-mechanical properties, which are due to the heterogeneous material, consisting of fibers and matrix, a heterogeneous temperature distribution and varying chemical reaction speeds throughout the mold [42]. Generally, the curing of fiber-reinforced thermosets consists of the curing process itself and the subsequent cooling to room temperature [43]. Curing is conducted at a globally constant temperature that is high enough to trigger the exothermic reaction. The reaction results in shrinkage and a change in material properties of the matrix – especially an increase in stiffness – while the properties of embedded fibers remain effectively unchanged. After the curing is finished, both polymer and fibers shrink when cooled. Their differing thermal expansion coefficients lead to differing shrinkage, however, which in turn creates additional ther-

4.3 Phase-Field Modeling of the Curing Process in Fiber-Reinforced Thermosets on a Microscale

mal eigenstresses. The resulting residual stresses partly transform into warpage or sink marks in polymer regions, particularly after demolding. Close to fibers, where the polymer is bonded and therefore constrained, cure shrinkage plays an important role in the pre-stressing and pre-damaging of manufactured parts [44, 45]. This is because the fibers generally experience compressive stresses, whereas the surrounding polymer is under tension. The magnitude of these stresses depends on the material properties of the fibers and matrix, and the thermoset matrix properties depend on the curing process [46]. This may lead to microcracking or interface debonding, even without external loading. This degrades the material properties and influences the behavior of the overall system. Along with these undesirable residual stresses, however, some stresses can have a positive effect. The hoop stresses around a reinforcing fiber, for example, may promote dissipation of pull-out energy and hence lead to an increase in toughness [47]. The diverse interdependencies that connect process design with the final product performance still make it common and necessary to improve the curing process and the choice of resin via trial and error [48]. A computational optimization of process design requires a variety of models to describe thermal, chemical, and mechanical effects and their interplay. Here, it is essential to better understand the curing process and its influences. If residual stresses and microcracks are significant, they must also be considered in follow-up simulations, such as structural analysis or fracture prediction. Common models, such as those found in [49, 50], are formulated within a thermodynamic framework and describe a thermo-mechanical material combined with a description of the curing reaction. The exothermic chemical reaction is often modeled using a phenomenological approach, and material properties are fitted to experimental data [51]. With growing complexity and the need for ever-increasing accuracy, most approaches need a large set of material parameters, which must either be determined in experiments or simulations. This step is essential for the outcome of curing simulations, but it is also complicated, since most properties are dependent on both curing degree and temperature. This chapter focuses on deriving an approach for modeling curing of fiber-reinforced thermosets based on the phase-field method. Herein, the phase-field method itself is used to capture the complex geometry of fiber bundles on a microscale. The material properties needed to simulate curing on a microscale are also identified.

4.3.2 Microscale Simulation on the Basis of the Phase-Field Method Many effects observed on a macroscale are induced on a microscale, and the formation and evolution of a material’s microstructure strongly influence a broad range of material properties. Hence, studying these processes in experiments and

169

170

Simulation of SMC and LFTP

simulations is important to further improve materials’ properties and materials’ modeling. One approach in modeling and simulating phenomena on a microscale is the phase-field method. It has the ability to describe complex systems consisting of regions with different properties and orientations via a set of order parameters – or phase-fields – in combination with an implicit tracking of interfaces between the regions. This ability has established the phase-field method as a means of describing microstructures and their evolution. By indicating regions physically separated and their interfaces using a diffuse transition region in which order parameters increase and decrease smoothly (see Figure 4.9), free boundary movement problems become numerically efficient [52]. Typical modeling applications include solidification processes, solid–solid phase transformations, growth and coarsening of precipitations, grain growth, martensitic phase transformations, and crack propagations [53, 54]. Due to the diffuse interface regions, interpolating material parameters between locally coexisting phases plays a major role, since these interfaces affect the overall system by influencing physical quantities and interface movement. By using thermodynamic reasoning, physical behavior, often formulated in a sharp interface context, can be mapped onto a diffuse interface introducing more advanced interpolation schemes in the phase-field context. If applied to momentum, mechanical jump conditions can be incorporated [55]. A Ginzburg–Landau-type integral collects all surface and bulk energy density contributions that describe the multiphase-field system. Together with anN-tuple of ˚ the phase-field order parameters  .X; t/ D  ˛ .X; t/ ; : : : ;  N .X; t/ , each of which describes the volume fraction of a phase, the domain parameterization leads to a free energy functional ℱ expressed for a volume:

 R ˚ F .; r; : : :/ D RV ˚fie .; r/ C f bulk .: : :/ dV  D V a.; r/ C 1 !ob ./ C f bulk .: : :/ dV ; 

(4.13)

where a.; r/ denotes the gradient energy density and !ob() ∕, the potential energy density [52]. The gradient term a widens the diffuse interface and is balanced by the potential term !ob. Together, they form the interfacial energy density fie yielding an interface of a defined width, which is controlled by the parameter . The bulk energy density f bulk comprises all the physical quantities involved, including the chemical and strain bulk energy densities, which are phase-inherent. Therefore, the volume-averaged strain energy density f el , which is composed of the ˛-phase contributions, is exemplarily written as

f el D

P

˛

 ˛ fel˛

with

P

˛

 ˛ D 1;

(4.14)

4.3 Phase-Field Modeling of the Curing Process in Fiber-Reinforced Thermosets on a Microscale

which represents a volume constraint on the volume fractions ’. Implicitly, this indicates that all  ˛ 2 Œ0; 1 and that norming is necessary in multiphase regions.

Using a variational approach, the evolution equations for each phase-field ’ are derived from the functional ℱ in Eq. (4.13). The variation ensures the energy minimization of the multiphase system towards a thermodynamic equilibrium. With an Allen–Cahn-type relaxation approach conserving the local volume fraction, we note according to [56] the following for each phase ˛:

@ ˛ 1 P ˛ˇ D M @t N  ˛¤ˇ



ıF ıF  ˇ ˛ ı ı



;

8 ˛ D 1; : : : ; N :

(4.15)

With ˛ − ˇ phase interactions, each of the N locally active phases contributes to the evolution of ’, where ıℱ  ∕  ı’ denotes the variation of the free energy functional with respect to ’. The proportionality constant M˛ˇ denotes the mobility of the ˛ − ˇ interface. If the functional ℱ has further dependencies, for example on the strain " or the absolute temperature , a variation of these variables results in constitutive relations, such as the stress–strain relation. To complete the framework, a variation by position X may be performed to gain knowledge about the balance laws involved, such as the linear momentum balance for solid mechanics.

Figure 4.9  Domain parameterization with order parameters φα and φβ for the polymer matrix phase and the fiber phase in a sharp and diffuse environment, respectively: (a) sharp interface representation and (b) diffuse interface representation

171

172

Simulation of SMC and LFTP

Because the curing process, which happens simultaneously throughout the whole domain, does not induce a solidification front, no evolving interfaces occur. This is why the phase-field method has not been applied to thermoset curing yet as opposed to a rare application to thermoplast solidification since [57]. Thus, in the following, the evolution equations for phases ˛ are only used to generate the initial configuration of the diffuse interface. The advantage of still using the phasefield method for the domain description lies in using the diffuse interfaces to capture the complex geometries occurring in densely packed, fiber-reinforced polymers. Without smoothly-changing order parameters, a proper mesh would be required, whose generation would pose a significant challenge [57], even when no re-meshing is needed due to the fixed interfaces.

4.3.3 Modeling the Curing Process In the previous section, it was pointed out that evolving interfaces are not involved in the curing process. Hence, the only relevant assumption to be considered is that energies in diffuse interface regions are volume-averaged, as noted in Eq. (4.14). Therefore, the following derivation is mainly done for a single phase ˛ and uses standard thermodynamic arguments (see, e.g., [58]). In the field of thermo-chemo-mechanics, the model follows the ideas and arguments of common approaches [49, 50], and is formulated for the regime of infinitesimal deformations. As indicated in the description of the curing process in Section 4.3.1, several thermoset material properties, such as stiffness, viscosity, and thermal conductivity, change during the exothermic curing reaction in the mold. These property changes must be captured by a dependence on the degree of cure and the temperature. In the following derivation, the property dependencies are neglected due to incomplete information on the shape of the dependencies (cf. Section 4.3.4) and to focus on the general and most important aspects of the derivation. Derivation from Thermodynamic Principles Reformulating the second law of thermodynamics and using the non-negativity of the entropy production rate yield the local form of the Clausius–Duhem inequality for each phase:

q  r  0:(4.16)   "P  P  P   Here, the Cauchy stress  and the strain rate "P form the stress power. Furthermore, we have the absolute temperature , the heat flux vector q, and the mass density  in combination with  and , the Helmholtz free energy density and the entropy density, respectively. Quantities may consist of their phase-inherent equiv-

4.3 Phase-Field Modeling of the Curing Process in Fiber-Reinforced Thermosets on a Microscale

alents (e.g., ) or may be continuously defined across phase boundaries (e.g., ). To further analyze the inequality, we assume  D  ."; "v;i ; ; q/ for the Helmholtz free energy to account for visco-elastic, thermal, and curing effects in the material, with the degree of curing q 2 Œ0; 1. Applying the time derivative for  results in



 

@ @"



  q  r @ P PN @ @  0;  "P  ¡  C  "P v;i   qP    iD1   @ @"v;i @q  (4.17)

where N denotes the number of Maxwell elements (cf. Visco-Elasticity section – see below) for a linear visco-elastic material. From this inequality, we obtain the thermodynamic relations

 D

@ @"

and

D

@ ;(4.18) @

which connect the stress and the entropy to the Helmholtz free energy, along with the dissipation inequality



PN

iD1



@ @ q  r  "P v;i   qP   0: @"v;i @q 

(4.19)

To satisfy the inequality, a stronger condition is used by requiring all three terms separately to be greater than zero. A common approach for heat conduction is Fourier’s law, which relates the heat flux vector q to the temperature gradient r via the constitutive relation q D r . The second-order tensor  is the thermal conductivity, which must be symmetric and positive semi-definite to fulfill the condition. The visco-elastic dissipation term may be analyzed separately for each Maxwell branch. The conjugate force @=@"v;i is reformulated with a potential !i, which depends on the viscous strain rate "P v;i . By setting ˝i D 1=2 "P v;i  Vi Œ"P v;i  ; an alterative formulation may be expressed for the viscous stress:  v;i D Vi Œ"P v;i . Inserting this formulation into Eq. (4.19) yields

Dv D

PN

iD1

"P v;i  Vi Œ"P v;i   0;

(4.20)

which satisfies the inequality for symmetric and positive semi-definite viscosities i. For the last term, which is related to the curing degree, the internal energy e in the relation of the Helmholtz free energy  D e    is replaced with the expression for the enthalpy H D e    ". By assuming the simple form H(q) H Htotq for the curing enthalpy (cf. Kamal–Malkin Model for Exothermic Reactions section – see below), the curing dissipation may be written as

Dc D

 o n P C0 C NiD1 Ci Œ ˇI   ."  ˛ /  H tot qP  0:(4.21)

173

174

Simulation of SMC and LFTP

Both the stiffness tensor ℂi and the tensor of thermal expansion ˛ are symmetric and positive semi-definite. We have the shrinkage ˇ due to the curing reaction and H tot D H.t D 1/ is the total releasable reaction enthalpy. For an irreversible exothermic reaction, the curing rate qP is always positive and hence, H tot < 0: To capture this isotropic shrinkage, the condition ˇ  0: ˇ

We state that the probability Pi(nˇ) of finding intact fibers in direction nˇ can be no higher than the probability Ps(nˇ) of fibers in that direction surviving a given external load, represented by I;eq nˇ ; smax . This key assumption leads to the following direction-dependent damage function and consistency condition:

       nˇ D Pi nˇ  Ps nˇ  0(4.79)

4.6 Mean-Field Damage Modeling of DiCoFRTS

Eq. (4.79) leads to a natural evolution for the orientation distribution of load-carrying fibers, which is, in general, anisotropic. For simplicity, it is assumed that fibers with damaged interfaces behave like matrix material. This behavior can be modeled by an artificial increase in the matrix volume fraction ( cPM  0), and a decrease in the fiber volume fraction ( cPF  0). The latter is given by

cF D cF0

PK

ˇ D1 c ˇ :(4.80)

4.6.3 Parameter Identification Matrix Damage The epoxy neat resin samples were cast in a net-shaped mold. The UPPH neat resin samples were manufactured by a project partner in the IRTG (Trauth [142]). Figure 4.37 shows the stress–strain behavior and the evolution of dM under the assumption that the non-linear behavior arises solely from stiffness degradation. For the computations, dM("M) was approximated using the ansatz that dM is zero until a damage initiation strain threshold is reached. This is followed by a sufficiently precise fit with a ninth-order polynomial for dM above the damage initiation threshold. The estimation of dM from only the secant modulus is, therefore, considered as sufficient.

