A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass (Mechanik, Werkstoffe und Konstruktion im Bauwesen) [1st ed. 2024] 3658420286, 9783658420284

Table of contents :
Danksagung
Abstract
Zusammenfassung
Contents
Glossaries
Abbreviations
Symbols
1 Introduction
1.1 Motivation
1.2 State of the Art
Optical Anisotropy in tempered Architecture Glass
Photoelastic Full-Field Methods
Evaluation Methods and Quality Assessment
1.3 Structure
1.4 Achievements of this Work
1.5 List of own Publications on this Ph.D. Thesis
2 Theoretical Principles
2.1 Basics of Linear Elasticity
2.2 Nature of Polarized Light
2.2.1 Nature of Light
2.2.2 Types of Polarized Light
2.2.3 Stokes Parameters
2.3 Polarization of Light
2.3.1 General
2.3.2 Polarization by Scattering
2.3.3 Polarization by Reflection
2.4 Brewster’s Angle
2.5 Passage of Light through Media
2.6 Basics of Photoelasticity
2.6.1 General
2.6.2 Artificial Birefringence
2.6.3 Stress-Optical Law
2.6.4 Plane and Circular Polariscope
3 Glass and their Photoelastic Behaviour
3.1 General
3.2 Residual Stresses
3.3 Photoelastic Behaviour
3.4 Visual Perception of Anisotropy Effects
4 Photoelastic Methods for Measuring Anisotropy Effects
4.1 General
4.2 Scattered Light Method
4.3 RGB Photoelasticity
4.4 Half-Wavelength and Multi-Wavelength Photoelasticity
4.5 Phase-Shifting Methods
4.6 PSM for Skylight Observation
5 Photoelastic Measurements on Tempered Flat Glass
5.1 Validation Experiments
5.1.1 Accuracy and Precision
5.1.2 Temperature Dependency
5.2 Specimen
5.3 Influence from Geometry Parameters
5.3.1 Thickness
5.3.2 Size
5.3.3 Holes and Cut Outs
5.4 Influence from Glass-Specific Parameters
5.4.1 Type of Glass
5.4.2 Tempering Level
5.5 Influence from Furnace Parameter
5.5.1 Glass Position
5.5.2 Glass Orientation
6 Experimental Field Studies on Tempered Flat Glass
6.1 Design and Construction the Test Facility
6.2 Setup and Specimen
6.3 Influence from the Building Environment and Use
6.3.1 Background Lighting
6.3.2 Reflection Disturbances
6.4 Influence from Viewing
6.4.1 Viewing Angle
6.4.2 Viewing Position
6.4.3 Viewing Direction and Sun Position
6.5 Influence from Skylight Polarization
6.6 Visual Intensity of Anisotropy Effects
6.7 Correlation between Measurement and Observation
7 Methods for evaluating Anisotropy Effects in Glass
7.1 Evaluation Zone
7.2 Statistical Method Quantile Value
7.3 Threshold Method Isotropy value
7.4 Texture Analysis
7.5 Method and Combined Textural Feature CCP
8 Evaluation and Concept
8.1 Assessment of Evaluation Methods
Iso75
x95
CCP
8.2 Anisotropy Quality of Tempered Flat Glass
8.3 Evaluation Concept
8.3.1 General
8.3.2 Definition of the Quality Classes
8.3.3 Requirements for the Measurement
8.3.4 Procedure of the Evaluation Concept
8.4 Discussion
9 Summary and further Research
Further Research
References
Own Publications
Standards
Bibliography
Appendix A Experiments Results
Appendix B Field Study Test Results

Citation preview

Mechanik, Werkstoffe und Konstruktion im Bauwesen | Band 70

Steffen Dix

A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass

Mechanik, Werkstoffe und Konstruktion im Bauwesen Band 70 Reihe herausgegeben von Ulrich Knaack, Institut für Statik und Konstruktion, Technische Universität Darmstadt, Darmstadt, Germany Jens Schneider, Institut für Statik und Konstruktion, Technische Universität Darmstadt, Darmstadt, Germany

