A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior [1st ed. 2020] 978-3-662-60275-1, 978-3-662-60276-8

Table of contents :
Front Matter ....Pages I-XVII
Introduction (Ralf Seemann)....Pages 1-3
State of the art (Ralf Seemann)....Pages 5-32
Overall concept of mechanical characterization (Ralf Seemann)....Pages 33-34
Mechanical characterization on constituent level (Ralf Seemann)....Pages 35-72
Mechanical characterization on structural element level (Ralf Seemann)....Pages 73-93
Mechanical characterization on sub-component level (Ralf Seemann)....Pages 95-103
Virtual testing approach for sandwich panel joints (Ralf Seemann)....Pages 105-153
Development of novel sandwich panel joints (Ralf Seemann)....Pages 155-161
Summary and outlook (Ralf Seemann)....Pages 163-164
Back Matter ....Pages 165-201

Citation preview

Produktentwicklung und Konstruktionstechnik

Ralf Seemann

A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior

16

Produktentwicklung und Konstruktionstechnik Band 16 Reihe herausgegeben vom Institut für Produktentwicklung und Konstruktionstechnik (PKT) der Technischen Universität Hamburg (TUHH), Hamburg, Deutschland unter der Leitung von Prof. Dr.-Ing. Dieter Krause

In der Buchreihe erscheinen die am Institut von Prof. Dr.-Ing. Dieter Krause erfolgreich betreuten abgeschlossenen Dissertationsschriften. Die Themen umfassen vorwiegend Arbeiten aus den beiden Forschungsschwerpunkten des Institutes, die methodische Produktentwicklung, insbesondere Themen zum Varianten- und Komplexitätsmangement sowie Methodenforschung für die Produktentwicklung im Allgemeinen und dem zweiten Forschungsthema der Strukturanalyse und Versuchstechnik mit Themen aus dem Bereich der Auslegung von Hochleistungswerkstoffen, wie CFK, Sandwich oder auch Keramik, sowie der Weiterentwicklung von Simulationsmethoden und Versuchstechnik für Spezialanwendungen. Bücher zu weiteren interessanten Themen oder Tagungsbände mit wissenschaftlichem oder mehr anwendungsorientiertem Charakter ergänzen die Buchreihe.

Weitere Bände in der Reihe http://www.springer.com/series/16305

Ralf Seemann

A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior

Ralf Seemann Institut für Produktentwicklung und Konstruktionstechnik (PKT) Hamburg University of Technology Hamburg, Germany

Produktentwicklung und Konstruktionstechnik ISBN 978-3-662-60275-1 ISBN 978-3-662-60276-8  (eBook) https://doi.org/10.1007/978-3-662-60276-8 Springer Vieweg © Springer-Verlag GmbH Germany, part of Springer Nature 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer Vieweg imprint is published by the registered company Springer-Verlag GmbH, DE part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior    

Vom Promotionsausschuss der Technischen Universität Hamburg zur Erlangung des akademischen Grades Doktor-Ingenieur (Dr.-Ing)

genehmigte Dissertation

von Ralf Seemann

aus Lübz

2019

1. Gutachter: Prof. Dr.-Ing. Dieter Krause 2. Gutachter: Prof. Tong-Earn Tay Tag der mündlichen Prüfung: 22.05.2019

Vorwort Die vorliegende Arbeit ist überwiegend während meiner Zeit als wissenschaftlicher Mitarbeiter am Institut für Produktentwicklung und Konstruktionstechnik der Technischen Universität Hamburg entstanden. Ich werde diese Zeit in guter Erinnerung behalten nicht zuletzt wegen der Menschen, die mich dabei begleitet haben. Im Folgenden möchte ich einige dieser Menschen kurz erwähnen. Herrn Prof. Dr.-Ing Dieter Krause danke ich für die Betreuung der Arbeit, für die Ermöglichung meiner zahlreichen Reisen nach Singapur und für die ein oder andere Lektion die auch im außerakademischen Bereich nützlich ist. Herrn Prof. Tong-Earn Tay von der National University of Singapore (NUS) danke ich für die Begutachtung der Arbeit und für den weiten Weg zur Promotionsprüfung nach Hamburg. Darüber hinaus danke ich auch Prof. Vincent Tan für die Hilfe bei der Durchführung meiner Gastaufenthalte an der NUS. Das Promotionsthema ist zu großen Teilen im Rahmen von Industrieprojekten entstanden. Hier möchte ich Herrn Peter Lampen für die Unterstützung bei der Durchführung von Strukturtests sowie für das stets offene Ohr danken. Ein weiterer Dank gilt Herrn Michael Quadbeck, durch dessen Einsatz mein letztes Forschungsprojekt erst ermöglicht wurde. Einen großen Beitrag haben auch viele Studierende im Rahmen von studentischen Arbeiten geleistet. Hier sind insbesondere Gerrit Brinckmann, Erik Fleming Lennart Gravert, Ina Hölscher, Hermann Hübner und Max Krause zu nennen. Auch möchte ich mich bei all meinen ehemaligen Kollegen bedanken. Ohne euch hätte die Arbeit nur halb so viel Spaß bereitet. Insbesondere danke ich Karen Malone für die Übernahme eines ungeliebten Forschungsprojektes. Benedikt Plaumann, Olaf Rasmussen und Jan Oltmann danke ich für die Unterstützung in allen praktischen und theoretischen Problemstellungen. Außerdem möchte ich Sebastian Ripperda danken. Auch wenn wir uns fachlich nur wenig austauschen konnten, so haben wir doch im Rahmen von Forschungsanträgen, Netzwerkabenden und Auslandsreisen immer ein gutes Team abgegeben. Schließlich möchte ich noch Karsten Albers erwähnen, der immer da war wenn man ihn im Prüffeld oder in IT-Fragen brauchte. Letztlich danke ich meiner Familie und insbesondere meiner Frau Shakina für die Ausdauer und Unterstützung bei der Beendigung dieser Arbeit.

Zusammenfassung Die Bestimmung der mechanischen Produkteigenschaften mithilfe von realen Tests ist einer der Hauptkostentreiber im Entwicklungsprozess von Leichtbauprodukten. Die Implementierung von virtuellen Testmethoden basierend auf der Finiten-Elemente-Methode kann wesentlich zur Reduzierung der Entwicklungskosten beitragen. Jedoch weisen insbesondere Verbundfasersandwichstrukturen ein kompliziertes Versagensverhalten auf. Dies macht Festigkeitsvorhersagen mit Hilfe von FE-Simulationen schwierig. Die vorliegende Arbeit bewältigt dieses Problem durch die Entwicklung eines virtuellen Testverfahrens für Sandwichstrukturen. Das Testverfahren basiert auf dem sogenannten Building Block Approach, welcher für die Entwicklung von Verbundfaserstrukturen vorrangig für Luftfahrtanwendungen entwickelt wurde. Er ist durch die typische Gliederung in Konstituenten, Strukturelementen, Sub-Komponenten und Komponenten als Komplexitätsebenen gekennzeichnet. Der Fokus des entwickelten virtuellen Testverfahrens liegt auf der Festigkeitsvorhersage von Verbindungselementen als typischer Schwachpunkt von Sandwichstrukturen. Es deckt daher Untersuchungen bis hin zur Sub-Komponentenebene ab, während die Untersuchungen auf Konstituenten- und Strukturelementebene durch einen hohen Detailgrad zur adäquaten Abbildung des komplizierten Versagensverhaltens an Verbindungstellen gekennzeichnet sind. In der vorliegenden Arbeit werden verschiedene Sandwichmaterialen und –konfigurationen experimentell und numerisch in den drei betrachteten Komplexitätsebenen untersucht. Mit den durchgeführten Studien wird ein virtuelles Testverfahren entwickelt. Auf Konstituentenebene werden der Kern, die Deckschichten und der Kleber untersucht, wobei der Fokus auf dem Kern liegt, da das lokale Versagen häufig durch die Kernmechanik dominiert wird. In diesem Zusammenhang wird eine detaillierte Meso-Modellierung für den Kern entwickelt, welche alle relevanten Kernschadensmechanismen abbildet. Auf Strukturelementebene werden verschiedene Sandwichpanels basierend auf standardisierten Biege- und Schubtests analysiert. Die Tests werden als virtuelle Tests basierend auf den Erkenntnissen der Konstituentenebene entwickelt. Es werden sowohl MesoKernmodelle als auch 3D-Kontinuumkernmodelle in einer vergleichenden Studie umgesetzt. Dabei können die zuvor bestimmten Materialparameter validiert werden. Auf SubKomponentenebene werden schließlich verschiedene Sandwich-Insertkonfigurationen sowie eine Eckverbindung experimentell untersucht. Basierend auf den vorherigen Komplexitätsebenen werden diese Verbindungselemente in virtuellen Tests umgesetzt. Dabei wurde eine gute Übereinstimmung zwischen realem und virtuellem Test festgestellt. Auf dieser Basis wurde das virtuelle Testverfahren abstrahiert und detailliert anhand eines Beispiels beschrieben. Abschließend wurde die Anwendung des Testverfahrens für die Entwicklung eines neuartigen Sandwichinserts demonstriert.

Table of contents 1

Introduction ........................................................................................................ 1 1.1 Motivation ........................................................................................................ 1 1.2 Thesis objectives............................................................................................... 2 1.3 Thesis structure ................................................................................................ 2

2

State of the art .................................................................................................... 5 2.1 Sandwich structures ......................................................................................... 5 2.1.1 Face sheets ............................................................................................ 5 2.1.2 Core ....................................................................................................... 7 2.1.3 Bonded sandwich panel ........................................................................ 8 2.1.4 Failure modes ...................................................................................... 11 2.2 Sandwich structure joints ............................................................................... 12 2.2.1 Inserts .................................................................................................. 12 2.2.2 Panel edges ......................................................................................... 15 2.2.3 Novel joint designs .............................................................................. 16 2.3 Computational analysis .................................................................................. 17 2.3.1 Finite Element Method........................................................................ 19 2.3.2 Literature survey on sandwich panel joint modelling ......................... 22 2.4 Virtual testing ................................................................................................. 23 2.5 Assessment of the state of the art and need for further research ................. 30

3

Overall concept of mechanical characterization ................................................. 33

4

Mechanical characterization on constituent level .............................................. 35 4.1 Sandwich core ................................................................................................ 35 4.1.1 Materials ............................................................................................. 36 4.1.2 Experimental analysis .......................................................................... 39 4.1.3 Numerical modelling on meso scale .................................................... 44

XII

Table of contents

4.1.4 Numerical modelling with 3D-contiuum elements .............................. 59 4.1.5 Conclusion ........................................................................................... 62 4.2 Face sheets ..................................................................................................... 62 4.2.1 Experimental analysis .......................................................................... 64 4.2.2 Numerical modelling and calibration................................................... 65 4.3 Adhesives ........................................................................................................ 68 4.3.1 Experimental analysis .......................................................................... 68 4.3.2 Numerical modelling and calibration................................................... 72 5

Mechanical characterization on structural element level ................................... 73 5.1 Panel flexure ................................................................................................... 73 5.1.1 Experimental analysis .......................................................................... 75 5.1.2 Numerical analysis ............................................................................... 79 5.2 In-plane shear ................................................................................................. 87 5.2.1 Experimental analysis .......................................................................... 87 5.2.2 Numerical analysis ............................................................................... 88 5.3 Additional test methods ................................................................................. 91

6

Mechanical characterization on sub-component level ....................................... 95 6.1 Threaded inserts perpendicular to the face sheet .......................................... 95 6.1.1 Out-of-plane tension (pull-out) ........................................................... 96 6.1.2 In-plane tension (shear)....................................................................... 99 6.2 L-Joints .......................................................................................................... 100 6.2.1 L-Joint bending test ........................................................................... 101 6.2.2 L-Joint shear test ............................................................................... 102

7

Virtual testing approach for sandwich panel joints .......................................... 105 7.1 Overview ....................................................................................................... 105 7.2 Phase 1 - Problem analysis ........................................................................... 106 7.3 Phase 2 - Definition of model framework ..................................................... 110 7.4 Phase 3 - Model development ...................................................................... 114

Table of contents

XIII

7.4.1 Investigation ...................................................................................... 115 7.4.2 Building blocks................................................................................... 125 7.4.3 Modelling database ........................................................................... 136 7.5 Phase 4 - Application of virtual test .............................................................. 136 7.6 Summary ...................................................................................................... 140 7.7 Validation based on different joint configurations ....................................... 141 7.7.1 Partially potted inserts ...................................................................... 141 7.7.2 Corner joints ...................................................................................... 148 7.7.3 Conclusion ......................................................................................... 153 8

Development of novel sandwich panel joints ................................................... 155 8.1 Virtual testing of design alternatives ............................................................ 157 8.2 Validation by experimental investigation ..................................................... 160

9

Summary and outlook ..................................................................................... 163

Literature .............................................................................................................. 165 Appendix A – Constituent level .............................................................................. 179 A1

Implemented material models of Nomex honeycomb ................................. 179

A2

Implemented material models for face sheets............................................. 183

A3

Implemented material models for adhesives ............................................... 187

Appendix B – Structural element level ................................................................... 192 B1 Sandwich bending test details.......................................................................... 192 B2 Comparison of modelling approaches in case of bending................................ 194 B3 Frame shear test details ................................................................................... 195 Appendix C – Sub-component level........................................................................ 196 C1 Damage progression for pull-out test on fully potted insert ............................ 196 C2 Implemented cohesive behavior of potting-face contact ................................ 197 C3 Experimental results in novel design study ...................................................... 198

Abbreviations ABAQUS Commercial FE-software ABS

Acrylonitrile butadiene styrene

AM

Additive manufacturing

BBA

Building block approach

CDP

Climbing drum peel test

CFRP

Carbon fiber reinforced plastics

CT

Computer tomography

DIC

Digital image correlation

DOE

Design of experiments

DoF

Degree of freedom

FAA

Federal Aviation Administration

FDM

Fused deposition modeling

FE

Finite element

FEA

Finite element analysis

FEM

Finite element method

FSDT

First order shear deformation theory

FST

Fire, smoke and toxicity

GFRP

Glass fiber reinforce plastic

HC

Honeycomb

HSDT

High-order displacement theory

IDH

Insert Design Handbook

LT

Transverse shear in core L-direction

MD

Machine direction

ML

Multiple layer

MPC

Multi point constraint

S4R

Under integrated 4-Node element type in ABAQUS

XVI

Abbreviations

SCB

Single cantilever beam test

SL

Single layer

SPC

Single point constraint

TUHH

Technische Universität Hamburg

UC

Unit cell

VUMAT User subroutine to define material behavior in ABAQUS/Explicit WT

Transverse shear in core W-direction

XD

Cross machine direction

Nomenclature Speed of sound of material for critical time increment calculation Compressive material strength Tensile material strength C

Damping matrix

E

Young’s modulus

F

Force/Load

G

Shear modulus

G1c

Mode I fracture toughness

K

Stiffness matrix Characteristic element length

M

Mass matrix

∆

Critical time increment

∆

Time increment

γ

Shear strain

ν

Poisson’s ratio Density of material

σt

Tensile strength of face sheet

σc

Compressive strength of face sheet

τ12

Shear strength of face sheet

1

Introduction

1.1 Motivation Due to their good weight specific mechanical properties, composite sandwich structures have become essential in modern commercial passenger aircraft. Typical applications include external secondary structure components and cabin interior parts (Figure 1). In fact, the vast majority of the cabin furnishing including floor to ceiling lining is made of composite sandwich panels. As secondary aircraft structure, the mechanical strength of the cabin monuments is not crucial for the flight safety of the aircraft. However, the passenger safety is closely linked to the integrity of the cabin.

Figure 1 Application of composite sandwich structures in case of the Airbus A380 according to Herrmann [Her05]

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_1

2

1 Introduction

As such, cabin monuments have to comply with strict legal airworthiness requirements not only in terms of flammability but also mechanical strength [EAS17]. Acceptable means of compliance include engineering evaluation for instance through calculation or testing. Furthermore, in order to ensure that compliance can be substantiated, concurrent determination of the mechanical product properties is required throughout the product development phase. Despite the fact that substantiation and concurrent analysis have seen increasing application of numerical analysis methods, time consuming and costly physical testing remains extensive during cabin development projects. Of particular interest are detailed tests on sandwich panel joints since full scale structures typically fail at these interfaces. In terms of airworthiness substantiation detailed tests programs are extensive, since minor changes in the joint configuration (i.e. sandwich panel composition, adhesive type, material supplier or reinforcement geometry) can often only be substantiated via testing. Analogously, concurrent mechanical analysis of design alternatives largely depends on physical tests. This is due to the complicated failure behavior of sandwich panel joints with multiple simultaneous damage mechanisms, which makes failure prediction via simulation challenging. However, virtual tests by means of simulation are desirable in order to reduce development time and cost, while increasing product quality due to front loading and predictive engineering.

1.2 Thesis objectives This thesis intends to provide a hierarchical virtual testing approach, which enables the prediction of the failure behavior and the strength of composite sandwich panels joints by means of validated non-linear FE-simulations. The approach generally assumes that there is an existing physical test which is to be replaced by simulation. It aims to provide guidance on the definition of a suitable level of detail for the simulation model depending on the complexity of the failure behavior in the investigated test. In addition, the approach outlines relevant hierarchy levels for the model development, while providing a reference for test and simulation procedures within each level. In this context multiple tests on sandwich structures along with the corresponding simulation models are suggested. Therefore, this thesis shall contribute material models and parameters for common sandwich materials in commercial aircraft cabins. The superordinate objective is to enable the reduction of physical tests in the development phase of sandwich constructions.

1.3 Thesis structure In chapter 2 the relevant theoretical background as well as state of the art concerning virtual testing of sandwich structures is described. This includes an introduction to sandwich structures in general and in particular to the different aspects of sandwich panel

1.3 Thesis structure

3

joints. In addition, a literature review on computational modelling of sandwich structures and virtual testing approaches is presented. The following chapters 4 to 6 are each dedicated to one of the three investigated hierarchy levels. Chapter 4 summarizes the performed experimental and numerical studies on various sandwich structures on constituent level. This includes face sheets, core and adhesives. Chapter 5 describes the investigations on structural element level, which corresponds to the bonded sandwich panel. In both chapters, virtual testing concepts are applied to derive suitable computational models, while information is transferred between the hierarchy levels. In chapter 6, experimental studies on sandwich panel joints are outlined. These include various configurations of standard potted inserts as well as mortise corner joints. These experimental studies on sub-component level serve as basis for the development and validation of the proposed virtual testing approach. Chapter 7 describes the developed approach for virtual testing of sandwich panel joints using a demonstration example. The investigations described in chapter 3 and 5 are integral part of this approach. Therefore, aspects of these chapters are revisited and put into perspective. In addition to the described demonstration example, further validation examples are outlined. Chapter 8 demonstrates the application of the established virtual testing approach in an engineering design study for the development of a novel sandwich panel joint.

2

State of the art

2.1 Sandwich structures Sandwich structures are based on the principle of separating two thin and stiff faces by a thick, mechanically weak lightweight core. Load transfer between these three components is achieved by adhesive bonding (Figure 2). This arrangement functions like an Ibeam, where as much material as possible is placed farthest away from the neutral axis, thus providing excellent weight specific bending stiffness and strength. The core primarily serves the function to transmit transverse shear and to prevent the thin faces from buckling, while the faces are mainly under normal stresses. Sandwich structures can be tailored for a great variety of applications. In particular, the core can fulfill additional functions, such as noise or thermal insulation. In the following, the main aspects of sandwich construction with focus on aircraft interior applications are introduced.

Figure 2 Sandwich construction

2.1.1 Face sheets A great variety of materials can be used as sandwich face, as long as it is available as thin sheet. Therefore, designers have the freedom to select a suitable material based on the

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_2

6

2 State of the art

primary requirements of a given application. These requirements may include, high stiffness and strength, impact resistance, surface finish and environmental resistance (UV, flammability etc.) [Zen97]. In lightweight design, fiber reinforced composites are among the most commonly used face sheet materials, while glass fibers are the most common reinforcement material. This is due to their good mechanical properties and environmental resistance at low price. In advanced aerospace applications carbon fiber reinforced plastics (CFRP) can also be found as face sheets, owing to their superior weight specific stiffness [Zen97]. In aircraft interiors, these two fiber materials make up the vast majority found as face sheet reinforcement, while glass fibers make up about 65% and carbon fibers most of the remainder [Red12]. Typically, aircraft interior face sheets are reinforced using woven fabrics, which are characterized by two orthogonally oriented fiber directions using warp and weft yarns. Woven fabrics are favorable for planar components, since they allow to apply two fiber directions in only one manufacturing step, while they can still be tailored according to the applied loads by adjusting the fiber content of the warp and weft yarns [Sch07]. Woven fabrics are available in an abundant variety of configurations. Typical weave patterns for application in aircraft interior sandwich face sheets are summarized in Table 1. Table 1 Typical weave patterns for aircraft interior sandwich face sheets [Hex10]

Four harness satin

Eight harness satin

Twill weave

Good pliability, also referred to as crowfoot

Best pliability; for curved surfaces

Good pliability; better drapability and fabric stability than harness satin patterns

Regarding the matrix for the composite face sheet, again a vast number of materials is plausible depending on the given application. Generally, it can be distinguished between thermoset and thermoplastic matrices. Thermosets are low-viscosity prepolymers that have been solidified through an irreversible chemical reaction to form a high weight polymer network. They are traditionally the most common matrix type in composite construction [Sch07]. In aircraft interiors phenolic thermosets are most commonly used, due to their excellent fire, smoke and toxicity (FST) properties [Tay10].

2.1 Sandwich structures

7

2.1.2 Core The core is probably the most important sandwich component, despite the fact that engineers tend to have the least knowledge of this component [Zen97]. Sandwich cores are very diverse, while two broad groups can be distinguished, the homogenous and the structured cores. In aerospace applications, the structured honeycomb cores are most commonly used [Zen97], [Bit97]. In addition, homogenous foam cores have recently also found some applications in aircraft structures [Sei06]. a)

b)

Figure 3 a) Sandwich core types; b) Honeycomb cell shapes [Bit97]

The most common honeycomb materials are aluminum and impregnated glass or aramid fiber mats, such as Nomex®. Honeycombs can be manufactured in a variety of cell shapes (Figure 3b). The mechanical properties of honeycomb cores can be further tailored using the density of the core. Kim and Lee [Kim97] established for instance that the compressive core properties linearly increase with the core density. In modern aircraft interior structures, Nomex honeycomb in regular or over-expanded shapes are typically used, while over-expanded honeycombs are primarily used for curved sandwich panels. Nomex1 is a non-metallic paper material, which is well known for its excellent fire-resistance. It comprises two forms of aramid polymer, the fibrids (small fibrous binder particles) and the floc (short fibers). These two components are mixed in a water-based slurry and machined to a continuous sheet. Subsequent high-temperature calendering results in a dense and mechanically strong paper material. Due to the calendering, the longer floc fibers align themselves in direction of the paper coming off the machine

1

Trademarked by E. I. du Pont de Nemours and Company

8

2 State of the art

[DuP03]. This leads to orthotropic mechanical properties of the paper, with the machine direction (MD) being superior in terms of modulus and strength if compared to the cross direction (XD) (E1 > E2 in Figure 4). Nomex is generally fabricated into honeycomb using the adhesive bonding method and the expansion process [Bit97]. Here, adhesive lines are placed on the paper material, before it is cut into sheets and stacked to form a solid block. Expanding this block leads to the desired honeycomb lattice, which is subsequently dipped in phenolic resin and oven cured so that it retains its shape. This process leads to uneven cell wall thicknesses with the bonded cell walls being twice as thick as the free single walls. Due to the orthotropic nature of the Nomex paper, the orientation of the material in the final honeycomb core is of interest. This depends on the orientation of the adhesive lines before stacking the paper sheets. In applications where honeycomb cores with large extend in L-direction are required, the adhesive is applied in cross line [Bit97]. This way the L-direction length of the honeycomb is not restricted by the width of the Nomex paper roll. It is assumed that this is the standard case for cabin interior applications, which require large planar segments. The manufacturing process along with the assumed material orientations is illustrated in Figure 4. Cell wall material sheets

Cured honeycomb core

E1

2t

E1

E2

tion machine direc (roll direction)

t

E2

Adhesive lines in crossline (web direciton)

W

T

cross direction (web direction)

Calendered paper roll

L

Figure 4 Manufacturing of Nomex honeycomb and material orientations [See17]

2.1.3 Bonded sandwich panel There are two main methods of bonding sandwich panels, vacuum bag processing and press moulding. In the vacuum bag process panels can be cured in an oven or in an autoclave for increased pressure (Figure 5). The vacuum bag is commonly used for curved shapes and press moulding for flat panels [Bit97], [Hex00]. In cabin interior applications both processes are common due the fact that both, curved and flat panels, can be found in cabin interior monuments. However, the load carrying sandwich components in partitions, galleys and hatracks are typically manufactured from flat panels. Regardless the

2.1 Sandwich structures

9

applied bonding method, cabin interior honeycomb sandwich panels are generally fabricated by co-curing the prepregs onto the honeycomb core in a single shot process [Bit97], [Hex00], [Bla06]. This method not only simplifies the lay-up but also reduces the weight of the bonded panel, since there is no adhesive added. The bond between face and core is achieved by adhesive fillets that form at the core-skin bond lines during the co-curing process. Therefore, the adhesive fillets consist of the thermoset used in the face sheet prepregs. The fillet condition defines the bond strength and depends on the used prepreg thermoset, the honeycomb quality as well as process parameters such as pressure and curing cycle [Yua08]. Therefore, the process parameters have to be tuned for application in sandwich components. Figure 6 illustrates desirable and undesirable fillet conditions for honeycomb sandwich panels.

Figure 5 Main honeycomb sandwich panel fabrication methods a) vacuum bag processing; b) flat press moulding according to Hexcel [Hex01] High core Short core uplift of skin no fillet

Excessive adhesive flow

Lack of adhesive flow

Uneven filleting

One-sided

Equally large fillets that thoroughly wet cell walls Well formed and desired adhesive fillets

10

2 State of the art

Figure 6 Fillet conditions depending on the process parameters according to Campbell [Cam04]

One additional effect has to be considered in the bonded sandwich panel. In the vacuum bag process the sandwich panel has two sides, the bag side and the tool side. In particular on the bag side the face sheet can sink into the honeycomb cells, since it is only supported by the cell walls. This effect is known as dimpling, pillowing or telegraphing (Figure 7). The flat press moulding is characterized by two tool sides, which reduces the telegraphing and leads to a better surface finish. However, the limited support of the cell wall edges results in uneven faces with a non-uniform face sheet thickness as well as a variation of the fiber volume fraction also on the tool side. This effect can considerably reduce the mechanical properties of the face sheets depending on its severity [Cam04]. Bag side

Core cells

Area prone to porosity

Tool side

Figure 7 Pillowing effect in vacuum bag process [Cam04]

Figure 8 illustrates the telegraphing effect based on a microscopic image of a face sheet section. The areas of pure resin and fabric reinforced resin can be clearly distinguished. It also becomes apparent that the face sheet thickness varies significantly, while in sandwich design the face sheet thickness is generally idealized assuming constant thickness. Cell wall Pure resin fillet

Fabric telegraphing

Idealized homogenous face sheet

Porosities

0.25 mm

Figure 8 Telegraphing effect in face sheets (uneven face sheet thickness and waviness of face sheet fibers on tool side)

2.1 Sandwich structures

11

2.1.4 Failure modes Sandwich panels are characterized by a multitude of failure modes, many of which being unique to sandwich structures. Identifying the different failure modes and damage mechanisms is crucial when analyzing sandwich structures. In the following the most important failure modes are illustrated and briefly described. This overview is derived from standard literature [Bit97], [Zen97], [Hex00]. Table 2 Failure modes in sandwich structures Local indentation Initiated by low compressive strength of the core One of the most critical damages due to initiation of face debonding Core shear failure Due to low shear strength of the core Common damage in bending and due to local loads around core reinforcements Face yield/fracture Resulting from tension, compression or shear, due to insufficient face sheet strength Global buckling Due to insufficient panel thickness or core shear modulus

Face dimpling (intracell buckling) Due to large core cells and thin face sheets. May propagate to surrounding cells

12

2 State of the art

Face wrinkling Either due to Face debonding resulting from low adhesive strength between face and core

or due to core crushing resulting from low compressive core strength

2.2 Sandwich structure joints The design of sandwich panel joints is crucial in sandwich construction and a considerable share of the total development time in sandwich construction is typically attributed to joint design. This is due to the sensitivity to localized loads, which is one of the major short comings of sandwich structures. This is a result of the low-density core, which does not provide enough stiffness to distribute loads adequately. High multiaxial stress concentrations in the vicinity of load introduction areas often lead to premature failure of the core, which quickly propagates and eventually causes catastrophic failure of the entire panel [Zen97]. However, when it comes to joining sandwich panels, local external load application is unavoidable. In order to prevent premature core failure, sandwich panel joints are locally reinforced. Depending on the type of joint, an abundant variety of joint designs can be found in the literature. In general sandwich panel joints can be distinguished between inserts that enable fastening of components onto the panel and joints along panel edges for assembling larger structures. A combination of both categories can also be found. In the following, the two categories are described in more detail.

2.2.1 Inserts In Zenkert’s Handbook of Sandwich Construction [Zen97] inserts are defined as local change in stiffness and strength of the sandwich panel, with the purpose of distributing localized loads. There are three groups of such fastener elements [ESA11]. One of the most common insert designs is illustrated in Figure 9. Here, a threaded circular insert is bonded into a sandwich panel using adhesive. This process as well as the adhesive itself are often referred to as “potting”. Since this is done post panel fabrication (post-fab), this method requires to locally remove the face sheet and core, for instance by means of milling, and to inject the adhesive into the cavity with the insert placed in its center. This method enables a great variety in insert designs covering a wide range of requirements for the fastener element. There are different potting methods depending on the

2.2 Sandwich structure joints

13

insert type. Generally, it is distinguished between, partially and fully potted as well as through-the-thickness bonded. In addition, there are further post-fab bonded insert designs such as so called “onserts” or flanged bushings.

Figure 9 Typical constituents of sandwich panel inserts [See14]

However, bonding is not essential and there are insert designs that do not require any adhesive. This second group comprises mechanically fastened inserts, which generally have a low structural performance, since they are lacking a planar load transmission into the face sheet. As third group, there are insert designs that require reinforcement of the panel during panel manufacturing (co-fab). This can be implemented using low density core filling or by bonding a rigid section as local core replacement during panel manufacturing. This method has the advantage that large high strength fastener elements can be implemented anywhere in the panel without damaging the face sheets. However, the panel manufacturing process is considerably more complicated and the positioning of the fastener elements tends to be less accurate. In addition, co-fab methods are generally less flexible in the overall sandwich structure production. Figure 10 illustrates the three different fastener methods with multiple examples for each group. This summary represents the view of the author and is derived from available literature, most notably [Hei09], [Zen97], [ESA11] and [Bit97]. The literature also provides guidance on the relative load carrying capabilities of the different insert types and in case of the Insert Design Handbook (IDH) [ESA11] comprehensive resources on design considerations for the selection of inserts are given. Regarding the loads, it can be distinguished between four loading conditions for sandwich fasteners, namely tension/compression, shear, torsion and bending (Figure 11). The latter two loading conditions are unfavorable for inserts and they are therefore avoided. This is achieved by fastening components onto the panel using multiple inserts. Such arrangements transform torsional loading of the component into shear for the individual inserts while bending is transformed into tension/compression [ESA11]. Therefore, shear and tension/compression are of primary interest in the design phase.

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Figure 10 Overview and classification of different sandwich insert types

There are no standardized tests for determining the mechanical strength of inserts and sandwich joints in general [Mun15]. However, in case of out-of-plane tension of sandwich inserts, there is a great number of studies in the literature, which all apply the same test setup. This setup follows suggestions given in the IDH [ESA11], which can be considered as quasi-standard. In case of shear loading, there are less examples in the literature, however the IDH also gives guidance for this test setup. The present work follows the IDH in both cases. More details on the implemented test setups are given in section 6, which covers the experimental investigation of sandwich panel joints.

2.2 Sandwich structure joints

15

Figure 11 Loading conditions of sandwich inserts according to [ESA11]

2.2.2 Panel edges Joints along panel edges are a common feature in sandwich structures and analogous to the previously introduced sandwich fasteners they require local reinforcement to prevent premature failure. This is due to the inevitable circumstance that in-plane loading on one panel of the joint results in out-of-plane loading on the other panel [Zen97]. This is illustrated in Figure 12 for three basic panel joint configurations.

Figure 12 Reaction forces in basic edge joint configurations according to [Zen97]

Similarly to sandwich inserts, edge joints exist in abundant variety, depending on the joint configuration, the required load carrying capability as well as manufacturing constraints. Figure 13 illustrates four typical panel edge joint designs in case of L-joints. Zenkert [Zen97] provides guidance on the reinforcement design depending on the joint configuration. Generally corner joints should be reinforced with a high density core in the horizontal panel to prevent core failure along with bonded fillets in the corners for improved load distribution in to the face sheets [Zen97]. Regarding experimental testing, corner joints are generally less documented in the literature if compared to inserts. The majority of available studies is concerned with T-joints, originating from ship building applications [The96], [Tur00], [Tof05], [Gie05]. L-joint testing is described by Mund et al. [Mun15] and Heimbs [Hei09]. Based on this literature, the critical load cases are established as shear and bending of the two panels. Due to a lack of standardized test methods, the listed literature serves as reference for the experimental testing in the present work.