Figure 4.37 Tensile behavior of the matrix systems

Fiber–Matrix Interface Strength Distribution The interface strength distribution is influenced by the fiber and matrix material properties, the fiber surface properties, the roving composition, the fiber sizing, and the process-dependent fiber impregnation characteristics. The characterization of the interface strength is challenging and, therefore, not directly characterized here. Instead, the interface properties are obtained from the literature and inverse parameter identification with tensile tests performed on the SMC compos-

219

220

Simulation of SMC and LFTP

ite. Characterizing the influence of shear and normal stress on the interface failure represents a key challenge. The literature commonly applies a linear criterion (m H 1, Eq. (4.74) and Eq. (4.76)), a quadratic criterion (m H 2), or a parabolic criterion (cubic contribution of shear stress and quadratic contribution of normal stress). Here, the more commonly applied quadratic criterion [143–146] is assumed. The contributions of the normal and shear stress on the failure behavior can be quantified by I0  ∕ I0. Experimentally, this relation was obtained in a lap shear test by Swentek [146] ( I0 =I0  1:6). Ogihara and Koyanagi [147] ( I0 =I0  1:31:8) and Tandon et al. [143] ( I0 =I0  1:22) measured the interface strength of epoxy and glass fibers using a fragmentation test on cruciform specimens with varying angles between the specimens’ arms. Koyanagi et al. [148] ( I0 =I0  1:3) compared the method to single-fiber pull-out tests under a combined stress state. In the following, I0 =I0 D 1:5 is assumed. The parameters O I;eq ; I0 ; I0 ; AI0 ; u ; o , and k describe the interface strength. If I0 ∕ I0 is given, three of the five remaining parameters are independent. Following Eq. (4.74) and Eq. (4.75), these independent parameters 1, 2, and 3 are

1 WD 2 WD

1 .AI0 / 1

1=k

.AI0 /1=k Ÿ3 WD k:

1 I0 O I;eq ; 0 I0 u ; 0

(4.81)  These three parameters were estimated by fitting the model to uniaxial tensile tests on bone specimens. An initially planar isotropic microstructure was assumed, since the flow lengths in the compression molding were short. Figure  4.39 and Figure 4.40 show the fits and experimental results for the epoxy-based and UPPHbased SMC composites with the low fiber volume fractions. The resulting interface strength distributions are plotted in Figure 4.38 under the assumption of a homogeneous interface stress distribution. Interpreting the interface strength distribution requires caution, since it does not capture the real distribution, but instead, also serves as an implicit model corrector. For example, the assumption of homogeneous matrix damage underestimates the composite stiffness degradation. Thus, the fitting procedure results in a lower interface strength distribution than the real distribution. The fitted interface strengths (Figure 4.38) show a significantly wider distribution than the interface strength typically measured in the literature (e.g., [149]), whose shape is similar to the strength distribution in Figure  4.35. This narrower strength distribution (Figure  4.35) results in stress–strain behavior of a bilinear nature.

4.6 Mean-Field Damage Modeling of DiCoFRTS

Figure 4.38 Interface survival probabilities (assumption: homogeneous stress distribution on the interface), resulting from fits in Figure 4.39 and Figure 4.40

4.6.4 Application Variation of Fiber Content The epoxy matrix SMC composite was available with two fiber contents. After fitting the model to the lower fiber content (43%), the model is applied to the higher fiber content (50%) under the assumption that the interface strength distribution is not affected by the fiber content and, thus, remains constant. Figure 4.39(a) shows the simulated and measured stress–strain behavior. The model slightly over-estimates the stiffness reduction for an increasing fiber volume fraction. Figure 4.39(b) depicts the estimated evolution of the total load-carrying fiber volume fraction cF and the relative matrix stiffness reduction dM. The matrix degradation is underestimated by the phase-averaged isotropic matrix damage model. As the fiber volume fraction increases, the matrix volume fraction decreases, and consequently, the influence of the underestimated matrix damage also decreases. The higher influence of the interface damage model, therefore, results in over-estimation of the overall stiffness reduction. Another source of the deviation between the experiment and the model prediction might be a fiber-content-dependent interface strength distribution. One possible explanation for an increase in the interface strength with increasing fiber content might be the improved fiber filament impregnation caused by roving dispersion during fiber–fiber interactions in the manufacturing process.

221

222

Simulation of SMC and LFTP

Figure 4.39 Validation of epoxy-SMC-based composite under uniaxial tension for two different volume fractions (interface strength distribution fitted to c0F D 43%)

Figure 4.40 Validation of UPPH SMC composite under a uniaxial and biaxial stress state (interface strength distribution fitted to uniaxial stress state)

Biaxial Tensile Loading Cruciform specimens that allow for comparably high biaxial and homogeneous stress permitted validation of the damage model in a biaxial stress state. The specimen’s arms were reinforced with continuous tapes manufactured in a co-molding process. A detailed discussion of the cruciform design and experimental procedure will be covered in an upcoming publication. These samples were only available for UPPH SMC-based composites, which have a B-stage (partially cured resin) that allows for co-molding with UD-reinforcements. Figure 4.40(a) displays the estimated evolution of total load-carrying fiber volume fraction cF and matrix damage dM. The evolution of interface and matrix damage is earlier and faster under biaxial tension than under uniaxial tension. The failure strain is significantly lower under biaxial tension (0.95% vs. 1.54%). The tensile strength is also lower under biaxial than

4.6 Mean-Field Damage Modeling of DiCoFRTS

under uniaxial tension (111 MPa vs. 136 MPa). The model predicts the stress under biaxial tension with a maximal relative error of about 4%. This result is satisfactory, considering the typically high fluctuations in the mechanical properties of SMC composites. An application of the model to four non-monotonic loading paths is presented.

4.6.5 Conclusions The elasto-damage model for SMC composites captures matrix damage and interface debonding on the microscale. A Mori–Tanaka homogenization scheme is applied to calculate the corresponding macroscopic behavior. The model accounts for an arbitrary, mold-flow-induced, inhomogeneous fiber orientation distribution of straight fibers. The complete model can predict the damage behavior of SMC composites for different matrix systems, fiber contents, and stress states. The applicability is only validated for a limited number of material combinations. Further validations are required to more precisely evaluate the model’s capabilities and limitations. Matrix damage is modeled as an isotropic degradation of the matrix stiffness based on the maximum principal matrix stress. This approach underestimates the stiffness degradation and does not adequately capture anisotropy due to microcracks. Interface debonding is modeled as a reduction of load-carrying fiber fraction in the directions exposed to sufficiently large equivalent interface stresses. Here, a Weibull interface strength distribution is assumed. It was shown that an approach that only takes account of the maximum equivalent stress occurring on the interface notably underestimates the interface survival probability. The inhomogeneous stress distribution was therefore assumed to be homogeneous around the transverse fiber axis. The interface damage model presented here leads to anisotropic stiffness degradation. Matrix and interface damage are coupled by the localization relation, which does not capture such phenomena as crack propagation from the matrix into the interface, or vice versa. Artificial regularization of the considered damage directions and a computationally-efficient model implementation permit application to larger components.

223

224

Simulation of SMC and LFTP

„„4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic Lukas Schulenberg, Thomas Seelig, Jörg Lienhard 4.7.1 Introduction This section presents an anisotropic visco-elastic–visco-plastic material model for injection-molded long-fiber-reinforced thermoplastics (LFTP) that can be applied in structural finite element (FEM) calculations applied to crash or impact. This publication is the completion of the elasto-plastic material model developed in [150], in which strain rate effects had initially been neglected. Here, the material model from [150] is enhanced to model viscous effects. This introduces new parameters adjusted using a fully strain-rate and stress-state dependent material characterization published in [151]. The goal is to reliably predict the deformation behavior of LFTP up to the point of failure. An efficient material model for structural impact or crash simulation is therefore developed that takes into account the local fiber orientation distribution (FOD) and fiber volume fraction. The macroscopic material model is partly based on analytical homogenization methods and phenomenologically extended to capture non-linear material behavior. A reliable prediction of the position-dependent fiber orientations can be obtained by means of injection molding simulations. The combined simulation of the mold-filling process and component crash based on FOD and fiber content allows one to consider the locally varying inhomogeneities. To calibrate the anisotropic visco-elastic–visco-plastic material model introduced in this section, experimental tests on three specimen types are needed. Parameters are calibrated by simulating the experimental characterization. Strain-rate dependent tensile and shear tests as well as punch tests are, by these means, reproduced satisfactorily.

4.7.2 Material and Microstructure An injection-molded LFTP plate of polypropylene with 30 wt% glass fibers (SABIC – STAMAX 30YK270), so-called PP-GF30, has been analyzed experimentally in [150] and [151] and is shown in Figure 4.41(a). The plate measures 300  mm  80 mm  2.8 mm. The material was injected through the whole width on the left side of the plate. Exemplary positions of three specimen types extracted from the LFTP plate are indicated (Figure 4.41(a)). The different specimen types generate

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

different stress states. In the case of quasi-static loading, the flat tensile test specimen (Figure 4.43(a)) is used to analyze both the loading and unloading paths. Experimental results from [150] and [151] will be illustrated in Section 4.7.4 together with the simulation results. Microstructural investigations via computer tomography (CT) scans of the injection-molded LFTP plate are used to determine microstructural parameters that are then incorporated into the material model. Relevant quantities, such as fiber orientation distribution (FOD) and local fiber volume fraction, are compared with the results of a process simulation (Figure 4.41(b)) [150]. The FOD variation through the thickness of the plate is shown in Figure 4.41(b) by means of the components of second order fiber orientation tensor N. CT scans indicated with dashed curves are compared to results from mold-filling simulations (solid curves). The process simulation itself was carried out by the Fraunhofer Institute for Industrial Mathematics ITWM in Kaiserslautern using the software Co­ Rheos (Complex Rheology Solver), [152] and [153]. The characteristic flow-induced layered structure of fiber orientations can be observed with a good correlation between experimental CT analysis and injection molding simulation.

Figure 4.41 (a) Injection-molded LFTP plate with indicated specimen types for different tests extracted from exemplary positions and (b) variation of FOD from CT-scan and mold-filling simulation [151]

The local fiber orientation tensors and fiber volume fraction calculated in the mold-filling simulation are included as variables in the material model of the structural FEM simulations. Therefore, each specimen (Figure 4.41(a)) in the FEM calculation (Section 4.7.4) carries the spatial heterogeneous information of fiber content and orientation. Details of the mapping procedure can be found in [152]. The aim of simulating the experimental material characterization tests is to determine all relevant mechanical properties of the material in order to reproduce these by a suitable material modeling.