Johann-Dietrich Wörner, Institut für Statik und Konstruktion, Technische Universität Darmstadt, Darmstadt, Germany Stefan Kolling, Fachbereich Maschinenbau & Energietechnik, Technische Hochschule Mittelhessen, Gießen, Germany

Institutsreihe zu Fortschritten bei Mechanik, Werkstoffen, Konstruktionen, Gebäudehüllen und Tragwerken. Das Institut für Statik und Konstruktion der TU Darmstadt sowie das Institut für Mechanik und Materialforschung der TH Mittelhessen in Gießen bündeln die Forschungs- und Lehraktivitäten in den Bereichen Mechanik, Werkstoffe im Bauwesen, Statik und Dynamik, Glasbau und Fassadentechnik, um einheitliche Grundlagen für werkstoffgerechtes Entwerfen und Konstruieren zu erreichen. Die Institute sind national und international sehr gut vernetzt und kooperieren bei grundlegenden theoretischen Arbeiten und angewandten Forschungsprojekten mit Partnern aus Wissenschaft, Industrie und Verwaltung. Die Forschungsaktivitäten finden sich im gesamten Ingenieurbereich wieder. Sie umfassen die Modellierung von Tragstrukturen zur Erfassung des statischen und dynamischen Verhaltens, die mechanische Modellierung und Computersimulation des Deformations-, Schädigungs- und Versagensverhaltens von Werkstoffen, Bauteilen und Tragstrukturen, die Entwicklung neuer Materialien, Produktionsverfahren und Gebäudetechnologien sowie deren Anwendung im Bauwesen unter Berücksichtigung sicherheitstheoretischer Überlegungen und der Energieeffizienz, konstruktive Aspekte des Umweltschutzes sowie numerische Simulationen von komplexen Stoßvorgängen und Kontaktproblemen in Statik und Dynamik.

Steffen Dix

A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass

Steffen Dix Hochschule München München, Bayern, Germany Vom Promotionszentrum für Ingenieurwissenschaften des Forschungscampus Mittelhessen zur Erlangung des akademischen Grades des Doktors der Ingenieurwissenschaften (Dr.-Ing.) genehmigte Dissertation von Steffen Dix M.Eng. aus Osterode am Harz. 1. Gutachten: Prof. Dr.-Ing. habil. Stefan Kolling (Technische Hochschule Mittelhessen, Gießen) 2. Gutachten: Prof. Dr. Peter J. Klar (Justus Liebig Universität, Gießen)

Tag der Einreichung: 30.11.2022 Tag der mündlichen Prüfung: 25.04.2023 Gießen 2023

ISSN 2512-3238 ISSN 2512-3246 (electronic) Mechanik, Werkstoffe und Konstruktion im Bauwesen ISBN 978-3-658-42028-4 ISBN 978-3-658-42029-1 (eBook) https://doi.org/10.1007/978-3-658-42029-1 Springer Vieweg © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 This work is subject to copyright. All rights are solely and exclusively licensed 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 Fachmedien Wiesbaden GmbH, part of Springer Nature. The registered company address is: Abraham-Lincoln-Str. 46, 65189 Wiesbaden, Germany Paper in this product is recyclable.