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2 State of the art

Figure 13 Typical L-joint designs derived from literature [Hex01], [Hei09], [Bit97]

2.2.3 Novel joint designs The previously introduced sandwich panel joint designs were established decades ago and they still dominate the industry. At the same time, there are only few studies on novel joint designs. Roth [Rot05] developed a new manufacturing method for throughthe-thickness reinforcement of established insert types by means of stitching. He reported considerably improved load introduction if compared to state-of-the-art inserts. However, stitching is mostly limited to foam core sandwich structures and cannot be readily transferred to honeycomb cores. Schwennen et al. [Sch16] implemented two novel co-fabrication processes based on resin transfer moulding for integrating highstrength inserts into carbon fiber foam core sandwich. Lim and Lee [Lim11] developed a novel lightweight insert for co-fabrication into honeycomb sandwich structures. The web of the insert is sealed and reinforced with carbon composite material. The new design achieved a weight reduction of 37 % through reduction of potting mass, while achieving similar tensile strength and 50% increased shear strength if compared to the reference insert. They complemented the development by the application of a linear FE-model. Block et al. [Blo05] developed carbon fiber tube inserts as alternative for through-thethickness and partially potted inserts in honeycomb sandwich structures for application in a spacecraft. They reported improved weight specific strengths given that the insert tube diameter is larger than 2x the honeycomb cell size. a)

b)

Figure 14 Examples of novel honeycomb insert designs, a) Carbon fiber tubes [Blo05] and b) Web reinforced insert [Lim11]

2.3 Computational analysis

17

Feldhusen et al. [Fel09] developed a mechanical joining technology for joining sandwich structures based on established design methodology. However, their solutions were only implemented for large scale aluminum-foam sandwich structures for civil engineering applications.

2.3 Computational analysis One of the foundations for computational analysis of sandwich structures is the first order shear deformation theory (FSDT) based on Mindlin & Reissner. The FSDT enables two dimensional models to simulate the transverse shear deformation of the core, which can contribute considerably to the total panel deformation due to the low shear modulus of typical sandwich cores. This is illustrated in Figure 15.

Figure 15 Sandwich panel deformation due to bending

The FSDT has been adapted for sandwich structures making assumptions such as, low inplane normal stiffness and infinite transverse stiffness of the core as well as thin face sheets if compared to the core height. The result is the so called sandwich theory which was established by Allen [All69] and Plantema [Pla66]. It was later complemented by high-order theories, which enable non-linear displacement fields of the core due to its soft nature. These high-order displacement theories (HSDT) are for instance required to model localized effects such as point loads. Based on these theories, there is an abundance of computational models described in the literature. Noor et al. [Noo96] distinguished between four categories; detailed models, 3D-continuum models, 2Dshell/plate models and simplified models. Simplified models are often derived from sandwich theory and generally enable to simulate specific isolated effects, such as bending deflection, wrinkling or buckling, often by means of analytical equations [Zen97]. There are also numerous simplified models for the estimation of the equivalent homogenized elastic and ‘plastic’ honeycomb core properties based on the cell geometry and material. Such models were proposed by Meraghni et al. [Mer99], Hohe and Becker [Hoh02] as well as Gibson and Ashby [Gib10]. These simplified models are important tools for preliminary design studies of sandwich plates. The three remaining categories are, today, commonly realized using the numerical Finite Element Method (FEM). 2D shell and plate models represent the most basic group of FE-models. They can be implemented as single layer equivalent or discrete multilayer models based on the FSDT or

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HSDT. However, in industrial applications single layer FSDT models are most common. They are readily available in commercial finite element software and enable to analyze large structures at low computational effort. While these models are effective in representing symmetric in-plane damage mechanism, they are limited in their capability to represent out-of-plane sandwich failure modes, like core crushing, face wrinkling and delamination. This can be overcome by implementing 3D-continuum models. By modelling the core with solid elements or quasi-solid elements in case of axial symmetry, various out-of-plane damage mechanisms can be simulated using effective homogenized mechanical core properties. Such a core is often coupled with 2D-shell elements for the faces, leading to the well-established Shell-Solid-Shell approach. The increased damage modeling capability of this approach, if compared to the simplified and 2D-models, results in increased computational effort. However, due to the homogenization of the core no buckling of the honeycomb cell walls can be represented. This can be achieved using detailed models, where the actual cellular core geometry is modelled. This is required to simulate the large local deformation of the core cell walls accurately. These meso-scale models require high computational effort, yet they have seen increasing applications in the recent past, due to increasing computational capabilities. Figure 16 illustrates the four introduced categories, while the relative damage modeling capabilities and computational effort are indicated using an arrow. In the following, the Finite Element Method is briefly introduced as fundamental tool in the present work before a literature survey on computational models for honeycomb sandwich panel joints is given.

Simplified models

2D shell and plate models

3D-Continuum models

Detailed models

Analytical equations

Global approximation, discrete layer

e.g. Shell-Solid-Shell

Meso/Micro scale

 

Increasing computational effort Increasing damage modeling capabilities

Figure 16 Categories of computational models for sandwich structures [See14]

2.3 Computational analysis

19

2.3.1 Finite Element Method The Finite Element Method enables to analyze the mechanical properties of complicated structures by discretizing the geometry into smaller segments also known as elements, which can be analyzed using basic engineering mechanics. The elements are linked via nodes while the relationship between the nodes is described by shape functions. The mechanical quantities of the system are determined by calculating the distribution of the nodes depending on the boundary conditions including external loads. The system is described with a set of differential equations, which can be written as the following equilibrium equation ([Nas15]) M∙u

C∙u

K∙u

F

2.1

Here, M refers to the mass matrix, C to the damping matrix, K is the stiffness matrix and F defines a set of external loads. , and are the acceleration, velocity and displacement of the nodes respectively. The equation above describes a linear static system. Modelling progressive damage mechanisms requires transient and non-linear relationships. Therefore, the displacement and its derivatives are time dependent while the stiffness and damping matrices as well as the external loads may depend on the displacement and velocity of the nodes (Eq 2.2) M∙u t

C u, u ∙ u t

K u, u ∙ u t

F u, u

2.2

Solving such transient systems requires discretizing the time into increments ∆ , while the system is solved for each point in time. There are two main types of time integration methods, the implicit and explicit one [Liu03]. Both methods have their pro’s and con’s and hence their specific areas of application depending on the problem to be solved. Generally, explicit methods are computationally more efficient for rapid and highly nonlinear phenomena such as impact or explosion. Implicit methods are advantageous for quasi-static problems with limited degree of non-linearity. This issue is illustrated in Figure 17 with the help two graphs. Figure 17 a) illustrates the suitable area of application for both methods depending on the velocity and degree of non-linearity of the investigated problem. Figure 17 b) displays the relationship between computational effort and complexity of the problem for both methods, while the complexity refers to the combination of velocity and degree of non-linearity. The computational effort largely corresponds to the computing time. However, the computing time not only depends on the model setup but also on the available computing resources. Therefore, computational effort is used as general term, which includes both aspects, computing time and computational resources. The computational effort is of particular interest in industrial applications where the simulation results are required to make design decisions in tightly scheduled development projects. From the graphs in Figure 17, it can be seen that there is a transition zone with applications where both methods are equally suitable. Virtual testing of sandwich structures often falls into this transition zone, with quasi-static tests

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being investigated while at the same many simultaneous non-linear effects have to be considered. This is also evident in the reviewed literature, where both methods can be found for the failure prediction of sandwich structures. There are various commercial finite element software packages available for each of the two methods. However, due to the fundamental differences, the available codes specialize in either one of the methods and finite element models are generally implemented for a specific integration scheme. Therefore, the integration method cannot be readily changed for an existing model. This requires at least some degree of model adaption. As a result of this, the applied integration method should be defined carefully prior to the model development. The following paragraphs briefly introduce the theory behind the two methods. a)

b)

Non-linearity

Computational effort

Rupture Damage

Explicit

Explicit

Implicit

Buckling Plastic Elastic

Implicit

Complexity

Static

Dynamic

Velocity

Static / Elastic

Non-linear dynamic

Figure 17 Comparison of implicit and explicit integration schemes; a) suitability depending on type of problem, b) Computational effort depending on type of problem according to Altair [Alt12]

Explicit time integration Using the explicit integration Eq. (2.2) is solved at time ∆ by extrapolating the state of equilibrium at time . The extrapolation is commonly based on the central difference method, which makes assumptions regarding the relationship between displacement, velocity and acceleration. Using this method, only the damping and mass matrix have to be inverted, making the equation solving computationally inexpensive as long as under integrated elements are implemented. However, the method is conditionally stable and requires time steps below a critical time step in order to give plausible results. The critical equals the time a stress wave takes to cross the smallest element in the time step ∆ and the charmesh [Liu03]. This time depends on the speed of sound of the material acteristic element length , while relates to the density and modulus of the material. ∆

∆

;



2.3

Therefore, the maximum allowable time step depends on the mesh size as well as the mass and stiffness of the elements. Generally, a large time step is desirable, since it reduces the total number of increments to be solved. However, often the mesh size and

2.3 Computational analysis

21

element stiffness are predefined and cannot be altered. Therefore, the time step can only be increased by increasing the mass of the elements. This process is called mass scaling and enables to reduce the computation time of the simulation. However, increasing the mass also increases the kinetic energy, which may destabilize the solution leading to invalid results. In addition, the time step directly affects the quality of the solution. Large time increments as well as a great number of time steps lead to increasing error. This is illustrated in Figure 18, where the vertical lines along with the capital letters A to D indicate the time increments. Therefore, applying explicit integration generally requires some preliminary sensitivity studies to determine a suitable time step. Small time increments

C B A

Error

D

Function value

Function value

Large time increments

Time

Time Actual curve progression

Explicit solution

Current system behaviour

Figure 18 Explicit time integration for large and small time increments

Implicit time integration Unlike the explicit solution, the implicit integration scheme attempts to solve Eq. (2.2) at time ∆ based on assumptions regarding the unknown system quantities of this following time step. Therefore, the implicit method requires equilibrium iterations, which approximate the solution until convergence is achieved. This process requires to invert the stiffness matrix K making the equation solving computationally expensive, while the equilibrium iterations may require multiple solver runs for each time increment (i.e. A1 – An in Figure 19). This is compensated by the fact, that the implicit method enables large time increments if compared to the explicit method (factor 100 to 1000 larger) [Liu03]. Furthermore, the implicit method is unconditionally stable regardless the time increment length, yet the increment length affects the quality of the solution and may depend on the convergence conditions. Figure 19 illustrates the implicit integration scheme for short and long time increments. Due to the mandatory equilibrium iterations, the implicit integration may encounter convergence problems, which prevent the solver from finding a solution.

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2 State of the art

Small time increments

A1 B1 An

Cn C1

D1

Bn

Function value

Function value

Large time increments

Dn

Time

Time Actual curve progression

Implicit solution

Iterative solutions

Figure 19 Implicit time integration for large and small time increments

2.3.2 Literature survey on sandwich panel joint modelling Sandwich panel joints generally require the capability to model out-of-plane failure. Therefore, the available models can be assigned exclusively to the 3D-continuum and detailed model groups. As previously mentioned, FEM models have become state of the art in sandwich modelling. However, among the earliest sandwich panel joint models is the model developed by Thomsen and Rits [Tho98], [Tho97] who applied an adapted high-order theory for sandwich bending. This model was developed specifically for ‘through the thickness’, ‘partially’ and ‘fully potted’ inserts making simplifications such as homogenized honeycomb properties and regular axisymmetric interface between potting and honeycomb. The model was implemented using first-order differential equations, which are solved numerically. It was intended for early design estimations and for deriving design guidelines. This model was later implemented by Bull and Thomsen [Bul08] in a design tool for preliminary dimensioning of inserts in sandwich panels, while the model performance was benchmarked with experimental data and FE-simulations. Furthermore, Smith and Banerjee [Smi12] applied the Thomsen and Rits model in order to investigate the reliability of the strength of sandwich panel inserts comparing different reliability analysis methods. The remaining reviewed studies relied on FEM with varying level of detail. Most of the early FE-models were quasi 3D continuum-models reducing the dimension based on axi-symmetry analogous to the previously described model of Thomsen. Therefore, these models were based on several simplifying assumptions and were primarily applied for preliminary design studies as well [Boz04], [Rag08], [Tso06], [The96]. A true 3D-continuum model for countersunk titanium fasteners in Nomex honeycomb sandwich panels was developed by Bunyawanichakul et al. [Bun05], [Bun08]. The model development was supported by constituent tests on the potting material and the honeycomb core. Nguyen et al. [Ngu12] studied various configurations of

2.4 Virtual testing

23

foam sandwich panel joints. They implemented a 3D-continuum model, while benchmarking different approaches for failure modeling. Heimbs and Pein [Hei09] developed simplified 3D continuum models of inserts and panel edge joints, while including spotweld elements for an implementation in a global non-linear model of aircraft interior components. Furthermore, they derived one of the first detailed models of a honeycomb sandwich insert, where the hexagon core cells are modeled accurately. Additional studies on such detailed meso-models for honeycomb sandwich inserts include the work of Bianchi et al. [Bia11], who investigated post and co-fab bonding procedures for honeycomb sandwich inserts with the help of linear FE-models. Roy et al. [Roy14] derived the orthotropic material properties of Nomex honeycomb cell walls by comparing experimental results of partially potted inserts with a detailed FE-model of the joint. Silmane et al. [Sli17] studied the sensitivity of the actual potting shape of aluminum honeycomb inserts with respect to the position of the insert within the hexagon grid. Other examples of detailed honeycomb joint models include the analysis of the thermal coupling of sandwich inserts used in satellites [Bou14] as well as an investigation of the potting shrinkage during insert manufacturing [Cou15]. In the reviewed literature, computational models of sandwich panel joints were applied for preliminary design studies or to gain better understanding of the governing damage mechanisms. Applications where the models were intended to partially replace structural experiments by means of virtual testing are not evident.

2.4 Virtual testing The term virtual testing originates from the aerospace industry where certification requirements demand extensive physical tests, which contribute to a large share of the development cost. Hence, this industry is particularly pushing towards partially replacing tests with virtual simulation models in order to reduce costs [Oke14]. This environment requires high confidence in the simulation results. Therefore, virtual testing goes beyond the mere application of simulation models. According to Cox et al. [Cox08] a virtual test must be a system of hierarchical models, engineering tests, and specialized laboratory experiments, supported by the application of information science, model-based statistical analysis, and decision theory. Wood [Woo12] summarized different sources and described virtual tests as capability to provide predictions for the physical behavior of structures, specifically the structural strength as well as progressive damage up to localized and eventually catastrophic failure, while emphasis is put on the combination of testing and simulation on all levels of the testing pyramid. Ostergaard et al. [Ost11] characterized virtual testing as concept with several attributes, which is to be understood as simulation using advanced non-linear finite element analysis. They also underlined the fact

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that it involves the combination of analysis software, methods, people skills and experience to enable structural strength predictions with high level of confidence. These and other available resources can be broken down two three key points 

Prediction of damage mechanisms and failure



Close interaction of simulations and physical tests



Hierarchical approach

The first point emphasizes that virtual testing is particularly targeted towards simulating damage mechanisms. This requires advanced non-linear finite element solutions. In addition, deep understanding of the actual damage mechanisms and their interactions is essential. The second point stands for the fact that physical tests are an integral part of a virtual test framework. Tests are inevitable for validation and calibration of the simulation but also for providing the basis for understanding the damage mechanisms that led to failure. The other way around simulation models support the test planning by providing preliminary information about critical load cases and suitable boundary conditions. Lastly the third point indicates that all tests, simulation models and analyses are structured hierarchically. There are two types of hierarchy, which are common in the context of virtual testing. The first is the multiscale analysis, where the hierarchy is according to the investigated length scale. It can be described as the sequential coupling of different analysis models at different scales and levels of fidelity [Ost11]. This often involves a combination of micro and macro mechanics to analyze structures in great detail [Abd09]. This can be done for instance by determining the properties of one entity (e.g. composite ply) at a suitable length scale, transforming the results into a constitutive model and transferring these homogenized information to the following length scale to analyze the physical behavior of a larger entity (e.g. laminate) [LLo13]. Typical length scales of multiscale analyses are illustrated in Figure 20 a). This type of hierarchy is widely established in the material science context, in particular for the development of novel composite materials which can greatly benefit from virtual testing methods [Gon07], [Oke14]. Therefore, applications that apply multiscale analysis often end at macroscale (coupon level). The second type of hierarchy is according to the level of structural complexity of the investigated entity. These complexity levels are also known as ‘building blocks’, which originates from the substantiation of aircraft components [Mil03]. Applications with building block hierarchy usually target larger length scales (structural level), while it is not required to cover multiple length scales in a sense where constituent models are derived and integrated between length scales. However, similarly to the multiscale analysis, a fundamental part of the building blocks is the integration of gained knowledge from one level to the other

2.4 Virtual testing

25

starting with small specimens followed by structural elements, sub-components, components, and eventually the full scale product [Mil03].

Figure 20 Hierarchy in virtual tests; a) multiscale analysis [Oke14]; b) building blocks [Mil03]

Therefore, the building blocks follow the testing pyramid, which is an established concept in the aerospace industry to minimize cost and effort of structural testing [Bre16]. Typical building blocks are illustrated in Figure 20 b). Regardless the type of hierarchy, it can be distinguished between bottom-up and top down progressing through the hierarchy levels [Cox08], [Oke14]. The former, is based on the determination of the mechanical constituent behavior from lower to higher hierarchy levels. In contrast, top down progressing begins with macroscopic analyses, which may be detailed by investigations at lower levels based on engineering necessity. Top down also includes deriving microscopic material behavior from macroscopic tests. Another aspect of virtual testing is the consideration of statistical uncertainties in boundary conditions, material properties, loads and geometry. Such a probabilistic analysis enables to predict the scatter in experimental results based on statistical data and mathematical algorithms [Mos95]. Due to its complexity, probabilistic analysis can be considered as distinct sub-field with its own extensive literature. This was out of the scope of the present work. Uncertainties were therefore not considered. Virtual testing approaches Several authors have synthesized the previously introduced aspects into comprehensive virtual testing approaches. An early example is the approach for constructing physical models of materials by Ashby [Ash92]. He summarized his approach using a flowchart with nine stages (Figure 21). The first three stages correspond to the problem analysis

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phase where the problem is firstly identified, then the requirements in terms of inputs and outputs are defined and lastly the physical mechanisms that govern the material behavior are identified. Subsequently, the model precision or level of detail is targeted. He stresses, that the model development should be an iterative process, where the first model is of less detail enabling to predict the outputs within only a factor of 10 in order to identify important variables. In the following model construction stage existing modeling approaches and material models are employed to generate the desired output. Stages 6 and 7 correspond to the model implementation, which are followed by the interrogation and application of the model. The Ashby flowchart is unique in a sense that it provides sequential steps, which may serve as general guide for developing physical models. In addition, the described concepts are so universal that they are still up-to-date three decades later.

Figure 21 Flowchart for constructing physical models of materials by Ashby [Ash92]

2.4 Virtual testing

27

Cox et al. [Cox08] established a schematic for virtual tests describing the interaction between the different components. This structure is illustrated in Figure 22. Here, the central column sums up typical hierarchical levels, which are linked by multiscale concepts. The definition of scales, phenomena to be modelled and idealizations at each scale depend on the physics discovered in multiple types of specialized laboratory experiments (right column). Lastly, there are different types of engineering tests, which provide data for model calibration via inverse problem methods. This calibration is additionally supported by the laboratory experiments.

Figure 22 Structure and components of virtual tests according to Cox et al. [Cox08]

LLorca et al. [LLo13] suggested a local-to-global virtual testing strategy complemented by virtual processing in order to account for relevant material aspects resulting from manufacturing processes. The approaches of Ashby, Cox et al. and LLorca et al. originated from materials science and therefore implemented a multiscale hierarchy. The hierarchy based on structural complexity has evolved into the Building Block Approach (BBA) [Mil03]. The building blocks are typically processed in a bottom up manner, while it is assumed that the structural behavior at lower levels is directly transferable to specimens at higher levels of complexity. Each building block is characterized by a synergetic combination of tests and simulations as well as supporting technologies, while there is no standardized methodology for determining what tests and analyses are required in the different building blocks or even what building blocks should be investigated in the

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first place. This is highly dependent on the particular details of the investigated structure and loadings. The original integration of the approach is illustrated in Figure 23. The BBA is primarily intended for the development of structural aircraft components made of composites. However, due to the parallel interactive integration of tests and simulations up to component level it can also serve as approach for developing virtual test frameworks. In this context, Davies and Ankersen [Dav08] proposed virtual testing to reduce the testing in the intermediate building blocks of the test pyramid. They demonstrated this by implementing a virtual test of a composite T-joint. Johnson et al. [Joh15] developed a crashworthy aerospace composite component documenting the parallel development of the component and the virtual test model using the BBA. There are also examples for virtual test approaches in the literature, which are based on a combination of multiscale analysis and building block approach. Ostergaard et al. [Ost11] proposed an analysis framework where global-to-local multiscale analysis is applied to identify regions of interest in top-down manner, while building blocks are implemented for method development and validation in order to establish a detailed model of the region of interest. Abdi et al. [Abd09] developed a multiscale progressive failure and probabilistic analysis, which is embedded in FAA composite material certification requirements based on the building block approach.

Figure 23 Integration of building blocks [Mil03]

Virtual testing of sandwich structures The literature provides some examples where virtual testing frameworks were implemented for sandwich structures. Heimbs [Hei08] investigated aircraft cabin interior monuments such as hatracks made of sandwich panels hierarchically, while each level was characterized by extensive experimental and numerical studies. He suggested a multiscale approach, which enables to determine macroscopic honeycomb properties from

2.4 Virtual testing

29

mesoscale simulations of the cellular core. Furthermore, different joint designs were investigated, and numerical models were derived for implementation in a full-scale model, which enables global failure prediction of the investigated monuments. While Heimbs did not explicitly abstract or describe his approach as a whole, his work certainly reflects a virtual testing approach in the previously outlined sense. In a similar work, Zinno [Zin10] developed a multiscale approach for the design of sandwich structures for application in passenger train carriages. He implemented a multiscale hierarchy that is suitable for sandwich structures and he outlined the experimental, theoretical and numerical studies required on each level (Figure 24). The work culminated in the design of a novel train roof made of sandwich panels, while particular focus was put on the joint design and impact toughness. In addition, there are several less extensive studies. Giglio, Manes and Gilioli [Gig12], [Gig12] consecutively investigated a Nomex honeycomb core under compression and a sandwich beam with the same core under bending using an experimental-numerical approach, while integrating the results from the lower core level to the following sandwich beam level. Other studies where detailed experimental-numerical investigations on the sandwich core were successfully integrated in bonded sandwich panel models include Castanie et al. [Cas13], [Hei13], [Men13], [Fis09], [Kil13]. These studies were focused on the prediction of impact damage. With regards to sandwich panel joints, Bunyawanichakul et al. [Bun05], [Bun08] developed a non-linear FE-model for the pull-out loading of potted honeycomb inserts by integrating sub-models of relevant constituents into a synthesized top level model. The sub-models included threepoint bending of the bonded sandwich and compression of the potting.

Figure 24 Multiscale approach for the design of sandwich structures by Zinno [Zin10]

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2.5 Assessment of the state of the art and need for further research The assessment of the reviewed state of the art with respect to the scope of the present thesis is categorized into three groups, virtual testing, computational modelling of honeycomb sandwich structures and sandwich panel joint design. Each group is addressed in the following. Virtual testing The general concept of virtual testing is well described in the literature. These resources provide a solid foundation for the implementation of a virtual testing approach for the proposed field of application. With regards to honeycomb sandwich structures, the works of Zinno [Zin10] and Heimbs [Hei08] describe adequate hierarchy levels to be considered. However, these two authors were focused on the prediction of the full-scale mechanical behavior (component level). Therefore, they did not study the failure behavior in the joints in detail. In contrast, the present work concentrates entirely on sandwich panel joints (illustrated in Figure 25). This is a much more localized scope, which requires a higher level of detail. This has an effect on the scope and the focus within the hierarchy levels. Such an implementation for detailed analysis of sandwich structure joints has not been described in the literature. Compo- i.e. nent Cabin Level 4 module Sub-components Level 3 Joints & Interfaces Structural elements Level 2 Bonded sandwich panels

Scope of the present work

Scope of Zinno and Heimbs

Level 1 Constituents Honeycomb, face sheets, adhesives Figure 25 Identified hierarchy levels for investigation of sandwich structures

Computational modelling of honeycomb sandwich structures As previously outlined, there are numerous studies on computational modelling of honeycomb sandwich structures. In order to put them in relation to the scope of the present work, the reviewed studies were classified according to the computational level and the hierarchy levels they address. The computational level is defined as the capability of the model to predict failure. Simple models merely enable preliminary estimations of the structural strength. More sophisticated models enable the prediction of damage initiation up until true failure prediction including progressive damage. This is illustrated in Figure 26 using a plot like graph, while only those models are classified that are directly

2.5 Assessment of the state of the art and need for further research

31

linked to failure modelling of sandwich panel joints. On the left of the graph, there is a cluster with authors, who solely model joints on sub-component level without covering multiple hierarchy levels. These models are limited in their capability to predict the failure of the joints. Only the detailed models of Roy et al. [Roy14] and Silmane et al. [Sli17] enable the prediction of damage initiation. The two virtual testing studies of Heimbs and Zinno stand out, since they cover all four hierarchy levels. To less extend this also applies to Bunyawanichakul et al. [Bun08], whose studies come closest to the scope of the present work. However, their 3D-continuum model was not able to capture the progressive damage of inserts and the preceding hierarchy levels were not investigated thoroughly. In the bottom right of the graph, there is a cluster of authors, who established detailed models of cellular sandwich cores and successfully implemented them into bonded sandwich panel models. These models have the highest computational level in the reviewed literature. However, they do not go beyond the bonded panel level. There is no computational model for sandwich panel joints that is able to predict progressive damage up until failure. Hierarchy levels / scope

Subcomponent

Structural element

Contstituent

Bianchi Tsouvalis Smith Thomsen Zinno Roy Silmane Heimbs Bunyawanichakul Castanie Kilchert/Fischer Giglio/Manes/Gilioli Present thesis

Component

Computational level

Damage Failure Preliminary initiation prediction design Figure 26 Overview and classification of computational models for detailed analysis of sandwich structures with focus on sandwich panel joints

Sandwich panel joint design Once implemented, virtual tests enable quick and inexpensive design studies. In this context, many of the reviewed models were implemented for parameter and sizing studies [Tso06], [Rag08], [Bul08] or strength variation studies [Rag08], [Sli17] on existing joint designs. While the models of these studies contribute to a better understanding of the

32

2 State of the art

mechanical effects, conclusions regarding the actual structural performance of the investigated joints are difficult to draw, due to the preliminary analysis character of the applied models. As a result of this, there is only one study known that applied a computational model for the development of a new joint design [Lim11]. Beyond that, there are few additional novel joint designs described in the literature, all of which depended on real-world testing for evaluating the mechanical performance. Furthermore, the available novel joint designs are mostly based on co-fabrication, which requires bonding during panel fabrication. For cabin interior applications this is less favorable since small lot sizes require flexible manufacturing processes, such as post fabrication bonding. Need for further research Figure 27 illustrates the assessment of the state of the art and the need for further research. With respect to the problem statement, the gap in the literature is visualized in qualitative manner. The present work attempts to close these gaps. With regards to virtual testing, a framework specifically for sandwich panel joints is proposed. This is a meaningful addition to the state of the art, since existing frameworks do not address the specific requirements for detailed sandwich panel models up until sub-component level. In the context of computational sandwich models, the present work closes the gap between existing detailed non-linear core models and the available sandwich panel joint models. Lastly, with respect to sandwich panel joint design, the understanding of the prevailing mechanical effects is improved by the application of failure predicting models. Furthermore, the development of a novel insert design using the implemented virtual testing framework is demonstrated. This is an addition to the limited literature on novel sandwich panel joints in particular for post-fabrication processes. No post-fabrication novel joint designs

Covered by available literature

Limited application of computational models

Not covered by available literature

Virtual testing of sandwich panel joints

No virtual testing approach for sandwich panel components

No failure predicting models for sandwich panel joints

Figure 27 Visualization of the need for further research based on the state of the art

3

Overall concept of mechanical characterization

In the framework of this thesis a multitude of experimental and numerical studies on sandwich structures were performed. With regards to the Building Block Approach and the previously introduced hierarchy levels (Figure 25) the performed studies can be associated with a specific level. The following chapters 4 to 6 are each dedicated to one of the three investigated hierarchy levels, constituents, structural elements and sub-components. Within these chapters the investigated materials are firstly summarized before the experimental setups and results are presented. In case of chapters 4 and 5, the performed experiments are subsequently implemented as virtual tests. This includes numerical studies for the implementation and verification of suitable material models and modelling approaches. Lastly, the numerical model parameters are calibrated based on the experimental results. Chapter 6 corresponds to the sub-component level and solely describes the experiments on different joint configurations. The development of virtual tests for this top-level is the objective of the proposed virtual testing approach. This is described in chapter 7 using the experimental results of chapter 6 as reference and for validation. Figure 28 illustrates the attribution of chapters 4 to 6 to the hierarchy levels. Chapter 6

Sub-components Joints & Interfaces

Chapter 5

Structural elements Bonded sandwich panels

Chapter 4

Constituents Honeycomb, face sheets, adhesives

Figure 28 Visualization of the overall concept for the mechanical characterization

The presented scope is part of a superordinate building block approach for aircraft cabin interior, which has been jointly developed at the Institute of Product Development and Mechanical Engineering Design at Technische Universität Hamburg. This approach addresses two main challenges in the product development of aircraft cabins. Firstly, the © Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_3

34

3 Overall concept of mechanical characterization

high product variety due to individual customer requirements and the optimization of lightweight structures to further increase fuel efficiency. Both aspects require increasing effort for structural simulation and testing in order to validate the mechanical product properties during the development phase. High product variety, results in additional effort due to airworthiness regulations, which require that every variant needs to be substantiated and lightweight design essentially depends on accurate mechanical characterization to reduce reserve factors. The superordinate approach tackles these challenges by providing methods for synergetic combination of test and simulation based on the building approach, with the objective of reducing the physical testing effort. The approach additionally considers both, static and periodic dynamic (i.e sustained engine imbalance) mechanical properties. This distinction is necessary since, the dynamic behavior is governed by mechanical effects which are usually neglected in static analyses (mass, damping etc.). At the same time, periodic dynamic characterization is generally less focused on damage prediction. As a result, the hierarchy levels and the investigations within the different levels differ significantly between static and dynamic contexts. The present thesis contributes to the superordinate approach by providing a virtual testing approach for sandwich panel joints, which enables the virtual evaluation of numerous design alternatives at reduced physical testing effort. Figure 29 illustrates the contribution of the present work to the superordinate approach.

Figure 29 Present thesis within superordinate building block approach for cabin interior [Kr16]

4

Mechanical characterization on constituent level

In composite sandwich construction, three main constituents are of primary interest on constituent level. These include core, face sheets and adhesives. In case plastics are used for load introduction elements, such as inserts, these materials may be also of interest on constituent level. Additionally, used metallic elements are usually the strongest component in sandwich construction. Therefore, they do not require a detailed analysis. In addition, elastic material properties are readily available for common metals. This chapter describes the mechanical characterization of the relevant constituents in the framework of the present thesis.

4.1 Sandwich core The two most important mechanical properties of the core are its transverse shear and out-of-plane compressive resistance. These are also the properties that are typically given by core manufacturers. For detailed analyses of sandwich joints, the out-of-plane tensile properties may be additionally of interest. Honeycomb cores have generally very low in-plane mechanical properties. Hence, they do not contribute to the overall in-plane strength of a sandwich panel and it is common practice to make assumptions regarding the in-plane properties rather than doing additional tests. Therefore, there are three tests that are of particular interest for the mechanical characterization of the core – transverse shear, flatwise compression and flatwise tension. In the performed experimental study, structural tests were only conducted on cured honeycomb cores. Additional tests on the core constituents Nomex and phenolic resin were left out for different reasons. Firstly, in the framework of the present thesis the macroscopic core behavior is of primary interest. Therefore, assumptions for the mechanical behavior of its constituents are tolerable, as long as the macroscopic behavior is predicted accurately. Another aspect is the accessibility of the base materials. Core manufacturers generally do not disclose details of their fabrication processes, making it difficult to acquire comparable sets of the constituents. In addition, there are some studies available in literature, which

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_4

36

4 Mechanical characterization on constituent level

served as reference for the base materials. Therefore, the constituent material properties are derived in top-down manner using the results of macroscopic core tests. This is done for the two core modelling approaches detailed meso-scale and homogenized 3Dcontinuum elements. In the following, the performed experimental and numerical studies are described.