225

226

Simulation of SMC and LFTP

4.7.3 Material Modeling To describe the macroscopic behavior of the investigated LFT material, a visco-elastic–visco-plastic material model is developed on the basis of experimental observations. Starting from the homogenization of the elastic properties, the model is phenomenologically extended to account for plasticity and strain-rate-dependent behavior. An approach to describe material damage is introduced. Anisotropic properties due to the FOD are considered in all sub-material models. Only the damage behavior is formulated by a quasi-isotropic approach. To approximate the elastic properties, microstructural information is used in an analytical homogenization scheme. Additional phenomenological parameters are introduced in the sub-models describing plasticity, viscous behavior, and damage. The aim of the new model is to obtain a micromechanically-based description of the material behavior and still retain a numerically efficient calculation in the framework of the FEM. The visco-elastic–visco-plastic material model is shown schematically as a 1D rheological model in Figure 4.42.

Figure 4.42 Schematic 1D representation of the rheological visco-elastic–visco-plastic model

The material model consists of three elasto-plastic sub-models symbolized by spring and friction elements and another three visco-elastic sub-models symbolized by spring and dashpot elements. For each of the sub-models, the strain rate tensor D is additively split into an elastic part Del and a plastic Dpl or viscous part Dvi:

D D Del C Dpl

or

D D Del C Dvi :(4.82)

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

The effective stress  is calculated by adding the individual partial stresses from the elasto-plastic sub-model and the visco-elastic sub-model. With the damage-effect tensor , the Jaumann rate  r of the effective stress is given by elasto-plastic sub-model

r

‚ …„ ƒ    pl pl pl D M1 W Œa1 C W .D  D1 / C a2 C W .D  D2 / C a3 C W .D  D3 / C    vi vi w0 C W .D  Dvi 1 / C w1 C W .D  D1 / C w2 C W .D  D3 / : „ ƒ‚ … visco-elastic sub-model

(4.83)

The scalar variables a1 ; a2 ; a3 in the elasto-plastic sub-model are the eigenvalues of the second-order fiber orientation tensor [150]. In the visco-elastic sub-model, the scalars w1 ; w2 ; w3 are phenomenological parameters to model the strain-rate  dependency. The approximation of the effective stiffness tensor C is described in Eq. (4.85). The material model is implemented via a user interface as user-defined material in the commercial FEM program LS-DYNA [154]. Homogenization of Linear Elastic Behavior The position-dependent stiffness tensor is approximated in two steps. First, applying the method by Mori and Tanaka [84] to a single fiber orientation, a transversely isotropic stiffness tensor C* is calculated as

C  D Œcf Cf W L C .1  cf / Cm  W Œcf L C .1  cf / I1 :(4.84) Here, cf is the volume fraction of the inclusion (fiber) and ℂf and ℂm are the isotropic stiffness tensors of the inclusion and the matrix, respectively.  is the strain localization tensor defined in [84]. It builds the relation between the constant strain within the inclusion "f, and the average strain in the matrix "m and includes the information about the fiber shape, approximated as a prolate ellipsoid characterized by its aspect ratio. This leads to the transversely isotropic effective stiffness tensor ℂ*, Eq. (4.84). In the second step, the heterogeneous anisotropic material properties can be described using FOD depicted as N and ℕ being the fiber orientation tensors of the second- and fourth-order, respectively [115]. The second-order tensor N is obtained from mold-filling simulations (Section 4.7.2) and ℕ is approximated from N using the so-called hybrid closure approximation (e.g., [115]). The transversely isotropic stiffness tensor ℂ* can then be orientation-averaged to ap proximate the local anisotropic stiffness tensor C with Cartesian components:

C



ijkl

  D b1 Nijkl C b2 Nij ıkl C Nkl ıij   C b3 Nik ıjl C Nil ıjk C Njl ıik C Njk ıil   C b4 ıij ıkl C b5 ıik ıjl C ıil ıjk :



(4.85)

227

228

Simulation of SMC and LFTP

The five scalars bi are related to the five independent components of the transversely-isotropic stiffness tensor ℂ* [150]. Elasto-Plastic Sub-Model The elasto-plastic sub-model was published in [150] and is briefly summarized here. For reasons of efficiency, plasticity is decoupled from the linear elastic homogenization and described phenomenologically. In the rheological models, plasticity is characterized by three friction elements (Figure 4.42), and each unit represents a different direction of anisotropy given by the three principal directions ei of the second-order fiber orientation tensor N. Direction tensors Bi are introduced by

Bi D ei

N

ei

^ .i D 1; 2; 3/(4.86)

and for each principal direction ei , Hill’s transversely isotropic yield criterion according to [155] is used:

ˆ. ; Bi / D .F C 2G/ tr.s2 / C 2.L  F  2G/ tr.s2  Bi / C .5F C G  2L/ tr2 .s  Bi /  y2 ."pl / :

(4.87)

Here, y is the yield stress, s is the deviatoric part of , and the parameters F, G, and L describe the degree of anisotropy. When the parameters are chosen to be F D G D 0:5 and L H 1.5, the criterion reduces to the isotropic von Mises criterion. Hardening depends on the effective plastic strain "pl and is approximated with a potential approach: q

y ."pl / D 0 C h "pl ;(4.88) where 0, h, and q are material parameters. The plastic strain-rate tensor of each plastic sub-model is obtained from the normality flow rule for each orientation with pl

Di D 

@ˆ . ; Bi /  : @

(4.89)

This leads to three stress tensors (Bi), which are calculated from the numerical solution of ˆ . ; Bi /  0 [150]. The effective stress tensor  ep of the rheological elasto-plastic sub-model (Figure 4.42) is calculated as the weighted average using the eigenvalues ai of the fiber orientation tensor N as weights:

 ep D a1  .B1 / C a2  .B2 / C a3  .B3 / :(4.90)

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

The notation (Bi) symbolizes the dependence of the stress tensors on the direction tensors Bi. It should be noted that no orientation-averaged yield surface is formulated in the material model. The parallel connection of three independent elasto-plastic material models (three rows from the top of the parallel network in Figure  4.42) approximates the average stress resulting from three flow criteria with a unidirectional fiber orientation. The parameters F, G, and L of Hill’s yield criterion are assumed to be the same for all three friction elements of the rheological network in Figure 4.42. This simplified orientation averaging for elasto-plastic material behavior makes the material model efficient by significantly reducing CPU time compared to incrementally-formulated semi-analytic elastoplastic homogenization methods (e.g., [156–158]). Visco-Elastic Sub-Model The experimental investigations [150, 151] demonstrated that the material exhibits viscous effects. These are analyzed by the stress–strain curves of the dynamic tensile tests at high strain rates (e.g., Figure 4.47), but also in loading and unloading tests (e.g., Figure 4.46). Strain-rate dependence is modeled by three Maxwell elements being connected in parallel to the elasto-plastic sub-model (Figure 4.42). The amount of three Maxwell elements fits just right to approximate the considered range of strain rate. Each Maxwell element i with i  (1,2,3) yields a strain rate tensor:

Di D w i C

1

ve

Wr C i

1 1 ve C W  i :(4.91) i

Note that in the framework of the parallel arrangement (Figure 4.42), Di equals the overall strain rate tensor D. The phenomenological parameters wi approximating the strain rate dependence are weighting coefficients of the anisotropic stiffness  tensors, C and i are the corresponding relaxation times. Both wi and i need to be determined with the help of the experimental material characterization. The  product of tensor C with the scalars wi describes the anisotropic visco-elastic formulation in terms of a convenience hypothesis. Each Maxwell element takes into account the full anisotropy according to the local FOD through the effective  stiffness tensors C . Three Maxwell elements have been chosen to describe the experimentally investigated strain rates with a range from 10−3 s−1 up to 102 s−1. The effective visco-elastic–visco-plastic stress tensor  is calculated by adding the stress tensors from the sub-models (Figure 4.42) as ve  D a1  .B1 / C a2  .B2 / C a3  .B3 / C  ve C  ve 2 C  3 (4.92) „ ƒ‚ … „1 ƒ‚ … D  ep D  ve

229

230

Simulation of SMC and LFTP

Continuum Damage Model To consider damage effects, a damage-affected stress tensor  d is expressed as

 d D M1 W  ;(4.93) where  is the stress tensor of the virgin material and  denotes a fourth-order damage effect tensor (e.g., [159]). Assuming that there are no interactions in the damage evolution between the various components of the stress tensor, six independent damage variables d˛ .˛ D 1; : : : ; 6/ are defined. By applying the generalized Voigt notation, this leads to the modified form of the damage effect tensor  with 2 3 1  d1 0 0 0 0 0 6 7 0 1  d2 0 0 0 0 6 7 6 7 0 0 1  d 0 0 0 6 7 3 (4.94) M1 D 6 7: 0 0 0 1  d4 0 0 6 7 6 7 4 5  0 0 0 0 1  d5 0 0 0 0 0 0 1  d6 In the undamaged state, all six damage variables d˛ are equal to 0. As soon as one component reaches the value 1, material failure occurs. Damage evolution and fail"E ure depend on R t the corresponding components of the Hencky strain tensor H , E where "H  0 Ddt is assumed for the implementation in LS-DYNA [154]. With the material parameters "f and g describing the failure strain and damage evolution exponent, the six damage variables are calculated as

d˛ D



j"max ˛ .t/j "f

g

:(4.95)

Here, the expression j"max ˛ .t/j describes the maximum value of the strain history. In addition, indicating the absolute value with j  j leads to a damage evolution through positively and negatively signed strains. This seems justified, since fibers in the material may crack under tension and buckle under compression. Since determining all anisotropic damage parameters is a major challenge, a simplified quasi-isotropic choice of parameters is suggested for this formulation. Thus, for the simplified case, the same failure strain "f and the same damage exponent g are used for all components of the stress tensor. For g > 1; a progressive, and for g < 1; a degressive damage evolution is described. With this simplified quasi-isotropic choice of damage parameters, the macroscopic failure behavior is defined independently of the FOD. To simulate the material characterization tests from Section 4.7.4, Eq. (4.95) is unable to adequately describe the damage and failure of the experiments. Therefore,

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

to distinguish the particular load case, the failure strain "f() and the damage evolution parameter g() are taken to be functions of the stress triaxiality  defined as 1

 D q3

tr . / 3 tr .s2 / 2

:(4.96)

Hence, for the different stress states, the failure strain "f() varies. The functional approach is adopted from Johnson and Cook [160] and pursues the assumption of smaller failure strains for larger stress triaxialities resulting from an increase in void growth and nucleation, which is typical for ductile metallic materials. In LFTP, the formation of microcracks in the fiber–matrix interface is the dominant mechanism of damage initiation (e.g., [161, 162]). At higher stress triaxialities, it can be assumed that this mechanism is dominant. The material can undergo large shear deformations without failing and the failure strain at  ≈ 0 thus increases significantly. To treat the strain-rate-dependent failure behavior of higher failure strains at higher strain rates (cf. Figure 4.47), a logarithmic approach is introduced:

P D "f .; "/

qs "f





"P ./  1 C n  ln "P 0



(4.97)

qs

The functional relation of "f ./ describes the stress-state-dependent failure strain for quasi-static loading being assigned to an experimentally determined P therefore changes quasi-static reference strain rate "P0 . The failure strain "f .; "/ logarithmically by the factor n with the change of the strain rate "P . If the maximum damage of d H 1 is reached at a Gauss point in the FEM calculation, the corresponding finite element is deleted.

4.7.4 Parameter Identification and Model Verification Three types of specimen (Figure 4.43) are needed to calibrate the material model in Section  4.7.3: a tensile test specimen (Figure  4.43(a)), a shear test specimen (Figure  4.43(b)), and a biaxial tensile test specimen (Figure  4.43(c)) used in a punch test. For a detailed description of the quasi-static and dynamic material testing, the reader is referred to [150] and [151]. To approximate the anisotropic stiffness tensor – Eq. (4.84) to (4.85) – the spatial variation of the FOD is mapped from the mold-filling simulation mesh to the FEM model according to the position on the plate. A mean value of the fiber length (2.7 mm) and fiber diameter (0.017 mm) lead to an aspect ratio of 158. The elastic material properties of glass and PP are taken from the supplier’s information and are given in Table 4.13.