Danksagung Die vorliegende Arbeit entstand im Rahmen einer kooperativen Promotion am Forschungscampus Mittelhessen, zwischen der Technischen Hochschule Mittelhessen (THM), der Justus-Liebig-Universität (JLU) in Gießen und der Hochschule München (HM). Zu dieser Zeit war ich als wissenschaftlicher Mitarbeiter am Labor für Stahlund Leichtmetallbau an der HM tätig. Sie basiert auf Ergebnisse, die ich in dem vom Bundesministerium für Wirtschaft und Klima geförderten Forschungsprojekten: „Gläsernes Glas – Online Prüfsystem zur flächigen und zerstörungsfreien Qualitätskontrolle von thermisch vorgespanntem Glasscheiben mittels spannungsoptischer Methoden“ (FKZ: ZF4051701GM5) und „BeNAF – Bewertungskriterien zur Normung von Anisotropie-Effekten bei thermisch vorgespanntem Flachglas“ (FKZ: 03TNH011A) sowie den Forschungsarbeiten im Fachverband konstruktiver Glasbau sammeln konnte. Mein Dank gilt allen, mit denen ich in dieser Zeit zusammengearbeitet habe und die zum Erfolg dieser Arbeit beigetragen haben. Mein herzlichster Dank gilt Herrn Prof. Dr.-Ing. habil. Stefan Kolling (THM) und Herrn Prof. Dr. Peter Klar (JLU) für die Übernahme der Betreuung meiner Arbeit. Ein ganz besonderer Dank geht an Herrn Prof. Dr.-Ing. Christian Schuler (HM), der mir die Möglichkeit zu diesem Promotionsvorhaben eröffnete. Durch seine fachliche und menschliche Betreuung konnte ich persönlich wachsen. Ihnen, Herrn Prof. Dr.-Ing. Jens Schneider, Herrn Prof. Dr.-Ing. Ulrich Knaack und dem ganzen Team der IMM und ISM+D sei gedankt für die konstruktiven Anregungen sowie die wertvollen Impulse auf den lehrreichen Doktorandenseminaren. Auch bedanke ich mich bei Herrn Prof. Dr.-Ing. Ömer Bucak und den Mitarbeitern der LSL GmbH für die Unterstützung bei der Errichtung des Außenprüfstandes. Ganz herzlichen Dank gilt auch den Studenten, Hilfskräften und allen voran meinen ehemaligen und aktuellen Kollegen. Abschließend möchte ich mich bei meinen stets motivierenden Freunden sowie bei meiner fürsorglichen und geduldigen Familie bedanken. Mein innigster Dank gilt meiner Frau Sarah und meinem Sohn Noah, euch ist diese Arbeit gewidmet.

Mertingen, im November 2022

Steffen Dix v

Abstract Optical anisotropy effects can occur in building envelopes made of tempered glass, which affect the desired transparency. The colored patterns are related to residual stress differences from the tempering process, resulting in optical retardation, which becomes visible in nature under partially polarized light. So far, the visual effect has been completely neglected in the evaluation of the building product and increasingly leads to complaints and disputes between the parties involved. This thesis extends the state of knowledge on the cause and perception of optical anisotropic effects and presents a concept for measuring and evaluating them in flat monolithic tempered architectural glass. Initially, an overview and description of current photoelastic measurement methods are given, and the accuracy of the used measurement setups is verified for the first time. The experimental basis for the concept is formed by extensive fullfield retardation measurements in the laboratory and field studies of the maximum visibility of the anisotropy effects in an outdoor test rig with accompanying polarization measurements of the sky. Various glass types, geometries, and tempering levels are selected based on typically used products, and their influence on the resulting retardation image is investigated. Determining a correlation of the retardation images with the reflection images of selected test specimens in the outdoor test rig complements the experiments. Based on this, digital evaluation methods are presented, further developed, and applied to the measured retardation images. From the critical analysis of these results, limit values for different anisotropy quality classes are derived, and the concept is complemented. With the implementation of the evaluation methods and the limit values in commercial anisotropy scanners, the quality of each glass pane can be determined directly after tempering in the future. By choosing the highest quality class A, it will be possible to significantly reduce anisotropy effects in constructions made of tempered glass panes.