4.1.1 Materials In the framework of the present thesis, Nomex honeycomb cores with a cell size of 3.2 mm and a density of 48 kg/mm³ manufactured by EURO-COMPOSITES [EUR10] are investigated. This core is typical for aircraft interior applications and complies with the Airbus specification ABS 5035 [Air14]. In honeycomb manufacturing, Nomex of the Type 412 is usually applied. Due to the dipping process during fabrication (see 2.1.2), Nomex honeycomb is a bonded composite material comprising two constituents, Nomex paper and phenolic resin as coating. Both constituents are described in the following before the analysis of the bonded honeycomb core is presented. Nomex T412 Nomex paper retains the typical asymmetric stress-strain behavior of its aramid fiber components, with high tensile strength and comparably low compressive strength [War01]. The mechanical material properties of Nomex T412 were provided on request by its manufacturer DuPont. They are summarized in Table 3 for different paper thicknesses. The indices in Table 3 refer to the material directions of the Nomex paper as described in Figure 4 on page 8. There are only few additional references for the mechanical properties of Nomex paper. One of which being the work of Roy et al. [Roy14], who investigated Nomex T410. When comparing both sources some differences become evident in particular when it comes to the material strength. This may be attributed to the fact that different Nomex Types are compared. Regarding Poisson’s ratio, Roy et al. determined ηNomex = 0.193, while DuPont did not provide any reference. Table 3 Material properties of Nomex T412 in compliance with ASTM D828 [AST97] acc. to DuPont Nomex Type

Thick. [µm]

Density [g/cc]

E1 [MPa]

E2 [MPa]

s1 [N/mm]

s2 [N/mm]

d1 [%]

d2 [%]

2T412

47 - 65

0.54-0.94

3000

1700

3.63

1.23

6.1

3.5

3T412

71 - 91

0.67-0.91

3000

2000

6.01

2.33

6.7

5.1

4T412

94 - 117

0.72-0.94

3100

2200

6.13

1.70

8.0

5.3

Phenolic resin Phenolic resin is a brittle synthetic polymer with low tensile strength if compared to its compressive strength [Pil10]. The literature provides a limited number of references for

4.1 Sandwich core

37

its mechanical properties. The following table summarizes the identified references, where E refers to the elastic modulus, sT and sC refer to the compressive and tensile strength and ν to Poisson’s ratio. Table 4 Available material data references for phenolic resin Reference

Resin type

E [MPa]

sT [MPa]

sC [MPa]

νphen

ρresin [g/cc]

Redjel [Red95]

84055 catalyzed by 3 per C 1650

5160

27

80

-

1.25

Roy et al. [Roy14]

Hirenol KRD-HM2

4940

-

-

0.389

1.34

Liu et al. [Liu15]

unknown

5800

60

180

0.389

1.38

Phenolic Resin Techn. Hand. [Nii07]

Moulded unfilled phenolic resin

6100

48-55

138172

-

-

It is unknown what exact type of phenolic resin was used for the fabrication of the investigated honeycomb core. According to Taylor [Tay10], solvent based systems such as provided by Durez1 and GP2 are typically applied. The Hirenol KRD-HM2, which was investigated by Roy et al. [Roy14], was developed for use in honeycomb manufacturing as well. It this therefore assumed that the phenolic resin in the honeycomb core of the present work is comparable to this type. Considering the available literature, it can be summarized that the Young’s modulus appears to be consistent in the range of 50006000 MPa. The strength seems to differ more significantly, while Redjel [Red95] reported considerably lower values. However, the references are consistent in the ratio of compressive and tensile strength sC / st ≈ 3. Bonded honeycomb core In order to characterize the bonded honeycomb core, polished honeycomb sections were investigated under the microscope (Figure 30). These sections were prepared directly from the cured sandwich panels, which were cut to obtain the specimens for the experimental study. The microscope measurements indicate that the cell size c of the investigated honeycomb core match the specification of the manufacturer (here c = 3.2 mm). However, in order to represent the actual honeycomb grid the two other edges a and b have to be adjusted leading to a non-regular hexagon, which is elongated in Ldirection. In Figure 30, multiple additional typical imperfections of honeycomb cells are evident. These include the curved free single cell walls as they are bent in the expansion process during fabrication. Other imperfections include uneven or pre-buckled cell walls as well as varying cell wall thicknesses resulting from inconsistent thickness of the Nomex paper and the phenolic resin coating. In present thesis, these thicknesses are

1

Manufacturer of thermoset resins, since 2013 part of Sumitomo Bakelite Co,Ltd - https://www.sbhpp.com

2

Georgia-Pacific Chemicals LLC, manufacturer of thermoset resins

38

4 Mechanical characterization on constituent level

therefore determined by averaging 50 measurements across different specimens. Lastly, there is typically significant resin accumulation in the corners, where the double walls separate into single walls. According to the microscope measurements, these accumulations make up the bulk of resin coating (about 80%) in case of the investigated honeycomb core. This is determined by approximating the area of the resin corners as triangle and averaging the triangle size of 50 corners over different specimens. These corner accumulations represent bonded pillars along the hexagon edges, thus considerably reinforcing the cell walls turning them into stiffened shells. According to Aminanda et al. [Ami05], these reinforcements significantly affect the out-of-plane strength of the honeycomb core. The actual hexagon geometry as derived from the microscopic images is summarized in Table 5 according to the nomenclature in Figure 30. Table 5 Hexagon geometry of the investigated honeycomb according to microscopic images a [mm]

b [mm]

c [mm]

ϕ [deg]

1.9

2.0

3.2

53.1

Single wall thickness [µm] 51 ±6

Double wall thickness [µm] 104 ±14

Resin coating [µm] 3 ±0.5

Resin accum. area [µm²] 43000 ±10000

Nomex paper

50 µm

Resin coating

ϕ

c

b a Approximated area of resin accumulation Figure 30 Microscopic image of polished honeycomb section

4.1 Sandwich core

39

4.1.2 Experimental analysis All experiments were conducted on honeycomb core specimens, which were cut directly from a cured sandwich panel comprising the investigated core and bonded glass fiber fabric reinforced phenolic resin skins. The skins consisted of prepregs complying with the Airbus standards ABS5047-02 and ABS5047-08 [Air15]. The nominal thickness of the tested core was 18.5 mm. The configuration of the sandwich panel, which served as source for all specimens is illustrated in Figure 31. For each test series four specimens were prepared. The conducted tests along with the obtained results are described in the following subsections. Test results are given as stress strain curves, where the stress corresponds to the cross-sectional area of the entire specimen.

Figure 31 Sandwich panel configuration, which served as source for the investigated specimens

Flatwise compression The flatwise compression test allows to determine the out-of plane compressive modulus and strength of the core. The test can be performed on “bare” core specimens or alternatively on cores that are bonded to plates or face sheets (“stabilized”). Since the specimens of the present study were cut from bonded sandwich panels, the obtained results represent stabilized compressive core properties. The test is standardized for instance by ASTM C 365 [AST00] or DIN 53291 [DIN291]. Table 6 summarizes the test parameters applied in the performed experimental study. Since the machine’s crosshead stroke was taken as displacement measurement, the machine stiffness has to be accounted for in the data post processing. This is done using a simple approach, where the machine stiffness is compensated by assuming a series of springs comprising the machine and the specimen. The measured force-displacement curves represent the combined stiffness of this series of springs. The machine stiffness can be determined by compressing the bare pressure plates. With this information the specimen stiffness can be calculated. The ratio of measured combined stiffness and actual specimen stiffness yields a factor which was used to scale the measured crosshead displacement, thus compensating the machine stiffness. The compensated results in terms of stress strain relationship of the four tested specimens are illustrated in Figure 32 while both, stress and strain, refer to the initial cross section and thickness of the specimens. The test results

40

4 Mechanical characterization on constituent level

indicate little over all scatter and reflect the typical curve progression of honeycomb compression tests. The focus of the present study is on the stress-strain relationship up until a strain of about 0.2. This enables the consideration of the initial stiffness, peak stress and the following plateau stress. The behavior of the final densification phase is not presented here, since it was not relevant for the scope of this thesis. Table 6 Summary of performed flatwise compression tests

Test standard

ASTM C 365 [AST00]

Specimen dimension

60 mm x 60 mm x18.5 mm

Loading rate

1 mm/min

Testing machine

Shimadzu AG 25TB

Load cell

Shimadzu SFL-25AG (25kN)

Disp. measurement

Machine crosshead stroke

a)

b)

Figure 32 a) Experimental setup compressive tests; b) determined stress strain relationships

Flatwise tension This test method primarily allows to determine the flatwise tensile modulus and strength of a sandwich core. In case a bonded sandwich panel is tested it may also enable to determine the bond between core and face sheets. In this test, the specimens are subjected to a tensile load normal to the sandwich plane, by means of self-aligned rigid loading plates in order to ensure centric load transmission. In the present work, the relative dis-

4.1 Sandwich core

41

placement of the loading plates was measured using an external laser displacement sensor. Therefore, no machine stiffness compensation is required. For this test, there are established standards such as ASTM C 273 [AST94] and DIN 53292 [DIN292]. The test details of the present study are summarized in Table 7. Table 7 Summary of performed flatwise tension tests

Test standard

ASTM C 273 [AST94]

Specimen dimension

60 mm x 60 mm x18.5 mm

Loading rate

2 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-10 kN

Disp. measurement

External laser sensor - Micro Epsilon optoNCDT 1630-20

b)

Figure 33 a) Experimental setup tensile tests; b) stress strain relationship of tested specimens

The test results in terms of macroscopic stress-strain relationship along with an image of the test setup are given Figure 33. Analogous to the previous compression tests, the stress and strain ware derived from the measured force-displacement curve. All tested

42

4 Mechanical characterization on constituent level

specimens failed due to tensile core rupture. The results indicate brittle material behavior with linear deformation up until catastrophic failure. This behavior has also been observed by other researchers [Hei08], [Liu15], [Roy14]. There is little to no scatter in terms of modulus, while the strength showed scatter of 15%. Transverse shear The transverse shear test enables to determine the shear modulus and strength parallel to the sandwich plane. Analogous to the flatwise tensions tests, the specimens were bonded to loading plates in order to transmit the shear loading, while the relative displacement of the loading plates was measured by an external laser sensor. As with the previous core tests, transverse shear is a standardized test (ASTM C 273 [AST00] and DIN 53294 [DIN294]). It should be noted that this test does not produce pure shear. However, according to the test standards, secondary stresses have minimum effect as long as the specimen length is sufficient. Since honeycomb cores have two distinct material directions (L and W) the transverse shear tests were performed for both material directions. In the following, WT and LT refer to transverse shear in L- and W-direction respectively. Additional test details are summarized in Table 8. The tests reveal the typical curve progression for Nomex honeycomb transverse shear tests, confirming previous studies on the same material [Hei08]. For both material directions, the linear elastic deformation is followed by shear buckling of the cell walls which leads to a considerable drop to a stress plateau. This plateau is held until the cell walls start to tear, which eventually leads to catastrophic failure. In case of LT-shear, the load drop due to buckling is more distinct, while the stress plateau ends at considerably lower strain if compared to WT-shear. The test results along with an image of the test setup are given in Figure 34. As with the previous tests, the derived transverse shear curves show little scatter in terms of stiffness, while the strength deviated noticeably (about 10%). Table 8 Summary of performed transverse shear tests

Test standard

ASTM C 273 [AST00]

Specimen dimension

150 m x 50 mm x 18.5 mm

Loading rate

2 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-10 kN

Disp. measurement

External laser sensor - Micro Epsilon optoNCDT 1630-20

4.1 Sandwich core

a)

43

b)

c)

Figure 34 a) Experimental setup of transverse shear tests; b) stress strain relationship of tested specimen in L-direction; c) stress strain relationship of tested specimen in W-direction

Summary The obtained test results are generally in the range of the given mechanical properties from manufacturers for the same Nomex honeycomb configuration, while all determined mechanical properties tend to be inferior if compared to typical manufacturers data. This is summarized in Table 9, where the test results are averaged over all specimens for each test and opposed to the data from two manufacturers. In case of tension, the manufacturers give no reference. It can be noted that the determined tensile properties exceed the compressive ones in terms of both, strength and modulus, by about 12%. This trend was has also been observed by Liu et al. [Liu15].

44

4 Mechanical characterization on constituent level

Table 9 Obtained test results in comparison to given properties from manufacturers Compression Bare

HRH-10

1/8-

3.0 [Hex99] ECA-3.2-48 [EUR10] Test results1

Shear

Stabilized

Tension

LT-Direction

WT-Direction

Str.

Str.

Mod.

Str.

Mod.

Str.

Mod.

Str.

Stabilized Mod.

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

2.07

2.24

137

1.21

41

0.69

24

-

-

2.10

-

-

1.32

48

0.72

30

-

-

-

2.15

131

1.28

36

0.60

20

2.45

148

4.1.3 Numerical modelling on meso scale In the recent past, numerous studies on detailed finite element modelling of sandwich core materials, such as honeycomb, have emerged. One of the most prominent applications is the out-of-plane impact modelling of sandwich structures, which is extensively reviewed by Castanie et al. [Cas13] in case of honeycomb cores and by Heimbs [Hei13] for fold cores. Nomex honeycomb is among the most studied sandwich core materials in the literature. Therefore, there are numerous studies which cover the prediction of the macroscopic core behavior using detailed meso-models. The majority of the available studies implement two-dimensional elements to model the cell wall material. Giglio et al. [Gig12] presented a comparative study on out-of-plane compression of Nomex honeycomb cores using two-dimensional and three-dimensional elements. They concluded that 2D and 3D elements enable the prediction of the first failure well, while 3D elements achieve better results in the following plateau of the stress-strain curve. However, they also reported high computational effort when running 3D element simulations. Regardless the element dimension, there are three prevailing approaches to modelling Nomex cell wallpaper material in the literature. The most simplistic approach is based on isotropic linearly elasto-plastic material behavior in a single layer. It therefore neglects not only the orthotropy of the Nomex paper but also its layered composition. This approach has been established to be sufficient for predicting the out-plane compression of Nomex cellular sandwich structures [Foo08], [Hei07], [Asp13], [Akt08], [Gig12], [Gig12]. The second approach, applies a single layer orthotropic linearly elasto-plastic material model, which provides more freedom for modelling the directional mechanical behavior [Roy14], [Roy13], [Roy14], [Hei08], [Ami05]. However, these single layer approaches are limited when it comes to the representation of the initial failure of the phenolic resin

1

Macroscopic test results serve as reference for the numerical 3D-continuum core model throughout the present work

4.1 Sandwich core

45

coating. The third approach tries to overcome this by implementing a three-layered property set with a brittle material model for the phenolic resin coating and an elastoplastic material model for the inner aramid paper [Fis09], [Kil13], [Bar11], [Liu15], [Liu15]. This approach promises a more realistic failure progression. Based on the reviewed literature, a suitable modelling approach for detailed meso-scale models is developed. This is described in the following. Model description Four-node planar elements of the S4R type are implemented for the cell walls. The cell geometry is defined according to the cross-sectional measurements given in Table 5. Mesh convergence studies show that a mesh size of 0.4 mm (equivalent to 5 elements along cell wall width) provides a good trade-off between convergence and computational effort in particular for application in larger sandwich models [See14]. Since on constituent level solely the sandwich core is investigated, a mesh size of 0.25mm (8 elements along cell wall width) is implemented in order to increase computational accuracy. This mesh size is comparable to previous studies on Nomex meso scale modelling [Roy14], [Gig12], [Hei08]. The honeycomb core is modelled excluding the face sheets. Rigid bond between face sheet and core is assumed. Therefore, the nodes in the top and bottom plane are each defined as rigid body. The bottom rigid body is constrained in all six degrees of freedom (DoF). The boundary conditions of the top nodes depend on the load case. In compression and tension a constant velocity is prescribed in T direction, while all remaining DoF are constrained. In case of transverse shear, a constant velocity is prescribed in W/L direction and all remaining DoF are constrained excluding the T direction. These boundary conditions are summarized in Figure 35. It should be noted that Figure 35 illustrates the FE-models using a coarse mesh for clarity on the displayed nodal constraints. Due to the fact that an explicit solver is applied for quasi-static simulations, mass scaling and increased loading rates are implemented to reduce the computational time. Appropriate parameters for both model parameters have been established through sensitivity studies, in order to make sure that the simulation results are not affected. In addition, hourglass control is activated using the ABAQUS default settings. Another measure for keeping the computational time within manageable limits is reducing the total model size if compared to the tested specimens. In case of honeycomb cells, this is generally done by defining a unit cell (UC) along with appropriate boundary conditions, which represent the periodicity of the cellular core. The boundary conditions depend on the implemented unit cell geometry and on the load case, while the defined unit cell geometries of the present work are illustrated in Figure 36. The considerations that lead to these unit cells have been described in [See17]. All simulations throughout the present thesis were performed using ABAQUS 6.14-1.

46

4 Mechanical characterization on constituent level

Figure 35 Implemented boundary conditions of the simulation models [See17]

Figure 36 Implemented unit cell geometries based on regular hexagons [See17]

Consideration of imperfections Detailed meso scale models can be combined with various modelling approaches for considering imperfections of cellular sandwich cores. It can be distinguished between local geometric and material imperfections and global imperfections regarding the overall hexagon grid. The former can be implemented by randomly distorting all cell wall

4.1 Sandwich core

47

nodes (‘node shaking’) [Hei08], assigning random material properties and/or wall thickness [Hei08], [Asp13], [Kar13], [Fis16], pre-buckled cell walls or cell wall waviness [Hei08], [Roy13], [Fis16], angular deviation of the cells [Fis16] and actually determined geometry imperfections using CT-scans [Hei08], [Fis09], [Fis16]. These approaches have proven to effectively approximate local imperfections of actual honeycomb cells. A more simplistic approach is applying cell geometry along with globally reduced material properties. Heimbs [Hei08] showed, that this approach enables a good correlation between numerical and experimental results, while still reproducing realistic buckling patterns. From the available literature, it can be concluded that to some extend model calibration is generally required in order to match test results, independently of the level of model detail or the implemented approach to modelling imperfections. Therefore, the latter simplified approach is implemented in the present work, since it appears to be most efficient and thus well suited for engineering applications. As a result, all derived honeycomb material properties of the present thesis represent reduced properties including local geometric and material imperfections. However, the imperfect global hexagon grid of the investigated specimens is considered by the implemented models (a ≠ b and ϕ ≠ 60° in Figure 30). This is required since this imperfection has a different effect on the macroscopic mechanical behavior depending on the loading direction. For instance, in case the hexagon grid is elongated in L-direction (ϕ < 60°), the superiority of the LT-shear strength if compared to WT is enhanced. This cannot be captured by globally reduced material properties. Preliminary numerical studies In case of the honeycomb core, additional preliminary studies were performed prior to the material parameter calibration. These included the determination of a suitable model scale as well as hexagon geometry. The performed preliminary studies are described in the following. Model scale A previous study from Wilbert et al. [Wil11] showed that despite the implementation of an appropriate unit cell along with periodicity conditions prescribed on the free honeycomb edges, the macroscopic stress-strain progression obtained from simulation models correlates with the number of included unit cells. They achieve convergence after a few iterations. However, their results could not be transferred to the present study, since different unit cells and boundary conditions were defined. In addition, the study of Wilbert et al. was restricted to out-of-plane compression. In the present work, an appropriate model scale was determined through convergence studies based on the previously established boundary conditions for all three considered load cases. For a more detailed description of the performed convergence studies it is referred to [See17]. The conclusively determined model scales for each load case are illustrated in Figure 37.

48

4 Mechanical characterization on constituent level

Figure 37 Implemented model scales for the different load cases

Cell geometry In most of the reviewed literature a regular hexagon geometry was implemented for detailed honeycomb simulations. There are few studies where curved or S-shape hexagon geometries, which more closely resemble actual honeycomb cells, were applied [Roy14], [Fis16]. In the framework of the present thesis, it was investigated what hexagon geometry is best suited for application in meso scale models. This was done in a comparative study, where three candidate geometries are benchmarked. The three geometries, include a regular hexagon (Reg) with a cell size as given by honeycomb manufacturers, an irregular hexagon (iReg) with dimensions as derived from microscopic images (see Table 5) and an irregular hexagon with curved cell walls (iRegC), which is modelled to resemble the actual cells. The three investigated hexagon geometries are illustrated in Figure 38 a) along with a microscopic image of an actual honeycomb cell. It should be noted, that the iReg and iRegC models have the exact same macroscopic density, while the Reg model is slightly denser due its generally smaller cell size. In the benchmark, simulations under compression, shear LT and shear WT were performed with the three candidate geometries. The models are based on the previously established model scales (Figure 37) and boundary conditions (Figure 35), while an isotropic elastic perfectly plastic material model is implemented. The macroscopic stress-strain simulation results in case of WT-shear are given in Figure 38 b) in comparison to the experimental curves. The general trend of these results is characteristic for all investigated load cases. The results indicate that the regular and irregular shapes yield the same curve progression, while the regular shape achieve higher strength and stiffness. This is anticipated, since the regular geometry has the highest density. In comparison, the curved geometry indicates considerably lower strength, despite having the same density as the irregular geometry. In addition, the stress-strain progression of the curved geom-

4.1 Sandwich core

49

etry differs significantly from the non-curved hexagon shapes, indicating different buckling progression due to the S-shape. In the simulation results it can be observed that in case of the S-shape (iRegC) geometry initial web crippling propagates immediately from the cell walls to the cell edges leading to a significant load drop. In case of the non-curved geometries, initial web crippling is at first contained within the cell walls only causing a kink in the stress strain relationship. The load can increase further up until the point where the yield strength of the material is reached and folding of the cell edges causes a load drop. This can be explained by the shell modelling approach, which leads to material concentration at shared angular edges. This additional material stiffens the cell walls. In case of the curved geometry the stiffening effect is less pronounced, since the cell walls join at very small angle resulting in a more distributed material overlap. a)

b)

Figure 38 a) Considered cell geometries for comparative study; b) Macroscopic stress-strain curve for the three investigated cell geometries in case of Shear WT (height 19mm) [See17]

In summary, the curved model leads to stress-strain relationships that differ considerably from the experimental results, despite having the most accurate geometry representation of the actual honeycomb cells. It appears that the curved shape requires a more refined modelling approach where the resin accumulations and coating are modelled in high detail. In contrast, the non-curved models reproduce the experimental stress-strain progression well. It seems that the strong vertical cell wall edges of the shell modelling approach represent the reinforcement and stiffening due to the resin accumulations in the actual honeycomb well. Therefore, the non-curved geometry should be favored for meso scale honeycomb models. When considering the regular and irregular hexagon shapes, the deviation in terms of strength and modulus peaks at about 10% in case of WT-shear. In order to avoid this error, it is recommended to account for globally stretched honeycomb grids when creating the honeycomb geometry. For a more detailed description of this comparative study it is referred to [See17].

50

4 Mechanical characterization on constituent level

Implementation of different modelling approaches In the preliminary studies, appropriate unit cells, boundary conditions, model scales and hexagon geometries have been determined. Based on this, the material and element section definition have been established. As previously described, there are three prevailing approaches for modeling Nomex honeycomb cores evident in the literature. These approaches are implemented and calibrated with the experimental results. In addition, one novel approach, which emerged very recently, is implemented. Figure 39 illustrates the four implemented approaches. They are subsequently described, including the implemented material and section definition. It should be noted, that the given material parameters are the result of calibration using the experimental data. SL isotropic

SL orthotropic

ML resin coat

ML resin corner

novel Figure 39 Implemented modelling approaches for benchmark [See17]

Single layer isotropic approach The first approach is based on a single layer (SL) section with an isotropic elastic perfectly plastic material model. This approach has been applied in the previously described preliminary studies. The material model is essentially defined by just three material parameters, young’s modulus Eiso, yield strength δiso and Poisson’s ratio ηiso. This approach neglects the multi-layer composition of the Nomex material. Therefore, the implemented material parameters represent homogenized parameters of the phenolic resin impregnated Nomex composite. This approach enables manipulation of the shear modulus and strength only via Poisson’s ratio, while the shear strength cannot be defined independently from the uniaxial strengths. Furthermore, compressive and tensile strength cannot be defined independently. The implemented material parameters are listed in Table 10 (left) and the material definition is plotted in Figure 40 a) in terms of a stress

4.1 Sandwich core

51

strain relationship in tension/compression. The homogenized density of the cell wall material is defined to match the nominal honeycomb density of the tested specimens (48 kg/m³). The cell wall thicknesses tsingle and tdouble are defined based on the previous microscopic measurements (Table 5), while the total wall thickness including the resin coating is considered. Single layer orthotropic approach In contrast to the previous isotropic material, the orthotropic material model enables independent definition of shear modulus and strength as well as tensile and compressive strength. Hence, it requires the definition of additional material properties. The calibrated material parameters are given Table 10 (right). The uniaxial stress strain relationship of the material is plotted in Figure 40 b). The implemented material is characterized by slight orthotropy, which represents the orthotropic nature of Nomex with different material behavior in machine (MD) and cross machine direction (XD) of the base material (see section 2.1.2). The calibrated elastic properties are in the range of the reviewed literature [Hei08a], [Roy13], while little reference is available for the strength properties. Analogous to the single layer isotropic approach, the implemented material behaves perfectly plastic. The wall thicknesses and material density are defined identical to the isotropic approach. Table 10 Calibrated homogenized material properties for single layer approaches Eiso ηiso δiso

Single Layer Isotropic 4000 MPa tsingle 0.057 mm 0.3 tdouble 0.110 mm 90 MPa ρ 1.1 g/cc

E1 E2 G12 ηorth tsingle tdouble

Single Layer Orthotropic 5000 MPa δ1t 90 MPa 4000 MPa δ1c 105 MPa 1450 MPa δ2t 60 MPa 0.2 δ2c 90 MPa 0.110 mm δ12 44 MPa 0.057 mm ρ 1.1 g/cc

Figure 40 Stress-strain relationship for single layer a) isotropic and b) orthotropic material models

52

4 Mechanical characterization on constituent level

Multi layer resin coating approach In this approach, the two constituents Nomex paper and phenolic resin are modelled separately, using multiple layers (ML) based on laminate theory. It therefore enables separate consideration of brittle failure of the resin coating and plastic deformation of the ductile aramid paper. However, this approach is generally limited to an even distribution of the resin coating over all cell walls with constant resin coating thickness. Yet, in section 4.1.1 it is established that the majority of the resin coating accumulates in the corners, while the resin coating in the middle of the cell walls is comparably thin. Implementing the multi layer approach with constant resin layer thickness requires to distribute the corner accumulation evenly over all cell walls, leading to a thick layer of coating. This can be avoided by implementing multiple shell sections with incrementally changing resin coating thickness. However, this would lead to a significantly more complicated model in terms of both, setup and calibration. Therefore, a constant resin thickness is implemented in the present work. The equivalent thickness of the resin coating is tphen = 0.012 mm after distributing the total resin volume. This equals four times the average resin thickness determined under the microscope. With this thickness the honeycomb core model has a combined density of 48 kg/m³ in case the given densities and layer thicknesses of both constituents are considered (see Table 11). The Nomex paper is modelled using the same orthotropic material model as for the single layer orthotropic approach. The linear elastic material properties are adopted from the Nomex manufacturer data sheet (Table 3). The yield strength values were calibrated based on the experimental data. The phenolic resin is modelled as isotropic brittle material, whereby the strength in tension (δphen,t) and compression (δphen,c) are defined independently. The elastic modulus, Poisson’s ratio and density are adopted from literature [Roy14], [Roy14]. As with the Nomex paper, the strength parameters were calibrated with the test data. The stress strain curves of the applied material models are illustrated in Figure 41. All applied material properties for the multi-layer resin coat approach are summarized in Table 11.

Table 11 Calibrated material properties for multi layer coating approach E1 E2 G12 ηorth tsingleNomex tdoubleNomex

Nomex paper 3000 MPa δ1t 1700 MPa δ1c 800 MPa δ 2t 0.2 δ 2c 0.051 mm δ 12 0.104 mm ρ

90 MPa 45 MPa 60 MPa 30 MPa 50 MPa 0.72 g/cc

Phenolic resin Ephen 4800 MPa ηphen 0.389 δphen,t 100 MPa δphen,c 190 MPa tphen 0.012 mm ρphen 1.342 g/cc

4.1 Sandwich core

53

Figure 41 Stress strain relationship of materials for ML resin coat approach a) Nomex paper and b) phenolic resin

Multi layer resin corner approach The last approach is intended to represent the resin accumulation in the hexagon corners in more detail. This enables to consider the uneven phenolic resin coat distribution of actual Nomex honeycombs. In order to achieve this, the previous multi layer approach is complemented with additional elements in the corners, which represent the resin accumulations, while the resin coating is modelled as thin as measured under the microscope. It is assumed that this approach performs better in case of shear loading if compared to the multi layer resin coat approach, since the artificially thickened resin coating of the resin coat approach particularly alters the shear properties of the honeycomb. Furthermore, this approach enables to model the actual curved hexagon geometry in more detail by considering the stiffening of the cell walls due to the resin corners. In order to investigate this, the ML resin corner approach is applied for two hexagon geometries, irregular and irregular curved (iReg and iRegC according to Figure 38). This approach can be considered novel, as there are very few and recent published studies that have implemented a similar concept, one of which being the work of Fischer et al. [Fis16]. In the present study, the resin accumulations are modelled as solid elements (Type C3D8R and C3D6), which are placed in the cell wall corners forming a prism with triangular cross section. The cross section area is defined according to the microscope measurements of the investigated honeycomb (Table 5). The element size is about 0.1 mm resulting in six elements within a cross section. The bond between these corner elements and the cell walls is modelled using tied contact formulations. The cell walls are modelled analogous to the previous approaches with 0.25 mm S4R elements. The implemented multi layer resin corner models are depicted in Figure 42 for both investigated hexagon geometries. The applied material models are equivalent to the multi layer resin coat approach. However due to the redistribution of the resin coating, the damage related material properties are adjusted to match the experimental results. The resulting calibrated

54

4 Mechanical characterization on constituent level

material properties are summarized in Table 12 while the stress-strain relationships of the applied material models are given in Figure 43.

Figure 42 Illustration of the multi layer resin corner approach for both investigated geometries [See17] Table 12 Calibrated material properties for multi layer resin corner approach E1 E2 G12 ηorth tsingleNomex tdoubleNomex

Nomex paper 3000 MPa δ1t 1700 MPa δ1c 1200 MPa δ 2t 0.2 δ 2c 0.051 mm δ 12 0.104 mm ρ

90 MPa 45 MPa 60 MPa 30 MPa 55 MPa 0.72 g/cc

Phenolic resin Ephen 4800 MPa ηphen 0.389 δphen,t 106 MPa δphen,c 155 MPa tphen 0.003 mm ρphen 1.342 g/cc

Figure 43 Stress strain relationships of implemented material models for ML resin corner approach a) Nomex paper and b) phenolic resin

4.1 Sandwich core

55

Results The simulation results are presented separately for the single layer and multi layer approaches. The correlation of simulation and experiments is benchmarked in terms of stress-strain relationship for all four considered load cases. This correlation is illustrated using three plots, where compression and tension in T-direction are combined in one plot and the shear directions are each given in separate graphs. The experimental results are plotted along with the simulation results. All obtained experimental curves are plotted (test scatter), while an average curve is highlighted. The simulations were carried out on a six core Intel Xeon X5680 workstation. Computational effort varies greatly between the different modelling approaches. Considering the compression load case, computation time is as low half an hour in case of the single layer approaches, while the multi layer corner approach requires more than six hours. SL approaches The simulation results in comparison to the experiments for both single layer approaches are given in Figure 44. The simulations generally approximate the curve progression obtained from the tests in all loading conditions. However, the sudden load drop shortly after maximum stress in the compression and tension tests is not captured by the simulations. It is assumed that this is due to the implemented perfectly plastic material model, which neglects brittle resin damage. The isotropic material model is established as not capable to match all loading conditions simultaneously. In the present work the material model is calibrated according to the compression experiments, which results in a good approximation of this one load case. However, at the same time the strength of all remaining load cases is overestimated. For shear loading the deviation is up to 15 %, which can be considered acceptable for preliminary or rough predictions. However, in case of tension the isotropic model exceeds the experimental curves by about 50 %. The orthotropic material model enables more freedom when calibrating the material model. Therefore, a good match of simulation and experiment is achieved for all loading conditions. However, there is one exception. The plateau stress under LT-shear is noticeably overestimated by the orthotropic material model (Figure 44 bottom left). This effect is attributed to the applied symmetry boundary conditions, which restricts the buckling and folding of the cell walls located in the symmetry planes. Additionally performed studies indicate that a larger scale along with applying a single symmetry plane would result in a better approximation of the plateau stress when using the same material parameters. Another noticeable effect is the underestimated plateau strength under compression in case of the orthotropic model, whereas the isotropic model matches the plateau of the experiments well in case of the investigated honeycomb material. This may be explained by the reduced tensile strength of the orthotropic model, which affects the cell wall folding after buckling initiation, resulting in an increased drop in macroscopic

56

4 Mechanical characterization on constituent level

stress after buckling initiation. Regarding the global damage patterns, it can be summarized that the single layer approaches approximates the buckling, folding and tearing Tension/Compression T

5 Test scatter Test average SL Isotropic SL Orthotropic

4

Stress [MPa]

3 2 1 0 -1 -2 -3 -0.2

-0.15

-0.1

-0.05

0

0.05

Strain [-] Shear LT

1.5

Shear WT

0.8

Stress [MPa]

Stress [MPa]

0.6 1

0.5

0.4

0.2

0

0 0

0.05

0.1

Strain [-]

0.15

0.2

0

0.05

0.1

0.15

0.2

Strain [-]

Figure 44 Comparison of simulation and experiment in case of the SL modeling approaches

mechanisms observed in the experiments well. This is depicted in Figure 46 in case of the orthotropic approach. However, it should be noted that the applied models do not include a failure criterion. Therefore, they cannot represent true cell wall tearing. Despite this, the implemented perfectly plastic material model results in a significant load drop in the tensile virtual tests thus macroscopically approximating tensile tearing (Figure 44 top right quadrant). ML approaches The simulation results in comparison to the experiments for both ML approaches are given in Figure 45. The ML approaches are capable of modelling the abrupt failure in tension and compression due to the consideration of brittle resin failure.

4.1 Sandwich core

57

Tension/Compression T

3

2nd peak Test scatter Test average ML Resin Coating ML Resin Corner iRegC ML Resin Corner iReg

Stress [MPa]

2 1 0 -1

Underestimated plateau strength

-2 -3 -0.2

-0.15

-0.1

-0.05

0

0.05

Strain [-] Shear LT

1.5

Shear WT

1

1

Stress [MPa]

Stress [MPa]

0.8

0.5

0.6 0.4 0.2

0

0 0

0.05

0.1

Strain [-]

0.15

0.2

0

0.05

0.1

0.15

0.2

Strain [-]

Figure 45 Comparison of simulation and experiment in case of the ML modeling approaches

As a result, these out-of-plane load cases are matched well by both implemented multi layer models. However, both ML models underestimate the plateau stress after buckling initiation in case of compression similar to the SL orthotropic approach. In terms of tension, it can be noted that the curve progression of the resin coat approach shows a second peak, which is unlike the experimental results (Figure 45 top). This can be explained by the failure progression of the constituents. The initial brittle failure of the resin coat does not cause immediate collapse of the Nomex paper. Instead the Nomex paper carries additional load until it yields, leading to the second drop. In contrast, the tensile failure progression of the resin corner approach only shows a kink due to brittle failure of the thin resin coat, while the stress increases further until the resin corner elements fail resulting in simultaneous Nomex paper collapse. Considering the two investigated hexagon geometries, it can be noted that the curved hexagon (iRegC) leads to higher compressive strength, while the tensile strength of the non-curved (iReg) and curved

58

4 Mechanical characterization on constituent level

(iRegC) hexagon configuration are about the same. This is attributed to the increased moment of inertia of the curved hexagon cell walls resulting in postponed web crippling of the compressed cell walls. However, in summary the two ML approaches lead to comparable results in tension and compression regardless the hexagon geometry. In case of shear the discrepancy between resin coat and resin corner approach is more pronounced. Once it fails due to shear, the thick resin layer of the resin coat approach leads to a distinct peak in the macroscopic stress-strain relationship. This peak is not evident in the test results. Therefore, the core’s shear strength is overestimated by the ML resin coating approach. 5 mm

Figure 46 Comparison of folding patterns in simulation and experiments [See17]

4.1 Sandwich core

59

The resin corner approach on the other hand is characterized by a considerably thinner layer of resin coat. Shear failure of this layer only results in a minor peak in the stressstain relationship. With the damage of the structure progressing, the resin corners eventually fail locally along with cell wall folding due to shear buckling. This local failure of the resin corner elements is depicted in Figure 47 in case of compression loading. In general, the resin corner approach approximates the experimental stress-strain curve well for both considered shear directions. In addition, the two investigated hexagon geometries lead to comparable results in case of transverse shear.