231

232

Simulation of SMC and LFTP

Figure 4.43 Specimens for material characterization extracted from the plate (Figure 4.41) showing (a) a tensile test specimen, (b) a shear test specimen, and (c) a punch test specimen

4.7.5 Quasi-Static Simulations

Figure 4.44 Finite element model of tensile test specimen showing element size and boundary conditions

Uniaxial loading and unloading tests have been performed to separate the effects of plasticity and damage [150]. These experimental results are used for fitting the parameters in the anisotropic plasticity model and lead to values of the parameters 0, F, G, L – Eq. (4.87) – and the hardening parameters h and q – Eq. (4.88) – shown in Table 4.13. Similarly, parameters are fitted for the damage and failure model "f and g at   1=3 (Figure 4.53). For the parameter fitting, the tensile test specimen

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

(Figure  4.43(a)) is discretized with 3288 eight-node hexahedral elements using reduced integration (Figure 4.44). In the central area of size 14  5  2.8 mm, the edges of the finite-elements measure 0.5 mm. In the simulations, the engineering strain is determined (in analogy to the experiments [150, 151]) from the relative displacements of two nodes at a distance of 10 mm in the loading direction. The engineering stress in the simulation is calculated from the sum of the nodal forces in one cross section perpendicular to the load direction divided by the un-deformed cross section. Displacement boundary conditions are applied to the surface nodes on the left- and right-hand side of the sample, as shown in Figure 4.44. According to the coordinate system, the displacements in the y-direction are constrained on the left-hand side, and a prescribed velocity V0 is applied in the y-direction on the right side. On both sides, displacements in the z-direction are fixed, and stress-free boundary conditions are applied in the x-direction, as well as on the rest of the sample surface. The FOD is obtained from the mold-filling simulation (Section 4.7.2) and is considered generally different in each finite element. Simulation results of the tensile tests with unloading at 0° and 90° to the flow direction at a nominal strain rate of "Pnom D 2  102 s1 are shown in Figure 4.45 with adjusted plasticity and damage parameters, Table 4.13 [150]. A slightly higher Young’s modulus for polypropylene compared to the values given by the supplier (Table 4.13) of Em H 1.8 GPa has been used in this particular case. This leads to better results, since visco-elastic effects have been neglected for now. The damage formulation according to Eq. (4.95) is used here with the same parameters ("f, g) for both simulations (0° and 90°) and gives good results, even for the anisotropic material behavior. The variation of "f and g over the stress triaxiality (Figure 4.54) is of little importance for the uniaxial tensile test.

Figure 4.45  Uniaxial loading and unloading tensile tests of PP-GF30; FEM simulations with the elasto-plastic material model (Em H 1.8 GPa)

233

234

Simulation of SMC and LFTP

Figure 4.46  U  niaxial loading and unloading tensile tests of PP-GF30; FEM simulations with the visco-elastic–visco-plastic material model (Em H 1.45 GPa)

Despite taking damage into account, the unloading path still shows a deviation between simulation and experiment in Figure 4.45. The hystereses in the experiments are not represented in the simulation results. To account for viscous effects, additional Maxwell elements of the visco-elastic sub-model are used. Figure 4.46 shows the simulated loading and unloading tests, considering viscous effects. The Young’s modulus of Em H 1.45  GPa taken from the supplier’s information (Table 4.13) is now used. With the help of visco-elastic Maxwell models, the stress response increases in the loading path and reduces in the unloading path. The parameters w1 H 0.3 and the relaxation time 1 D 1  102  s are therefore adjusted to reproduce viscous effects at the lowest testing speed. All other parameters of the plasticity and damage model adjusted in Figure 4.45 remain unchanged. 4.7.5.1 Simulations of Dynamic Tests Tensile Tests To adjust the remaining parameters of the second and third Maxwell elements, tensile tests under higher loading rates are simulated. The change in the elongation of failure with increasing strain rate is captured by the parameter n in the strain-rate-dependent failure criterion according to Eq. (4.97). The simulation results of the dynamic tensile tests at 0° and 90° to the flow direction are shown in Figure 4.47 and Figure 4.48 together with the experimental results according to [151]. The experimental results are represented by polynomial fit curves indicating the averages of different specimen positions on the plate [151]. For the simulation results in Figure 4.47 and Figure 4.48, the FOD from the mold-filling simulation for the specimen positions on the plate as shown in Figure 4.41 (0° and 90°) are used. Simulated stress–strain curves and failure strains are in a good agreement with experimental observations.

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

Figure 4.47 Experiments and simulations of dynamic tensile tests at 0° to the flow direction performed on a tensile test specimen according to Figure 4.43(a)

Figure 4.48 Experiments and simulations of dynamic tensile tests at 90° to the flow direction performed on a tensile test specimen according to Figure 4.43(a)

Shear Tests The shear test specimen (Figure 4.43(b)) is discretized with 6228 hexahedral elements with reduced integration, as shown in Figure 4.49, with the applied boundary conditions according to the experimental set-up [150, 151]. The element size in the area of the local deformation is 0.5 mm. The simulated technical shear angle ” is determined from the relative nodal displacements with a distance of 2.5 mm (Figure 4.50) being analogous to the experimental tests set up [151]. The shear stress determined in the simulation is the sum of the nodal forces of a cross section perpendicular to the load direction divided by the area of the shear zone of 2.8 mm  3 mm (Figure 4.50). The shear tensile test is used to determine the parameters of the damage and failure model at  ≈ 0 (Figure  4.53 and Figure 4.54) and the yield stress under shear loading (parameter L H 4 in Table 4.13) of the elasto-plastic material sub-model, Eq. (4.90). In Figure 4.50, the simulated curves of the engineering shear stress versus the shear angle ” are compared with

235

236

Simulation of SMC and LFTP

the experimental results. Again, experimental results are represented by polynomial-fitted curves with error bars according to [151].

Figure 4.49 Finite element model of a shear test specimen showing element size and boundary conditions, numbers in mm

The test at the lowest strain rate is well reproduced only up to the maximum force (Figure 4.50, gray curve). The effect of high local shear deformation until failure for the lowest testing velocity is – in contrast to the more brittle failure under loading of the higher testing velocity – not represented well with the material model developed here. In addition, as a consequence of the convenience hypothesis, Eq. (4.91), the simulated curves in Figure 4.50 show a change in the initial tangent slope with the strain rate, which is not observed in the experiments.

Figure 4.50 Experiments and simulations of dynamic shear tests at 0° to the flow direction performed on a shear specimen according to Figure 4.43(b)

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

Punch Tests

Figure 4.51 (a) Finite element model of a punch test showing the FEM discretization and (b) the constraints according to the experimental test settings

The punch test is designed to produce a high biaxial stress state, which generally corresponds to a value of   2=3. The tests are carried out on circular samples with a diameter of 90 mm (Figure 4.43(c)). Experimental results are used for the damage model calibration (Figure 4.53); see also [150, 151]. The set-up of the numerical model of the punch test is shown in Figure 4.51. The specimen is discretized with 59010 eight-node fully-integrated hexahedral elements, since slightly higher hourglass energies had been observed with the use of under-integrated elements. An automated meshing software (HyperMesh, Altair Computing Inc., Troy, Michigan, USA) is used. In the center region of the specimen, the element size is 0.5 mm, with six elements across the sample thickness (Figure 4.51(a)). Bottom and top fixation are modeled as rigid bodies for fixing the sample according to the experimental set-up, see Figure 4.51(b). For the contact definitions, a penalty contact is used [154]. To clamp the sample between the rigid plates, a high friction coefficient of 0.99 is applied. A low coefficient of friction of 0.1 is assumed for the contact between the indenter and the specimen. Experimental measurements and simulation results of the punch tests with the indenter force as a function of the indenter displacements are shown in Figure 4.52(a). The punch tests are performed with four different indenter velocities V0, as marked in different colors in Figure 4.52(a). Experimental results are represented by polynomial-fitted curves with error bars [151]. With increasing load speed, the force–displacement curves become increasingly sharper at the maximum force, as indicated by the upward-shifted error bars.

237

238

Simulation of SMC and LFTP

Figure 4.52 (a) Force–displacement curves of experiments and simulations of dynamic punch tests; comparison of fracture pattern from (b) simulation and (c) experiment at indenter velocity V0 D 7  102 mm=s just after maximum force

As a comparison of the initial tangent slopes and maximum forces of the experimentally determined force–displacement curves and the numerical results shows (Figure 4.52(a)), the calculations are in a reasonable agreement with the experimental results. Due to an early and very fine crack initiation in the experiments, the slope gets successively flatter up to the maximum force in all experiments. As finite elements are deleted in the simulation, the force drops abruptly. After reaching its maximum, the force drop in the simulations is significantly overestimated. Due to the coarse mesh (element size 0.5 mm), neither the fine crack initiation nor the crack propagation can be simulated adequately. Nevertheless, a comparison of the fracture pattern at maximum force between simulation and experiment (Figure 4.52(b),(c)) shows reasonable agreement. All adjusted parameters of the developed material model are summed up in Table 4.13. For the stress-state-dependent damage and failure model, Figure 4.53 and Figure 4.54 visualize the calibration procedure. All phenomenological material parameters are adjusted by inverse simulations. The strain evolution of one finite element in the area of failure is also plotted in Figure 4.53. Table 4.13  Material Model Parameter for PP-GF30 at Room Temperature Sub-model

Material model parameter

Elasto-plastic

Ef ; Em

f ; m

0

h

q

F

G

L

0.23, 0.39

10 MPa

0:47

0:27

2:5

0:5

4

Visco-elastic

73 MPa, 1.45 MPa w1

1

w2

2

w3

3

0:3

1 £ 10  s

0:3

3  103s 

Damage

"f

Figure 4.53

2

g

Figure 4.54

0:25

2

8  10

"P0

 s

4 −1

3  10 s 

n

2:8  102

4.7 Material Modeling of Long Fiber-Reinforced Thermoplastic

Figure 4.53  Failure strain "f and simulated evolution of principle strain "I in one finite element at the location of damage initiation in the respective specimen

Figure 4.54  Stress-state-dependent damage evolution parameter g

4.7.6 Conclusions In this section, pre-existing approaches to model the anisotropic behavior of fiber-reinforced materials were modified, and developed further towards a new material model for LFTP. The following improvements of the presented material model should be emphasized: ƒƒA mold-filling simulation provided the FOD, which is spatially varying and considered over the entire plate thickness. ƒƒA clear focus is placed on the robustness and efficiency in the context of applied component design for simulations with explicit FEM codes.