vii

Zusammenfassung In Gebäudehüllen aus thermisch vorgespannten Gläsern können optische Anisotropie-Effekte auftreten. Diese farbigen Muster, welche die gewünschte Transparenz des Glases beeinträchtigen, stehen im Zusammenhang mit Eigenspannungsdifferenzen aus dem thermischen Vorspannprozess. Die dadurch resultierenden optischen Gangunterschiede können durch in der Natur vorkommendes, teilpolarisiertes Licht sichtbar werden. Bisher wird dieser optische Effekt bei der Bewertung des Bauprodukts komplett vernachlässigt und führt daher zunehmend zu Reklamationen und Streitigkeiten zwischen den Baubeteiligten. Die vorliegende Arbeit erweitert den Wissensstand zur Ursache und Wahrnehmung der optischen Anisotropie-Effekte und stellt ein Konzept zur Messung und Bewertung dieser in flachem thermisch vorgespannten Architekturglas vor. Beginnend mit einem Überblick über spannungsoptische Messmethoden und deren Art der Messwertbildung wird erstmalig die Genauigkeit einiger Messaufbauten verifiziert. Experimentelle Grundlage für das Konzept bilden umfangreiche vollflächige Gangunterschiedsmessungen im Labor und Feldstudien zur maximalen Sichtbarkeit der Anisotropie-Effekte in einem Außenprüfstand mit begleitenden Polarisationsmessungen des Himmels. Unter Berücksichtigung der im Bauwesen üblichen Bauprodukte wird eine Vielzahl an unterschiedlichen Glastypen, Geometrien und Vorspanngrade ausgewählt und deren Einfluss auf das entstehende Gangunterschiedsbild untersucht. Die Bestimmung einer Korrelation der Gangunterschiedsbilder mit den Reflexionsbildern ausgewählter Probekörper im Außenprüfstand komplementieren die Experimente. Darauf aufbauend werden digitale Auswertemethoden vorgestellt, weiterentwickelt und auf die gemessenen Gangunterschiedsbilder angewendet. Aus der kritischen Analyse dieser Ergebnisse werden Grenzwerte für unterschiedliche AnisotropieQualitätsklassen abgeleitet und das Bewertungskonzept vervollständigt. Mit der Implementierung der Auswertemethoden und der Grenzwerte in kommerzielle Anisotropie-Scanner kann zukünftig die optische Qualität jeder Glasscheibe direkt nach dem Vorspannen bestimmt werden. Durch die Wahl der höchsten Qualitätsklasse A wird ermöglicht, Anisotropie-Effekte in Konstruktionen aus thermisch vorgespannten Glasscheiben signifikant zu reduzieren.

ix

Contents Glossaries

xv

1 Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Achievements of this Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 List of own Publications on this Ph.D. Thesis . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 5 7 7

2 Theoretical Principles 2.1 Basics of Linear Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Nature of Polarized Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Nature of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Types of Polarized Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Stokes Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Polarization of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Polarization by Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Polarization by Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Brewster’s Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Passage of Light through Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Basics of Photoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Artificial Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Stress-Optical Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.4 Plane and Circular Polariscope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 12 12 14 14 18 18 19 21 22 24 25 25 26 27 28

3 Glass and their Photoelastic Behaviour 3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Photoelastic Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Visual Perception of Anisotropy Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 33 37 40 42 xi

xii

Contents

4 Photoelastic Methods for Measuring Anisotropy Effects 4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Scattered Light Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 RGB Photoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Half-Wavelength and Multi-Wavelength Photoelasticity . . . . . . . . . . . . . . . 4.5 Phase-Shifting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 PSM for Skylight Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 45 49 52 54 58

5 Photoelastic Measurements on Tempered Flat Glass 5.1 Validation Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Accuracy and Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Temperature Dependency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Influence from Geometry Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Holes and Cut Outs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Influence from Glass-Specific Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Type of Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Tempering Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Influence from Furnace Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Glass Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Glass Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61 61 61 64 66 67 67 68 69 70 70 72 73 73 73

6 Experimental Field Studies on Tempered Flat Glass 6.1 Design and Construction the Test Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Setup and Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Influence from the Building Environment and Use . . . . . . . . . . . . . . . . . . . . . 6.3.1 Background Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Reflection Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Influence from Viewing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Viewing Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Viewing Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Viewing Direction and Sun Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Influence from Skylight Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Visual Intensity of Anisotropy Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Correlation between Measurement and Observation . . . . . . . . . . . . . . . . . . . .