Figure 47 Failure of resin corner elements under compression loading at strain = 0.04 [See17]

4.1.4 Numerical modelling with 3D-contiuum elements As established in section 2.3.1, 3D-continuum elements are generally also capable to model out-of-plane core damage mechanisms, while at the same time requiring less modelling and computational effort if compared to detailed meso-scale models. In applications where core damage is only of secondary interest, this simplified modelling approach might be the preferred choice. Therefore, a homogenized core model is derived and calibrated using the experimental results. This is done using a single element of the C3D8R type, which is subjected to the four loading conditions compression, tension and both transverse shear directions (Figure 48). The boundary conditions of the model are defined analogous to the previous meso scale model (Figure 35), except that no symmetry planes are defined. As material, a generic orthotropic elasto-plastic material model suitable for 3D-continuum elements is implemented. One of the advantages of this approach is that material properties given by manufacturers or macroscopic tests, such as summarized in Table 9 on page 44, can be directly implemented in the material

60

4 Mechanical characterization on constituent level

model definition, since these properties reflect a homogenized core. Therefore, the calibration process is considerably simplified. However, the orthotropic material model additionally requires the input of in-plane properties as well as Poisson’s ratios, which are usually not covered by macroscopic tests. This is because the in-plane properties have limited impact on the macroscopic sandwich behavior. It is therefore common practice to make assumption regarding these properties. Bitzer [Bit97] suggests to use 1% of the known out-of-plane properties for the respective in-plane properties, while he suggests a Poisson’s ratio of 0.1. This approach is applied in the present work. Alternatively, analytical formulae can be applied to estimate these unknown properties. Such analytical relationships have been published by various authors. Steenackers et al. [Ste16] and Heimbs [Hei08] gave an overview on such formulae. The results of the implemented model in terms of stress-strain relationship in comparison to the experimental results are given in Figure 49. In these graphs two sets of simulation results are illustrated. One reflects the results of a calibrated material model based on the obtained experimental results. The second set represents a simulation which was based on material properties given by manufacturers (Table 9, p. 44). Since manufacturers do not indicate the plateau stress after initial core damage, the material was simplified using an elasto-perfectly plastic material model. The two implemented simulation models generally lead to a good match of the experimental results. Compression

Tension

Shear LT

Shear WT

Figure 48 Implementation of single element model for calibration of the 3D-continuum approach

4.1 Sandwich core

61

In case of WT shear, the simulation based on manufacturers data exceeds the strength of the calibrated simulation, since the provided WT-shear strength is higher than the experimentally obtained shear strength. The simplified perfectly plastic model does not enable to model decreasing stress due to cell wall buckling or tearing. This is evident in the respective stress-strain progression. In contrast, the calibrated plastic model enables to approximate the actual curve progression of the experiments including the plateau stress. Therefore, the simulation results of the calibrated material model agree better with the experimental results. Both implemented material models are given as ABAQUS input format in Appendix A1. In terms of computational effort, the implemented 3Dcontinuum model is not representative, since only single elements were studied for material calibration.

Figure 49 Comparison of simulation and experiment in case of the 3D-continuum core model

62

4 Mechanical characterization on constituent level

4.1.5 Conclusion Meso-scale models have proven to be well suited to represent the honeycomb behavior including realistic folding mechanisms. It is advisable to implement hexagons with straight cell walls, while accounting for possible stretching of the entire hexagon grid. This geometry along with a single layer orthotropic elasto-plastic material model leads to a good approximation of experimental results at comparably low modelling and computational effort. The ML approaches have proven to require considerably more effort in terms of modelling, calibration and computation, while providing little advantage in model accuracy. Therefore, the SL approaches are recommended when implementing meso scale models for sandwich panel joints. The macroscopic experimental results can also be approximated with homogenized 3D-continuum elements in combination with an orthotropic elasto-plastic model.

4.2 Face sheets On constituent level, the face sheets can be treated as a regular composite material. Therefore, standard test methods for determining the tensile properties of composite materials, such as ASTM D 3039 [AST00] or EN ISO 527-5 [ISO527] were applied. Determining the compressive properties is more challenging, particularly for thin layups such as sandwich face sheets commonly used in aircraft interior. Therefore, the four point bending test on bonded sandwich panels has been established as common method for determining the compressive properties of sandwich face sheets [Zen97]. In addition, tests on the bonded panel have the advantage that the telegraphing effect is included in the determined material properties. The same applies for determining the shear properties of the face sheets. Therefore, it is common practice in the sandwich construction industry to determine the face sheet properties directly from structural tests on the bonded sandwich panel. This is described in chapter 5. Despite this, the face sheets were additionally investigated on constituent level in the framework of the present thesis. This was done to validate existing material data and to generate a reference for the subsequent bending tests. In addition, the objective was to quantify the effect of face sheet telegraphing on the mechanical properties. In the following, the performed experiments and numerical studies are presented. Materials In the present work a total of three different E-glass prepreg fabric materials are investigated. All of which are typical in aircraft interior applications and comply with Airbus material performance specifications, while there are different manufacturers that supply prepregs according to these specifications. Table 13 summarizes the investigated materials. In the framework of the present thesis, the face sheets are generally referred to

4.2 Face sheets

63

according to their Airbus specification. Prepreg manufacturers only give vague or incomplete mechanical material properties. Aircraft interior manufacturers obtain relevant material properties from their own substantiation testing procedures. Due to collaboration with the industry, these properties are available in the framework of this thesis. However, they are subject to non-disclosure agreements and cannot be published. However, there are a few references in the literature, where similar materials were studied. Nast [Nas97] investigated prepregs of the ABS5047-02 and ABS5047-08 types and experimentally determined elastic properties.

Table 13 Investigated face sheet materials

Airbus specification

Manufacturer spec.

Description

ABS5047-02

Gurit – PHG600-44-50 [Gur09]

Woven fabric of E-glass filament yarn Style 120, 105 g/m2, crowfoot 1/3, preimpregnated with 53% phenolic resin

ABS5047-07

ISOVOLTA – AIRPREG PY 8137 [Iso12]

Woven fabric of E-glass filament yarn Style 7781, 296 g/m2, 8H satin, preimpregnated with 40% phenolic resin

ABS5047-08

Gurit – PHG600-68-50 [Gur09]

Woven fabric of E-glass filament yarn Style 7781, 296 g/m2, 8H satin, preimpregnated with 53% phenolic resin

Zinno et al. [Zin10] investigated pre-impregnated satin-weave E-glass fiber reinforced phenolic resin for application in honeycomb sandwich panels of rail transportation vehicles. They derived elastic and strength values from tensile and shear material tests. Heimbs [Hei08] investigated ABS5047-08 prepregs in tensile, compression and shear tests providing a full set of material properties. The available material data is summarized in Table 14. The material is generally characterized by linear deformation until brittle failure when loaded uniaxially in warp or weft direction, while the strength under tension is noticeably higher if compared to compression. Under in-plane shear the material shows considerable plasticity before failure. This shear plasticity is well known for woven fabric composites [Nai94]. In case of the investigated sandwich panels, the face sheets are always bonded on to the honeycomb core so that the warp direction of the prepregs is aligned with the W-direction of the core (weft is aligned with L-direction respectively). This is illustrated in Figure 50. Therefore, the core orientations W and L may also refer to face sheet orientations throughout the present thesis.

64

4 Mechanical characterization on constituent level

Table 14 Available material properties of glass fiber fabric reinforced phenolic resin Notation

E1 [MPa]

E2 [MPa]

G12 [MPa]

ν12 [-]

ABS5047-02 [Nas97]

20100

19500

3720

ABS5047-08 [Nas97]

24600

23100

ABS5047-08 [Hei08]

24745

GFRP [Zin10]

25540

σ1 [MPa]

σ2 [MPa]

τ12 [MPa]

Ply th [mm]

0.08

-

-

-

0.09

5630

0.12

-

-

-

0.19

23043

3842

0.07

352

325

46

-

22970

3410

0.15

326

288

41

0.25

Figure 50 Face sheet orientation after bonding to the core

4.2.1 Experimental analysis The sandwich face sheets were studied based on the tensile testing standard EN ISO 5275. In a first experimental study, a layup with one ply each of ABS5047-02 and ABS504708 was investigated. This is a standard layup in aircraft interior applications and it is also found in the panels that served as base material for the honeycomb core tests described in the previous section (see Figure 31). In order to quantify the telegraphing effect on the mechanical properties two sets of cured prepregs were studied. The first set was initially bonded on to a honeycomb core (ECA-3.2-48) and subsequently peeled off. It therefore, retains the honeycomb pattern as well as the uneven thickness and telegraphing. The second set was flat pressed using the same curing cycle as the sandwich panel of the first set. According to EN ISO 527-5 polymer tabs were bonded to the face

4.2 Face sheets

65

sheets in order to prevent gripping damage. For both material directions three specimens each were prepared and tested. The key test parameters are summarized in Table 15. Test results along with images of the test setup are given in Figure 51. In addition, microscopic images of longitudinal cross sections of the specimens are illustrated. Here, the imperfections of the honeycomb bonded prepreg in comparison to the flat pressed prepreg become evident. These imperfections are also reflected in the results, which indicate that the flat pressed prepreg outperforms the honeycomb bonded prepreg in terms of strength by about 20% for both material directions. The difference in stiffness is particularly pronounced in case of the L/weft-direction (20%) while in W/warp-direction the stiffness varies by about 5%. Scatter among the tests results of one configuration is below 7%. The results are given based on force-strain instead of stress-strain relationships. This is due to two reasons. Firstly, both tested materials are nominally identical, allowing to compare the mechanical performance also based on force results. Secondly, the bonding process leads to inconsistent face sheet thickness in case of the honeycomb bonded prepregs. Therefore, both materials would have different thicknesses, which may lead to misleading results when comparing stress-strain relationships. Assuming that a honeycomb bonded face sheet retains its mechanical properties after peeling it off the core, this initial study shows the significant effect of the honeycomb bonding process on the mechanical face sheet properties. It therefore justifies the industry standard to rely on bonded sandwich panel tests for determining the face sheet properties. In addition to this comparative study, a single ply of honeycomb bonded ABS5047-07 prepreg was investigated in the same manner. The obtained force-strain relationships are given in Appendix A2. Table 15 Summary of test parameters for face sheet tensile tests

Test standard

EN ISO 527-5 [Eur97]

Specimen dimension

Type A, 250 mm x 15 mm

Loading rate

5 mm/ min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-10 kN

Strain measurement

Strain gauge, HBM 1-LY18-6/120

4.2.2 Numerical modelling and calibration The thin sandwich face sheets are typically modelled using general purpose shell elements analogous to the meso-scale honeycomb core models of section 4.1.3. A suitable

66

4 Mechanical characterization on constituent level

material model is selected according to the characteristics known from the performed tests and literature. These characteristics largely coincide with UD-composite materials, which require orthotropic elasticity and brittle failure, while tensile and compressive strength are given separately. Such material models are standard in commercial FE-solvers. However, the shear plasticity of fabric composites is generally not covered by these UD-material models. In ABAQUS\Explicit this behavior can be modeled using a pre-compiled user subroutine (VUMAT)1, which is based on the continuum damage mechanics model of Johnson [Joh01]. This VUMAT is described in more detail in Appendix A2. Honeycomb bonded prepreg (HC)

1mm

Flat pressed prepreg (FP)

1mm

Figure 51 Comparison of HC pressed and flat pressed prepregs in terms of tensile properties

For comparison with the test results and for calibration of the material properties the performed tests are remodeled in ABAQUS/Explicit using S4R elements and the aforementioned VUMAT subroutine. Due to the small specimen size, the test is modelled in

1

VUMAT for Fabric Reinforced Composites, since ABAQUS 6.8

4.2 Face sheets

67

full scale. The prepreg thickness is set uniformly according to Nast [Nas97]. Due to the simple specimen geometry and uniform stress state, mesh convergence is achieved using a coarse mesh with 5 mm element size. Mass scaling and increased loading rate are implemented based on sensitivity analyses. The prescribed boundary conditions along with the calibrated uniaxial material properties for warp and weft material directions are depicted in Figure 52. The calibration was done based on the honeycomb bonded prepregs and the material properties given in the literature (Table 14) as starting point. Good agreement between simulation and experimental results is achieved after calibration. If compared to the material properties given in the literature, the calibrated values are in the same range, but tend to be about 15% higher in terms of tensile strength. The compressive face sheet strength along with the shear properties are investigated in the next building block, which is described in section 5.

Tx = v Ty,Tz = 0 Rx,Ry,Rz = 0

y x Tx,Ty,Tz = 0 Rx,Ry,Rz = 0

ABS5047-02

ABS5047-08

E1 [MPa]

21100

26100

E2 [MPa]

19500

23000

ν12 [-]

0.15

0.15

σ1t [MPa]

270

400

σ2t [MPa]

230

300

Ply thickness [mm]

0.09

0.19

Figure 52 Comparison of simulation and experiment with calibrated material properties

68

4 Mechanical characterization on constituent level

4.3 Adhesives As described in section 2.2, adhesives are used to locally reinforce sandwich panels. In this function, the added adhesive essentially forms a plastic component, which is bonded to the face and the core after curing. Since this plastic component is in the load path, its mechanical properties are of interest. However, adhesive manufacturers often do not provide basic mechanical properties, such as Young’s modulus or yield strength of cured adhesives. Therefore, the mechanical characterization of this material is necessary on constituent level. This is presented in the following. Materials In the framework of the present thesis three different types of adhesive are investigated, all of which are two component thermoset systems which are qualified for use as structural adhesive in aircraft construction. These adhesives have in common, that they are suitable for bonding a wide variety of metals, plastics, foams, composites and rubber and that they cure at room temperature. As such they are commonly used for bonding in sandwich panels. Table 16 summarizes the three investigated adhesives. Table 16 Investigated adhesives

Notation Ureol 1356 A/B [Hun04]

Manufacturer Huntsman Advanced Materials

Description Polyurethane adhesive

Scotch-Weld™ EC-9323 B/A [3M 13]

3M Company

Epoxy adhesive

Automix VE24430 (AB8162)

Delo Industrial Adhesives

Epoxy adhesive, experimental stage

4.3.1 Experimental analysis The primary objective of the experimental analysis was the determination of the tensile and compressive stress-strain relationship of the materials. Following Rolfes et al. [Rol08] it is assumed that the investigated thermosets behave isotropically. Therefore, the relationship between Young’s modulus E and shear modulus G is defined by Poisson’s ratio as follows. (4.1)

2 1 Considering, that Poisson’s ratio for structural adhesives typically varies between 0.3 and 0.5 [Sil05], there is only a small range of values the shear modulus can take up in case Poisson’s ratio is unknown. Therefore, the determination of the Poisson’s ratio is not of primary interest. However, for reference it was determined in case of the Scotch-Weld™

4.3 Adhesives

69

EC-9323 B/A adhesive. The specimens were manufactured using molds, which were custom made to represent the specimen geometry according to the respective ASTM standard. The molds were fabricated using a 3D-printer (Designjet Color 3D printer; HewlettPackard Development Company, Palo Alto, California). The adhesives were cured at room temperature for a minimum of 14 days. After unmolding, the cured specimens were grinded using sandpaper, in order to smoothen the outer surfaces. For all investigated adhesives, three specimens each were fabricated for compression and tension tests. The outer dimensions of all specimens were measured to determine the crosssectional area of the specimens. The performed tests are described in the following. Tensile properties The tension tests were performed based on the ASTM standard for plastics ASTM D638 [AST02]. The specimens were clamped using self-tightening wedge grips. Accurate strain measurement was ensured by uniaxial strain gauges. In case of Scotch-Weld™ EC-9323 B/A transverse strain gauges were applied along with axial ones in order to determine Poisson’s ratio (see Figure 53). Additional test details are summarized in Table 17. Figure 53 illustrates the experimental results in terms of tensile stress strain relationship for all three tested adhesives. In addition, the test setup along with a specimen after rupture is displayed in case of Scotch-Weld™ EC-9323 B/A. Table 17 Summary of performed tensile tests on adhesives

Test standard

ASTM D638 [AST02]

Specimen dimension

Type 1 (13 mm x 3.2 mm cross section, 57 mm length of narrow section)

Loading rate

5 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-10 kN

Strain measurement

Strain gauge, HBM 1-LY18-6/120

The two epoxy resins behave similar with comparable Young’s modulus and tensile strength, while the 3M Scotch adhesive outperforms the thermoset from Delo by about 10% in terms of strength. The Ureol adhesive behaves completely different, with low modulus and strength if compared to the epoxy-based resins. Furthermore, it is characterized by non-linear ductile behavior already at low strains, making it difficult to determine a Young’s modulus from the experimental data. All specimens are characterized by porosity due to trapped air during curing (Figure 53, right). This is a well-known phenomenon that also occurs during application in sandwich construction. It is therefore assumed that the obtained results are representative.

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4 Mechanical characterization on constituent level

Figure 53 Test results of tensile adhesive tests (left), Test setup and specimen after testing in case of Scotch-Weld™ EC-9323 B/A (right)

Compressive properties The compression tests were performed according to the standard ASTM D695 [AST02] using typical pressure plates. The strain measurement was based on the displacement reading of the machine crosshead. Therefore, the machine stiffness was determined for the test setup and compensated during post processing of the data. Further test parameters are summarized in Table 18. Table 18 Summary of performed compressive tests on adhesives

Test standard

ASTM D695 [AST02]

Specimen dimension

Circular cross section Ø 20 mm; length 40 mm

Loading rate

1 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-50 kN

Displacement measurement

Machine crosshead

The experimental results in terms of compressive stress-strain relationship for the three tested adhesives are given in Figure 54 along with images of the test specimen before and after testing in case of Scotch-Weld™ EC-9323 B/A. The compression results show the same trend as the tensile tests. Ureol has a comparably low stiffness and strength while, Delo and Scotch show similar stiffness. However, in terms of strength the results from the tensile tests flip, with Delo epoxy showing higher strength than the Scotch epoxy.

4.3 Adhesives

71

After test Before test Figure 54 Test results of compressive adhesive tests (left), Test setup and specimen after testing in case of Scotch-Weld™ EC-9323 B/A (right)

Summary The tests results show scatter between 2-5 %. This can be explained by the air pockets in the material, which appear to be random in size and distribution. In addition to the mechanical properties the density of the materials was determined from the specimens. All test results are summarized in Table 19. The three investigated materials indicate significantly different behavior in tension and compression. Ureol is clearly distinguished due to its low modulus and tensile strength, while the two epoxy adhesives are comparable with regards to the investigated basic material properties. Poisson’s ratio for Scotch-Weld™ EC-9323 B/A was determined at 0.44 based on an additional transverse strain gauge. This value serves as reference in the following simulations also for the remaining two adhesives, which were not tested with transverse strain gauges. Table 19 Material properties of investigated adhesives

Scotch 9323

E [MPa] 2600

σyield,t [MPa] 20

σyield,c [MPa] 30

Delo VE24430

2980

15

Ureol 1356 A/B

920

3

Notation

0.44

ρadhesive [g/cc] 1.2

35

-

1.1

20

-

1.6

ν12 [-]

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4 Mechanical characterization on constituent level

4.3.2 Numerical modelling and calibration Since the adhesive forms a voluminous plastic component after bonding in the sandwich panel, it is modeled using 3D-continuum elements (C3D8R), similar to the homogenized core model in section 4.1.4. As in the previous face sheet simulation, the conducted tests are modeled in full scale and mesh size convergence is achieved with relatively coarse elements (3 mm). The boundary conditions of the compression and tension simulation models are summarized in Figure 55. The mechanical behavior of the adhesives requires a material model that provides elastic-plastic behavior with different yield strengths, flow and hardening in compression and tension. In ABAQUS this can be modeled using the ‘Cast Iron Plasticity’ model. Here, the uniaxial yield stress along with the corresponding plastic strain can be given in tabular form separately for tension and compression. The yield stress and plastic strain pairs can be derived from the obtained stress-strain relationships of the experiments (Figure 53 and Figure 54). These stress-strain curves represent the engineering stress-strain relationship, where both, stress and strain, are based on the initial cross section and initial gauge length. a)

b)

Tx = v Ty,Tz = 0 Rx,Ry,Rz = 0

Tz = v Rx,Ry,Rz = 0

z x

y x Tx,Ty,Tz = 0 Rx,Ry,Rz = 0

Tz = 0 Rx,Ry,Rz = 0

Figure 55 Simulation model of adhesive tests, a) tensile test and b) compression test

However, FE-solvers require the input of the “true” yield stress- plastic strain relationship. The conversion of “engineering” stress/strain into “true” stress/strain is described in Appendix A3. With the implemented true yield stress progression from the experiments the simulation model is capable to reproduce the experimental stress strain relationship accurately. The implemented material models for all three investigated adhesives including stress-strain relationships are given in detail in Appendix A3.

5

Mechanical characterization on structural element level

In sandwich construction, the structural element level coincides with the bonded sandwich panel, which represents the combination of the two main constituents, face sheet and core. It is generally assumed that the material properties and modelling approaches, which are derived on constituent level, enable to predict the material behavior on structural element level. The investigations within this second building block were firstly intended to validate this assumption. In addition, the objective was to consider additional relevant aspects that can only be investigated on structural element level. Furthermore, as it is shown in chapter 4, the material properties of the face sheets are degraded due to the core bonding process. Therefore, investigations on structural element level serve as primary source for face sheet properties, which include this degradation. In the framework of the present thesis, two structural element test setups are investigated in experimental and numerical studies. This is described in the following.

5.1 Panel flexure In bending or flexural tests, beams are typically subjected to flatwise flexure. In sandwich construction, bending is probably the most important test on structural element level and numerous comprehensive studies on the flexural behavior of honeycomb sandwich panels are available. This is because flexural tests can cover a variety of key material properties. Due to the mechanical working principle of sandwich beams, bending tests are not only applied to determine or validate the flexural stiffness of the sandwich construction but also the shear modulus and strength of the core as well as face sheet modulus and strength [Zen97]. In addition, bending tests may also indicate failure of the face to core bond as well as core compression due to local indentation. Due to the numerous failure mechanisms, failure mode maps are commonly applied to predict the failure mode of bending test setups [Dan02], [Pet99], [Zin10], [Oth08], [Bel09]. In the present work, an extensive joint experimental and numerical study on sandwich bending was

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_5

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performed in order to validate numerical models of the investigated materials. This is described in the following. Materials and configurations

3

ABS 5047-07

4

ABS 5047-08

d

5

7

e

B26-W020

9

B19-L101 19 mm

6

B19-W101

26 mm

B19-W003

B19-L003 19 mm

ABS 5047-02

B26-L101

2

19 mm

7 mm 19 mm

B26-W101

1 B07-L001

c

b

26 mm

B07-W001

f 8

10 mm

7 mm

a

26 mm

In the framework of the bending study, different configurations of sandwich panels, which comprise the previously investigated constituents, are studied. The tested specimens originate from six different sandwich base panels with different core heights and face sheet lay-ups. The base panels and the tested configurations are summarized in Figure 55. Four of these panels are studied in both core orientations L and W (panels a to d), while two panels are studied solely in W-orientation (panels e and f). Therefore, there is a total of ten configurations. All panels were industrially manufactured in a flat press process and comply with aviation quality standards. The nomenclature of each configuration reflects the nominal panel thickness, core orientation and face sheet layup.

B10-W010

10

Core Wdirection

Core Ldirection

ABS 5035-A4

Specimen nomenclature B19-L101 No. of ABS5047-08 plies No. of ABS5047-07 plies No. of ABS5047-02 plies Core orientation Nominal panel thickness Test identifier (B=bending)

Figure 56 Summary of investigated materials and sandwich configurations

In order to support the bending study, the specimens were investigated under the microscope. For bending test specimens, the composition of the face sheets is of particular interest, since they strongly influence the flexural panel performance. Figure 57 illustrates exemplified microscopic images of three of the investigated face sheet layups. These images indicate that with the number of face sheet prepregs, the thickness of the phenolic resin fillet layer tends to increase. This is due to increased excess resin of the additional prepregs, which forms larger fillets in the co-curing bonding process. The

5.1 Panel flexure

75

nominal average face sheet thickness typically coincides with the fabric layer and thus does not include the fillet layer, since it does not add to the total panel thickness. In addition, it’s contribution to the macroscopic stiffness of the face sheet is negligible, due to the low modulus of pure phenolic resin. B07-L001 (1 layer)

B19-L101 (2 layers)

0.5mm

0.5mm

B19-L003 (3 layers) 0.5mm

phenolic resin fillet fabric layer

Figure 57 Microscopic images of face sheets of bending specimens

5.1.1 Experimental analysis The bending tests of the present work were performed according to the ASTM C393 [AST00] standard. The dimensions of the test specimens as well as the implemented test setups varied, in order to ensure that different failure modes occur during testing. In general, three specimens were prepared for each configuration, except for B26-W101 and B26-L101 where only two specimens were available. The panels were tested in three different test setups (Figure 58). The majority of the specimens were tested in a four point (4P) bending setup on a Shimadzu AG 25TB universal testing machine. This enables a uniform bending moment between the loading cylinders, which is generally preferred to determine the face sheet strength. The 7 mm panels were tested on the same machine using a three-point (3P) bending setup. This allowed to prepare smaller specimens from the limited base panel material. Lastly, the two configurations with ABS5047-07 as face sheets were tested in a four-point bending fixture on a Galdabini Quasar 100. In this setup, additional loading plates were placed between loading cylinders and panel in order prevent local indentation of the core. The test details for each setup including fixture and panel dimensions are given in detail in appendix B1. The displacement was measured via the machine crosshead in all three test setups. As in the previously described compression tests of the constituents, the machine stiffness was determined and compensated during post processing. The test results for all configurations are given in Figure 59 and Figure 60 as force-displacement relationships. Three different failure modes are identified throughout all tests, local core indentation, core shear and face sheet failure.

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5 Mechanical characterization on structural element level

Table 20 Summary of performed bending study

Test standard

ASTM C393 [AST00]

Specimen dimension

Width 50 mm, length 200 – 300 mm Width 75 mm, length 400 mm

Loading rate

5 mm/min | 10 mm/min

Testing machine

Shimadzu AG 25TB | Galdabini Quasar 100

Load cell

Shimadzu SFL-25AG (25kN) | HBM S9M 10 kN

Displacement measurement

Testing machine crosshead

a)

b)

c)

Figure 58 a) Four-point bending including loading plates on Galdabini (B26-W020); b) Four-point bending on Shimadzu (B19-W003); c) Three-point bending on Shimadzu (B07-W001)

5.1 Panel flexure

77

1

1 2 2

Face sheet failure

Core shear

Core indentation

Figure 59 Experimental results of 4P-bending tests without loading plates

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5 Mechanical characterization on structural element level

1

1

2 2

Face sheet failure

Core shear

Core indentation

Figure 60 Experimental results of 4P-bending tests with loading plates and 3P-bending tests Core shear can be easily identified by slowly progressing shear buckling of the cell walls, leading to a plateau in the force-displacement curve (e.g. B19-W003). The other two failure modes are more difficult to distinguish, as they succeed one after another almost instantly. As a result, force-displacement curves as well as visual damages after testing look similar. However, face sheet failure tends to lead to a more significant load drop if compared to local indentation. In addition, face sheet failure can be generally identified by a distinct bang during testing, which is typically not evident with core indentation. The identified failure modes for each configuration are indicated in and Figure 59 and

5.1 Panel flexure

79

Figure 60 with the help of pictograms. The experimental results are characterized by little scatter in terms of bending stiffness (below 5%). The scatter in terms of strength is slightly more pronounced (up to 10%). An exception is specimen B19-L101-03, which is an outlier in terms of strength due to premature failure in form of local core indentation, while the other two tested specimens of the same configuration indicate face sheet failure. The obtained test results generally reflect the expectations and thus appear to be plausible. Thin panels with comparably weak face sheets (B10, B07) fail due to face sheet rupture, while the B26 and B19 panels fail due to local core indentation, unless loading plates were applied to prevent this. Core shear failure is only evident with strong face sheets and in W-orientation where the core shear strength is the lowest.

5.1.2 Numerical analysis Due to the importance of bending tests in sandwich construction, there are several numerical studies on flexural bending of honeycomb sandwich beams available in the literature. These studies can be subdivided according to the applied core modelling approach. Heimbs [Hei06] and Zinno et al. [Zin11] model flexural tests of Nomex honeycomb sandwich beams using 3D-continuum elements for the core. Their models are intended to enable validation of existing material properties, while the focus is on the global panel response. Other models are targeted towards localized effects such as indentation or wrinkling. They therefore apply detailed meso-models. Giglio et al. [Gig12] investigated indentation in case of three point bending of a Nomex core with aluminum face sheets. They conclude that the friction parameter between load cylinder and face sheets has significant impact on the indentation pattern of the simulation. They suggest a friction parameter between 0 and 0.3. Staal [Sta06] studied face wrinkling of Nomex honeycomb panels with GFRP face sheets using detailed meso models and 3D-continuum models. He reports that a meso-model has no benefits over 3D-continuum models for the prediction of face wrinkling. In the present work all ten tested configurations are implemented in a virtual testing framework. The objective is to validate and benchmark previously derived modelling approaches and material properties. Therefore, the bending tests are implemented at meso-scale as well as using 3D-continuum elements for the core. The experimentally observed failure modes enable to validate and benchmark the model performance regarding the out of plane compressive and transverse shear strength of the core models. In addition, the compressive strength of the face sheets is calibrated and the implemented modelling approach for the face to core bond is evaluated. In the following, the implemented models are described in detail before the simulation results are presented in comparison to the experimental results. Such a comparative study of both core modelling approaches for bending analyses has not been described in the literature before and can be considered as notable contribution to the state of the art.

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5 Mechanical characterization on structural element level

Model description The virtual testing framework is based on a realistic representation of the experimental bending setup. This means, that the implemented model includes the load and support cylinders and the load is applied via contact formulations to the sandwich beam. Such model setup enables to consider local indentation of the core as well as stress concentrations in the face sheet within the contact area. Analogous to the test, the load cylinders are prescribed with a translatory vertical constant velocity v, while the remaining five DOF are constrained. The support cylinders are constrained in all six DOF. The contact between face sheet and cylinders is implemented as standard penalty contact with a friction coefficient of 0.2. In order to reduce computational effort, symmetry of the specimen and loading condition are utilized where applicable. In case of the four-point bending setups, two symmetry planes are implemented leading to a quarter model (Figure 61 a). In case of the three-point bending setup, the single load cylinder is located in the center of the beam. Therefore, only one symmetry plane along the longitudinal axis (x-z plane) is implemented in order to limit interference of the symmetry boundary conditions with the core cell wall folding due to local indentation beneath the load cylinder (Figure 61 b). In case of the four-point bending setup with additional loading plates, the loading plates are represented by 3D-continuum elements (Figure 61 c), while the contact formulation is adopted from the face-cylinder contact. The element and material modelling are adopted from the previous constituent level. The face sheets are modelled using S4R elements and the built-in user subroutine for fabric reinforced composites (see section 4.2.2). An element size of 2.0 mm is determined via convergence studies. The shell thickness is modelled based on the nominal face sheet thickness. The fillet layer (see Figure 57) is therefore physically neglected and its mechanical contribution is smeared into the face sheet. The face sheet properties are derived from the constituent level with the exception of the compressive strength, which was calibrated using the bending tests. The core is modelled as determined on constituent level using two approaches. As meso-scale model it is modelled using S4R elements (element size 0.4 mm) with accurate cell wall representation and with a single layer orthotropic-plastic material model (for material properties see Table 10 on p. 51). In addition, the core is implemented with C3D8R elements using the previously implemented macroscopic orthotropic elasto-plastic material model (section 4.1.4). Table 21 Calibrated compressive strengths of the studied face sheet prepregs ABS 5047-02 σ1c [MPa] σ2c [MPa] 180 150

ABS 5047-07 σ1c [MPa] σ2c [MPa] 220 150

ABS 5047-08 σ1c [MPa] σ2c [MPa] 250 200

5.1 Panel flexure

81

a) Cylinders C3D8R Rigid body

Honeycomb Tz = v S4R/C3D8R Tx,Ty = 0 Orth. plastic Rx,Ry,Rz = 0

Face sheets S4R Orth. fabric Tx,Ty,Tz = 0 Rx,Ry,Rz = 0

z y b)

x

Cylinder-face Penalty contact Friction 0.2

Face-core bond Tied contact

c)

Figure 61 Implemented FE-models for virtual bending tests; a) Model description in case of four-point bending; b) Three-point bending model; c) Four-point bending with loading plates The element size of the 3D-continuum core is 1 mm in the vicinity of load and support cylinders. This element size indicates converged results regarding local core indentation. In the far field the element size is defined so that there are five elements along the core height in order to ensure a good approximation of the shear stress. Therefore, the far field element size is variable throughout the implemented models depending on the core thickness. The contact between locally refined and coarse far field mesh is implemented as tied contact. This 3D-continuum core modelling approach is illustrated in Appendix B2. Regardless the core modelling approach, the bond between core and face sheets is

82

5 Mechanical characterization on structural element level

modelled as tied contact. In case of the meso-scale model, the top cell wall edges coincide with the face sheet. It is therefore a node to surface contact, while the 3D-continuum model is implemented with a surface to surface contact. Applying a tied contact appears reasonable, since there was no core-face debonding evident in the experiments. Lastly, the load cylinders are modelled as rigid bodies with an element size of 1.0 mm, thus enabling a good geometry approximation. The implemented virtual testing framework is illustrated in Figure 61 a) in case of the meso-scale core and four-point bending setup. The 3D-continuum model is essentially the same, just with 8-node hexahedron elements instead of the detailed core. In all simulations, mass scaling and increased loading rates are implemented based on sensitivity studies in order to reduce the computational effort. Results The simulation results in terms of force-displacement curves are given in Figure 62 and Figure 63 in comparison to the experimental results for each of the investigated bending configurations. Figure 64 illustrates the failure modes of the detailed simulation approach in comparison to the experiments. A comparative study on the visual damage mechanisms of the two implemented modelling approaches is given in Appendix B2. Analogous to the previously described simulations on constituent level, all simulations were carried out on a six core Intel Xeon X5680 workstation and computational effort varies greatly between the different models and modelling approaches. In case of the 3D-continuum approach the computation time ranges between 20 minutes in case of smaller models with little deformation until failure (e.g. B19-L101) and 2 h in case of larger models with large deformations (e.g B26-W010). In contrast the computation time of the detailed models varies between 2 h and 14 h. Discussion The simulated bending stiffness is consistent for both models in all configurations and matches the experimental results well. The only exceptions are the two B07 configurations, where both simulation models lead to a 5% reduced bending stiffness if compared to test results. However, regarding the failure mode and the bending strength, both models partly differ considerably depending on the configuration. Generally, the detailed model tends to result in equal or higher strengths if compared to the 3D-continuum model. In case of the two W020 configurations, which were tested using the 4Pbending setup including loading plates, both models predict the correct failure mode with comparable strength matching the experimental results well (deviation below 10 %). This is due to the fact that these configurations are dominated by face sheet failure, which could be calibrated by setting the compressive face sheet strength of the material model accordingly. The same applies for the thin B07 configurations.