239

240

Simulation of SMC and LFTP

ƒƒAnisotropic visco-elastic–visco-plastic behavior is described with a convenience hypothesis and presents a new modeling approach for LFTP. It has been shown that the experiments over a wide range of strain rate can be simulated with sufficient accuracy utilizing this simplified visco-elastic approach. Only the simulations of strain-rate-dependent shear tests indicate a shortcoming of the visco-elastic–visco-plastic material formulation. ƒƒDamage evolution and failure is modeled using a quasi-isotropic strain-rate-dependent approach, and this simplification also yields good agreement with experimental results. This is due to the fact that failure strains under tensile load at 0° and 90° to the flow direction do not differ significantly in the examined LFTP material. It can be assumed that simulations lead to poor results when the stress distribution over the sample thickness is no longer constant (e.g., bending). For the inhomogeneous FOD across the plate thickness, the isotropic damage and failure criterion would probably show insufficient accuracy. For this, further investigations into anisotropic damage behavior of LFTP should be considered. The present simulation results of all characterization tests show that the model approach proposed here can be used successfully in a crash or impact simulation in order to predict the non-linear anisotropic and strain-rate-dependent material behavior of injection-molded LFTP. References [1]

Hohberg, M., Kärger, L., Henning, F., Hrymak, A., Process simulation of sheet molding compound (SMC) as key for the integrated simulation chain. NAFEMS Semin. Simulation von Compos. – Be­ reit für Ind. 4.0? (2016) Hamburg, pp. 61–67

[2] Henning, F., Bücheler, D., Ugresic, V., Hrymak, A., Hohberg, M., Expanding Applications Areas for Sheet Molding Compound (SMC) Through New Material Compositions and New Hybrid Processes. 33rd Annu. Meet. Polym. Process. Soc. (2017) Cancun, Mexico [3] Hohberg, M., Fengler, B., Saburow, O., Meyer, N., Wittemann, F, Dörr, D., Kärger, L., Henning, F., Durchgehende CAE-Kette durch die Verknüpfung des Design, der Prozess-und der Struktursimulation zur ganzheitlichen Bewertung von langfaserverstärkten Duromeren und Thermoplasten. DVM-Workshop Qualif. von Kunststoffstrukturbauteilen mittels Integr. Pfinztal, Germany (2018) [4] Marker, L.F., Ford, B., Flow and curing behavior exhibited by SMC during molding. Mod. Plast. (1977) 54, pp. 64–70 [5] Barone, M.R., Caulk, D.A., The effect of deformation and thermoset cure on heat conduction in a chopped-fiber reinforced polyester during compression molding. Int. J. Heat Mass Transf. (1979) 22, pp. 1021–1032 [6] Perez, C., Ramirez, D., Osswald, T.A., Mechanistic model simulation of a compression molding process. Annu. Tech. Conf. – ANTEC (2015) [7] Kim, J., Shiau, Y.C., Lee, L.J., Im, Y.T., Compression molding simulation of chopped fiber reinforced polymeric composites in plate-rib type geometry. Polym. Compos. (1992) 13, pp. 97–107 [8] Xu, J., Kim, J., Ho, T., Lee, L.J., Compression molding of sheet molding compounds in plate-rib type geometry. Polym. Compos. (1993) 14, pp. 51–58

References

[9] Christensen, S.K., Hutchinson, B., Sun, E.M., Osswald, T.A., Davis, B.A., Fiber-matrix separation in ribbed SMC and BMC parts. Annu. Tech. Conf. – ANTEC (1997) [10] Orgéas, L., Geindreau, C., Auriault, J.-L., Bloch, J.-F., Upscaling the flow of generalised Newtonian fluids through anisotropic porous media. J. Non-Newton. Fluid Mech. (2007) 145, pp. 15–29 [11] Silva-Nieto, R.J., Fisher, B.C., Birley, A.W., Predicting mold flow for unsaturated polyester resin sheet molding compounds. Polym. Compos. (1980) 1, pp. 14–23 [12] Lee, C.-C., Folgar, F., Tucker, C.L., Simulation of Compression Molding for Fiber-Reinforced Thermosetting Polymers. J. Eng. Ind. (1984) 106, p. 114 [13] Osswald, T.A., Tucker, C.L., Compression Mold Filling Simulation for Non-Planar Parts. Int. Polym. Process. (1990) 5, pp. 79–87 [14] Twu, J.-T., Hill, R.R., Wang, T.J., Lee, L.J., Numerical simulation of non-isothermal SMC (sheet molding compound) molding. Polym. Compos. (1993) 14, pp. 503–514 [15] Barone, M.R., Caulk, D.A., Kinematics of flow in sheet molding compounds. Polym. Compos. (1985) 6, pp. 105–109 [16] Barone, M.R., Caulk, D.A., A Model for the Flow of a Chopped Fiber Reinforced Polymer Compound in Compression Molding. J. Appl. Mech. (1986) 53, p. 361 [17] Kotsikos, G., Gibson, A.G., Investigation of the squeeze flow behaviour of Sheet Moulding Compounds (SMC). Compos. Part A Appl. Sci. Manuf. (1998) 29, pp. 1569–1577 [18] Dumont, P., Orgéas, L., Le Corre, S., Favier, D., Anisotropic viscous behavior of sheet molding compounds (SMC) during compression molding. Int. J. Plast. (2003) 19, pp. 625–646 [19] Odenberger, P.T., Andersson, H.M., Lundström TS. Experimental flow-front visualisation in compression moulding of SMC. Compos. Part A Appl. Sci. Manuf. (2004) 35, pp. 1125–1134 [20] Barone, M.R., Osswald, T.A., Boundary integral equations for analyzing the flow of a chopped fiber reinforced polymer compound in compression molding. J. Non-Newton. Fluid Mech. (1987) 26, pp. 185–206 [21] Osswald, T.A., Tseng, S.-C., Compression molding, in Flow and Rheology in Polymer Composites Manufacturing, Advani, S.G. (Ed.) (1994) Elsevier, Amsterdam, pp. 361–413 [22] Abrams, L.M., Castro, J.M., Predicting molding forces during sheet molding compound (SMC) compression molding. I: Model development. Polym. Compos. (2003) 24, pp. 291–303 [23] Jeffery, G.B., The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid. Proc. R. Soc. A Math. Phys. Eng. Sci. (1922) 102, pp. 161–179 [24] Folgar, F., Tucker, C.L., Orientation Behavior of Fibers in Concentrated Suspensions. J. Reinf. Plast. Compos. (1984) 3, pp. 98–119 [25] Wang, J., O’Gara, J.F., Tucker, C.L., An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence. J. Rheol. (N. Y. N. Y.) (2008) 52, pp. 1179–1200 [26] Phelps, J.H., Tucker, C.L., An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics. J. Non-Newton. Fluid Mech. (2009) 156, pp. 165–176 [27] Bertóti, R., Böhlke, T., Flow-induced anisotropic viscosity in short FRPs. Mech. Adv. Mater. Mod. Process. (2017) p. 3 [28] Silva-Nieto, R.J., Fisher, B.C., Birley, A.W., Rheological characterization of unsaturated polyester resin sheet molding compound. Polym. Eng. Sci. (1981) 21, pp. 499–506 [29] Lee, L.J., Marker, L.F., Griffith, R.M., The rheology and mold flow of polyester sheet molding compound. Polym. Compos. (1981) 2, pp. 209–218 [30] Marjavaara, B.D., Ebermark, S., Lundström, T.S., Compression moulding simulations of SMC using a multiobjective surrogate-based inverse modeling approach. Mech. Compos. Mater. (2009) 45, p. 503 [31] Castro, J.M., Tomlinson, G., Predicting molding forces in SMC compression molding. Polym. Eng. Sci. (1990) 30, pp. 1568–1573

241

242

Simulation of SMC and LFTP

[32] Hohberg, M., Kärger, L., Bücheler, D., Henning, F., Rheological In-Mold Measurements and Characterizations of Sheet-Molding-Compound (SMC) Formulations with Different Constitution Properties by Using a Compressible Shell Model. Int. Polym. Process. (2017) 32, pp. 659–668 [33] Keckl, C., Einfluss der Eindickung von dichtereduzierten Sheet Moulding Compound auf die Form­ teilwelligkeit (2016) Institute of Vehicle System Technology (FAST), Department of Mechanical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Doctoral Thesis [34] Hohberg, M., Kärger, L., Henning, F., Hrymak, A., Rheological measurements and rheological shell model Considering the compressible behavior of long fiber reinforced sheet molding compound (SMC). Compos. Part A Appl. Sci. Manuf. (2017) 95, pp. 110–117 [35] Guiraud, O., Dumont, P.J.J., Orgéas, L., Favier, D., Rheometry of compression moulded fibre-reinforced polymer composites: Rheology, compressibility, and friction forces with mould surfaces. Compos. Part A Appl. Sci. Manuf. (2012) 43, pp. 2107–2119 [36] Dumont, P., Orgéas, L., Favier, D., Pizette, P., Venet, C., Compression moulding of SMC: In situ experiments, modelling and simulation. Compos. Part A Appl. Sci. Manuf. (2007) 38, pp. 353–368 [37] Hohberg, M., Kärger, L., Henning, F., Hrymak, A., Comparison of the Flow and Rheological Behavior of Two Semi-Structural Sheet-Molding-Compound (SMC) Based on a Hybrid Resin and Glass or Carbon Fibers. 33rd Annu. Meet. Polym. Process. Soc. (2017) Cancun, Mexico [38] Hohberg, M., Experimental investigation and process simulation of the compression molding pro­ cess of Sheet Molding Compound (SMC) with local reinforcements (2019) Institute of Vehicle System Technology (FAST), Department of Mechanical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Doctoral Thesis, to be published [39] Hohberg, M., Process simulation of hybrid SMC structures with local continuous fiber reinforcements. Connect. (2015) Moldflow User Meet. Frankfurt [40] Hohberg, M., Kärger, L., Hrymak, A., Henning, F., Process simulation of Sheet Moulding Compound (SMC) using an extensional viscosity model. 14th Int. Conf. Flow Process. Compos. Mater. (2018) Luleå, Sweden [41] Chung, D.H., Kwon, T.H., Invariant-based optimal fitting closure approximation for the numerical prediction of flow-induced fiber orientation. J. Rheol. (N. Y. N. Y.) (2002) 46, pp. 169–194 [42] Osswald, T.A., Menges, G., Materials Science of Polymers for Engineers, 3rd edition (2012) Han­ser, Munich [43] Lange, J., Toll, S., Månson, J.-A.E., Hult, A., Residual stress build-up in thermoset films cured above their ultimate glass transition temperature. Polymer (Guildf.) (1995) 36, pp. 3135–3141 [44] Gentz, M., Armentrout, D., Rupnowski, P., Kumosa, L., Shin, E., Sutter, J.K., Kumosa, M., In-plane shear testing of medium and high modulus woven graphite fiber reinforced/polyimide composites. Compos. Sci. Technol. (2004) 64, pp. 203–220 [45] Gentz, M., Benedikt, B., Sutter, J.K., Kumosa, M., Residual stresses in unidirectional graphite fiber/polyimide composites as a function of aging. Compos. Sci. Technol. (2004) 64, pp. 1671–1677 [46] Zhao, L.G., Warrior, N.A., Long, A.C., A micromechanical study of residual stress and its effect on transverse failure in polymer–matrix composites. Int. J. Solids Struct. (2006) 43, pp. 5449–5467 [47] Steven Johnson, W., Lagace, P., Masters, J., Nimmer, R.P., Fiber-Matrix Interface Effects in the Presence of Thermally Induced Residual Stresses. J. Compos. Technol. Res. (1990) 12, p. 65 [48] Halley, P.J., Mackay, M.E., Chemorheology of thermosets – an overview. Polym. Eng. Sci. (1996) 36, pp. 593–609 [49] Paradis, A., On the Comprehension of Time in Continuum Mechanics. Time (2008) 59, pp. 1–5 [50] Mahnken, R., Thermodynamic consistent modeling of polymer curing coupled to visco–elasticity at large strains. Int. J. Solids Struct. (2013) 50, pp. 2003–2021 [51] Ruiz, E., Trochu, F., Thermomechanical Properties during Cure of Glass-Polyester RTM Composites: Elastic and Viscoelastic Modeling. J. Compos. Mater. (2005) 39, pp. 881–916