77 77 79 81 81 82 84 84 85 87 89 91 94

99 7 Methods for evaluating Anisotropy Effects in Glass 7.1 Evaluation Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.2 Statistical Method - Quantile Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Contents

7.3 7.4 7.5

xiii

Threshold Method - Isotropy value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Texture Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Method and Combined Textural Feature CCP . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8 Evaluation and Concept 109 8.1 Assessment of Evaluation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 8.2 Anisotropy Quality of Tempered Flat Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 8.3 Evaluation Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.3.2 Definition of the Quality Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.3.3 Requirements for the Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8.3.4 Procedure of the Evaluation Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 9 Summary and further Research

127

References

133

A Experiments Results

145

B Field Study Test Results

147

Glossaries

Abbreviations Evaluation C CCP CP DIPM GLCM Iso75 x95

textural feature contrast combined textural feature textural feature cluster prominence digital image processing methods grey level co-occurrence matrix isotropy value at 75 nm 95 percent quantile value

General 2D 3D AE ECDF FEM GT LUT TF TL

two dimensional three dimensional absolute error empirical cumulative distribution function finite element method glass type lookup table tempering facility tempering level

Materials CF FTG HSG LE

clear float fully-tempered glass heat-strengthened glass low-emissivity xv

Glossaries

xvi

LI LSG PVB SC SLS

low-iron laminated safety glass Polyvinylbutyral solar control soda-lime-silica glass

Optics HWP MWP PPSM PSM RGBP RSK SLM

half-wavelength photoelasticity multiple-wavelength photoelasticity pixelated phase-shifting phase-shifting method RGB photoelasticity Rayleigh sky model scattered light method

Symbols

General A I T ¯ x α λ σ σ τ i, j l n t v w x y z

area invariant temperature mean value relative retardation eigenvalue Cauchy’s stress tensor stress, standard deviation shear stress indices length number thickness velocity width abscissa of Cartesian coordinate system ordinate of Cartesian coordinate system applicate of Cartesian coordinate system

Glossaries

xvii

Optics A C H I N R S T ∆ Θ ΘS α αB αe β δ ϵ γ λ ω ψ ρe , ρ v τe , τ v θ φ ⃗ E ⃗ H ⃗ S c f n p s t

splitted light vector photoelastic constant polarized vector Intensity fringe order reflectance Stokes Parameter transmission phase difference sun zenith distance (RSK) angle between sun and observing point (RSK) angle of incidence Brewster’s angle solar absorptance angle of refraction relative retardation ellipticity angular distance (RSK), angle sun to facade orientation wavelength circular frequency ellipse angle, isoclinic angle solar reflectance solar transmittance azimuth angle (Sky-PSM) azimuthal angle (PPSM) light, electric vector magnetic vector Stokes vector speed of light in vacuum frequency refractive indices degree of polarization speed of light in a material time

1 Introduction 1.1 Motivation Nowadays, extraordinary building envelopes consisting of over-seized glass panes are realized, which decisively shape the urban landscape. Annealed float glass is fragile and breaks under tensile stress depending on the load duration. The glass dimensions required for these high-quality facade projects can only be achieved sensibly with tempered glass due to its high strength and thermal shock resistance compared to annealed float glass. Increasing the strength by a factor of approximately 1.6 for heat-strengthened glass (HSG) and about 2.7 for fully tempered glass (FTG) makes it possible to design lighter structures and reduce CO2 emissions by using thinner glass and slimmer steel and aluminum profiles. The all-glass constructions built in the last 30 years involving the transfer of the static load-bearing capacity could only be built with thermally tempered glass, see Fig. 1.1. Tempered glass panes are indispensable, especially in structural glass engineering, since the connection of the load-bearing structures is achieved almost exclusively by mechanical supports in the hole and edge areas. Drilled glass made of annealed float glass is not an option due to the stress increase at the drill hole and the low strength under permanent load. All-Glass Structures made of Tempered Glass

Figure 1.1 All-Glass shell structure over the courtyard of the Maximilian Museum in Augburg, Germany (a). Load-bearing glass structure of the Apple Cube, Apple retail store 5th avenue in New York, USA (b).