5.1 Panel flexure

83

Test scatter Test average Continuum core Detailed core

Face sheet failure

Core shear

Core indentation

Figure 62 Experimental and numerical results for 4P-bending tests without loading plates

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5 Mechanical characterization on structural element level

Test scatter Test average Continuum core Detailed core

Face sheet failure

Core shear

Core indentation

Figure 63 Experimental and numerical results for 4P-bending tests with loading plates and 3Pbending tests

However here, the two simulation models yield different results in terms of both, failure mode and strength. The 3D-continuum model fails prematurely due to local core indentation leading to reduced strength if compared to the experiments. This is particularly evident for B07-L001. The detailed model on the other hand indicate face sheet failure and thus predicts the bending strength accurately within less than 10% of the experimental results. In case of the B26 configurations both models indicate core indentation, while the 3D-continuum model fails earlier. However, in this case both modelling approaches suggest bending strengths within 10% of the experiments, leading to a good agreement between test and simulation. Regarding the B19-101 configurations, the two

5.1 Panel flexure

85

simulations models once again indicate local core indentation, while the detailed model achieves higher strengths. b) a)

c)

Figure 64 Comparison of experimental and numerical results in terms of failure mechanisms and damage patterns in case of the detailed modelling approach, a) local indentation of loading cylinder (B19-W101-4P); b) core shear failure (B19-W003-4P) and c) face sheet failure (B10-W010-4P-LoadPlate)

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5 Mechanical characterization on structural element level

Yet here, the simulation results collectively underachieve the experimental results. However in case of B19-L101, the experiments suggest inconsistent failure modes leading to high scatter. The two simulation models accurately match the single test specimen, which failed due to local indentation. As for B19-W101, the detailed model suggests about 15% lower bending strength if compared to the experiments. Lastly there are the B19 configurations with three prepreg layers. In case of B19-L003, the strength of both simulation models is considerably lower than in the test, while the failure mode of local indentation is predicted correctly. This is possibly due to the thick phenolic resin fillet layer of this configuration (see Figure 57 on p. 75), which is not considered in the simulations models. It is assumed, that this fillet layer postpones local core indentation in the actual specimens. Regarding B19-W003, the 3D-continuum model appears to correctly predict the initiation of core shear failure. However, the homogenized hexahedron elements are not capable to represent the distributed large-scale core shearing due to cell wall buckling. Instead, the 3D-continuum elements shear locally underneath the load cylinders, leading to premature failure. This is illustrated in Appendix B2. In contrast, the detailed model represents the actual failure pattern well (see Figure 64 b) and thus also reproduce the experimental force-displacement curve progression. However, the simulation model exceeds the force plateau of the experiments by about 15%. This can be explained by the fact that the calibrated detailed honeycomb core model, which is described in section 4.1.3, also exceeds the experimental strength in case of WT-shear on constituent level (see Figure 44). This is because the derived detailed constituent core model represents a trade-off between multiple loading conditions. Summary Generally the detailed modelling approach enables a good overall match of the experimental results in terms of both, visual damage patterns (Figure 64) and force-displacement curve progression (Figure 62 and Figure 63). Therefore, the previously determined material models and properties could be validated. Discrepancies between simulation and test are due to remaining limitations in the model detail and general material and test uncertainties. In contrast, the 3D-continuum modelling approach reveals several short comings in the performed bending study. The derived homogenized core model tends to result in premature local core indentation. However, this is not evident in all configurations. Furthermore, this modelling approach does not appear to be suitable to model the complicated stress state in the vicinity of the loading cylinders once shear failure is initiated. However, based on the performed study the 3D-continuum approach seems well suited for preliminary conservative predictions or optimization studies, especially considering that the computational time is up to 10 times lower if compared to the detailed models.

5.2 In-plane shear

87

5.2 In-plane shear The in-plane shear strength and stiffness of sandwich panels are important design parameters in terms of both, global panel behavior and local effects in the vicinity of joints. Shear tests are therefore standard in sandwich construction [Ada14]. Due to the low inplane stiffness and strength of the core, the in-plane behavior of the panel is dominated by the face sheets. However, the core should not be neglected entirely since its properties may have an effect on the face wrinkling [Sta06]. In the framework of the present thesis, two panel configurations were investigated in terms of in-plane shear. This is described in the following. Materials and configurations The investigated panel configurations reflect the main face sheet layups of the present thesis. Since the core height and orientation have negligible effect on the in-plane shear behavior of the panel, no core variations were considered. As a result, only two panel configurations are investigated under shear, both of which have also been studied in bending. These configurations are summarized in Figure 65, while the nomenclature is derived from the bending tests without specifying the core orientation.

Figure 65 Investigated panel configurations for in-plane shear testing

5.2.1 Experimental analysis The in-plane shear tests of the present study were performed according to ASTM D8067/D8067M [AST17]. This is a recently published standard test method for the determination of shear strength and modulus of sandwich panels using a picture frame fixture. Since the panel shear behavior is governed by the face sheets, this test essentially enables to determine the shear strength and modulus of the faces while considering degradation due to telegraphing. The test requires square test specimens with notched corners, which are clamped between four pairs of pinned fixture rails. The pins in the corners of the rails allow relative rotation of the rails. Therefore, when the frame is loaded in uni-axial tension tensile forces act along all four edges of the specimen in 45° angle to the applied tension. This leads to predominating shear stress in the specimen.

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5 Mechanical characterization on structural element level

Table 22 Summary of performed frame shear tests

Test standard Specimen dimension

ASTM D8067/D8067M [AST17] 400 mm x 400 mm, Type A no edge doublers, potting in the clamping area

Loading rate

10 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-50 kN

Strain measurement

Strain gauge, HBM 1RY18-6/120 (rosette)

According to ASTM D8067/D8067M, the specimens are usually reinforced in the clamping area along the edges in order to locally increase the face sheet thickness and to prevent premature failure in the bearing holes. In addition, potting or other kinds of filling may be required in the core in between the fixture rails in order to avoid core crushing during fastening. The specimens in the present work were reinforced with bonded aluminum bars as edge filler. These bars not only prevent core crushing but also bearing failure of the fastener holes. A drawing of the prepared specimens is given in Appendix B2. For each of the tested configurations three specimens were prepared. In compliance with ASTM D8067/D8067M, three-dimensional strain gauges were applied to determine the shear strain γ. This is further explained in Appendix B3. The key test parameters are summarized in Table 22. The test results are given in Figure 66 in terms of force strain relationship. Here, the force relates to the tensile force measured by the machine load cell. Both tested configurations generally indicate the same ductile shear behavior, which is typical for fabric reinforced composites. The failure mode for all tested specimens is shear rupture of the face sheet at the interface of edge filling and core (Figure 66, right), while no debonding is evident prior to catastrophic failure. Scatter in the results is below 5% in terms of both, modulus and strength. The shear properties of the material are derived in a numerical study by calibrating the material model using the test results. This is described in the following.

5.2.2 Numerical analysis As in the previous bending study, the picture frame shear tests are implemented in a virtual testing framework which closely follows the actual test setup. Due to the limited effect of the core on the panel shear behavior, a 3D-continuum model is implemented.

5.2 In-plane shear

89

The symmetry of the specimen and loading condition is utilized by implementing a quarter model in order to reduce computational time. The steel fixture is modelled using beam elements (B21) with an equivalent cross section as the actual rails. a)

b)

Cracks at transition between filler and core Figure 66 a) Force strain relationships of the two investigated panel configurations; b) image of the test setup in case of the S10-010 configuration after catastrophic failure

The hinge joint is implemented as CONN3D2 element. The specimen is attached to the fixture via rigid multi point constraints (MPC) in all fastener holes. These boundary conditions reflect the test setup with one end of the fixture being constrained in all DoF except Z-rotation (SPC). The load is applied as guided prescribed velocity v on the other end of the fixture. All specimen components such as core, face and edge filling, are bonded among one another via tied contacts (kinematic coupling). The implemented model is summarized graphically in Figure 67. The material modelling is adopted from the previous numerical studies. The edge filling bars and fixture rails are modeled linear elastically using standard properties for aluminum and steel respectively. The core is modeled using calibrated macroscopic material properties (section 4.1.4), while the face sheets are modeled with the pre-compiled VUMAT for fabric reinforced composites. Uni-

90

5 Mechanical characterization on structural element level

axial face sheet properties are adopted from the bending study as well as the tensile face sheet tests described in section 4.2. The same applies for numerical parameters such as mass scaling and loading rates. The shear properties of the material model were calibrated based on the picture frame test results, while available material data from literature served as reference for the calibration. Key material properties of the investigated prepregs after calibration are given in Table 23, where G is the shear modulus and S shear stress at the onset of shear damage. The ultimate shear strength depends on the definition of the shear damage model parameters and cannot be explicitly given as input parameter. The calibrated material model is given as input deck format in appendix A2. Table 23 Key shear properties of the face sheets as derived from virtual testing framework Prepreg / Face

G [MPa]

S [MPa]

Ply thickness [mm]

ABS5047-02

3400

45

0.09

ABS5047-07

4980

40

0.25

ABS5047-08

5600

70

0.19

The simulation results in comparison to the test results after calibrating the shear parameters are given in Figure 68 a). The calibrated model leads to a good match of numerical and experimental force-strain relationships. In addition, the failure mode is reproduced well by the numerical model. This is illustrated in Figure 68 b). In sum, the applied pre-compiled VUMAT can be established as well suited to model the shear behavior of the face sheets. Hinge joint CONN3D2

Shear frame B21 Isotropic elastic Circ. section R = 7mm

Edge filling C3D8R Isotropic Elastic 3mm Elemsize

Fastener Rigid MPC

Honeycomb C3D8R Orth. Plastic 5mm Elemsize

Face sheets S4R Orth. fabric 5mm Elemsize

y

z x

Ty = v Rx,Ry = 0 Tx,Ty = 0

symmetry

Tx,Ty,Tz = 0 Rx,Ry = 0

Figure 67 Implemented finite element model for picture frame shear test

5.3 Additional test methods

a)

91

b)

Configuration S10-010

y x

z

Shear damage 0%

100%

Figure 68 Comparison of simulation and experiment; a) in terms of force strain relationship and b) in terms of failure mode

5.3 Additional test methods There are additional tests on structural element level, which may be considered in virtual testing frameworks for sandwich structures. The subsequently introduced test setups are not described in detail in the present thesis, since they have proven to be less relevant with regards to the investigated joint configurations. However, due to their general relevance in sandwich construction they are briefly outlined. Uniaxial testing of sandwich panels Uniaxial tests on sandwich panels can be an alternative for determining the face sheet properties, which, in the present thesis, was done based on bending tests and tensile tests of the face sheet prepregs. The standardized edgewise compression test [AST99] enables to directly determine the in-plane uniaxial compressive properties of the panel. Depending on the specimen dimension and composition, the test can yield diverse failure modes such as compressive face sheet rupture, face sheet wrinkling and dimpling

92

5 Mechanical characterization on structural element level

and even global buckling. Therefore, it may provide a good validation basis for the compressive face sheet behavior within virtual testing frameworks. However, in the present work the compressive face sheet behavior is of secondary interest, since the investigated joints do not exhibit such damage mechanisms. Therefore, the characterization via bending tests is considered sufficient. The non-standardized tensile test of bonded sandwich panels typically fails due to tensile rupture of the face sheet. Since face sheet failure in bending tests is generally caused by compressive yield, this test may supplement flexural tests or edgewise compression tests by providing the tensile strength of face sheets including degradation due to honeycomb bonding. However, in the framework of the present thesis, these properties are determined based on tensile tests on formerly bonded face sheets. Therefore, this test is not further investigated. Edgewise compression test ASTM C364 [AST99]

Tensile test on bonded panel No standard

Figure 69 Uniaxial tests on bonded sandwich panels

Both introduced uniaxial tests are illustrated in Figure 69. They have the advantage that the test specimens can be prepared with little effort and the test setup is characterized by clearly defined load paths. Therefore, they are well suited for remodeling in a virtual test framework and subsequent calibration based on experimental results. Face sheet to core debonding The characterization of the face to core bond is a key mechanical property in sandwich construction. Mode I fracture is generally regarded as most critical debonding process for sandwich panels. For quality control and relative comparison, the climbing drum peel (CDP) test has been established as standard test method to evaluate mode I fracture properties of sandwich panels [Net07], [AST12]. However, incorporating face-core debonding in a virtual test environment requires the input of the mode I fracture toughness G1c (critical strain energy release rate). In case of monolithic laminates, the G1c value

5.3 Additional test methods

93

is typically determined using the double cantilever beam (DCB) test. However, in case of sandwich structures several studies suggest that the DCB yields significant scatter, thus limiting its quantitative value [Rat11]. In order to overcome this the single cantilever beam (SCB) test has been proposed. This test appears most suited for a virtual testing framework, since it provides reliable determination of G1c. Furthermore, it can be easily implemented as virtual test in order to validate the behavior of the implemented fracture mechanics model. The introduced mode I fracture tests are illustrated in Figure 70. In the framework of the present thesis, mode I fracture is evident in multiple joint configurations. However, it only occurs in the post failure regime. It is therefore of secondary interest, since the primary objective is the prediction of catastrophic failure. As a result of this, mode I fracture is not studied in detail. Yet, in applications where face to core debonding is a dominant damage mechanism prior to catastrophic failure, an additional investigation based on the SCB is recommended. Climbing drum peel test ASTM D1781-98 [AST12]

Double cantilever beam (DCB) ASTM D5528-01 [AST99]

Single cantilever beam (SCB) No standard

Figure 70 Mode I fracture tests on sandwich panels (delamination / debonding of face and core)

6

Mechanical characterization on sub-component level

The sub-component level is typically concerned with all joints and fasteners within sandwich constructions. In the framework of the present thesis various configurations of common sandwich fastener designs were investigated in experimental studies. These experimental studies serve as reference for the development and validation of a virtual testing approach, which is described in chapter 7. The performed experimental studies are described in the following. They are clustered according to the studied type of fastener or joint.

6.1 Threaded inserts perpendicular to the face sheet As established in section 2.2.1, out-of-plane tension/compression and in-plane shear are the most important loading conditions for threaded inserts placed perpendicular to the face sheets. This is also evident in the fact that most available studies focus on these load cases. Song et al. [Son08] studied various configurations of potted inserts in Nomex honeycomb sandwich panels with carbon epoxy face sheets. They reported that the pull-out strength strongly correlates with core density and height as well as the face sheet thickness. The shear-out joint strength on the other hand is dominated by the face thickness. Kim and Lee [Kim08] investigated the effect of the insert geometry on the load introduction of partially potted inserts in composite sandwich panels. Demelio et al. [Dem01] looked at various combinations of honeycomb sandwich panel fasteners under pull-out and shear static and fatigue loading. They pointed out that core height and skin reinforcements have the most significant impact on the fatigue strength. Bianchi et al. [Bia11], compared hot and cold bonded procedures of honeycomb sandwich insert manufacturing. They reported that the stiffness of the potting material strongly correlates with the insert pull-out strength. Heimbs and Pein [Hei09] investigated the failure behavior of sandwich inserts under pull-out and shear, pointing out the different damage mechanisms. In the present work both, pull-out and shear tests are considered. In the

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_6

96

6 Mechanical characterization on sub-component level

following, the investigated materials and configurations are introduced before the experimental studies are described. Materials and configurations The investigated configurations essentially comprise the previously introduced materials, while both, fully and partially potted inserts were investigated. Figure 71 illustrates the investigated configurations and materials. The fully potted type is studied in three configurations where only the core height varies (Figure 71 a). The partially potted type is investigated in a single configuration (Figure 71 b). Typical inserts for application in aircraft interior are studied. The Shurlok SL607-08-6S is a standard steel insert, which is suitable for a wide variety of panel thicknesses. The ABS1005-08078T is a lightweight plastic insert with bonded threaded steel bush. The nomenclature of the configurations is adopted from the previous investigation levels. FP-10-101 a) 10 mm ABS 5047-02 ABS 5047-08

SL607-08-6S

FP-19-101

Fully potted

Ureol

19 mm ABS5035-A4 FP-26-101 26 mm

b)

PP-26-010

ABS1005-08078T Delo

ABS 5047-07 Partially potted ABS5035-A4

26 mm Figure 71 Investigated materials and panel configurations for inserts perpendicular to face sheets a) fully potted and b) partially potted configurations

6.1.1 Out-of-plane tension (pull-out) Out-of-plane tension is also referred to as pull-out test. It is a common and well-studied test setup for sandwich fasteners. Despite this, there is no standardized test method

6.1 Threaded inserts perpendicular to the face sheet

97

available. However, the reviewed studies generally followed the same setup, which is also suggested in the ESA Insert Design Handbook (IDH) [ESA11] and the Shurlok Design Manual [Shu96]. The IDH additionally provides manufacturing drawings for all required parts of this setup. The test requires quadratic sandwich panel specimens with a bonded insert and fastened screw in the center. During the tests the specimen faces a fixture with a circular hole while quasi-static crosshead movement of the testing machine pulls the fastened screw and thus the insert out of the panel until catastrophic failure. Table 24 sums up the test details of the performed pull-out tests. The tests were performed in two test series on different testing machines. The fully potted configurations were tested on a Zwick-Roell T1-FR050TH.A1K equipped with 25 kN load cell, while a total of 21 specimens were prepared for each configuration. The partially potted configuration was tested on a Galdabini Quasar 100 testing machine using an HBM S9M-10 kN load cell, while 12 specimens were prepared. Table 24 Summary of performed insert pull-out tests

Test standard

Based on IDH [ESA11]

Specimen dimension

100 mm x 100 mm / Thickness depending on configuration

Fixture hole diameter

D = 80 mm

Loading rate

10 mm/min

Testing machine

Galdabini Quasar 100 / Zwick-Roell T1FR050TH.A1K

Load cell

HBM S9M-10 kN / 25 kN Zwick load cell

Displacement measurement

Machine crosshead

The test results of the four tested configurations are given in Figure 72 in terms of forcedisplacement relationships. Regarding the fully potted inserts all three investigated configurations exhibit the same bi-linear curve progression and damage mechanisms before catastrophic failure. However, it becomes apparent that with increasing core height, the stiffness degradation after damage initiation increases, leading to a less pronounced second linear regime with reduced slope in case of the thicker panels. The partially potted configuration is characterized by more rapidly progressing damage mechanisms leading to catastrophic failure shortly after damage initiation. All tested configurations are subject to considerable scatter regarding the peak force as well as damage initiation force

98

6 Mechanical characterization on sub-component level

(up to 40%). Images of the test setup are given in Figure 73. A more detailed analysis of the experimental results is given in the following chapter as part of the proposed virtual testing approach.

Figure 72 Experimental results of the four tested insert configurations under pull-out loading a)

b)

Figure 73 Pull-out test setup a) top view and b) bottom view (FP-19-101)

6.1 Threaded inserts perpendicular to the face sheet

99

6.1.2 In-plane tension (shear) The in-plane tension test is also referred to as shear or parallel tension test. Analogous to the pull-out test there are no clearly defined test standards, however there are references in the literature. For instance, the IDH [ESA11] suggests two setups, both of which are found in the reviewed technical literature. In the present work the shear test is roughly based on the ASTM F606-95b [AST95]. This test requires rectangular specimens that contain two inserts with a defined distance to each other and to the edges. A rectangular steel plate with a bore hole is loosely fastened via a screw onto each insert allowing rotation of the specimen. The steel plates are clamped in the machine using self-tightening wedge grips. The crosshead movement of the machine exerts a tensile load to the panel resulting in a shear dominated loading for both inserts. In case of partially or fully potted inserts, the setup is non-symmetric and does not allow pure tensile loading of the panel. Therefore, the panel is additionally loaded in bending. Table 25 gives a summary of the performed insert shear tests. In the present work only the partially potted insert configuration was tested in shear. Analogous to the pull-out test of this configuration, the shear tests were performed on a Galdabini Quasar 100 testing machine using an HBM S9M-10 kN load cell, while 12 specimens were tested. Table 25 Summary of performed insert shear tests

Test standard Specimen dimension Distance between inserts

Based on ASTM F60695b [AST95] 100 mm x 190 m x 26 mm L = 85 mm

Loading rate

10 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-10 kN

Displacement measurement

Machine crosshead

The experimental results are given in Figure 74 a) in terms of force-displacement relationships. Figure 74 additionally illustrates the test setup along with the prevailing visual damage pattern. The specimens exhibit significant scatter in terms of both, strength and stiffness. It is assumed that misalignment of the steel plates is largely responsible for the scatter of up to 20%. All specimens are characterized by face shear rupture and face

100

6 Mechanical characterization on sub-component level

wrinkling due to core crushing on the compression side of the insert. The experimental results are described in more detail in the problem analysis step of the virtual testing approach, which is introduced in the following chapter. a)

b)

c)

Figure 74 a) Experimental results of insert shear tests, b) Test setup and c) failure mode

6.2 L-Joints L-joints are a common feature in aircraft cabin components. Therefore, a typical L-joint configuration is included in the present work. As introduced in section 2.2.2, critical load cases for sandwich corner joints include shear and bending. The literature provides limited references for structural testing of L-joints. Mund et al. [Mun15] tested foam based sandwich L-joints with a bonded extrusion comparing different test setups. In these tests one panel is mounted vertically onto a fixture, while the free horizontal panel is loaded vertically similar to a cantilever beam. However, this setup results in a combined bending and shear loading, making it difficult to characterize the failure modes systematically. Heimbs and Pein [Hei09] characterized the damage mechanisms of three different L-joint designs using a systematic analysis method where the joints are investigated separately under shear and bending in two specifically designed experimental setups. These setups serve as reference for the present work. In the following, the investigated materials are introduced before the experimental setups and results are described. Materials and configurations One configuration of a mortise joint comprising a 26 mm panel bonded to a 10 mm panel is investigated. In this configuration, the 10 mm panel contains two 10 x 60 mm pockets while the 26 mm is prepared with two respective tenons. The specimens have legs of equal length and consist of materials which have already been studied on sub-component and constituent level. In order to reinforce the free edges of the specimens for load

6.2 L-Joints

101

introduction solid sections were bonded into both panels locally replacing the honeycomb core. These sections are made of laminated plastic based on the Airbus standard ABS5722 A250 [Air12], which is a common material for reinforcing sandwich panels in aviation. The applied materials and specimen dimensions are summarized in Figure 75.

Figure 75 Investigated materials and panel configuration for corner joints in case of bending setup

6.2.1 L-Joint bending test In the implemented bending test setup the free joint edges rest on linear bearings while the load is applied to the corner via a loading plate. Therefore, both legs of the specimen are bent open with increasing crosshead displacement. The linear bearing support is implemented using plates which rested on a pair of cylinders. The tests were performed on a Galdabini Quasar 100 universal testing machine, while a total of 10 specimens were tested. A summary of the test details is given in Table 26. The test results in terms of force-displacement curves are illustrated in Figure 76. In this experimental setup, the specimens exhibit a damage tolerant behavior with no catastrophic failure at high displacements up until 25 mm. The curve progression after first failure is characterized by a moderate load drop followed by moderate load increase, leading to a parabolic shape. The dominant associated damage mechanism is core crushing in the corner. In particular the thinner panel penetrates into the core of the thicker panel leading to local in-plane core crushing and delamination of the face sheet. Therefore, the joint strength is limited by the low in-plane strength of the core. Significant scatter is evident in terms of force at first failure, while the initial stiffness appears to be constant. This indicates that the

102

6 Mechanical characterization on sub-component level

specimens were placed consistently in the fixture, yet the local conditions in the bonded section appear to be inconsistent leading to different force levels at failure initiation. It is assumed that one main aspect here is the condition of the bond between the face sheets of both panels. Table 26 Summary of performed L-joint bending tests

Specimen dimension

Based on Heimbs and Pein [Hei09] 200 mm x 140 mm x 140 mm

Loading rate

10 mm/min

Testing machine

Galdabini Quasar 100

Load cell

HBM S9M-10 kN

Displacement measurement

Machine crosshead

Test standard

a)

b)

Figure 76 a) Experimental results of L-joint bending test, b) L-joint bending test setup

6.2.2 L-Joint shear test In the shear setup, the 26 mm panel is clamped horizontally onto a base plate using a beam, while a constant distance between clamping beam and vertical 10 mm panel is maintained. The clamping force is limited in order to prevent core crushing. For the shear tests a bore hole is added in the center of the solid edge filling of the vertical 10 mm panel. A tensile load is applied to this bore hole via a bolt. The tests were performed on

6.2 L-Joints

103

the same machine using the same parameters as the L-joint bending tests. (Table 27). The experimental results are given in Figure 77. Table 27 Summary of performed L-joint shear tests

Test standard Specimen dimension Distance to fixture Loading rate

Based on Heimbs and Pein [Hei09] 200 mm x 140 mm x 140 mm D = 5 mm 10 mm/min

Testing machine

Galdabini Quasar 100

Load cell Displacement measurement

HBM S9M-10 kN

a)

Machine crosshead b)

Figure 77 a) Experimental results of L-joint joint shear test, b) L-joint shear test setup

The curve progression is generally similar to the bending tests. The joint failure is again dominated by core failure of the thick panel. However, in this case it is transverse shear. Therefore, the joint shear strength is considerably higher if compared to the bending strength of the same panel. After the first load drop due to failure initiation the load increases despite progressing shear failure of the core. This is due to the top face sheets of the tenon, which are still intact increasingly becoming loaded in tension. The tests were aborted in this final stage. It is assumed that catastrophic failure would have occurred once the bond of the upper face sheet ruptures.

7

Virtual testing approach for sandwich panel joints

This chapter describes the developed approach for virtual testing of sandwich panel joints using the sub-component tests of chapter 6 as example and for validation. The investigations in chapter 4 and 5 are integral parts of this approach. Therefore, aspects of these chapters are revisited and put into perspective of the approach. In the following, an overview over the approach and it’s four phases is given in section 7.1. Then each phase is described in section 7.2, 7.3, 7.4 and 7.5 using a demonstration example. Sections 7.6 and 7.7 summarize and conclude with additional case studies as validation.

7.1 Overview The approach is based on the premise, that there is a reference physical test, which represents the top level of the building block pyramid in the investigated scope. It is assumed that measurement results and documentation of the reference test are available based on a reference test article. In order to implement a virtual test method, which can replace or complement the physical test, the virtual testing approach suggests four phases which are schematically illustrated in Figure 78. Physical reference test 

Measurement results



Test documentation



Strucutral tests and analysis methods Iteration

1 



Problem analysis Definition of application & requirements Identification of mechanical effects

2  

Definition of model framework Definition of level of detail Selection of time integration/solver

3

Model development 

Building blocks



Investigations



Material Data and Modelling Base

Figure 78 Schematic of the developed approach

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_7

4

Application of virtual test method 

Parameter studies



Evaluation of design alternatives

106

7 Virtual testing approach for sandwich panel joints

The four phases relate to the nine steps of Ashby’s flowchart [Ash92], while each phase integrates multiple steps of Ashby. In Phase 1, the field of application for the virtual test is defined. Based on this, the requirements are derived before the relevant mechanical effects of the reference physical test are identified. In Phase 2, the model framework is defined. This includes the definition of the level of detail which enables to capture the relevant mechanical effects. In conjunction, the time integration method and hence the solver is selected. The most extensive part of the virtual testing approach is the following hierarchical model development in Phase 3, which generally follows the Building Block Approach. In the final Phase 4 the developed models are applied for design studies, according to the initially defined field of application. Depending on the performance of the virtual test method additional iteration loops are required, which lead back to Phase 2. In the following sections, the four phases are described in detail based on an integrated example, which is subsequently introduced. Demonstration example As demonstration example, the fully potted insert SL607-08-6S under pull-out loading is selected (Figure 79). This is a common insert type, which has been studied by various authors, making it a suitable example. The corresponding experimental study is described in section 6.1.1 (p. 96). For the implementation as virtual test, all three investigated core heights for this insert configuration are considered. FP-10-101 10 mm FP-19-101 19 mm

Face sheets ABS 5047-02 ABS 5047-08

Insert SL607-08-6S Adhesive Ureol

Fully potted

FP-26-101

Pull-out test

Core ABS5035-A4

26 mm

Figure 79 Demonstration example for the virtual testing approach

7.2 Phase 1 - Problem analysis In the problem analysis phase, the application and requirements for the virtual test are initially defined. Subsequently, the relevant mechanical effects are identified. Existing measurement results and documentation of the reference test serve as input for this identification. In case the available data is not sufficient to identify all relevant mechanical effects, additional structural tests and/or analysis methods are required. The process step of structural tests and analysis methods is described in detail in section 7.4, since it is typically executed within the investigations during the model development. However,

7.2 Phase 1 - Problem analysis

107

since it may be required during the problem analysis it is introduced here. Phase 1 ends once the mechanical effects are identified and the list of relevant effects is established. This procedure is illustrated in Figure 80 as flow chart. In the following, the different process steps are described. 1

2 Problem analysis

Definition of model framework

3

4 Model development

Application of virtual test method

Physical reference test

Start

Field of applicaiton and requirements

Physical test results

Structural tests and analysis methods

Definition of application and requirements

Identification of mechanical effects

no Mechanical effects identified

yes

List of relevant effects

End

Figure 80 Flow chart of Phase 1

Definition of application and requirements Based on the definition of virtual tests given in 2.4, the primary requirement is typically that the model is capable to predict the progressive damage up until catastrophic failure as in the reference test. However, depending on the intended application of the model the prediction of damage initiation may be sufficient, while other applications may require the prediction even of the post failure behavior. This aspect can be referred to as degree of damage modelling, while a high degree corresponds to representing the complete damage progression beyond failure. Another important requirement concerns the computational effort. For instance, models intended to be applied in optimization studies have to be run hundreds or thousands of times, thus requiring little computational effort. In other applications long computing times of several days may be tolerable allowing high detail and accuracy. Regardless the degree of damage modelling and computational effort, the present approach distinguishes between the following typical application scenarios 

Studying unknown configurations of existing panel joints



Benchmarking alternatives for novel insert designs

In the former scenario, reference constituents are replaced in order to draw conclusions regarding their effect on the strength of the joint. This resembles a parameter study, since replacing constituents corresponds to changing material parameters of the model. The latter scenario extends the application towards the development of novel insert designs, where the effect of different designs on the joint strength is benchmarked based

108

7 Virtual testing approach for sandwich panel joints

on virtual tests. Therefore, this typically involves drastic changes in the geometry of the joint. Lastly, in case the virtual test is intended to predict uncertainties, the corresponding requirements for the probabilistic analysis need to be defined in Phase 1 as well. Therefore, the three main aspects that should be addressed by the requirement definition are as follows 

Degree of damage modelling



Computational effort



Uncertainty (not covered in this work).

With regards to the demonstration example, the intended application is the evaluation of the effect of different constituents (face sheet, honeycomb core, adhesives and inserts) on the pull-out strength. Therefore, only a limited number of design alternatives are to be studied. At the same time, the model should be able to predict the point of catastrophic failure. A computational time in the range of about 2 h to 4 h per simulation is targeted. This allows to perform a full parameter study containing several simulations runs over night. The model is supposed to run on a state-of-the-art Intel i7 workstation. No uncertainty analysis is considered. Identification of relevant mechanical effects In the second part of the problem analysis phase the governing mechanical effects are identified based on available results and documentation of the reference test. These effects generally correspond to the damage mechanisms, which contribute to the overall failure behavior. The required test documentation generally includes the force-displacement or stress-strain relationship, which characterizes the mechanical response and damage progression of the specimen. In addition, live examination results such as video recording as well as pre- and post-test analysis of the specimens are required. The exact set of required test documentation and analyses depends on the investigated specimen and the evident damage mechanisms. Common analysis methods are introduced in section 7.4, where the process of structural tests and analysis methods as part of the model development phase is described. Once the mechanical effects and damages are identified, they are mapped onto the test progression in order to ensure that the sequence of the effects is understood. This can be done by sub-dividing the force displacement curve into stages and assigning the different effects to these stages. Depending on the required degree of damage modelling, the relevant mechanical effects are lastly established. Phase 1 concludes with a list of relevant mechanical effects, which have to be implemented in order to represent the failure behavior observed in the reference test. In case of the demonstration example, the reference test was observed simultaneously from the top and the bottom by two cameras with 120 fps. This ensures that the behavior of both faces is captured throughout the test. Since the damage progression in the

7.2 Phase 1 - Problem analysis

109

tests is relatively slow, there was no need for high speed cameras. The pre-test analysis was limited to visual inspection and measuring the key geometric dimensions. The posttest analysis was primarily based on visual inspection of a section cut of the specimen. An image of a section with the identified damage mechanisms is given in Figure 81 a) in case of the 19 mm configuration. In order to assign the damage mechanisms to the test progression, the force displacement curve of the reference test is subdivided in five characteristic stages. Images of the specimen exterior in each stage are given in appendix C1. b)

a) Shear buckling of cell walls 2

3

Face rupture

5

Face shear damage 3

5

4 4 3 2

Debonding of adhesive and face sheet 3

4

Debonding of core and face sheet 5

5

1

Figure 81 Identification of mechanical effects in reference test; a) section of specimen after the test; b) single force displacement curve of FP10-101 with assigned progression stages

A single force displacement curve, which represents the curve progression of all tested configurations is illustrated in Figure 81 b). Out of the identified damage mechanisms, all but the core damage can also be observed in the videos of the live observation. Therefore, these mechanical effects can be easily assigned to the test progression. Mapping the core damage is more difficult, since it cannot be observed from the exterior. However, based on available literature assumptions are made that enable to assign the core damage with high certainty. The five test progression stages and the corresponding mechanical effects are explained in the following. Stage ① represents the linear elastic displacement of the undamaged structure. Stage ② describes the quadratic flattening of the curve due to shear buckling of the honeycomb cell walls adjacent to the adhesive. In case of honeycomb sandwich inserts this was reported by several authors as first damage mechanism [Hei09], [Roy14], [Son08] and it also reflects the expectation, that the core as weakest component experiences damage first. During the tests, no additional damage was visible from the exterior up until this point.