References

[52] Nestler, B., Garcke, H., Stinner, B., Multicomponent alloy solidification: Phase-field modeling and simulations. Phys. Rev. E – Stat. Nonlinear, Soft Matter Phys. (2005) 71, pp. 1–6 [53] Moelans, N., Blanpain, B., Wollants, P., An introduction to phase-field modeling of microstructure evolution. Calphad. (2008) 32, pp. 268–294 [54] Schneider, D., Schoof, E., Huang, Y., Selzer, M., Nestler, B., Phase-field modeling of crack propagation in multiphase systems. Comput. Methods Appl. Mech. Eng. (2016) 312, pp. 186–195 [55] Schneider, D., Schwab, F., Schoof, E., Reiter, A., Herrmann, C., Selzer, M., Böhlke, T., Nestler, B., On the stress calculation within phase-field approaches: a model for finite deformations. Comput. Mech. (2017) 60, pp. 203–217 [56] Steinbach, I., Pezzolla, F., A generalized field method for multiphase transformations using interface fields. Phys. D Nonlinear Phenom. (1999) 134, pp. 385–393 [57] Kyu, T., Chiu, H.-W., Guenthner, A.J., Okabe, Y., Saito, H., Inoue, T., Rhythmic Growth of Target and Spiral Spherulites of Crystalline Polymer Blends. Phys. Rev. Lett. (1999) 83, pp. 2749–2752 [58] Li, X., Lowengrub, J., Rätz, A., Voigt, A., Solving PDE’s in Complex Geometries: A Diffuse Domain Approach. Commun. Math. Sci. (2009) 7, pp. 81–107 [59] Haupt, P., Wegner, J., Continuum Mechanics and Theory of Materials, 2nd edition, Haupt, P. (Ed.) (2002) Springer Berlin, Heidelberg [60] Kamal, M.R., Sourour, S., Ryan, M., Integrated thermo-rheological analysis of the cure of thermosets. SPE Tech. Pap. (1973) 19, p. 187 [61] Bernath, A., Kärger, L., Henning, F., Accurate Cure Modeling for Isothermal Processing of Fast Curing Epoxy Resins. Polymers (Basel) (2016) 8, p. 390 [62] DiBenedetto, A.T., Prediction of the glass transition temperature of polymers: A model based on the principle of corresponding states. J. Polym. Sci. Part B Polym. Phys. (1987) 25, pp. 1949–1969 [63] Tsouvalis, N., Margelis, G., Dellis, D., Residual Stresses in Composite Materials: A Review (2009) Athens, Greece [64] Johnston, A.A., An integrated model of the development of process-induced deformation in autoclave processing of composite structures (1997) Department of Metals and Materials Engineering, The University of British Columbia, PhD Thesis [65] Bogetti, T.A., Gillespie, J.W., Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates. J. Compos. Mater. (1992) 26, pp. 626–660 [66] White, S.R., Kim, Y.K., Process-Induced Residual Stress Analysis of AS4/3501-6 Composite Material. Mech. Adv. Mater. Struct. (1998) 5, pp. 153–186 [67] Simon, S.L., Mckenna, G.B., Sindt, O., Modeling the evolution of the dynamic mechanical properties of a commercial epoxy during cure after gelation. J. Appl. Polym. Sci. (2000) 76, pp. 495–508 [68] Adolf, D., Martin, J.E., Calculation of Stresses in Crosslinking Polymers. J. Compos. Mater. (1996) 30, pp. 13–34 [69] Prasatya, P., McKenna, G.B., Simon, S.L., A Viscoelastic Model for Predicting Isotropic Residual Stresses in Thermosetting Materials: Effects of Processing Parameters. J. Compos. Mater. (2001) 35, pp. 826–848 [70] O’Brien, D.J., Mather, P.T., White, S.R., Viscoelastic properties of an epoxy resin during cure. J. Compos. Mater. (2001) 35, pp. 883–904 [71] Kim, Y.K., White, S.R., Stress relaxation behavior of 3501-6 epoxy resin during cure. Polym. Eng. Sci. (1996) 36, pp. 2852–2862 [72] Ding, A., Li, S., Wang, J., Ni, A., Zu, L., A new path-dependent constitutive model predicting cure-induced distortions in composite structures. Compos. Part A Appl. Sci. Manuf. (2017) 95, pp. 183–196 [73] Svanberg, J.M., Holmberg, J.A., Prediction of shape distortions Part I. FE-implementation of a path dependent constitutive model. Compos. Part A Appl. Sci. Manuf. (2004) 35, pp. 711–721

243

244

Simulation of SMC and LFTP

[74] Li, D., Li, X., Dai, J., Process Modelling of Curing Process-Induced Internal Stress and Deformation of Composite Laminate Structure with Elastic and Viscoelastic Models. Appl. Compos. Mater. (2017) pp. 1–18 [75] Nielsen, M.W., Prediction of process induced shape distortions and residual stresses in large fibre reinforced composite laminates: With application to Wind Turbine Blades (2013) Manufacturing Engineering, Department of Mechanical Engineering, Technical University of Denmark, PhD Thesis [76] Yuan, Z., Wang, Y., Yang, G., Tang, A., Yang, Z., Li, S., Li, Y., Song, D., Evolution of curing residual stresses in composite using multi-scale method. Compos. Part B Eng. (2018) 155, pp. 49–61 [77] Hexcel. 3501-6 Epoxy Matrix – Material Datasheet [Internet] (2016) Available from: https://www. hexcel.com/user_area/content_media/raw/HexPly_35016_eu_DataSheet.pdf. [78] Kaliske, M., Rothert, H., Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Comput. Mech. (1997) 19, pp. 228–239 [79] Jin, K.K., Oh, J.H., Ha, S.K., Effect of fiber arrangement on residual thermal stress distributions in a unidirectional composite. J. Compos. Mater. (2007) 41, pp. 591–611 [80] Voigt, W., Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper. Ann. Phys. (1889) 274, pp. 573–587 [81] Reuss, A., Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM – Zeitschrift für Angew. Math. und Mech. (1929) 9, pp. 49–58 [82] Hashin, Z., Shtrikman, S., A variational approach to the theory of the elastic behaviour of polycrystals. J. Mech. Phys. Solids (1962) 10, pp. 343–352 [83] Eshelby, J.D., The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems. Proc. R. Soc. A Math. Phys. Eng. Sci. (1957) 241, pp. 376–396 [84] Mori, T., Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. (1973) 21, pp. 571–574 [85] Benveniste, Y., A new approach to the application of Mori-Tanaka’s theory in composite materials. Mech. Mater. (1987) 6, pp. 147–157 [86] Brylka, B., Charakterisierung und Modellierung der Steifigkeit von langfaserverstärktem Polypropyl­ en (2017) Institute of Engineering Mechanics (ITM), Department of Mechanical Engineering, Karls­ruhe Institute of Technology (KIT), Karlsruhe, Doctoral Thesis [87] Zheng, Q.S., Du, D.X., An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution. J. Mech. Phys. Solids (2001) 49, pp. 2765–2788 [88] Du, D.X., Zheng, Q.S., A further exploration of the interaction direct derivative (IDD) estimate for the effective properties of multiphase composites taking into account inclusion distribution. Acta Mech. (2002) 157, pp. 61–80 [89] Müller, V., Böhlke, T., Prediction of effective elastic properties of fiber reinforced composites using fiber orientation tensors. Compos. Sci. Technol. (2016) 130, pp. 36–45 [90] Hershey, A.V., The Elasticity of an isotropic aggregate of anisotropic cubic crystals. J. Appl. Mech. ASME (1954) 21, pp. 236–240 [91] Kröner, E., Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Ein­ kristalls. Zeitschrift für Phys. (1958) 151, pp. 504–518 [92] Laws, N., On the thermostatics of composite materials. J. Mech. Phys. Solids (1973) 21, pp. 9–17 [93] Lielens, G., Pirotte, P., Couniot, A., Dupret, F., Keunings, R., Prediction of thermo-mechanical properties for compression moulded composites. Compos. Part A Appl. Sci. Manuf. (1998) 29, pp. 63–70 [94] Pierard, O., Friebel, C., Doghri, I., Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation. Compos. Sci. Technol. (2004) 64, pp. 1587–1603 [95] Doghri, I., Friebel, C., Effective elasto-plastic properties of inclusion-reinforced composites. Study of shape, orientation and cyclic response. Mech. Mater. (2005) 37, pp. 45–68

References

[96] Willis, J.R., Variational and related methods for the overall properties of composites. Adv. Appl. Mech. (1981) 21, pp. 1–78 [97] Mura, T., Micromechanics of defects in solids (1987) Springer, Dordrecht, Netherlands [98] Torquato, S., Random Heterogeneous Materials, 16th edition (2002) Springer, New York, NY [99] Wang, H.W., Zhou, H.W., Mishnaevsky, L., Brøndsted, P., Wang, L.N., Single fibre and multifibre unit cell analysis of strength and cracking of unidirectional composites. Comput. Mater. Sci. (2009) 46, pp. 810–820 [100] Moulinec, H., Suquet, P., A fast numerical method for computing the linear and nonlinear mechanical properties of composites. Comptes Rendus l’ Acad. des Sci. Ser. IIbMecanique Phys. Chim. Astron. (1994) 318, pp. 296–302 [101] Moulinec, H., Suquet, P., A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Eng. (1998) 157, pp. 69–94 [102] Andrä, H., Grzhibovskis, R., Rjasanow, S., Boundary Element Method for Linear Elasticity with Conservative Body Forces, in Advanced Finite Element Methods, Apel, T., Steinbach, O. (Ed.) (2013) Springer Berlin, Heidelberg, pp. 275–297 [103] Fliegener, S., Micromechanical finite element modeling of long fiber reinforced thermoplastics (2015) Institute for Applied Materials – Computational Materials Science (IAM-CMS), Department of Mechanical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Doctoral Thesis [104] Schneider, M., An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems. Comput. Methods Appl. Mech. Eng. (2017) 315, pp. 846–866 [105] Tjong, S.C., Xu, S.A., Li, R.K.Y., Mai, Y.W., Mechanical behavior and fracture toughness evaluation of maleic anhydride compatibilized short glass fiber/SEBS/polypropylene hybrid composites. Compos. Sci. Technol. (2002) pp. 831–840 [106] Thomason, J.L., Investigation of composite interphase using dynamic mechanical analysis: Artifacts and reality. Polym. Compos. (1990) 11, pp. 105–113 [107] Kostka, P., Holeczek, K., Höhne, R., Filippatos, A., Modler, N., Extension and application of dynamic mechanical analysis for the estimation of spatial distribution of material properties. Polym. Test. (2016) 52, pp 184–191 [108] Brylka, B., Schemmann, M., Wood, J., Böhlke, T., DMA based characterization of stiffness reduction in long fiber reinforced polypropylene. Polym. Test. (2018) 66, pp. 296–302 [109] Walpole, L.J., On bounds for the overall elastic moduli of inhomogeneous systems—I. J. Mech. Phys. Solids (1966) 14, pp. 151–162 [110] Kehrer, L., Thermomechanical mean-field modeling and experimental characterization of long fi­ ber-reinforced sheet molding compound composites (2019) KIT Scientific Publishing, Schriftenreihe Kontinuumsmechanik im Maschinenbau Nr. 15, Doctoral Thesis [111] Menard, K.P., Dynamic mechanical analysis: a practical introduction (2008) CRC Press [112] Trauth, A., Weidenmann, K.A., Continuous-discontinuous sheet moulding compounds – Effect of hybridisation on mechanical material properties. Compos. Struct. (2018) 202, pp. 1087–1098 [113] Castañeda, P.P., The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids (1991) 39, pp. 45–71 [114] Hill, R., Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Solids (1963) 11, pp. 357–372 [115] Advani, S.G., Tucker, C.L., The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites. J. Rheol. (N. Y. N. Y.) (1987) 31, pp. 751–784 [116] Kabel, M., Böhlke, T., Schneider, M., Efficient fixed point and Newton–Krylov solvers for FFTbased homogenization of elasticity at large deformations. Comput. Mech. (2014) 54, pp. 1497–1514