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_1

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2

1 Introduction

Maximum transparency is expected from the glass used in architecture. However, the standard tempering process for architectural flat glass creates minor fluctuations in the lateral stress distribution resulting in birefringence and undesired optical iridescence, also known as anisotropy effects. In general, the optical properties of an anisotropic material are not symmetrical to a plane or an axis. Optical anisotropy, as it is also known in crystals in nature, occurs in glass due to artificial stress birefringence. These optical phenomena can become visible as a characteristic pattern in the facade in the form of grey, white or rainbow-colored spots, rings or stripes under certain light incidence, weather conditions and daytimes, see Fig. 1.2. Even though anisotropy effects do not constitute a defect in the sense of product standards, architects, building owners, facade consultants, and, increasingly, building users perceive this effect as a visual disturbance. Tempered Glass Panes with Optical Anisotropy Effects

Figure 1.2 Facade with tempered glass panes, strong (arrows 1) and weak (arrows 2) optical anisotropy effects. Image were taken without a polarizing filter in Luxembourg (Courtesy: Ruth Kasper, Ref. Feldmann et al. (2017a)).

Architects often requested a visual assessment of birefringence effects based on mock-ups in the past. However, this is not recommended because it is expensive and yet there is a very high risk that higher anisotropy effects will occur under unfavorable conditions and that the evaluation is subjective on the part of the observer. A new concept that objectively evaluates the phenomenon is necessary. Motivated by recent advances in full-field digital photoelasticity, it is possible to quantify the effects by measuring the optical retardation in the laboratory. The investigation aims to develop a concept to measure and evaluate optical anisotropy effects from residual stress difference as well as to classify the quality of monolithic

1.2 State of the Art

3

tempered glass. The measurement techniques are intended to generally apply to residual stress differences in tempered glass and predict the maximum intensity of anisotropy effects. The evaluation is to consider the level and the distribution of optical retardation. The aim is to classify in anisotropy quality class with which by choosing the highest quality a reduction of optical effects occurs and defects on site are avoided.

1.2 State of the Art The current challenges for quantifying and predicting anisotropy effects in glass are their unknown multiplicity and variability in nature. The formation of the residual stress state of glass with the generation of optical retardation and the observation, in reality, is subject to many influences. In the following, recent studies and unsolved problems in describing, measuring, and evaluating anisotropy effects in tempered glass are presented. Although a general consideration of tempered glass is intended, this study focuses on flat architectural glass. Optical Anisotropy in tempered Architecture Glass The basic physical effect, stress birefringence, was already discovered by Brewster (1815a) and is applied in photoelasticity to visualize and measure stresses in complex components (Ramesh and Sasikumar (2020), Ajovalasit et al. (2015b), Solaguren-Beascoa Fernández et al. (2010)). External or residual stresses in glass cause artificial birefringence depending on the principal stresses and their orientation. If polarized light hits this glass, it can be split according to the principal stresses when it enters the glass pane. Assuming that there is a difference between the two principal stresses, the two partial light beams pass through the glass at different velocities, resulting in optical retardation (Illguth et al. (2015), Feldmann et al. (2017a)). The conventional tempering process for FTG and HSG cannot be completely homogeneous, so the generated stress state will differ minimally across the thickness and area. The minimum residual stress difference is sufficient to produce optical retardations whose height varies over the glass sheet area. Suppose the tempered glass pane is now installed in the facade under natural partially polarized daylight. In that case, the retardation pattern causes a color pattern that can be perceived by the human eye in the interference colors, according to Michel-Levy (Sørensen (2013), Illguth et al. (2015)). While a wealth of knowledge exists on optics, photoelasticity, and the formation of the stress state of tempered glass, little exists on the distribution of retardations and their optical anisotropy effects in natural environments. Although the phenomenon is already known (Können (1985)), it is neglected because its control and