110

7 Virtual testing approach for sandwich panel joints

Stage ③ represents another linear regime, where the load increases despite previous core damage. In this stage, the shear transmission of the damaged core is reduced, leading to a change of the load path. From this point onwards, the bond between adhesive and lower face experiences increased stress. This is also visible in the exterior live observation of the test, where the bonded surface area between these two constituents is decreasing throughout this stage (Figure 73, page 98). At the same time, the core damage progresses and shear damage initiation of the increasingly stressed top face sheet is visible by the end of the stage. Stage ④ marks catastrophic failure of the structure, which is evident by a sudden 50% load drop. This failure occurs not before adhesive and bottom face sheet have fully debonded. Stage ⑤ represents the post failure regime. Here, rupture of the upper face sheet and debonding of upper face sheet and core occurs. Since it is not required to predict the post failure regime accurately, the two effects in stage ⑤ are of secondary interest in the example. The relevant mechanical effects are therefore all effects, that occur in stages ②-④. The virtual test method is required to enable the prediction of these mechanical effects. They are summarized as follows. 

Core shear failure



Face shear damage



Adhesive to face debonding

With the mapping of the damage mechanisms to the test progression and the identification of the relevant mechanical effects the problem analysis phase concludes. The following section addresses the definition of the model framework for the virtual test.

7.3 Phase 2 - Definition of model framework The objective of Phase 2 is to set the framework for the FE-models to be developed in Phase 3. The definition of the model framework depends on the previously identified list of relevant mechanical effects. It can be subdivided in three general steps. Firstly, the level of detail of the virtual test model is defined. Subsequently, the time integration method is selected. The combination of level of detail and time integration method makes up the model framework. In the last step, the model framework is evaluated. In case the framework is evaluated as not suitable, an iteration loop leading back to the definition of level of detail is required. This last step is implemented to ensure that the model framework is defined with care. If the framework is changed later on, considerable rework is required. A flow chart of phase 2 is illustrated in Figure 82.

7.3 Phase 2 - Definition of model framework

1

111

2

3

Definition of model framework

Problem analysis

4 Model development

Application of virtual test method

Start

Definition of level of detail



In-plane damage



Out-of-plane damage



Symmetry about panel plane



Axisymmetric loading



Detailed meso-scale

3D-continuum

Quasi 3D-continuum (axisymmetric)

2D-shell

 

Isotropic materials

In-plane and out-ofplane damage



Large core deformation with multiaxial loading

Orthotropic materials



Optimization of cellular cores

Selection of time integration Explicit

Implicit



More than two nonlinear effects



Up to two non-linear effects



High loading rates



Quasi-static loading

no Preliminary evaluation 

Convergence



Compuational effort

Framework suitable

yes

End

Figure 82 Flow chart of Phase 2 with illustration of different modelling approaches

Definition of level of detail The definition of the level of detail corresponds to the four groups of computational models of sandwich structures which are introduced in section 2.3 (Figure 16, p. 18). The present work focuses on virtual tests by means of FE-models. Therefore, only the introduced FE-modelling approaches are considered. The given flow chart illustrates the different levels of detail based on standard inserts under pull-out loading as example. If compared to Figure 16, the quasi 3D-continuum models are here distinguished as separate level of detail. Therefore, the presented virtual testing approach suggests four levels of detail to choose from in Phase 2. These are described further in the following. 2D-shell and plate models can be used efficiently in applications where symmetric inplane damage mechanisms are dominant. However, the 3D-continuum and detailed models are generally most suited for advanced non-linear simulations such as required for virtual tests, since they also enable to adequately represent out-of-plane damage

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mechanisms. This is also evident in the reviewed literature where most introduced models for sandwich joints correspond to one of these three levels of detail. The quasi-3Dcontinuum models have the lowest computational cost and are therefore most suited for preliminary design and optimization studies. However, the geometry representation is limited to axisymmetric joint designs. This is not the case for honeycomb sandwich inserts, which have an irregular interface between potting and core. This effect can be modelled with true 3D-continuum and detailed models. The advantage of the detailed models is their capability to model the buckling of the cell walls due to core shear accurately. This yields better results when high shear deformation beyond core damage initiation occurs. Furthermore, the accurate geometry representation is considered to be superior in multiaxial stress states of the core. Due to the homogenization, 3D-continuum models are limited in representing these effects, as it was shown in the performed bending study (section 5.1.2) In addition, detailed models enable to perform design studies with cellular cores for instance for the development of novel core geometries. Expectedly, detailed models require by far the highest modelling and computational effort. Therefore, the expected computing time of the eventually implemented virtual test strongly correlates with the core modelling approach. This is also shown in the performed bending study, where the detailed core models required 5-10 times more computational time. Therefore, detailed models generally yield computing times in the range of several hours. They are therefore less suitable for extensive optimization studies. In this case 3D-continuum models are the preferred choice, since they can be optimized to run in a matter of minutes. However, this comes at the cost of reduced degree of damage modelling. In addition, 3D-continuum models are generally sufficient for homogenous cores such as foam and in case of honeycomb when the core deformation after damage initiation is limited. Selection of time integration The second step of Phase 2 addresses the definition of the time integration scheme for the virtual test. As discussed in 2.3.1 both, implicit and explicit integration, have their specific field of application where they are most suited. However, virtual tests often stand in between. In case of quasi-static tests, the implicit method is generally favorable. However, with increasing non-linearity of the simulation, implicit solving encounters increasing difficulty with regards to convergence. As depicted in Figure 17 on page 20, single non-linear effects up until rupture can often still be represented. However, virtual testing of sandwich panel joints often involves multiple non-linear effects from the different constituents. Furthermore, including the fixture in the simulation often requires implementing a penalty contact, thus further adding a non-linear effect beyond the material behavior of the constituents. A high degree of non-linearity generally corresponds to the number of non-linear effects to be reflected in the model. This is where the robustness of explicit solvers is advantageous. As rule of thumb it has been established

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that more than two non-linear effects should be implemented using explicit integration. Implementing an explicit simulation model is also advantageous when it comes to detailing an existing model by integrating additional mechanical effects in a later stage. Therefore, the explicit integration scheme can be considered more robust for future model refinement. However, for quasi-static problems with few non-linear effects, the implicit integration scheme remains favorable. Preliminary evaluation The model framework has to be consistent throughout the model development. It defines critical model aspects such as material models, elements and contact formulations. Changing the framework during the model development should be strictly avoided. Therefore, the last step of Phase 2 is the evaluation of the defined model framework. This step corresponds to a final check, where the following question is raised. Is the model framework suitable for the intended virtual test? Generally, the definition of the level of detail and integration scheme is suitable as long as the guidelines summarized in Figure 82 are followed. However, it is possible that some degree of uncertainty remains due to a lack of literature or past experiences. In this case a comparative study where the performance of the integration schemes and/or levels of detail is benchmarked using a representative model for the top-level virtual test should be performed. In this context, performance refers to both, computational effort and the capability to represent the relevant mechanical effects. A prominent issue here, is convergence in case implicit integration is selected. At the same time, the computational effort should be evaluated, to ensure that the expected computation time is likely within limits regarding the requirements. Phase 2 concludes when the defined model framework is evaluated to be suitable for the following model development. With regards to the demonstration example, a detailed meso-scale model in combination with the explicit integration scheme is defined. This enables to represent the nondiscrete nature of the potting to core interface and the considerable non-linear core deformation before catastrophic failure as identified in the problem analysis phase. Explicit integration is selected, due to fact that in the majority of the reviewed studies on nonlinear cellular sandwich core modelling the explicit method was implemented. Furthermore, the problem analysis phase has reveals at least three non-linear material effects that have to be implemented in order to predict the point of catastrophic failure. Definition of modelling approach 2D-shell

Quasi 3D-continuum (axisymmetric)

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Figure 83 Defined model framework for demonstration example

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These include, core shear buckling, face shear damage and face to potting adhesive debonding. In addition, there is a contact between specimen and fixture, which may have to be implemented as well in order to represent the reference tests appropriately. This is considered as high degree of non-linearity thus pointing towards the application of the explicit method, despite the quasi-static nature of the reference test. Based on the available literature and past experience, no additional performance study is performed. Figure 83 illustrates the defined model framework based on the previously introduced flow chart.

7.4 Phase 3 - Model development The objective of the model development phase is the implementation of the reference test as FE-simulation and thus as virtual test. This requires a complete set of material and modelling parameters, which adequately represent the physical test configuration. These material and modelling parameters are determined in investigations. The investigation represents the central reoccurring procedure in the development phase. The investigations are structured hierarchically based on the building block approach, where the top-level corresponds to the reference test. Each investigation is associated with a specific building block, while there can be multiple investigations for a single building block. The building blocks are addressed consecutively bottom-up. When traversing the building blocks, it is defined what investigations are required. Each investigation typically corresponds to a mechanical effect or a set of material properties, which is not yet part of the modelling database. However, an investigation may also be the synthesis and verification of available model parameters from a lower building block to a higher level. 1

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Figure 84 Flow chart of the model development phase (Phase 3)

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The procedure for the investigations is based on close interaction between simulation and available physical test data with the objective to virtually represent the physical tests. The building blocks and the corresponding investigations are continued until the top-level and thus the reference test is implemented as virtual test. The gained knowledge of the investigations is transferred into the modelling database. Therefore, the effort in future virtual test implementations is reduced in case existing material properties and modelling aspects can be adopted. A flow chart for Phase 3 is given in Figure 84. In the following, the general procedure for investigations is described before the building blocks and the modelling database are described.

7.4.1 Investigation The objective of an investigation is generally the determination of verified model parameters for the top-level virtual test. The required model parameters and the corresponding investigations are defined in the preceding building block considerations. There are three main steps in each investigation. In the first step structural tests and analysis methods are performed. The obtained test results serve as physical benchmark for the following virtual representation. In the second step the performed physical tests are modeled as virtual test. The FE-modelling is accompanied by numerical studies, which are intended to establish suitable material models and to reduce the computational effort of the model according to the requirements defined in Phase 1. The second step concludes with simulation results. The third step is concerned with the model calibration and verification. This is done by matching the physical test results with the simulation results. In case the simulation does not represent the physical test sufficiently, it is returned to the previous step and the implemented FE-model is adjusted. This calibration is repeated until the simulation results match the test results. The outcome of the investigation is a set of verified model parameters, which is transferred to the modelling database. The general procedure for investigations in Phase 3 is illustrated in Figure 85. Physical test results

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Figure 85 General procedure for investigations in Phase 3

This procedure can be applied universally for any investigation in any building block. However, the extent of the different steps varies depending on the complexity of the

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investigation. For instance, more complicated material models (i.e. orthotropic including fracture) naturally require more structural tests and thus more FE-models and numerical studies for deriving all material parameters if compared to simple material models (i.e. isotropic elastic). Similarly, the number and type of analysis methods may differ depending on the composition of the specimen and the failure behavior. In the following, the three steps are described using the example of the detailed honeycomb core of the reference test configuration. This is an extensive constituent level example, which gives a good overview over the different studies that may be required for building block investigations. The mechanical characterization of the applied honeycomb core including the implemented numerical models are described in section 4.1. Therefore, many references to this section are made in the following paragraphs. Structural tests and analysis methods Structural tests and analysis methods are the foundation of any Phase 3 investigation. In addition, this step can also be found in Phase 1. This is due to the fact that the results of the top-level physical reference test are required as input for the identification of mechanical effects. The structural tests can be generally subdivided in standard material tests and custom component tests. The tests in the two lower building blocks tend to belong to the former category, while the top-level reference tests are usually custom tests, which are designed for a specific joint type. These tests result in progressive forcedisplacement or stress-strain relationships, which characterize the mechanical behavior of the tested structure. In parallel to the structural tests, analysis methods are performed with the objective to determine the composition and geometry of the tested structure as well as to understand the failure behavior. Structural tests and analysis methods

Structural tests Standard material tests

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Microscopy Section cuts Thermography CT-scan

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Figure 86 Flow chart of structural tests and analysis methods process step

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The analysis methods can be subdivided in live examination and pre- and post-test analysis. In its most basic form, live examination simply means visual observation of the reference test. This is typically documented using video images if necessary from multiple angles. It is preferable, if the video images can be related to the test progress, for instance by displaying live test parameters such as force and displacement in the field of view of the cameras or by feeding this information directly to the camera system. Due to the often rapid progression of damage, many applications require high-speed cameras to capture all relevant effects. Video images of the specimen can also be used for digital image correlation (DIC) given that the specimens are prepared for such analysis. This enables to determine strain fields over large areas of the specimen. Another form of live examination of the reference test is recording the acoustic emission, which can help to identify specific damages such as fiber rupture in the face sheet. Pre- and post-test analyses ensure that the state of the specimen before and after testing is captured and documented. Pre-test analysis is required to determine the necessary geometric input to for the computational model. In addition, significant imperfections or pre-damages are determined. The post-test analysis identifies all damages after testing. Both analyses apply similar methods, such as visual inspection, light microscopy, computer tomography (CT) and thermography. The sum of analysis results and test results yields the physical test results, which is the main output of this process step. Figure 86 illustrates a flow chart of the structural tests and analysis methods step. As initially introduced, the detailed honeycomb core of section 4.1 shall serve as example to further explain the first step of building block investigations. Figure 87 displays the performed structural tests and analysis methods for deriving a constituent material model for the honeycomb Nomex cell walls. Four structural tests were performed. These represent standard sandwich core tests, which also correspond to the main damage mechanisms that can occur it sandwich cores. It is assumed, that the constituent cell wall material model can be applied universally if it is capable to reproduce the mechanical behavior in all four tests. The performed tests yield four force-displacement relationships, which are converted into stress-strain curves based on the specimen geometry (see Figure 32, Figure 33 and Figure 34 from page 40 onwards). Structural tests Flatwise compression

Transverse shear L

Force-displ.

Transverse shear W

Analysis methods Flatwise tension

Pre-test insepection

Live examination

Microscopy

Video images

Figure 87 Overview of the performed structural tests and analysis methods in case of the of detailed honeycomb core example

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Regarding the analysis methods, no additional post-test inspection was performed. This is not necessary since the recorded life examination video images provide sufficient detail regarding the damage mechanism. However, pre-test inspection was performed based on polished sections of the tested honeycomb cells, which were investigated under a light microscope. This is described in section 4.1.1. As a result of this analysis, the irregular hexagon shape, cell wall thicknesses and resin distribution are characterized. In sum, the first step of a building block investigation provides experimental data, which characterizes a material or a mechanical effect for instance by means of stress-strain or force-displacement relationships. This is complemented by analysis method results such as video recordings, which provide reference for the progressive failure behavior. Additional analysis methods such as pre-test light microscopy may provide geometric data for the FE-model representation. FE-modelling and numerical studies In the second step, the previously performed tests are remodeled using FEM based on the defined model framework of Phase 2. The objective is to implement a FE-model, which represents the failure behavior of the physical tests adequately. This step can be subdivided in two parts. The FE-modelling initially merely corresponds to generating a geometry representation of the specimen and if applicable the fixture using finite elements. In parallel, multiple numerical studies are performed based on the generated FErepresentation in order to define all additional model parameters. FE-modelling & numerical studies

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Figure 88 Flow chart for the FE-modelling and numerical studies process step

The modelling database serves as input for the numerical studies and may provide reference for some model parameters, thus reducing the effort for numerical studies. The

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combination of geometry representation and model parameters yields the virtual test, which in turn produces the virtual test results. Figure 88 illustrates a flow chart of the FE-modelling and numerical studies process step. In the following, the FE-modelling and the numerical studies are further explained based on the detailed honeycomb example. Figure 89 gives an overview of the performed modelling and numerical studies in case of this example. Numerical studies

FE-modleling Parametric FE-geometry representaiton

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Figure 89 FE-modelling and numerical studies in case of the detailed honeycomb example

FE-modelling The objective of the FE-modelling sub-step is the implementation of the preceding test setups as virtual tests. The first task here is to generate a geometric representation of the test article and if applicable the fixture using finite elements, while the previously defined model framework largely dictates the element types to be used. In addition, the available physical test results provide input regarding the geometry of the tested specimens based on pre-test inspection. In order to turn the FE-geometry representation into a virtual test, additional model parameters are required. These are determined in the numerical studies sub-step. Regarding the detailed honeycomb example, a parametric FE-geometry representation was implemented in order to enable quick generation of different geometries for the numerical studies. The parametric FE-model requires the hexagon geometry based on the lengths of the hexagon sides as input (a, b and c in Figure 90). This unit cell can be repeated in W- and L-direction of the core to generate arbitrary model scales. In addition, the mesh size and the core height can be set as input parameter. This parametric FE-model is illustrated in Figure 90. It was used to implement the finite elements of all four tested configurations, flatwise tension and compression, transverse shear in L- and W-direction.

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Figure 90 Parametric FE-geometry representation of detailed honeycomb example

Numerical Studies Numerical studies can be considered as preliminary studies with the objective to understand and quantify the impact of relevant model parameters on the virtual test results. Based on this, the numerical studies are ultimately intended to help to define or select the respective modelling aspects in such a way that the requirements and relevant mechanical effects from Phase 1 can be reflected adequately in the virtual test. In addition, the numerical studies ensure that the obtained virtual test results are not dependent on the setting of certain numerical parameters. Therefore, many numerical studies are concerned with the convergence of numerical parameters such as mesh size, loading rate or mass scaling. In addition, numerical studies address modelling aspects in a broader sense such as boundary conditions, material models and element types. In this context, numerical studies are intended to optimize model parameters for computational effort. This is mainly due to the model calibration in the following step, which requires numerous simulation runs and therefore benefits from short simulation times. The numerical studies can be categorized in three groups, numerical parameters, system boundaries and material modelling. Numerical study

FE-geometry representation

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Figure 91 General procedure for numerical studies

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An overview of the categories along with a list of relevant parameters for each category is given in Figure 88. The numerical studies generally follow the same procedure, which is illustrated in Figure 91. This procedure begins with the definition of a benchmark model parameter set. This corresponds to selecting reasonable dummy values for all relevant model parameters as given in Figure 88. Therefore, the benchmark parameter set is defined based on experience (i.e. from modelling database) and it may require some trial and error to find suitable parameters. In parallel, a certain number of increments or variants is defined for the model parameter to be studied. For instance, this could be mesh size increments or different material models. Subsequently, the benchmark model parameter set is implemented together with the FE-geometry representation and the simulation is performed n times, depending on the number of increments or variants for the studied model parameter. The obtained simulation results are then evaluated based on the requirements of Phase 1 and the model parameter, which best suits the requirements, is selected. The numerical study sub-step concludes when all relevant model parameters are defined. In the following, the three categories of numerical studies are described in more detail based on the detailed honeycomb example. Numerical parameters There are general numerical parameters, which greatly influence the accuracy of the simulation results and at the same time the computational effort. It is therefore common practice to perform convergence analyses, in order to determine suitable parameter settings. In case of the explicit integration method, mass scaling and increased loading rate are standard methods to reduce the computational time of quasi-static simulations. Mass scaling achieves this by increasing the nodal mass of the model in order to increase the critical time step, while an increased loading rate leads to a reduced time period of the simulation. Therefore, both parameters reduce the number of required time increments. However, they also influence the kinetic energy of the system. Excessive mass scaling and loading rate lead to unstable and inaccurate results. This is illustrated exemplary in Figure 92, where one of the performed sensitivity studies for the detailed honeycomb investigation is illustrated based on flatwise compression. The implemented benchmark parameters in terms of mesh size and boundary conditions are described in section 4.1.3 from page 44 onwards. The model scale was defined as depicted in Figure 37 on page 48 and a SL isotropic material model was used as benchmark. Four increments of mass scaling were studied, while the results are given as stress-strain curves in Figure 92. It can be seen that a time increment of 1e-4 s leads to inaccurate results. Therefore, the time increment should have an upper limit of about 1e-5 s. In case of implicit time integration similar sensitivity studies may be required in order to determine a reasonable amount of damping for stabilization of non-linear simulations. Regardless the time integration method, sensitivity studies regarding the mesh size (mesh convergence) are always recommended. Regarding the honeycomb core of

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the demonstration example, mass scaling and loading rate were investigated in sensitivity studies. The mesh size was implemented based on available literature.

Figure 92 Mass scaling sensitivity study for compression of honeycomb cells

System boundaries Another aspect that often requires numerical studies is the system boundary of the virtual test. The general objective is to determine system boundaries which provide full scale equivalent results at significantly reduced computational effort. In this context, it is generally desirable to exclude the fixture of a test setup in order to reduce the model size and complexity. However, depending on the test setup, the fixture may have a noticeable effect on the overall damage behavior. This can be determined in numerical studies, where the results off possible system boundary definitions are benchmarked. These studies typically include different levels of detail for the fixture (fixture modelling) and different sets of boundary conditions, which are meant to replace the fixture entirely. In this context, symmetry boundary conditions can also be considered for reducing the model scale. In case periodic or repetitive structures are investigated, the system boundary consideration can be extended to the implementation of periodic boundary conditions, which enable to greatly reduce the model scale without affecting the results. Therefore, the required model scale often correlates with the implemented boundary conditions and both model parameters are investigated jointly. Regarding the detailed honeycomb example, scale analyses were performed with two different sets of boundary conditions and three scale increments, while no geometric fixture was considered. In case of the periodic honeycomb structure, the model scale refers to the number of cells included in the model. Such scale analyses were done for all four virtual test setups, in order to reflect the different test configurations. The results of the performed study are illustrated in Figure 93 for the flatwise compression load

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case. It is shown that the model scale can be reduced from full scale (about 300 cells) to just eight honeycomb cells when using symmetry boundary conditions as described in Figure 35 (p. 46). The full system boundary analysis for detailed honeycomb cores is described in [See17]. 01L01W

02L03W

10L17W Full scale specimen

Figure 93 Numerical study on boundary conditions and model scale for flatwise compression on a honeycomb core

Material modelling Lastly, the material modelling approach typically requires additional numerical studies. An import input for this is the model framework from Phase 2, which largely predefines element types and the overall modelling approach. Despite this, there is still considerable freedom regarding the exact material model, the element formulation (i.e. under integrated vs. fully integrated), the section definition in case of composites and the consideration of imperfections. Since, these aspects are closely related they often have to be considered together. Hence, they jointly make up the material modeling approach. The objective of the material modelling studies is to preselect the mentioned modelling aspects such that the relevant mechanical effects of Phase 1 can be qualitatively represented. However, there is no calibration based on the physical test results. This is done in the following model calibration and verification sub-step. In case of the investigated honeycomb core, four material modelling approaches were implemented and benchmarked regarding computational results and effort (Figure 39, p. 50). In addition, the imperfect actual honeycomb cell geometry was compared with idealized hexagon geometries (Figure 38, p. 49). These studies result in the implementation of a homogenized single layer orthotropic material model based on irregular hexagon geometry. Such extensive numerical studies, as described for the honeycomb core

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require a multitude of variations of the implemented FE-model. This is aided by the derived parametric FE-model as illustrated in Figure 90. The second step concludes with a FE-model, which remodels the performed structural tests and qualitatively reproduces the occurring damage mechanisms and the recorded curve progression. The implemented model is optimized for computational effort and relevant numerical parameters have been demonstrated to converge. Model calibration and verification With an adequate FE-model implemented, the last step is the calibration of the model using the experimental results of the first step. Cox [Cox08] recommends that this task should be carried out using a formal approach like inverse problem methods. Such a model-based approach enables to quantify the degree to which a model parameter can be determined. Inverse problem methods are for instance described by Aster et al. [Ast13] and Tarantola [Tar04]. However, Cox also pointed out that these methods are difficult to implement for complex non-linear experiments. Inverse problems can also be solved using simpler methods such as curve fitting by minimizing the deviance between experimental and model results. Due to the universal applicability of curve fitting methods, they are suggested as primary calibration approach in the present work. The respective flowchart for the calibration and verification process step is illustrated in Figure 94.

Structural tests and analysis methods

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Figure 94 Flow chart for the model calibration and verification process step

In this process the physical and virtual test results are initially simply matched. This includes both, the results in terms of force-displacement (or stress-strain) relationship and in terms of visual damage patterns. Subsequently the agreement of virtual- and experimental test results is evaluated based on the requirements of Phase 1. In case the virtual test results fulfill the requirements, the model and the applied model parameters are considered verified. If this is not the case, an iterative calibration is performed. This can

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be supported by using integrated parameter fitting algorithms, which run the FE-model multiple times optimizing model parameters until convergence for predefined result figures is achieved. Computer aided engineering software packages often provide such capabilities (e.g. HyperStudy1). However, in order to perform such curve fitting, the model parameters to be adjusted have to be established, if not yet done. This can be done with the help of a design of experiment (DOE) study, which reveals the impact of several model parameters on the virtual test results. The model parameters that are typically adjusted to calibrate the model are material or cohesive parameters (i.e. modulus, strength or fracture toughness), while the corresponding material or cohesive model has been selected based on the previous numerical studies. In case of the investigated honeycomb core, there are four non-linear experimental curves (from the four test setups, see Figure 32 to Figure 34), which have to be fitted using a single set of material parameters for the cell wall material. This is a complicated task for curve fitting algorithms. Therefore, curve fitting has been performed by manual iteration based on a DOE study. The virtual test results of the implemented material modelling approaches after calibration are illustrated in Figure 44, page 56 and Figure 45, page 57. In addition, it has been shown that the calibrated model is capable to reflect the visual damage patterns as in the experiments (Figure 46). The third step and therefore the investigation concludes with a calibrated model of the investigated structural test. The applied model parameters have been verified and they are transferred into the Modelling Database for implementation in the following building blocks or in future virtual tests.

7.4.2 Building blocks The consideration of the building blocks is the starting point of the model development phase. The developed approach suggests three building blocks that need to be addressed (see Figure 95). The constituents generally refer to the involved materials for core, face sheets, adhesives and local reinforcements (i.e. inserts). Therefore, the primary objective of the constituent level is the implementation of suitable material models for all materials that can be found in the reference test configuration. The structural elements level is primarily concerned with bilateral bonding of the constituents and the effect of the bond on the combined mechanical properties. Therefore, the modelling of bonded zones is of primary interest. In addition, it is common practice to derive the degraded properties of bonded face sheets on structural element level (see section 4.2 on

1

Altair® HyperStudy® is a multi-disciplinary, design exploration, study and optimization software. (Altair, 1820 E. Big Beaver Rd., Troy, MI)

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p. 62). Lastly, the structural element level also enables to validate the material models determined on constituent level. On sub-component level, the objective is to synthesize the previous derived model parameters into the top-level virtual test. Furthermore, the bond between adhesive and face sheet is often characterized on sub-component level as well. This is due to the fact, that the strength of this bond is the result of the complete configuration including reinforcement and core. Therefore, this mechanical effect often cannot be isolated on structural element level. Figure 95 summarizes the described considerations within the building blocks. Model synthesis

Face to adhesive bond – cohesive model Bonded face sheet – material model

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Reinf. to core bond – cohesive model

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Figure 95 Generic overview of applicable investigations within the building blocks

An important aspect when traversing the building blocks is the definition of required investigations for each building block. The previously defined model framework and the identified relevant mechanical effects are major input parameters for this step. A selection of applicable material models as well as element and fracture formulations are predefined by the model framework while the required degree of damage modelling for the different constituents and structural elements is defined by the identified relevant mechanical effects. Therefore, there may be constituents, which simply require an isotropic elastic material model, while others may require a complicated orthotropic plastic material model including fracture mechanics. The same applies for structural elements, where the bond between constituents can be modelled as kinematic coupling or using cohesive behavior. All of these aspects translate to sets of model parameters, which are required as input for the top-level finite element model. For all model parameters that are unknown, investigations are required. Therefore, the available modelling database is cross referenced with the required model parameters in order to determine the required investigations. Figure 96 illustrates the procedure for defining the required investigations. This procedure is performed within each building block.

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Mechanical effects (Phase 1)

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Figure 96 Procedure for defining the required investigations within building blocks

When applying this procedure for the demonstration example, there is a total of five investigations required. This is illustrated in Figure 97. In the following, the considerations that lead to the definition of these investigations are described for each building block. The subsequent considerations are described from a perspective where it is assumed that there are no material and model parameters available except for general literature or manufacturer’s data. Face to adhesive bond – cohesive model

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Figure 97 Performed investigations in case of demonstration example

Constituent level The demonstration example (Figure 79, p. 106) comprises four constituents, honeycomb core, face sheets, adhesive and the insert. Each of them is addressed in the following paragraphs. Honeycomb core The honeycomb core has been declared a critical constituent for the overall damage progression, since core shear damage is the first damage mechanism in the reference test. At the same time, there are no applicable detailed material models for investigated core available in the literature. Therefore, the core has been investigated based on tensile, compressive and shear tests in order to derive a suitable modelling approach for the cell wall material. This investigation is described in section 4.1 from page 35 onwards.

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Face sheets The material properties of bonded face sheet prepregs are not available for the investigated face sheet layup. Yet, the face sheets have been identified as critical for the damage progression of the reference test. In particular, the shear damage initiation of the upper face sheet at the boundary of potting and core appears to influence the damage progression in stage ③ of the force displacement curve (see Figure 81 b), p. 109). Therefore, an investigation has been carried out to determine the face sheet material properties (section 4.2). However, on constituent level only tensile tests were performed because the face sheets are very thin making it difficult to perform compressive and shear tests on unsupported specimens. The tested specimens were removed from a bonded sandwich panel in order to account for degradation due to sandwich bonding. Based on the tensile tests, the elastic modulus and tensile strength in both material directions have been determined (Figure 52, p. 67). Adhesive/Potting In Phase 1, no damage of the adhesive has been identified. Therefore, the adhesive is of secondary concern on constituent level. However, from the literature review it is known that the material properties of the potting can have a considerable impact on the joint strength [Bia11]. In case of the demonstration example, there are no mechanical properties available from the manufacturers data sheet of Ureol [Hun04]. Polyurethane adhesives can have a wide range of mechanical properties depending on the chemical composition [Ran02]. Therefore, material properties cannot just be derived from polyurethane adhesives of other manufacturers. As a result of this, the adhesive has been investigated on constituent level based on standard test methods for plastic materials. This investigation is described in section 4.3. A suitable material model has been implemented and calibrated to represent the experimentally observed material behavior. The ABAQUS input deck definition of the adhesive material is given in appendix A3. Insert Analogous to the adhesive, no damage of the steel insert has been identified in Phase 1. It is therefore assumed that elastic material parameters are sufficient for the implementation in the final virtual test model. Elastic material parameters of steel can be derived from standard literature. Therefore, no additional investigation is required for the insert. Summary On constituent level a total of three investigations have been defined, each addressing the material properties of one constituent. The insert has not been further investigated, since no damage is evident and material properties are readily available. For the Nomex honeycomb a robust material model has been established and calibrated. Regarding the face sheets, only the elastic modulus and the tensile strength have been determined and

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calibrated. The compressive strength and the shear modulus characterization have been determined in the following structural elements building block. Structural element level Considering the bilateral adhesive bond between the constituents, the debonding of face and adhesive/potting has been established as the only relevant mechanical effect during the problem analysis. Therefore, the remaining interfaces between the constituents can be modelled as tied contact (kinematic coupling). As described earlier, the face to adhesive bond is generally addressed on sub-component level. Hence, the only investigation which has been performed on structural element level is the completion of the face sheet material model based on tests on the bonded sandwich panel. Here, the face shear properties are of particular interest, since face shear failure has been established as relevant mechanical effect. In addition, the compressive strength of the face sheets has not been determined on constituent level. In order to determine the missing material properties, the corresponding investigation has been based on two structural tests. These are described in the following. Sandwich panel bending The first structural test of the investigation is flexural bending, which enables to determine the compressive strength of the prepregs. The full study, which contains additional face sheet lay-ups is described in section 5.1. This study confirmed and validated the elastic face sheet and core properties from the constituent level. In addition, the existing face sheet material model has been complemented by the compressive damage behavior. Regarding the core, it is shown that the honeycomb modelling approach determined on constituent level is able to predict the correct failure mode also on structural element level. Frame shear In order to determine the shear properties of the face sheets, sandwich panels with the same lay-up as in the reference test were additionally subjected to in-plane shear according to the standardized picture frame shear test. Using inverse problem methods, the existing face sheet model has been complemented by the elastic and plastic shear properties based on the experimental results. The fully calibrated face sheet material model reproduces the performed shear test results in terms of both stress-strain relationship and face sheet fracture progression. The corresponding experimental and numerical studies are described in detail in section 5.2. Summary The structural element building block concludes with validated elastic constituent material properties of face sheet and core as well as a fully calibrated face sheet material model including compressive and shear strength properties. Since no fracture of the core

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to face adhesive bond is considered, this interface is modelled as kinematic coupling using a tied contact. The performed bending study indicates that this simplified interface model reproduces the mechanical behavior well. Sub-component level Considering the determined relevant mechanical effects of the reference test, the cohesive model for the debonding of face and adhesive/potting is yet to be determined. This is done on sub-component level, because it is difficult to conceive a customized investigation that isolates this effect allowing to characterize it on structural element level. A corresponding test setup, which enables to study the debonding of face and potting would have to be similar or even equal to the reference test. The determination of the corresponding cohesive model is the only investigation in the last building block and the synthesis of the model parameters determined on lower building blocks is included in this investigation. Since, the sub-component level coincides with the reference test, the physical test results have been available as input for Phase 1 and the structural tests and analysis methods process step of the investigation procedure is generally not necessary for sub-component level investigations (see Figure 98). Physical test results Structural tests and analysis methods

FE-modelling & numerical studies

Reference test input

Virtual test results

Model calibration and verification

Figure 98 Process steps of sub-component level investigations

Regarding the demonstration example, the implementation of the top-level virtual test has not been described in the previous chapters. This is done in the following based on the two remaining steps of the investigation procedure. FE-modelling & numerical studies The top-level FE-model is implemented based on the previous building blocks. Therefore, basic numerical parameters such as mass scaling, loading rate and element size are adopted from the structural element building block. Additional mesh convergence studies regarding the face sheet and core have been performed in order to determine an appropriate local mesh refinement. Other performed numerical studies include the consideration of the fixture, which eventually is included in combination with a penalty contact. This is done in order to represent the effect that the specimen can lift off the fixture

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such that it is held primarily by the fixture’s edge instead of the entire initial contact surface. This is illustrated in Figure 99 in comparison to single point constraint boundary conditions, which would restrict the overall panel bending. Single point constraints

Fixture included

F

F

Penalty contact

Figure 99 Effect of different boundary conditions for pull-out test

In an additional numerical study it has been shown that the insert itself can be replaced by a rigid body without affecting the results of the virtual model. Therefore, this is implemented in order to reduce the computational time. The interface definition for the face-to-core bond is adopted from the previous building block and modelled as tied contact. The same applies for the potting-to-core interface, which doesn’t indicate any damage in the reference test. Lastly, the contact between face and potting is implemented as contact surface with cohesive behavior, in order to enable debonding based on a traction separation law. In a final numerical study, different cohesive behavior definitions have been implemented and benchmarked with the objective to select a suitable setup. Eventually, damage initiation has been defined based on a maximum stress criterion and damage evolution based on linear softening. The corresponding cohesive behavior model parameters are calibrated in the following step. Figure 100 summarizes the performed numerical studies in the final investigation on sub-component level. Numerical studies Numerical parameters Sensitivity studies 

Local mesh refinement

System boundaries 

Fixture modelling

Material modelling 

Rigid body as insert



Cohesive model

Figure 100 Performed numerical studies as part of the sub-component investigation in case of the demonstration example

The complete implemented sub-component level model is illustrated Figure 101. The model utilizes the symmetry of the specimen and loading condition resulting in a quarter model with two symmetry planes. The fixture is fully constraint, while the center node of the insert rigid body is constraint in the lateral translatory directions and a constant velocity is prescribed in vertical direction. In the following, the calibration and verification of the top-level virtual test model are described.