245

246

Simulation of SMC and LFTP

[117] Granta. CES EduPack Materials Selector [Internet] (2016) Available from: http://www.grantadesign.com/education/edupack/coretools.htm [118] Böhlke, T., Brüggemann, C., Graphical Representation of the Generalized Hooke’s Law. Tech. Mech. (2001) p. 21 [119] Schemmann, M., Görthofer, J., Seelig, T., Hrymak, A., Böhlke, T., Anisotropic meanfield modeling of debonding and matrix damage in SMC composites. Compos. Sci. Technol. (2018) 161, pp. 143–158 [120] Meraghni, F., Desrumaux, F., Benzeggagh, M.L., Implementation of a constitutive micromechanical model for damage analysis in glass mat reinforced composite structures. Compos. Sci. Tech­ nol. (2002) 62, pp. 2087–2097 [121] Jendli, Z., Fitoussi, J., Meraghni, F., Baptiste, D., Anisotropic strain rate effects on the fibre–matrix interface decohesion in sheet moulding compound composites. Compos. Sci. Technol. (2005) 65, pp. 387–393 [122] Larbi, A.B.C., Sai, K., Sidhom, H., Baptiste, D., Constitutive Model of Micromechanical Damage to Predict Reduction in Stiffness of a Fatigued SMC Composite. J. Mater. Eng. Perform. (2006) 15, pp. 575–580 [123] Fitoussi, J., Bocquet, M., Meraghni, F., Effect of the matrix behavior on the damage of ethylene-propylene glass fiber reinforced composite subjected to high strain rate tension. Compos. Part B Eng. (2013) 45, pp. 1181–1191 [124] Fitoussi, J., Bourgeois, N., Guo, G., Baptiste, D., Prediction of the anisotropic damaged behavior of composite materials: introduction of multilocal failure criteria in a micro-macro relationship. Comput. Mater. Sci. (1996) 5, pp. 87–100 [125] Fitoussi, J., Guo, G., Baptiste, D., Determination of a tridimensional failure criterion at the fibre/ matrix interface of an organic-matrix/discontinuous-reinforcement composite. Compos. Sci. Tech­ nol. (1996) 56, pp. 755–760 [126] Fitoussi, J., Guo, G., Baptiste, D., A statistical micromechanical model of anisotropic damage for S.M.C. composites. Compos. Sci. Technol. (1998) 58, pp. 759–763 [127] Meraghni, F., Blakeman, C.J., Benzeggagh, M.L., Effect of interfacial decohesion on stiffness reduction in a random discontinuous-fibre composite containing matrix microcracks. Compos. Sci. Technol. (1996) 56, pp. 541–555 [128] Derrien, K., Fitoussi, J., Guo, G., Baptiste, D., Prediction of the effective damage properties and failure properties of nonlinear anisotropic discontinuous reinforced composites. Comput. Meth­ ods Appl. Mech. Eng. (2000) 185, pp. 93–107 [129] Desrumaux, F., Meraghni, F., Benzeggagh, M.L., Micromechanical Modelling Coupled to a Reliability Approach for Damage Evolution Prediction in Composite Materials. Appl. Compos. Mater. (2000) 7, pp. 231–250 [130] Desrumaux, F., Meraghni, F., Benzeggagh, M.L., Generalised Mori-Tanaka scheme to model anisotropic damage using numerical Eshelby tensor. J. Compos. Mater. (2001) 35, pp. 603–624 [131] Jendli, Z., Meraghni, F., Fitoussi, J., Baptiste, D., Multi-scales modelling of dynamic behaviour for discontinuous fibre SMC composites. Compos. Sci. Technol. (2009) 69, pp. 97–103 [132] Kammoun, S., Doghri, I., Brassart, L., Delannay, L., Micromechanical modeling of the progressive failure in short glass–fiber reinforced thermoplastics – First Pseudo-Grain Damage model. Com­ pos. Part A Appl. Sci. Manuf. (2015) 73, pp. 166–175 [133] Baptiste, D., Non Linear Behavior Micromechanical Multi-Scale Modelling of Discontinuous Reinforced Composites. Mater. Sci. Forum (2003) 426–432, pp. 3939–3944 [134] Zaïri, F., Naït-Abdelaziz, M., Gloaguen, J.M., Bouaziz, A., Lefebvre, J.M., Micromechanical modelling and simulation of chopped random fiber reinforced polymer composites with progressive debonding damage. Int. J. Solids Struct. (2008) 45, pp. 5220–5236

References

[135] Pinter, P., Dietrich, S., Bertram, B., Kehrer, L., Elsner, P., Weidenmann, K.A., Comparison and error estimation of 3D fibre orientation analysis of computed tomography image data for fibre reinforced composites. NDT E Int. (2018) 95, pp. 26–35 [136] Motaghi, A., Hrymak, A.N., Microstructure characterization in direct sheet molding compound. Polym. Compos. (2019) 40, pp. E69–E77 [137] Benveniste, Y., Dvorak, G.J., Chen, T., On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media. J. Mech. Phys. Solids (1991) 39, pp. 927–946 [138] Castañeda, P.P., Suquet, P., Nonlinear Composites. Adv. Appl. Mech. (1997) 34, pp. 171–302 [139] Duschlbauer, D., Pettermann, H., Böhm, H., Mori–Tanaka based evaluation of inclusion stresses in composites with nonaligned reinforcements. Scr. Mater. (2003) 48, pp. 223–228 [140] Weibull, W., A Statistical Distribution Function of Wide Applicability. J. Appl. Mech. (1951) 18, pp. 293–297 [141] Ju, J.W., Lee, H.K., A micromechanical damage model for effective elastoplastic behavior of ductile matrix composites considering evolutionary complete particle debonding. Comput. Methods Appl. Mech. Eng. (2000) 183, pp. 201–222 [142] Trauth, A., Personal Communication within a cooperation of GRK 2078 (2017) [143] Tandon, G.P., Kim, R.Y., Bechel, V.T., Fiber–Matrix Interfacial Failure Characterization Using a Cruciform-Shaped Specimen. J. Compos. Mater. (2002) 36, pp. 2667–2691 [144] Koyanagi, J., Nakatani, H., Ogihara, S., Comparison of glass-epoxy interface strengths examined by cruciform specimen and single-fiber pull-out tests under combined stress state. Compos. Part A Appl. Sci. Manuf. (2012) 43, pp. 1819–1827 [145] Ogihara, S., Koyanagi, J., Investigation of combined stress state failure criterion for glass fiber/ epoxy interface by the cruciform specimen method. Compos. Sci. Technol. (2010) 70, pp. 143–150 [146] Swentek, I.N., On the Interfacial Fracture Mechanics of Long-fibre Reinforced Polymer Composites (2014) Mechanical and Materials Engineering, The Univeristy of Western Ontario, PhD Thesis [147] Ogihara, S., Koyanagi, J., Investigation of combined stress state failure criterion for glass fiber/ epoxy interface by the cruciform specimen method. Compos. Sci. Technol. (2010) 70, pp. 143–150 [148] Koyanagi, J., Nakatani, H., Ogihara, S., Comparison of glass–epoxy interface strengths examined by cruciform specimen and single-fiber pull-out tests under combined stress state. Compos. Part A Appl. Sci. Manuf. (2012) 43, pp. 1819–1827 [149] Broutman, L.J., Measurement of the Fiber-Polymer Matrix Interfacial Strength. Interfaces Com­ pos. ASTM International (1969) p. 27–41 [150] Schulenberg, L., Seelig, T., Andrieux, F., Sun, D.-Z., An anisotropic elasto-plastic material model for injection-molded long fiber-reinforced thermoplastics accounting for local fiber orientation distributions. J. Compos. Mater. (2016) 51, pp. 2061–2078 [151] Lienhard, J., Schulenberg, L., Strain rate dependent multiaxial characterization of long fiber reinforced plastic. Compos. Part B Eng. (2018) 141, pp. 164–173 [152] Sun, D.-Z., Schulenberg, L., Lienhard, J., Andrieux, F., Huberth, F., Andrä, H., Niedziela, D., Shklyar, I., Steiner, K., Wirjadi, O., Peter, G., Prätzel-Wolters, D., IGF-Vorhaben 17334 N: Entwicklung einer Methode zur Crashsimulation von langfaserverstärkten Thermoplast (LFT) Bauteilen auf Basis der Faserorientierung aus der Formfüllsimulation. Forschungsvereinigung Automob. e.V., Fat-schriftenr. 284 (2016) p. 147 [153] Niedziela, D., Strautins, U., Hosdez, V., Kech, A., Latz, A., Improved multiscale fiber orientation modeling in injection molding of short fiber reinforced thermoplastics: Simulation and experiment. 1st Conf. Multiphysics Simul. – Adv. Methods Ind. Eng. (2010) p. 10. [154] LIVERMORE Software Technology Corporation (LSTC). LS-DYNA Keyword Users Manual Volume I (revision: 5471) (2014) Livermore, California

247

248

Simulation of SMC and LFTP

[155] Aravas, N., Finite elastoplastic transformations of transversely isotropic metals. Int. J. Solids Struct. (1992) 29, pp. 2137–2157 [156] Doghri, I., Ouaar, A., Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms. Int. J. Solids Struct. (2003) 40, pp. 1681–1712 [157] Doghri, I., Tinel, L., Micromechanical modeling and computation of elasto-plastic materials reinforced with distributed-orientation fibers. Int. J. Plast. (2005) 21, pp. 1919–1940 [158] Doghri, I., Tinel, L., Micromechanics of inelastic composites with misaligned inclusions: Numerical treatment of orientation. Comput. Methods Appl. Mech. Eng. (2006) 195, pp. 1387–1406 [159] Murakami, S., Continuum Damage Mechanics (2012) Springer, Dordrecht, Netherlands [160] Johnson, G.R., Cook, W.H., Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. (1985) 21, pp. 31–48 [161] Sato, N., Kurauchi, T., Sato, S., Kamigaito, O., Microfailure behaviour of randomly dispersed short fibre reinforced thermoplastic composites obtained by direct SEM observation. J. Mater. Sci. (1991) 26, pp. 3891–3898 [162] Schulenberg, L., Sun, D.-Z., Seelig, T., Numerical Modelling of Damage Initiation and Failure of Long Fibre-Reinforced Thermoplastics. Probl. Deform. und Bruchverhalten von Kunststoffen (2017) Merseburg, pp. 83–92

5

Designing CoDiCoFRP Structures

„„5.1 Introduction Luise Kärger 5.1.1 Challenges Combining continuous and discontinuous fibers in structural composite components increases both the component’s lightweight potential and the engineer’s design freedom. The additional design freedom, however, comes at the price of greater variety in the design parameters, which are strongly interdependent and thus difficult to optimize simultaneously. The DiCoFRP manufacturing process in conjunction with the DiCoFRP part geometry define the distribution of discontinuous fibers within the part. In turn, the distribution of fibers and the part geometry define the structural capacity. Additionally, curing and cooling cause geometrical distortion and inner stresses, which also influence the structural capacity. For CoDiCoFRP structures, the structural capacity is further controlled by the position and orientation of local continuous fiber patches. The position of these local CoFRP patches is influenced by the forming process, which again depends on the geometry of the part. These multiple interdependencies of structural design aspects, process design aspects, and material design aspects greatly complicate the overall product development. In theory, the simultaneous optimization of all material, process, and structural design parameters would be desirable to permit a holistic design of CoDiCoFRP products. However, integrating all relevant design aspects sufficiently and efficiently into a product development process is still a distant goal. Structural optimization is an essential part of the product development process. It allows improvement of the product’s weight-specific performance in an early design phase. In this regard, topology optimization is generally used to create a first conceptual design. Topology optimization is well-established, provided isotropic or homogeneous anisotropic linear elastic material behavior can be assumed. If the mate-

250

5 Designing CoDiCoFRP Structures

rial anisotropy varies with process conditions and with the topology itself, as is the case for long-fiber-reinforced polymer structures, topology optimization becomes much more complex and represents a challenge that has hardly been addressed. Various suggestions have been made to increase the quality of topology optimization by incorporating manufacturing constraints [1]. These constraints, such as mold opening direction, minimum rib width, or other structural conditions, are typically independent of the iteratively-changing topology or process conditions. Since the fiber orientations in FRP components substantially influence the mechanical properties, several approaches have been developed to enhance structural optimization for FRP [2–4]. Most of these approaches address laminated CoFRP components or CoFRP patches and do not consider manufacturing effects. Particularly, optimization with interrelated process and structural simulation or with multiple objectives for both the FRP production and structural performance is a very new field. For CoFRP, a framework for an integrated optimization workflow including a continuous virtual process chain (CAE chain) has been proposed and exemplified by automated forming optimization and subsequent structural simulation [5]. However, an overall automatic optimization that includes all simulation steps with physics-based material models is computationally too expensive to be executed at once with currently available high-performance hardware. Since the computational effort is even higher for CoDiCoFRP components, reasonable abstraction and simplification, along with selection of the most relevant process, material, and structural design aspects, are imperative for an overall adequate product design. For industrial applications in particular, the complex interdependencies of CoDiCoFRP processes and structural behavior need to be represented in a feasible way, one that is accessible and manageable for design engineers. Here, design guidelines are the most common instrument to transfer detailed knowledge to engineering applications. These include information on the manufacturing process technologies, material behavior, and structural design. Additionally, a number of numerical and analytical methods exist to describe the physical correlations. These can potentially be used for physics-based optimization. However, the road from scientific knowledge generation and method development to industrial method application is long. Thus, the suitable selection and preparation of relevant information represents an important, but challenging task of knowledge management. In addition to a profound and clearly arranged knowledge management system (KMS), flexible solutions are needed to successively extend the existing KMS with new research results. The number of existing design guidelines for CoFRP and DiCoFRP structures (e.g., VDI, AVK, cf. Section 5.4) can be viewed as a puzzle comprising diverse types of data having differing objectives, grades of detail, and validity. This makes it hard for design engineers to find the required and suitable piece of information. Currently, information is most often provided in the form of texts and images that are hardly adaptable to new research results. Particularly in the case of CoDiCoFRP, where no established design guidelines exist, one needs a dynamic

5.1 Introduction

knowledge management system that reasonably and flexibly combines existing knowledge about CoFRP and DiCoFRP with new research results on CoDiCoFRP.

5.1.2 Approaches An integrated design of CoDiCoFRP products requires the consideration of all process, material, and structural design aspects that define the final capacity of the hybrid composite product. Due to the combination of continuous and discontinuous fiber reinforcements, the CoDiCoFRP manufacturing process comprises the three distinct process steps of DiCoFRP compression molding, CoFRP forming, and solidification of both composite polymers. All three influence the anisotropic material behavior and the structural performance of the final part. Therefore, they must all be taken into account when designing a new CoDiCoFRP product. However, as explained in Section 5.1.1, simultaneous optimization of the structural capacity and all process steps is not yet possible. Therefore, the Research Area Design (RAD) of the IRTG aims at a stepwise refinement of multi-objective, multi-step optimization methods to integrate an increasing number of relevant design aspects into a single optimization. Furthermore, the convergence, robustness, and general applicability of the developed iterative multi-step optimization procedures need to be evaluated. The first generation of the IRTG Research Area Design focuses on CoFRP patch optimization (Section 5.2), DiCoFRP topology optimization (Section 5.3), and CoDiCoFRP knowledge management (Section  5.4). Accordingly, the following subsections address these three topics, and considering the manufacturing process plays an important role in each of the three sections. An overview of the three subprojects is given in Figure 5.1. Section 5.2 proposes a multi-objective CoFRP patch optimization method including a kinematic forming simulation to compute the final patch position and orientation. Moreover, a curing simulation is incorporated to consider warpage during optimization. The objective functions of the multi-objective parameter-based optimization include the global strain energy of the CoDiCoFRP part, the warpage, and the CoFRP material consumption. In the structural analysis, the primary CoFRP material orientation depends on the incorporated forming simulation. In contrast, the DiCoFRP part of the CoDiCoFRP structure is assumed to maintain constant topology and homogeneous anisotropic material behavior, as pre-predicted by a pre-processing DiCoFRP molding simulation (cf. Section 4.2). Therefore, process-dependent topology optimization of the DiCoFRP part is addressed in Section 5.3. Here, an iterative two-step optimization method is proposed, which incorporates a DiCoFRP molding simulation for the intermediate topology solutions within the overall optimization workflow. The topology optimization aims at an optimum rib structure of the DiCoFRP part, where the governing optimization algorithm is based on an optimality criterion to minimize the global strain energy for a given load case and a given material consumption. In summing

251

252

5 Designing CoDiCoFRP Structures

up the CoDiCoFRP research achievements, Section 5.4 focuses on the development of a dynamic knowledge management system that can be used by design engineers in the earliest phase of CoDiCoFRP product development processes. Here, existing design guidelines for CoFRP and DiCoFRP are analyzed and evaluated. Furthermore, qualitative interviews and quantitative surveys with representatives from industry in Germany and Canada are conducted to identify the industrial demands for worthwhile design guidelines. On this basis, a decision-support system, called CoDiCo-FiberFox, is developed to provide situation-specific information on FRP material and product development. Furthermore, a concept is included to successively integrate new research results into the knowledge platform.

Figure 5.1 Cooperation within the Research Area Design in the framework of the IRTG

„„5.2 Production-Oriented Dimensioning of Local Patchesunder Consideration of Distortion and Manufacturing Constraints Benedikt Fengler, Luise Kärger, Frank Henning, Andrew Hrymak 5.2.1 Introduction Optimization methods are an essential part of the product development process when the goal is to improve product performance. Since composite materials offer a wide range of design parameters, composite-specific optimization approaches are necessary to fully exploit the capability of these material classes. In addition, the optimization quality can be increased by incorporating manufacturing constraints into the optimization.

5.2 Production-Oriented Dimensioning of Local Patches

To date, the development of optimization strategies for composite materials has mostly focused on continuous fiber-reinforced composites. Le Riche and Haftka [6] introduced a method for the optimization of the stacking sequence for a laminate, using an evolutionary algorithm. A topology optimization approach for composite materials was presented by Blasques and Stolpe [7]. In their work, they utilized the classical laminate theory to set up a material database with different layups, which is then used during the optimization to find the optimum layup for each region. Kaufmann et al. [8] improved the quality of their results by considering draping effects during a weight optimization. Here, the draping is modeled before the optimization to create a material database, which is then used during the optimization loop. Skordos et al. [9] combined a kinematic draping simulation with an evolutionary algorithm to optimize the draping process itself. Here, they used the starting point, applied pre-shear, and draping direction as design parameters to minimize the maximum and average shear angles. The optimization of local reinforcements has been done with two aims: to improve structural performance and repair damaged structures. Focusing on the repair of damaged structures, Mathias et al. [10] developed a 2D patch optimization approach, in which they used a spline curve to define the patch geometry. The control points of the spline curve are used as design variables for the optimization. A different approach for optimizing repair patches was presented by Ramji et al. [11, 12], who used parametric models of different initial geometries. The aim here was to find the best of several predefined geometries and, for this geometry, to then determine the best set of parameters. Therefore, they utilized 2D parametric patch models. An approach to optimize local reinforcements was proposed by Zehnder and Ermanni [13]. In their work, they focused on optimizing the stacking sequence of predefined patches, whose shapes are not changed during the optimization. In a later work, they extended their method by a spline-based geometry optimization of the patch [3]. They applied a parametric CAD model to create the patch geometry and did not include a draping simulation in their optimization. In both cases, an evolutionary algorithm was used to perform the optimization. Rettenwander et al. [14] proposed an approach for optimizing the position and stacking sequence of local reinforcements. Since they focused on two-dimensional structures only, they did not include a draping simulation in their optimization. A multi-objective optimization method for composite materials was introduced by Walker and Smith [15]. This work combined an evolutionary algorithm with a finite element simulation to simultaneously optimize the weight and mechanical performance of a plate structure. Using fiber orientation and laminate thickness as optimization parameters, a Tsai-Wu failure criterion is included as an optimization constraint. Thereby, they used discrete design variables for orientation and thickness to reduce the design space. Zhang et al. [16] employed a weighted-sum approach for the multi-optimization of patches. In their approach, however, a patch is

253

254

5 Designing CoDiCoFRP Structures

defined as an area of a composite layup with a uniform stacking sequence and the geometry must therefore be subdivided a-priori into patches. This segmentation is then maintained during the optimization, while the orientation of each ply serves as an optimization parameter. The influence of the number of design variables on the performance of an evolutionary algorithm for composite optimization was investigated by Vo-Duy et al. [17]. They consider weight and natural frequency as objectives and varied the number of design parameters from one to three. Although several approaches for positioning local reinforcements can be found in the literature, the consideration of manufacturing influences and draping effects on the optimization has not been covered so far. The consideration of manufacturing effects during the optimization is an important aspect, since it leads to more reliable and easier-to-manufacture results. Incorporating a warpage simulation in the optimization workflow also allows one to incorporate further restrictions from the manufacturing process.

5.2.2 Draping Simulation Method A draping simulation is needed to predict the final shape and fiber orientation of continuous fiber-reinforced composites. The methods developed for draping simulations of continuous fiber-reinforced materials can be divided into mechanical and kinematic methods. Although mechanical methods can provide good predictions of material behavior during the forming process, where effects like wrinkling can be predicted [18], a thorough understanding of the material behavior is essential. Furthermore, these methods are usually computationally expensive. Since many simulations are needed for the optimization approach proposed in this chapter, a kinematic draping method will be used. This seems reasonable, since the detailed behavior of the fabric during the forming process is not the main focus, but rather the prediction of the patch’s final geometry. The kinematic draping simulation method was first introduced by Mack and Taylor [19]. In their work, they described the governing assumptions for the kinematic draping method, which are also applied here: 1. the fibers are inextensible, 2. warp and weft crossing points act as pivoting points, 3. no slipping occurs at these pivoting points, 4. the distance between two pivoting points is much less than the smallest curvature radius of the surface, 5. the fabric is in contact with the surface of the initial component (tool) everywhere. In addition, the assumption of a simple shear deformation of the patch is applied to describe the deformation of a unidirectional textile rather than a woven textile. The

5.2 Production-Oriented Dimensioning of Local Patches

necessary input parameters for the kinematic draping simulation are the patch’s midpoint M, orientation ', length l0, and width w0. Based on these assumptions, the following equations can be derived according to Fengler et al. [20]. First, the distance between two consecutive nodes a and a of the patch must be equal to a predefined mesh size m:

ˇ ˇ ˇa  a ˇ D m:(5.1)

In addition, the calculated node must be on the initial component’s surface   a D F a ; a ;(5.2) 3 2 1

, and a are the x, y, and z components of the calculated where a ; a 3 1 2

, and F(x, y) represents the interpolation of the z component of the node a surface of the initial component. In addition, the patch’s initial orientation ' must be maintained. Based on this, the initial paths A and B can be calculated, cf. Figure 5.2(a).

Figure 5.2 (a) Definition of the initial paths A and B for the kinematic draping simulation and (b) visualization of the calculation process for all other nodes [20]

The nodes from the initial paths are used to calculate all other nodes. The principal process is illustrated in Figure 5.2(b). The assumption of simple shear leads to the following equations for calculating the patch nodes:

ˇ ˇ ˇa  a ˇ D m ;(5.3) ˇ ˇ ˇa  a ˇ D m;(5.4) with i D 1; 2; : : :

l0 w0 ; j D 1; 2; : : : :(5.5) m m

Here, Eq. (5.3) and (5.4) state that the distance between adjacent paths remains constant in the perpendicular directions A and B and that the initial fiber length remains constant. In addition, Eq. (5.2) must be fulfilled for each node of the patch.

255

256

5 Designing CoDiCoFRP Structures

Rearranging Eq. (5.2), (5.3), and (5.4) leads to the following system:

 2  2 B.jC1/>

0 D a

2 (5.6) C a

0 D a

2 (5.7) C a ;(5.8) 0 D a