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Face C3D4 | Orth. fabric (VUMAT) 0.4-2mm elemsize

Tx,Ty,Tz,Rx,Ry,Rz = 0

Fixture-face Penalty contact Face-core bond Tied contact

Fixture C3D4 | Isotr. elastic 5mm elemsize

Tz = v Tx,Ty = 0

Potting-core bond Tied contact

Honeycomb core S4R | Orth. plastic 0.4/1.5mm elemsize Adhesive/Potting C3D8R | Isotr. bi-plastic 0.3mm elemsize

Insert Rigid body

z x

Face-potting bond Cohesive contact

y

Figure 101 Implemented sub-component level model for demonstration example (acc. to [See15])

Model calibration and verification The model parameters of the cohesive model include the cohesive stiffness, the maximum stress for damage initiation and the rate of cohesive stiffness degradation once damage is initiated. These parameters are calibrated based on all three considered insert configurations simultaneously (see Figure 79). The calibration is done manually supported by preliminary DoE studies, which help to understand the effect of each individual parameter on the macroscopic simulation results. The calibrated cohesive behavior is given in ABAQUS input deck format in appendix C2. The virtual test results in terms of force-displacement relationship are given in Figure 102 for the three investigated insert configurations. The simulation predicts the overall curve progression for all three panel configurations. Therefore, the virtual model is generally capable of representing all damage mechanisms correctly. In particular the initial stiffness as well as the initiation of core shear damage is reproduced with less than 5% deviation. In addition, the displacement and force at catastrophic failure are predicted correctly within the scatter of the test results, while the strength is on the upper boundary of the scatter band. However, it can be pointed out that the stiffness in the second linear regime of the curve progression (stage ③) is generally overestimated by the simulation. This discrepancy becomes increasingly pronounced with increasing panel thickness. However, the trend that the stiffness in stage ③ is decreasing with increasing core height is also evident in the simulation.

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PullOut | FP-10-101

2000

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Force [N]

1500

Test scatter Test average Simulation

3 5

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1

500

0 Stiffness deviation in stage 3

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2 3 Displacement [mm]

PullOut | FP-19-101

2000

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PullOut | FP-26-101

2000

1500 Force [N]

1500 Force [N]

4

1000

500

1000

500

0

0 0

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2 3 Displacement [mm]

4

5

0

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2 3 Displacement [mm]

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5

Figure 102 Reference test results in comparison with virtual test results for reference test

In sum, the virtual test model predicts the test results best in case of the 10 mm panel, while the difference between test and simulation increases with the panel thickness. In order to evaluate the virtual model performance in terms of visual damage patterns, Figure 103 illustrates the damage of virtual and physical test in case of the 10 mm panel configuration after testing. Furthermore, Figure 104 illustrates the visual damage during the virtual test for each of the previously defined five damage progression stages. These damage illustrations confirm that the virtual test represents all identified damage mechanisms correctly. Even the delamination of core and face in the post failure regime is evident by tensile failure of the core. The remaining differences between test and simulation in particular in case of the thicker panels, is assumed to origin from the exact mechanics of core shear failure. The implemented cell wall material modeling approach leads to a less distinct load drop after shear buckling of the cell walls if compared to the experimental results (Figure 44, p. 56). Hence, the stiffness of the linear regime in stage ③ is overestimated. A more refined core model is likely to yield better results, yet this

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would require considerably more computational effort. At the same time, it is shown that the implemented model is capable of predicting the strength and the damage progression of all three considered configurations with a single set of material and model parameters, while the simulation time is between 1h-2h on a state of the art 4 core CPU workstation depending on the panel thickness. Therefore, the model is considered to fulfill the requirements and the top-level virtual test is considered verified. Face shear damage

Face rupture

Face damage 0%

100%

Debonding of adhesive and face sheet

Figure 103 Comparison of physical and virtual test results in terms of visual damage patterns in case of the 10 mm specimen after testing

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Stage ① No visible damage

Stage ② Core shear buckling initiated No face sheet damage visible Stage ③ Core shear buckling progressed and potting-face debonding initiated Top face shear damage visible Stage ④ Potting-face debonding almost completed Face shear damage progressed Stage ⑤ Face sheet rupture visible Debonding of face and core visible due to tensile core failure beneath top face Figure 104 Visual damage in virtual test for the five identified progression stages in case of FP-10101

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7.4.3 Modelling database The modelling database is an integral part of Phase 3. It can be considered as knowledge base that contains all available model parameters for the implementation of virtual tests. There are two types of input sources for the modelling database. Firstly, there are verified model parameters resulting from previous proprietary investigations. Secondly, there are published model parameters provided by available literature. This also includes technical data sheets from material manufacturers. In this context the term “model parameter” not only refers to actual parameters such as material properties or loading rate, but also model aspects such as the definition of boundary conditions or the selection of a suitable material model. The general structure of the different modelling parameters follows the previously introduced categories of numerical studies. Figure 105 illustrates the input and content of the modelling database. The available model parameters are an important input for the definition of the investigations within each building block, since investigations are generally only required for unknown model parameters. In case the needed parameters are not available, the modelling database may also provide model parameters for investigations thus reducing the effort for numerical studies within future investigations. Previous investigations

Available literature

Sets of verified model parameters

Published model parameters

Modelling database

Numerical parameters



Mass scaling



Loading rate



Mesh size



Convergence

System boundaries

Material modelling

Boundary conditions



Material model



Cohesive model



Model scale





Fixture modelling

Section/Element type



Imperfections



Figure 105 Input and content of modelling database

7.5 Phase 4 - Application of virtual test In the final application phase, the virtual test model is used in design studies based on the defined application scenario from Phase 1. There is no generic procedure to follow in this phase, since the application is very specific depending on the intended use of the virtual test. However, considering the overall approach Phase 4 is crucial since here it is

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proven whether that the virtual test can be applied as intended. If this is not the case, it is returned to Phase 2, where it is evaluated whether an adjustment to the defined model framework is required before the model development phase is initiated once again. Figure 106 illustrates Phase 4 embedded in the overall approach. End yes Virtual test applicable?

no

1

2 Problem analysis

Definition of model framework

3

4 Model development

Application of virtual test method

Field of applicaiton and requirements

Figure 106 Embedding of Phase 4 in overall approach

In case of the demonstration example, the primary field of application is the prediction of different joint configurations. In order to demonstrate this, the effect of the face sheets, the adhesive and the core on the pull-out strength is studied based on the developed virtual test. This is described in the following for each studied constituent. Insert variations are not studied the same way, since simply changing the material of the insert is not expected to have much impact on the results and changing the insert type requires additional modelling effort. Instead the effect of the insert is studied in a more extensive design study in chapter 8. Face sheets Regarding the face sheets three prepreg lay-ups are considered. The standard configuration of the reference test being Face 101 is complemented by face sheets with additional ABS 5047-08 layers leading to the lay-ups Face 102 and Face 103 (Table 28). Table 28 Considered lay-ups for face sheet parameter study

The results of this parameter study are given in Figure 107 in terms of force-displacement curves analogous to the previous section. Increasing the number of face sheet layers leads to postponed initial core shear failure, which eventually translates into increased absolute strength. However, from Figure 107 it can also be seen that the increase in joint

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strength due to stronger face sheets appears to be limited since the strength increase from the 102 to the 103 lay-up is smaller if compared to just adding one layer to the reference lay-up (101 to 102).

Figure 107 Simulation results for face sheet parameter study

Core Analogous to the face sheets, two additional core types are investigated in order to quantify the core impact on the insert pull-out strength. All investigated core types are summarized in Table 29, while the nomenclature of the cores is based on the Airbus specification ABS 5035 [Air14]. The ABS 5035-A4 core is used in the reference test. Hence, the material model of the cell walls for the detailed core model has been calibrated in section 4.1 based on experimental results. The additionally considered core types of the parameter study have the same cell size as the reference core (3.2 mm). They differ in the density, which is achieved by applying different Nomex paper thick-

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nesses and resin coat volumes during manufacturing. However, for the additionally investigated core types no experimental studies have been performed on constituent level. Instead, the implemented material modelling approach of the reference test is adapted for the additional cores based on the macroscopic material properties given by manufacturers (Euro Composites [EUR10] and Hexcel [Hex99]). The cell wall material models have been calibrated to match these key properties. The ABAQUS input deck code for the two additional cores are given in Appendix A1. The results of the core parameter study are given in Figure 108. The core density greatly impacts the strength of the joint. This is due to the fact that the core density strongly correlates with its shear strength and the shear strength directly influences the failure initiation of joints in case of out-of-plane loading. As a result, the virtual model indicates that the joint strength can be increased by about 35-55% when using a 96kg/m³ instead of the 48kg/m³ core, while higher core density tends to be more effective with increasing core height. Reducing the core density has the opposite effect respectively.

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Figure 108 Simulation results for core parameter study Table 29 Investigated cores in core parameter study Compression Density [kg/m³]

Stabilized

Shear LT-Direction

Tension WT-Direction

Stabilized

Str

Mod

Str

Mod

Str

Mod

Str

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

[MPa]

ABS5035-A11

29

1.00

55

0.65

20

0.35

12

1.10

2

48

2.15

131

1.28

36

0.60

20

2.45

ABS5035-C31

96

6.20

410

2.50

90

1.40

50

6.50

ABS5035-A4

Adhesives The impact of the potting material is evaluated based on the three investigated potting materials of the present work. Therefore, the virtual model is also run with the calibrated material models of Delo VE 24430 and Scotch 9323 instead of Ureol (see section 4.3). The simulation results in comparison to the reference simulations for all three core heights are given in Figure 109. The increased elastic modulus of the Delo and Scotch epoxy adhesives leads to considerable increase in joint strength due to increased stiffness in the second linear regime after core shear failure. At the same time, the Delo and Scotch adhesives result in almost identical curve progressions. Therefore, the adhesive material noticeably impacts the overall joint strength, while Ureol appears to provide too little stiffness. At the same time, it is shown that little variations in the mechanical behavior of the adhesive as with Delo and Scotch can be neglected.

7.6 Summary With Phase 4 the virtual testing approach concludes. In case of the demonstration example it is shown that the virtual testing approach leads to a simulation model, which is capable to satisfy the requirement of predicting the ultimate strength of honeycomb sandwich inserts. Furthermore, no further iteration is required since the developed virtual test is fully compatible with the intended application scenario. This is achieved with an explicit detailed model, which is assembled based on five investigations within the building blocks. In order to validate this approach additional sub-component tests from chapter 6 are implemented as virtual test as well. This is described in the following sub-section.

1

Material properties are taken from manufacturers data sheets

2

Material properties are determined from tests in the framework of the present work (section 3.1)

7.7 Validation based on different joint configurations

141

Figure 109 Simulation results for adhesive parameter study

7.7 Validation based on different joint configurations The validation is based on reference tests for partially potted inserts and corner joints. The implementation of these tests as virtual test using the developed approach is outlined in this sub-section. However, the following validation is focused on Phase 1 – Phase 3, since the primary objective is to demonstrate the capability to implement virtual tests and not to demonstrate the application of virtual tests in design studies.

7.7.1 Partially potted inserts In case of partially potted inserts, two reference tests have been implemented as virtual test. These include out-of-plane tension and in in-plane shear. The corresponding reference tests are described in section 6.1 from p. 95 onwards. Figure 110 summarizes the material configuration of the joint and the test setups.

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Configuration ABS1005-08078T Delo

Loading 1

PP-26-010

Out-ofplane tension

Partially potted

Loading 2

ABS5035-A4

In-plane shear

26 mm

ABS 5047-07

Figure 110 Investigated configuration and loading conditions for validation of virtual testing approach based on partially potted inserts

Out-of-plane tension In case of out-of-plane tension, the requirements and application scenario for the virtual test are defined analogous to the previous demonstration example. The intention is to develop a virtual test which is capable to predict catastrophic failure at computation times between 2-4h. The reference tests were video recorded and a section cut of the specimens after testing was prepared and analyzed (Figure 111, left). The characteristic force displacement curve progression has been studied and the identified damage mechanisms are assigned to the curve progression stages (Figure 111, right). In comparison to the fully potted inserts, the partially potted curve is not characterized by further increasing load after initiation of core shear buckling (stage ②) as first damage mechanism. Instead, the load drops significantly shortly after core damage initiation (stage ③). This is due to tensile failure of the core below the potting, which initiates catastrophic failure accompanied by face sheet failure in in the post failure regime (stage ④). Therefore, there are only two relevant mechanical effects, core shear buckling and tensile core failure. Face sheet failure 4 Debonding of core and face sheet 4 Shear buckling 2 of cell walls

3 2

3 4 1

Tensile failure of core 3

Figure 111 Problem analysis for partially potted inserts under pull-out loading

7.7 Validation based on different joint configurations

1. Problem analysis  Prediction of catastrophic failure  2-4h computational time

2. Definition of model framework  Detailed model  Explicit solver

 Two relevant mechancial effects

Modelling database 

Detailed core model ABS 5035-A4

143

3. Model development  Four additional investigations  Core model is adopted from modelling database

Level 3

Sub-component

Level 2

Structural Structural elements elements

Level 1

Constituents

Adhesive Delo – material model

4. Application of virtual test method 

Parameter studies



Evaluation of design alternatives

Model synthesis Bonded face sheet ABS 5047-07 Compr & shear properties

1

Face sheet ABS 5047-07 tensile properties

4

3

2

Figure 112 Summary of applied virtual testing approach in case of out-of-plane tension of partially potted inserts

In Phase 2, the model framework is defined based on a detailed model and an explicit solver, which is also equivalent to the previous demonstration example. This is due to the similar failure progression with the core being the crucial constituent. Regarding Phase 3, there is a total of four investigations required. On constituent level, the developed detailed core model can be reused from the modelling database, while the adhesive and the tensile face sheet properties have to be determined in investigations. Regarding the insert itself, there is no additional investigation necessary. However, since the insert is made of polymer, the insert is not modelled as rigid body. Instead it is accurately represented using solid elements based on a linear elastic material model with a Young’s modulus of 4000 MPa. This is an estimation, since there is no information on the exact material available. However, the problem analysis does not indicate any damage of insert or adhesive. Therefore, estimating the insert stiffness appears sufficient. On structural element level, the compressive and shear properties of the face sheets are investigated. Lastly, on sub-component level the top-level model is synthesized based on the modelling database and the lower levels. The overall model resembles the previous fully potted virtual test (Figure 101), with the main difference that the cohesive contact of potting and lower face is replaced with a tied contact between potting and core in order to account for the partial potting. The application of the virtual testing approach is summarized in Figure 112, while the implemented overall model for the investigated partially potted insert is illustrated in Figure 113. The numerical modelling of this insert configuration has been published in more detail in a separate publication [See18].

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Face

Tx,Ty,Tz = 0 Rx,Ry,Rz = 0

S4R | Orth. fabric (VUMAT) 0.4-2mm elemsize

Fixture to Face Penalty contact Face-core bond Tied contact

Fixture C3D8R | Isotr. elastic 5mm elemsize

Tz = v Tx,Ty = 0

z

x y

Honeycomb S4R | Orth. plastic 0.4/1.5mm elemsize Potting C3D10M | Isotr. bi-plastic 0.8mm elemsize

Insert C3D8R | Elastic 0.5mm elemsize

Potting-core bond Tied contact

Figure 113 Virtual test model for partially potted insert under out-of-plane tension [See18]

The results of the simulation model are displayed in Figure 114. The implemented model proves to accurately represent the test results in terms of both, force-displacement relationship and visual damage mechanisms. In terms of strength and stiffness the model results align with the average test results with only about 2% deviation. The post failure behavior is not matched with the same accuracy. However, this is not the requirement for the model. Regarding the damage mechanisms, it can be summarized that the model reproduces not only the two relevant mechanical effects in the correct order, but also the remaining damage mechanisms such as face sheet damage and debonding of face and core (Figure 114, left). However, this debonding is represented in the model as tensile failure of the core. Therefore, it can be concluded that the implemented partially potted model agrees well with the reference test and the given example validates the approach.

7.7 Validation based on different joint configurations

Tensile core failure

145

Shear buckling of Face sheet failure cell walls Face damage 0%

100%

Figure 114 Virtual testing results of partially potted inserts under out-of-plane tension [See18]

In-plane shear The in-plane shear virtual test is implemented based on the same requirements and application scenario as the previous out-of-plane tension virtual test (catastrophic failure prediction and computation times between 2-4h). During the corresponding reference tests the failure behavior could not be observed directly due to the fixture, which covered the area of externally visible damage. Therefore, the identification of mechanical effects relies on the inspection of the specimens after testing (Figure 115). From this it is concluded that the damage is dominated by shear and compression failure of the face along with some cracks of the potting on the tension side of the insert. The damage solely occurs at one of the two inserts of the specimens. Considering the force displacement progression (Figure 115, right), four stages are identified. The initial linear elastic deformation (stage ①) is followed by quadratic flattening (stage ②) before catastrophic failure occurs (stage ③). Stage ④ marks the post failure regime. Load application

3 2

Face shear failure 2

Potting damage 4

1

4

Face compression 3 failure

Figure 115 Problem analysis for partially potted inserts under in-plane shear loading

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It is assumed that stage ② represents the initiation of shear damage of the faces due to shear plasticity, which typically leads to a quadratic stress-strain relationship (see section 5.2). However, catastrophic failure occurs suddenly, almost brittle unlike pure shear failure, which is characterized by considerable plasticity before failure. Therefore, it is assumed that compressive face failure in direction of the load eventually leads to catastrophic failure of the specimens in stage ③. The observed adhesive damage is likely to be confined to the post failure regime in stage ④. Therefore, there are two relevant mechanical effects, face shear damage and face compressive failure. In sum, Phase 1 reveals that the damage progression in this in-plane reference test is mostly governed by the faces and to lesser extent by the adhesive. Due to its low in-plane mechanical properties, the core has little impact on the global structural behavior. Therefore, it is not necessary to model the core in detail. However, it is required to represent the specimen with a 3D-continuum model in order to enable the non-symmetric load introduction and thus the actual stresses in face sheet and potting. Regarding the solver, the model is implemented based on explicit time integration in order to be able to adopt model parameters from the previous out-of-plane tension test. With the model framework established in Phase 2, the subsequent model development phase requires only two investigations, since the adhesive and face sheet material models can be adopted from the modelling database. On constituent level there is an investigation for the implementation of a 3D-continuum model of the core required, since the modelling database only contains a detailed material model for the core at this point. This investigation is described in section 4.1.4. on page 59, while the derived material model is given as ABAQUS input deck in appendix A1. 1. Problem analysis  Prediction of catastrophic failure  2-4h computational time

2. Definition of model framework  3D-continuum model  Explicit solver

 Two relevant mechancial effects

3. Model development

4. Application of virtual test method

 Two additional investigations  Face sheet and adhesive properties adopted from modelling database

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Sub-component

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

Evaluation of design alternatives

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3D-continuum core model ABS 5035-A4

1

Figure 116 Summary of applied virtual testing approach for partially potted inserts under shear

7.7 Validation based on different joint configurations

147

The second investigation is the synthesis of the top-level model. This investigation has been characterized by numerical studies regarding mesh size and boundary conditions. The implemented model utilizes the half symmetry of the loading condition and specimen. One of the two inserts serves as bearing and is constraint in-plane, while out-ofplane deflection is enabled. The other insert is prescribed with a constant velocity in longitudinal panel direction while the transverse direction is constraint. This allows bending of the panel, which is also evident in the tests. All adhesive bonds in the model are represented by tied contacts, since no debonding is evident in the tests. The application of the developed virtual testing approach for this validation example is summarized in Figure 116, while Figure 117 illustrates the final model with all basic details. Face S4R | Orth. fabric (VUMAT) 0.4-2mm elemsize

z y

x

Potting C3D8R | Isotr. bi-plastic 0.8mm elemsize

Tx = Ty = 0 Insert C3D8R | Isotr. Elastic 0.8mm elemsize

Tx = -v; Ty = 0 All adhesive bonds as tied contact

Core C3D8R | Orth. Plastic 3mm elemsize

Figure 117 Implemented FE-model for shear test of partially potted inserts

The virtual test results of the implemented model are depicted in Figure 118. The virtual test agrees well with the test results in terms of both, visual damage mechanisms and force displacement curve. All three experimentally identified damage mechanisms are evident in the simulation and their sequence aligns with the assumptions made in the problem analysis. Regarding the force displacement curve the simulation indicates a stiffness, which is on the upper end of the scatter of the test results. However, the average strength in terms of failure load is matched accurately by the model. Therefore, it is concluded that the given example validates the approach as well as the previously determined model parameters.

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Face damage

Load application 0%

Face compression damage

Potting damage

100%

Face shear damage

Figure 118 Simulation results of partially potted inserts under shear, left: damage mechanisms, right: force-displacement curve

7.7.2 Corner joints All previously described application examples for the developed virtual testing approach are based on typical sandwich fasteners perpendicular to the face sheets. In order to extend the validation of the approach, it is also applied to typical corner joints. In this context a mortise and tenon L-joint, which is tested in shear and bending, is included in the validation study. The respective experimental study is described in section 6.2 from page 100 onwards. The application of the virtual testing approach for both loading conditions is summarized in Figure 119. In the following, the virtual test implementation for both loading conditions is described starting with the mechanical effect identification. 1. Problem analysis  Prediction of catastrophic failure  2-4h computational time  One relevant mechancial effect each

2. Definition of model framework  Hybrid model with detailed and solid core areas  Explicit solver

3. Model development  One additional investigation  All material properties adopted from modelling database

4. Application of virtual test method 

Parameter studies



Evaluation of design alternatives

Modelling database 

Adhesive material model Delo

Level 3

Sub-component



Detailed and Solid core model ABS 5035-A4

Level 2

Structural Structural elements elements



Face sheet material model ABS 5047-07

Level 1

Constituents

Model synthesis

Figure 119 Summary of applied virtual testing approach for corner joint examples

1

7.7 Validation based on different joint configurations

149

Shear test Figure 120 a) depicts a representative force-displacement curve and the visual damage pattern for the L-joint shear test. The curve progression is subdivided in four stages. Following the linear elastic regime (stage ①), stage ② represents failure initiation due to a combination of shear buckling and compressive core crushing of the honeycomb cell walls in the contact zone of fixture and specimen. During the tests, shear buckling progresses rapidly, while it remains localized in the unclamped area (Figure 120 a, bottom). This leads to a sharp load drop, which is followed by a force plateau (stage ③), where core shear damage progresses until tearing of the cell walls results in a dysfunctional core. a)

b)

2 2

4

3

4

3

1

1

Figure 120 Problem analysis for investigated corner joints, a) L-joint shear and b) L-joint bending

Stage ④ represents the final curve section where the load increases due to the face sheets of the tenon, which are still bonded to the vertical panel and eventually become increasingly loaded in tension. Since the failure progression largely depends on the core damage, a detailed core model based on explicit integration is defined as level of detail. In order to reduce the number of degrees of freedom (DoF), only a section of the clamped horizontal core is modeled in detail. The remaining core sections are modeled

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7 Virtual testing approach for sandwich panel joints

using 3D-continuum elements. Therefore, the model framework is essentially a hybrid. The bond between detailed and 3D-continuum core is implemented using tied contacts. This has been verified in numerical studies. The majority of required model parameters for the top-level model is available in the modeling database from previous investigations. Solely the material model of the laminated plastic as edge reinforcement has to be newly implemented. However, this component does not impact the overall failure progression. Therefore, it is modelled using a linear elastic material model with a Young’s modulus of E = 8000 MPa based on available literature [Lam17]. Therefore, there is only the model synthesis investigation in Phase 3 of the virtual testing approach. The fixture is included in the model, in order to account for the local core compression in the contact zone at the edge of the fixture. The symmetry of specimen and loading condition is applied by implementing a half-model with respective symmetry boundary conditions. Additional boundary conditions are applied to the load introduction area in order to account for the guidance given by the test setup. All model details are given in Figure 121.

Figure 121 Implemented virtual test models for corner joints

7.7 Validation based on different joint configurations

151

The simulation results are displayed in Figure 122 a) in terms of force-displacement curve and visual damage pattern. The simulation matches the test results with regards to initial stiffness accurately. The strength is generally overestimated while still being in the range of the test scatter. There is significant scatter in the tests, which is assumed to be largely originating from the specimen placement in the fixture. This is due to the lack of stoppers which handicap repeatable specimen placing. Since the simulation indicates a strength at the upper end of the scatter range, it is assumed that the specimens with lower strength represent unfavorably placed specimens. Regarding the further curve progression, the simulation indicates a less distinct load drop and plateau in stage ③. Instead the simulation goes directly into stage ④ with increasing load after the load drop. The visual damage pattern of the simulation matches the observations during the tests well. In sum, the virtual test agrees well with the physical test. The deviation in the post failure regime of the later stages is tolerable since the primary objective is to forecast the strength. In addition, the simulation indicates all relevant mechanical effects in correct sequence. Therefore, the given example validates the developed approach. Bending test Analogous to the shear tests, the bending tests are analyzed by characterizing the forcedisplacement curve and the visual damage patterns during the test. This is illustrated in Figure 120 b). The curve progression generally resembles the force-displacement relationship of the shear tests. Therefore, it is split in the same four stages. However, the governing mechanical effects during the test are different. Stage ① represents elastic deformation, while stage ② describes the in-plane core crushing of the 26 mm panel due to penetration of the 10 mm panel. This damage mechanism is generally undesirable, since it leads to premature catastrophic failure, which is governed by the low inplane material properties of the core. In the tests, this is caused by unfavorable bonding of the panels such that there is a gap between the outer faces of the bonded panels. This enables unconstraint penetration of the core. Stage ③ represents debonding of core and face of the penetrated panel leading to a force plateau. Stage ④ describes the final curve section with increasing load, due to densification of the penetrated core as well as change in angle of the penetrating panel. Figure 120 b) illustrates the core penetration and core to face debonding. Therefore, the test results indicate that the failure progression is entirely dictated by core mechanics. As a result of this a detailed model with explicit time integration is defined as model framework. However, in order to reduce computation time, the core is only modelled in detail in the contact area of both panels in order to ensure accurate mechanics in the penetration zone. The remaining core is modeled using 3D-continuum elements leading to a hybrid model. The implemented simulation model for the bending test is illustrated in appendix Figure 121. It largely coincides

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7 Virtual testing approach for sandwich panel joints

with the shear test model. The load is applied via a rigid plate which is prescribed a constant velocity compressing the joint based on a penalty contact. All implemented material models and contact definitions are identical to the L-joint shear tests. a)

b)

Figure 122 Simulation results for corner joints, a) L-joint shear and b) L-joint bending

Figure 122 b) illustrates the simulation results as force-displacement curve and visual failure mode. The simulation reproduces the test results well in terms of initial stiffness, while the strength of the joint is underestimated by about 10% if compared to the test average. Following the first damage mechanism the simulation indicates a load drop which is followed by load increase and decrease leading to an oscillation pattern. The force level of this oscillation agrees well with the average plateau of the test results (stage ③). However, the amplitude of the oscillation appears to be high if compared to the test results. It is assumed that this results from the disregard of the face to core adhesive bond. Due to the complicated mechanisms in the contact zone, the required computational time for this simulation exceeds 100 h in case the post failure regime shall be included in the simulation. The point of catastrophic failure can be predicted with computation times within the limits of the defined requirements. Regarding the visual failure modes, the model indicates the same damage mechanisms as the physical tests

7.7 Validation based on different joint configurations

153

with the exception of the face to core debonding which is not implemented by means of a cohesive contact. However, analogous to the virtual tests of inserts under out-of-plane tension (Figure 104, p. 135), the core locally fails in tension, which is another form of core to face debonding. In summary, good agreement between physical and virtual test can be attested. Therefore, the implemented model proves to be capable to also reproduce undesirable failure modes, which are caused by poor manufacturing and the virtual testing approach can be considered further validated.

7.7.3 Conclusion It is shown that the virtual testing approach enables to predict the mechanical damage behavior of four independent reference tests with varying material configurations and damage mechanisms. When considering the validation examples in sequence it can be seen that the modeling database grows and fewer investigations become necessary during the model development phase (see Figure 112, Figure 116 and Figure 119). In addition, since the different implemented models comprise reoccurring constituents, the derived material models and parameters can be validated. Overall the four given examples represent a solid validation foundation and it is concluded that the proposed approach is validated.

8

Development of novel sandwich panel joints

Chapter 8 describes the application of the established virtual test of inserts under outof-plane tension for the development of a novel sandwich panel joint design. The premise of this study is based on the general mechanic that the effective potting radius of the insert directly affects the core shear buckling as first damage mechanism. Increasing the potting radius increases the number of cell walls adjacent to the potting thus increasing the initial stiffness of the insert and postponing shear failure of the core. These two effects typically result in an increased overall strength of the insert configuration. This is illustrated in Figure 123.

Figure 123 Proposed effect of increased potting radius on insert pull-out strength

In the state of the art there are two common solutions, which allow increasing the potting radius of existing inserts. Firstly, the core can be locally densified with core filler compound. This is typically done during panel manufacturing. When the insert is placed in the densified area, the core filler serves as potting thus increasing the potting radius. The same can be achieved using post-fabrication processes. In this case the core surrounding the bore hole for the insert is removed using a special tool. This generates a larger cavity, which is filled with potting mass during insert bonding. This post-fabrication solution is often referred to as “Undercut” and it is generally favorable since it enables to use standard panels thus increasing flexibility. However, there are two drawbacks. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_8

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Firstly, this solution requires an additional manufacturing step for removing the core. Secondly, filling the cavity with potting can considerably increase the mass of the panel considering that there may be dozens of inserts in a single panel. To overcome these drawbacks a novel insert design, which attempts to utilize the design freedom of additive manufacturing (AM), is proposed. The idea behind this design is to increase the potting radius by increasing the radius of the insert itself, while the load from the insert center to the outer walls is to be transmitted by a weight optimized topology. In order to achieve this, a topology optimization has been implemented based on a linearized model of the previously investigated partially potted inserts under pull-out. The inner volume of the insert is defined as design space while the outer walls are defined as non-design space in order to ensure a fully enclosed structure. The optimization is run considering both, pull-out and shear out loading. The performed topology optimization is described in Figure 124. The optimization results indicate an hourglass shape for the design space.

Final result

Design space evolution Figure 124 Topology optimization for novel insert design

In order to evaluate the performance of this novel insert, a virtual test study has been implemented, in order to compare the novel design to the state of the art using FE-models on sub-component level. Furthermore, the virtual test study has been reproduced experimentally with the objective of validating the virtual tests. The considered materials are consistent with the materials, which have been studied throughout the present thesis. The only exception is the insert material. Unlike the previously described joint configurations, a thermoplastic material (Acrylonitrile butadiene styrene - ABS) is considered, since the first prototypes of the novel insert were to be manufactured via Fused Deposition Modelling (FDM) using ABS as material. Respective additive manufacturing

8.1 Virtual testing of design alternatives

157

machines have been available in the framework of the present work. This enables flexible manufacturing of complicated insert geometries, such as the proposed novel insert design. The eventually considered material configuration is summarized in Figure 125. In the following, the performed virtual and experimental studies are described.

Figure 125 Considered material configuration for novel insert design

8.1 Virtual testing of design alternatives Based on the topology optimization results, a novel insert design has been derived. This design is referred to as hourglass due to its characteristic shape. For the evaluation of the performance of this novel design, a reference configuration is defined based on a typical threaded insert (Shur-Lok SL607 [Shu96]). The sizing of the proposed hourglass insert is defined with the intention to considerably increase the effective potting radius if compared to the reference insert. The implemented geometries of the reference and the hourglass insert are given in Appendix C3. These two inserts are assumed to be bonded in a 100 mm x 100 mm sandwich panel using a standard insert bonding process. In addition to these two configurations, a third configuration is considered. Here the reference insert is assumed to be bonded using the previously introduced undercut process, while the potting radius is defined to be equivalent to the hourglass alternative. All three considered alternatives are illustrated in Figure 126. It can be seen that the hourglass design requires a large bore hole, which may affect the face sheet integrity, while the undercut design adds significant potting mass. Figure 126 also illustrates that the presented design study is merely the application of the previously developed virtual tests. Therefore, Phase 1-3 are not executed and the virtual tests of the selected design alternatives are directly implemented based on the available modelling database. Apart from the constituent composition, the implemented models are equivalent to the previously investigated partially potted insert (Figure 113, p.144). The ABS of the insert is implemented using a linear elastic isotropic material model with Young’s modulus =1.03 g/cm³ taken from Brostow [Bro07]. Therefore, it is E = 2000 MPa and density assumed that the insert itself does not contribute to the catastrophic failure of the joint.

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8 Development of novel sandwich panel joints

1. Problem analysis  Prediction of catastrophic failure  2-4h computational time

2. Definition of model framework  Detailed model  Explicit solver

 Three relevant mechancial effects

Modelling database 

Adhesive material model Scotch9323



Detailed and Solid core model ABS 5035-A4



Face sheet material model ABS 5047-02 ABS 5047-08

3. Model development

4. Application of virtual test method

 No investigation, just implementation



 All material properties adopted from modelling database

Reference

Hourglass

Undercut

22.0g

Investigation of three insert designs

32.6g

28.7g

Figure 126 Application of virtual test for design study on partially potted inserts

The simulation results in terms of force displacement curves are given in Figure 127 a), while Figure 127 b) depicts the weight specific force displacement relationship based on the estimated weight of each design alternative. Both illustrations present the same trends. The configurations with increased potting radius achieve comparable strengths, which are considerably higher if compared to the reference. This strength advantage is reduced when considering the weight specific strength, while in this case the Hourglass configuration is superior to the Undercut. The force displacement results of the three alternatives indicate that the Hourglass and Undercut design exhibit a consistent failure mode which is unlike the failure mode of the Reference. a)

b)

Figure 127 Virtual testing results; a) force-displacement curve and b) weight specific force-displacement curve

8.1 Virtual testing of design alternatives

159

This is confirmed by the visual output of the virtual tests, which are given in Table 30. From this it is concluded that the Reference exhibits the same damage progression as the previously investigated partially potted inserts (compare with Figure 114, p. 145). However, the Hourglass and Undercut alternatives ae equally distinct. Here the final load drop is not caused by tensile failure of the core under the potting. Instead, buckling of the lower face sheet causes catastrophic failure (see Table 30). In sum, the virtual test study suggests that Undercut and Hourglass design yield comparable strengths. Therefore, the large borehole of the Hourglass insert does not appear to negatively affect the pull-out strength. Considering that the Undercut weights about 12% more than the Hourglass design, the latter is superior in terms of light weight design. In comparison to the Reference, both designs with increased potting radius suggest a considerable increase in weight specific strength (up to 100%).

Table 30 Visual damage in the post failure regime of all three design alternatives Reference

Tensile core rupture

Hourglass

Undercut

Buckling

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8 Development of novel sandwich panel joints

8.2 Validation by experimental investigation The virtual tests were reproduced in an experimental study. Therefore, the developed Hourglass and the defined Reference insert were fabricated using a commercial 3Dprinter based on ABS (Designjet Color 3D printer; Hewlett-Packard Development Company, Palo Alto, California). Subsequently, the three investigated design alternatives were manufactured according to the configuration given in Figure 125. The required cavity for the Undercut design was generated manually using an angled chisel. Three specimens were manufactured for each design. The load introduction into the 3D-printed inserts was implemented by means of SPAX® screws. This proved to be the strongest connection if compared to other options such as threaded inserts for plastics or Heli-Coils®. All specimens were tested under pull-out loading according to the test parameters given in Table 24 on page 97. The corresponding test setup is illustrated in Figure 128 in case of the Hourglass design. Except for the Reference design, the test results are inconsistent regarding the observed damage patterns and thus the curve progression. This is a result of premature failure due to insert rupture or screw shearing at high load levels. This failure can be explained by the reduced strength resulting from the non-homogeneous nature of FDM-fabricated parts [Iva13]. In case of the Undercut design, the result variability is enhanced due to manufacturing inconsistency regarding the shape of the cavity and thus the potting. A detailed analysis of the test results is given in Appendix C3. Since no material failure of the insert has been implemented in the virtual tests, the experimental results indicate lower pull-out strengths than the simulation. Pull-out jig

Fixture

SPAX® screw

ABS printed insert

Figure 128 Test setup for experimental study on novel hourglass insert design

Therefore, the experiment test curve with the highest peak force for each alternative has been selected for comparison with the virtual test results, as these best performing

8.2 Validation by experimental investigation

161

specimens come closest to the idealized virtual tests. The comparison of virtual and experiment is illustrated in Figure 129. a)

b)

Reference Test Reference Sim.

Hourglass Test Hourglass Sim.

Undercut Test Undercut Sim.

Figure 129 Comparison of experimental with virtual test results; a) force-displacement curve and b) weight specific force-displacement curve

When considering the force-displacement relationship, the virtual test matches the experiment accurately in case of the Reference. This is confirmed by the visual damage progression. This agreement is reduced when considering the weight specific force-displacement curve. This can be explained by the difference between the estimated mass of the virtual test specimen (22.0 g) and the determined weight of the physical specimen (24.6 g). The weight estimation of the virtual test study is generally lower than the physical specimens (about 10%). Regarding the alternatives with increased potting radius, the virtual tests indicate significantly higher peak forces if compared to the experiments. This is expected due to undesired premature failure of the inserts, which is not represented in the simulation. Therefore, the virtual tests cannot be fully validated in case of the Hourglass and Undercut alternatives. However, the general curve progression trends of virtual and physical tests are comparable for all considered designs. Hourglass and Undercut design present similar force-displacement curves with almost equal peak forces in case of both, virtual and physical tests, while the Hourglass design indicates a better performance when considering the weight specific force-displacement curve. In addition, it is assumed that without premature insert failure both alternatives would have achieved higher peak forces, thus approaching the predictions from the virtual tests. However, in sum the performed experimental study only enables a qualitative comparison with the virtual test results. A comprehensive validation based on test results without premature insert failure remains.

9

Summary and outlook

The determination of the mechanical properties by means of physical testing is a major cost driver in the development process of lightweight products. The implementation of virtual tests based on FE-simulations can be a significant contributor to reducing the development cost. However, composite sandwich structures are characterized by a complicated failure behavior, making reliable predictions via FE-simulations challenging. The present work addresses this problem by establishing a virtual testing approach for sandwich structures. The approach is based on the building block approach for the development of aircraft composite structures. Its structure therefore reflects the common classification in constituents, structural elements, sub-components and components as structural complexity levels. The focus of the approach lies on the prediction of the strength of structural joints as general weak point in sandwich constructions. It therefore addresses analyses up until sub-component level, while the investigations on constituent and structural element level are characterized by sufficient level of detail to enable the representation of the complicated failure behavior in sandwich panel joints. In the present work, various sandwich materials and configurations were investigated in experimental and numerical studies covering all three considered structural complexity levels. The performed studies were synthesized into the proposed approach. On constituent level, the core was of primary interest since its mechanics often govern failure initiation of sandwich structures. In this context, a detailed meso-scale honeycomb core model, which enables accurate representation of all core damage mechanisms, was established. In order to provide a computationally less expensive alternative, a 3D-continuum core model was additionally implemented. The material parameters of both core models were calibrated using macroscopic experimental results based on standardized sandwich tests. In addition to the core, the face sheets and typical structural adhesives were investigated on constituent level. For the face sheets, it was established that the sandwich panel bonding process leads to considerable degradation of the tensile face sheet modulus and strength. The obtained test results were implemented in a suitable fabric composite material model. The adhesives were investigated in tension © Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8_9

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9 Summary and outlook

and compression. An isotropic material behavior with different plastic hardening in tension and compression was determined and implemented in a suitable material model with the experimental stress-strain data as tabular input. On structural element level, various bonded sandwich panel configurations were investigated based on standardized flexural bending and in-plane shear tests. The performed bending tests exhibited three failure modes, face sheet compressive rupture, local core indentation and core shear failure. In the corresponding numerical study, the tests were implemented as detailed meso-scale model and 3D-continuum model. Here, the material parameters from the previous constituent level could be validated, while both models agreed well with the test results. However, the 3D-continuum model generally proved to be less accurate in particular in case of core shear failure. In the in-plane shear tests, the shear plasticity and strength of the face sheets was experimentally determined and subsequently implemented in the face sheet material model. On sub-component level, fully and partially potted sandwich panel insert configurations were tested under out-of-plane pull out and in-plane shear loading. In addition, a mortise and tenon corner joint was investigated under shear and bending. Based on the findings of the previous building blocks, these sub-components tests were implemented as simulation models using a common virtual testing approach. Good agreement between physical and virtual tests was achieved. The virtual testing approach encompasses experimental and numerical investigations on all three introduced complexity levels. It provides guidance on the general procedure within the complexity levels as well as on the definition of a suitable level of detail for the investigated sub-component. The proposed approach was described in detail using one of the sub-component tests as demonstration example. Lastly, the application of the approach was demonstrated based on the development of a novel sandwich panel insert design. The presented research could be extended in different areas. In the investigated subcomponent tests, debonding of face and core was not a decisive damage mechanism. Therefore, it is not reflected in detail in the virtual testing approach. However, it is generally known as key aspect in sandwich construction and could be added in the future. In addition, the consideration of uncertainties is a natural next step for the proposed virtual testing approach. This would allow to predict the scatter of mechanical properties, which is important for airworthiness substantiation applications. Lastly, the successful implementation of detailed meso-scale honeycomb models on sub-component level paved the way for optimization studies, where the core is locally adapted for mechanically efficient load introduction. In combination with the design freedom of additive manufacturing, novel adaptive core geometries could be developed with the help of the established approach.

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Supervised students projects related to this thesis [Kra14]

Krause, M.: Virtuelles Testen von Inserts in Honigwabensandwichpaneelen, Bachelor thesis at TUHH, Hamburg 2014

[Ana15]

Anand, A.: Non-Linear Numerical Modelling of Nomex Honeycomb Cores, Project thesis at TUHH, Hamburg 2015

[Gra15]

Gravert, L.: Bestimmung und Verifikation der mechanischen Materialeigenschaften eines Harzsystems für nicht-lineare FEM Berechnungen, Project thesis at TUHH, Hamburg 2015

[Men16]

Menzel, M.: Numerische Simulation von Sandwichbiegeversuchen mittels Detailmodellen in ABAQUS\Explicit, Bachelor thesis at TUHH, Hamburg 2016

[Hoe16]

Hölscher, I.: Experimentelle und numerische Untersuchung von neuartigen generativ gefertigten Inserts für Sandwichstrukturen, Bachelor thesis at TUHH, Hamburg 2016

[Bri16]

Brinckmann, G.: Numerische Simulation des Pull-Out- und Scherversuchs von Partially Potted Sandwichinserts mittels ABAQUS/Explicit, Project thesis at TUHH, Hamburg 2016

[Fle16]

Fleming, E.: Numerische Simulation von Mortise-Eckverbindungen bei Honigwabensandwichplatten mittels ABAQUS/Explicit, Bachelor thesis at TUHH, Hamburg 2016

Appendix A – Constituent level

179

Appendix A – Constituent level A1 Implemented material models of Nomex honeycomb Detailed/meso scale models _______________________________________________________________________ Single Layer Isotropic *MATERIAL,NAME=NOMEX_SL_ISOTROPIC *ELASTIC, TYPE=ISOTROPIC 4000,0.3 *DENSITY 1.19e-09 *PLASTIC, HARDENING = ISOTROPIC 90, 0.0

_______________________________________________________________________ Single Layer Orthotropic *MATERIAL,NAME=NOMEX_SL_ORTHOTROPIC *ELASTIC, TYPE=LAMINA 5000, 4000, 0.2, 1450, 1450, 1450 *DENSITY 1.19e-09 *DAMAGE INITIATION, CRITERION=HASHIN 90, 105, 60, 90, 44, 44 *DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR 100000, 100000, 100000, 100000

_______________________________________________________________________ Multi Layer Resin Corner *Material, NAME = PHENOL_ML_RESIN_CORNER *ELASTIC, TYPE = ISOTROPIC 4800 , 0.39 *DENSITY 1.35e-09 *PLASTIC, HARDENING = ISOTROPIC 155, 0.0 *TENSILE FAILURE 106 *DAMAGE INITIATION, CRITERION = DUCTILE 0.001, *DAMAGE EVOLUTION, TYPE = ENERGY, SOFTENING = LINEAR ,,,, © Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8

180

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*MATERIAL,NAME=NOMEX_ML_RESIN_CORNER *ELASTIC, TYPE=LAMINA 3000, 1700, 0.2, 1200, 1200, 1200 *DENSITY 1.19e-09 *DAMAGE INITIATION, CRITERION=HASHIN 90,45,60,30,55,55 *DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR 100000,100000,100000,100000

_______________________________________________________________________ Multi Layer Resin Coat *Material, NAME = PHENOL_ML_RESIN_COAT *ELASTIC, TYPE = ISOTROPIC 4800 , 0.39 *DENSITY 1.35e-09 *PLASTIC, HARDENING = ISOTROPIC 190, 0.0 *TENSILE FAILURE 100 *DAMAGE INITIATION, CRITERION = DUCTILE 0.001, *DAMAGE EVOLUTION, TYPE = ENERGY, SOFTENING = LINEAR ,,,, *MATERIAL,NAME=NOMEX_ML_RESIN_COAT *ELASTIC, TYPE=LAMINA 3000, 1700, 0.2, 800, 800, 800 *DENSITY 1.19e-09 *DAMAGE INITIATION, CRITERION=HASHIN 90,45,60,30,50,50 *DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR 100000,100000,100000,100000

_______________________________________________________________________

Appendix A – Constituent level

181

Additional cores which have been calibrated using manufacturers data sheets _______________________________________________________________________ ABS 5035-A1 *MATERIAL,NAME=NOMEX_ABS5035-A1 *ELASTIC, TYPE=LAMINA 4000, 3000, 0.2, 1450, 1450, 1450 *DENSITY 1.19e-09 *DAMAGE INITIATION, CRITERION=HASHIN 90,105,60,80,44,44 *DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR 100000,100000, 100000,100000 *PARAMETER thicknessDoubleWall = 0.070 thicknessSingleWall = 0.035

_______________________________________________________________________ ABS 5035-C3 *MATERIAL,NAME=NOMEX_ABS5035-C3 *ELASTIC, TYPE=LAMINA 8000, 7000, 0.2, 2250, 2250, 2250 *DENSITY 1.19e-09 *DAMAGE INITIATION, CRITERION=HASHIN 100,100,80,180,60,60 *DAMAGE EVOLUTION, TYPE=ENERGY, SOFTENING=LINEAR 100000,100000, 100000, 100000 *PARAMETER thicknessDoubleWall = 0.150 thicknessSingleWall = 0.075

182

Appendix A – Constituent level

3D-continuum models _______________________________________________________________________ Elasto perfectly plastic material according to the manufacturer’s data sheet *MATERIAL, NAME= NOMEX_SOLID_MANUFACTURER *ELASTIC, TYPE=ENGINEERING CONSTANTS 1, 1, 137, 0.01, 0.01, 0.01, 0.1, 40, 25 *DENSITY 4.8e-11 *PLASTIC, HARDENING = ISOTROPIC 2.2, 0.0 *POTENTIAL 1,1,1,1,1,0.5

_______________________________________________________________________ Calibrated plastic material according to the experimental results *MATERIAL, NAME= NOMEX_SOLID_CALIBRATED *ELASTIC, TYPE=ENGINEERING CONSTANTS 1, 1, 137, 0.01, 0.01, 0.01, 0.1, 38, 22 *DENSITY 4.8e-11 *PLASTIC, HARDENING = ISOTROPIC 2.15, 0.0 2.15, 0.020 1, 0.05 1, 0.2 0.001 , 0.7 0.0001, 0.9 *POTENTIAL 1,1,1,1,1,0.48

_______________________________________________________________________

Appendix A – Constituent level

183

A2 Implemented material models for face sheets VUMAT for fabric reinforced composites With ABAQUS/Explicit 6.8 a built-in VUMAT user subroutine for fabric reinforced composites has been implemented. This subroutine can be activated by naming the material such that it starts with the string ABQ_PLY_FABRIC (for instance ABQ_PLY_FABRIC_ABS). This homogenous orthotropic elastic material model enables progressive stiffness degradation due to fiber or matrix damage. In addition, it allows plastic deformation under shear loading. This is what sets it apart from the standard UD-composite material of ABAQUS. Throughout the present work it is applied for the face sheets. The syntax of the input format is given below *MATERIAL,NAME=ABQ_PLY_FABRIC *DENSITY ρ *USER MATERIAL, CONSTANTS=40 ** Line 1: +1E, +2E, +12ν, 12G, -1E, -2E, -12ν ** Line 2: +1X, -1X, +2X, -2X, S ** Line 3: +1Gf, -1Gf, +2Gf, -2Gf, 12α, 12dmax ** Line 4: σy0, C, p ** Line 5: lDelFlag, dmax , εplmax , εmax , εmin *DEPVAR, DELETE=16 16 LINE: 1 Elastic properties Pos. Symbol Description 1 +1E Young’s modulus along tensile fiber direction 1 2 +2E Young’s modulus along tensile fiber direction 2 3 +12ν Poisson ratio 4 12G Shear modulus 5 −1E Young’s modulus along compressive fiber direction 1 6 −2E Young’s modulus along compressive fiber direction 2 7 −12ν Poisson ratio 8 Not used

184

Appendix A – Constituent level

LINE: 2 Damage initiation coefficients Pos. Symbol Description 1 +1X Tensile strength along fiber direction 1 2 −1X Compressive strength along fiber direction 1 3 +2X Tensile strength along fiber direction 2 4 −2X Compressive strength along fiber direction 2 5 S Shear stress at the onset of shear damage 6-8 Not used LINE: 3 Damage evolution coefficients Pos. Symbol Description Energy per unit area for tensile fracture along fiber direction 1 1 +1Gf 2 -1Gf Energy per unit area for compressive fracture along fiber direction 1 Energy per unit area for tensile fracture along fiber direction 2 3 +2Gf Energy per unit area for compressive fracture along fiber direction 2 4 -2Gf 5 12α Parameter in the equation of shear damage 6 12dmax Maximum shear damage 7-8 Not used LINE: 4 Shear plasticity coefficients Pos. Symbol Description Initial effective shear yield stress 1 σy0 2 C Coefficient in hardening equation 3 p Power term in hardening equation 4-8 Not used LINE: 5 Controls for material point failure Pos. Symbol Description 1 lDelFlag Element deletion flag: lDelFlag=0: Element is not deleted (default) lDelFlag=1: Element is deleted when either fiber fails, d1 = dmax or d2 = dmax or when εpl = εplmax lDelFlag=2: Element is deleted when both fibers fail d1 = d2 = dmax or when εpl = εplmax 2 dmax Maximum value of damage variable used in element deletion criterion 3 εplmax Maximum value of equivalent plastic strain for element deletion criterion. (A value of zero means εpl is not used as criterion for element deletion) Maximum (positive) principal logarithmic strain beyond which the ele4 εmax ment will get deleted. Ignored if zero, not specified, or lDelFlag=0. 5 εmin Minimum (negative) principal logarithmic strain beyond which the element will get deleted. Ignored if zero, not specified, or lDelFlag=0. 6-8 Not used

Appendix A – Constituent level

185

In the following all implemented material models for the three investigated face sheet materials are given in ABAQUS input format ABS 5047-02 *MATERIAL,NAME=ABQ_PLY_FABRIC_ABS5047_02 *DENSITY 1.8e-09 *USER MATERIAL, CONSTANTS=40 ** Line 1: +1E, +2E, +12nu, 12G, -1E, -2E, -12nu 21100, 19500, 0.15, 3400,21100, 19500, 0.15 ** Line 2: +1X, -1X, +2X, -2X, S 270,180,230,150,35 ** Line 3: +1fG, -1fG, +2fG, -2fG, 12a, max12d 9,9,9,9,0.4,1 ** Line 4: 0~ys, C, p ** Line 5: 1 *DEPVAR, DELETE=16 16

_______________________________________________________________________ ABS 5047-07 In case of the ABS5047-07 prepreg, additional tensile tests on honeycomb bonded face sheets are performed and the material model is calibrated accordingly. The results are given in the following figure.

ABS5047-07 E1 [MPa]

23200

E2 [MPa]

21500

ν12 [-]

0.15

σ1t [MPa]

322

σ2t [MPa]

250

Ply thickness [mm]

0.25

186

Appendix A – Constituent level

*MATERIAL,NAME=ABQ_PLY_FABRIC_1_ABS5047_07 *DENSITY 1.8e-09 *USER MATERIAL, CONSTANTS=40 ** Line 1: +1E, +2E, +12ν, 12G, −1E, −2E, −12ν 23200,21500,0.15,4980,23200,21500,0.15 ** Line 2: +1X, −1X, +2X, −2X, S 322,220,250,180,40 ** Line 3: +1fG, −1fG, +2fG, −2fG, 12α, max12d 9,9,9,9,0.41,1 ** Line 4: 0~yσ, C, p ** Line 5: 1 *DEPVAR, DELETE=16 16

_______________________________________________________________________ ABS 5047-08 *MATERIAL,NAME=ABQ_PLY_FABRIC_ABS5047_08 *DENSITY 1.8e-09 *USER MATERIAL, CONSTANTS=40 ** Line 1: +1E, +2E, +12?, 12G, -1E, -2E, -12ν 26100, 23100, 0.15, 5600,26100, 23100, 0.15 ** Line 2: +1X, -1X, +2X, -2X, S 400,250,300,200,70 ** Line 3: +1fG, -1fG, +2fG, -2fG, 12a, max12d 9,9,9,9,0.4,1 ** Line 4: 0~ys, C, p ** Line 5: 1 *DEPVAR, DELETE=16 16

Appendix A – Constituent level

187

A3 Implemented material models for adhesives The adhesive material models were implemented based on experimental data of standardized tension and compression tests on plastic materials. Since, FE-solvers typically require the input of true yield stress and strain data, the experimentally determined engineering stress and strain have to be converted. This process is described in the following before the determined material models for the three investigated adhesives are given in ABAQUS input format. Extraction of true yield stress and strain from test data In the following a brief overview on how to determine the true stress as function of plastic strain based on uniaxial test data. Relevant materials mechanics relationships are introduced. For a more detailed derivation of the given equations it is referred to material mechanics standard literature such as Ghavami [Gha15]. The true strain in case of tension is given by Eq. 1 ln

,

ln

ln

ln

∆

(1)

Where is the infinitesimal elongation, is the instantaneous length, the initial length and ∆ the elongation. Substituting the engineering strain ∆ / in Eq. 1 yields the following. ln 1

,

(2)

The compressive true strain is respectively given by Eq. 3. ln

,

ln

∆

ln 1

(3)

The true stress is the instantaneous load acting on the instantaneous cross section of the specimen. It therefore takes into account the changing cross sectional area during uniaxial material testing. Assuming that the volume remains constant, the true stress can be obtained from the engineering stress using Eq. 4 and 5 respectively. ∙

,

,

∙

∙ ∙

∙ 1

( 4 )

∙ 1

( 5 )

188

Appendix A – Constituent level

It should be noted that these equations are only valid up until necking of the material. From the converted true stress-strain relationship the yield stress as function of the plastic strain can be extracted as pairs of values. This is illustrated graphically in in the following figure using the example of Ureol under compression. The eventually implemented material models are given in appendix A3.

Yield stress

Plastic strain

20.1871

0.0

26.9850

0.0049

30.2125

0.0175

31.5531

0.0398

41.0303

0.3378

Appendix A – Constituent level

Delo Automix VE24430 *MATERIAL, NAME = DELO Automix VE24430 *ELASTIC, TYPE=ISOTROPIC 2979,0.44 *DENSITY 1.1e-09 *CAST IRON PLASTICITY 0.44 *CAST IRON TENSION HARDENING 15.1978,0.0000 18.6105,0.0003 20.2216,0.0007 21.6817,0.0012 24.0311,0.0024 26.8457,0.0044 28.6718,0.0067 29.3644,0.0093 *CAST IRON COMPRESSION HARDENING 35.0000,0.0000 45.7944,0.0010 55.2648,0.0025 60.1967,0.0041 61.2367,0.0050 65.1955,0.0081 67.2350,0.0151 69.2260,0.0615 73.8889,0.0956

189

190

Scotch-Weld™ EC-9323 B/A *MATERIAL, NAME= Scotch-Weld 9323 *ELASTIC, TYPE=ISOTROPIC 2529.75,0.44 *DENSITY 1.2e-09 *CAST IRON PLASTICITY 0.44 *CAST IRON TENSION HARDENING 20.1978,0.0000 24.6105,0.0003 28.2216,0.0007 30.6817,0.0012 32.0311,0.0024 33.8457,0.0044 34.6718,0.0067 34.5644,0.0093 *CAST IRON COMPRESSION HARDENING 30.0000,0.0000 35.7944,0.0014 38.9944,0.0035 40.2648,0.0052 41.5648,0.0075 42.8967,0.0121 43.9783,0.0211 44.1955,0.0312 44.4833,0.0414

Appendix A – Constituent level

Appendix A – Constituent level

Ureol 1356 A/B *MATERIAL, NAME=Ureol *ELASTIC, TYPE = ISOTROPIC 921, 0.45 *DENSITY 1.6e-09 *CAST IRON PLASTICITY 0.45 *CAST IRON TENSION HARDENING 2.95141 , 0.0 6.11236 , 0.00527 8.22624 , 0.01587 9.36693 , 0.02703 10.6476 , 0.04919 12.4176 , 0.10669 15.0393 , 0.26637 *CAST IRON COMPRESSION HARDENING 20.1871 , 0.0 26.9850 , 0.0049 30.2125 , 0.0175 31.5531 , 0.0398 41.0303 , 0.3978

191

192

Appendix B – Structural element level

Appendix B – Structural element level B1 Sandwich bending test details

Notation B19-L101_01 B19-L101_02 B19-L101_03 B19-W101_01 B19-W101_02 B19-W101_03 B26-L101_01 B26-L101_02 B26-W101_01 B26-W101_02 B19-L003_01 B19-L003_02 B19-L003_03 B19-W003_01 B19-W003_02 B19-W003_03

t [mm] 19.5 19.5 19.4 19.5 19.4 19.4 26.3 26.3 26.3 26.3 19.3 19.2 19.2 19.2 19.3 19.3

b [mm] 50.1 50.1 50.1 50.1 50.1 50.1 49.2 49.2 49.2 49.2 50.2 50.1 50.2 50.1 50.1 50.1

l [mm] 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250 250

Failure Compressive face sheet rupture Compressive face sheet rupture Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Local core indentation Core shear Core shear Core shear

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8

Appendix B – Structural element level

193

Notation B07-L001_01 B07-L001_02 B07-L001_03 B07-W001_01 B07-W001_02 B07-W001_03

t [mm] 7.5 7.4 7.4 7.5 7.5 7.5

b [mm] 49.9 49.9 49.9 49.9 49.9 49.9

l [mm] 190 190 190 190 190 190

Failure Compressive face sheet rupture Compressive face sheet rupture Compressive face sheet rupture Compressive face sheet rupture Compressive face sheet rupture Compressive face sheet rupture

Notation B10-W010_01 B10-W010_01 B10-W010_01 B26-W020_01 B26-W020_02 B26-W020_03

t [mm] 10.1 10.1 10.1 25.1 25.1 25.1

b [mm] 74.8 74.8 74.8 74.8 74.8 74.8

l [mm] 420 420 420 420 420 420

Failure Compressive face sheet rupture Compressive face sheet rupture Compressive face sheet rupture Core shear followed by face sheet Core shear followed by face sheet Core shear followed by face sheet

194

Appendix B – Structural element level

B2 Comparison of modelling approaches in case of bending The bending tests are virtually implemented using two different modelling approaches for the core. The following table compares the two approaches in terms of the visual failure mode for the three dominating kinds of failure. Both models enable to reproduce the correct failure mode. Furthermore, in case of local indentation and face sheet failure, the two approaches lead to comparable visual failure patterns. The limitations of the 3Dcontinuum core are most evident in case of core shear. The 8-node hexahedron elements are not capable to capture the distributed shearing of the core. Instead the shearing is limited to only one row of elements directly underneath the load cylinder. This eventually leads to local compressive core indentation and thus to premature failure.

B19-L003 Core shear failure

B07-L001-3P Face sheet failure

B19-L101 Local core indent.

Detailed core

3D-continuum core

Appendix B – Structural element level

195

B3 Frame shear test details Fame shear test specimen drawing (panel thickness variable depending on tested panel configuration). 400 375 330

90

270

Edge filling (alumnium)

R 25

Engineering shear strain γ calculated from rectangular rosette with ε1, ε2 and ε3 being the strains measured at the rosette legs according to the image on the right [AST17].

196

Appendix C – Sub-component level

Appendix C – Sub-component level C1 Damage progression for pull-out test on fully potted insert Stage 1

Linear elastic deformation No visible damage Stage 2 Initiation of core shear damage No damage visible from exterior Stage 3 Continuous debonding of potting and face Face shear damage visible Stage 4 Potting-face debonding almost completed Debonding and face damage progressed Stage 5 Post failure regime Top face sheet damage clearly visible, Potting debonded from face

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8

Appendix C – Sub-component level

197

C2 Implemented cohesive behavior of potting-face contact The bond between face and potting in the fully potted insert configurations was implemented using surface-based cohesive behavior properties. The corresponding surface interaction input deck definition (ABAQUS) is given below. This represents the calibrated contact properties. *SURFACE INTERACTION, NAME=COHESIVE_BOTTOM *COHESIVE BEHAVIOR, eligibility=ORIGINAL CONTACTS 20000,20000,20000 *DAMAGE INITIATION, CRITERION=MAXS 1,1,1 *DAMAGE EVOLUTION, TYPE=DISPLACEMENT, SOFTENING=LINEAR 0.8 *DAMAGE STABILIZATION 1e-06

198

Appendix C – Sub-component level

C3 Experimental results in novel design study The following graph summarizes the experimental results of all tested specimens in the framework of the novel insert design study. There is significant scatter in particular in case of the reinforced configurations (Hourglass and Undercut). This scatter is evaluated based on visual inspection of the specimens after testing. This evaluation is summarized in the table on the following page. 3000 2500

Reference_01 Reference_02 Reference_03 Hourglass_01 Hourglass_02 Hourglass_03 Undercut_01 Undercut_02 Undercut_03

Force [N]

2000 1500 1000 500 0 0

2 4 Displacement [mm]

6

Despite the noticeable scatter in terms of force-displacement relationship, the reference configurations are characterized by consistent failure. Therefore, it is assumed that the scatter is simply due to uncertainties of the material especially regarding the bonding. All three hourglass configurations present a different failure mode, while each specimen failed prematurely. Hourglass_01 and _03 have a similar curve progression, while specimen 01 failed due to screw shear off and specimen 03 due to insert rupture. Specimen 02 is an outlier, which failed due to debonding of insert and adhesive. This was caused by the Spax screw which pierced through the insert penetrating the adhesive, thus leading to an initial crack between insert and adhesive. The undercut configurations are characterized by the most significant scatter. This is due to poor and inconsistent manufacturing in particular in terms of removing the core for the undercut cavity. A lack of specialized tools made this manufacturing step difficult. This results in considerably varying potting conditions. Only specimen Undercut_03 can be considered close to the desired Undercut potting condition. This is also evident in the force displacement relationship, which develop the characteristic curve progression only in case of specimen 03. However, catastrophic failure is here also caused by insert rupture analogous to the hourglass configurations. The remaining Undercut specimens can be considered outliers due to poor manufacturing. For comparison with the virtual tests, a single characteristic curve for each configuration is selected (gray highlights in following table).

Appendix C – Sub-component level

199

Reference_01 3000

Reference_01 Reference_02 Reference_03

2500

Force [N]

2000

24.2g Reference_02

1500

24.6g

1000 500 0 0

-Shear/tensile core failure - Face sheet rupture -Shear/tensile core failure - Face sheet rupture

Reference_03 1

2 3 4 Displacement [mm]

5

24.3g

-Shear/tensile core failure - Face sheet rupture

Hourglass_01 3000

30.9g

2500

Force [N]

2000

- Core shear failure - Screw shear off

Hourglass_02

1500

30.6g

1000 Hourglass_01 Hourglass_02 Hourglass_03

500 0 0

2 4 Displacement [mm]

6

- Core shear failure - Debonding of insert

Hourglass_03 31.9g

- Core shear failure - Insert rupture

Undercut_01 3000

30.2g

2500

Force [N]

2000

Undercut_02

1500

37.5g

1000 Undercut_01 Undercut_02 Undercut_03

500 0 0

-Shear/tensile core failure - Face sheet rupture

1

2 3 4 Displacement [mm]

5

- Core shear failure - Insert rupture

Undercut_03 33.1g

- Core shear failure - Insert rupture

Lebenslauf

Name Vorname Staatsangehörigkeit Geburtsdatum Geburtsort, -land

Seemann Ralf deutsch 16.05.1985 Lübz, Deutschland

09.1991 - 07.1995

Grundschule II in Lübz

08.1995 - 06.2004

Eldenburg-Gymnasium Lübz

07.2004 - 03.2005

Grundwehrdienst bei der Marine in Plön und Eckernförde

04.2005 - 09.2005

Praktikum Fertigungstechnik - Hydraulik Nord in Parchim

10.2005 - 08.2011

Maschinenbaustudium - Technische Universität Hamburg Abschluss: Diplom-Ingenieur

09.2011 - 12.2016

Wissenschaftl. Mitarbeiter - Technische Universität Hamburg

01.2017 - heute

Berechnungsingenieur bei Diehl Aviation in Hamburg

© Springer-Verlag GmbH Germany, part of Springer Nature 2020 R. Seemann, A Virtual Testing Approach for Honeycomb Sandwich Panel Joints in Aircraft Interior, Produktentwicklung und Konstruktionstechnik 16, https://doi.org/10.1007/978-3-662-60276-8