4

1 Introduction

prevention during production was probably considered impossible. It was not until the improvement of furnace technology and the invention of the first photoelastic measurement methods that various authors (Henriksen and Leosson (2009), Illguth et al. (2015), Pasetto (2014), Dehner and Schweitzer (2015)) started to address the phenomenon. Some of these authors give hints based on selective practical examples and physical relations, under which anisotropy effects can become visible. Scientific studies investigating and observing retardations in tempered glass panes and their direct visual impact on anisotropy effects are unknown. Photoelastic Full-Field Methods Photoelastic methods for full-field retardation measurements are known or were co-developed in the preliminary work of this thesis (Dix et al. (2017a)). The first technique, which was able to measure optical retardation in large-seized glass panes, point by point, was presented with the linkage of the Phase-Shifting Method (PSM) and a CNC control (Dehner and Schweitzer (2015)). At the same time, the RGB photoelasticity (RGBP) was tested in Illguth et al. (2015), which enabled full-field and fast image acquisition. Recognizing the potential for quality assurance, several measurement systems (Decourcelle et al. (2017), Vogel (2017)) were then developed, based on novel measurement approaches, such as the multiple wavelength method (Dix et al. (2017a), Hidalgo and Elstner (2018)) or the pixelated phase shifting method (Katte and Saur (2018)). Evaluation Methods and Quality Assessment The output of the measurement results is in the form of an image or in matrix notation as a comma-separated value file with the single values as retardation in the unit ’nm’. Digital image processing methods (DIPM) can be used to evaluate retardation images. Statistical methods, like the determination of mean or quantile values on retardation images, are proposed in Illguth et al. (2015) and applied to two exemplary glass panes. Another method, the isotropy value method, is presented using an exemplary glass pane in Dehner and Schweitzer (2015). Here, the isotropy value is the percentage area of a glass pane that should be free of optically perceptible anisotropies under unfavorable lighting conditions. The method is based on the threshold method, for which a threshold value must be specified. However, this value is not specified and is therefore not comprehensible. The application of texture analysis (Haralick et al. (1973)), with its advantage of considering homogeneity and spatial distribution of retardation values, is tested for the first time in Hidalgo and Elstner (2018) on 55 samples of the same size. By the formation of a Grey-Level Co-occurrence Matrix (GLCM) in which retardation values

1.3 Structure

5

are compared in a defined distance and direction, statements about the texture can be determined with an evaluation of the textural features Contrast (C) and Cluster Prominence (CP). The retardation images were acquired within this thesis at the University of Applied Sciences Munich and were provided to Hidalgo and Elstner (2018). The approach is very promising, but the computation time of the evaluation algorithm is yet too slow, and the results are abstract and scaledependent and, therefore, difficult to compare. The influence of the different setting parameters of the GLCM is unknown for the application of retardation images. There is a lack of literature on the evaluation of optical anisotropy effects in thermally toughened glass (Illguth et al. (2015), Dehner and Schweitzer (2015), Hidalgo and Elstner (2018)) since, according to the current product standards (EN 12150 (2015), EN 1863 (2012)) and guidelines (Bundesverband Flachglas (2009)), it is not considered a defect but a characteristic feature of tempered glass. Therefore, there are no benchmarks for good, normal, or insufficient anisotropy quality. There are also no studies that have performed a larger number of retardation measurements on tempered glass that could be used to define it. A concept for measuring, evaluating, and assessing anisotropy effects in tempered architectural glass has not yet been introduced.

1.3 Structure A concept for measuring and evaluating optical anisotropy effects in tempered architectural glass does not exist and will be developed in this thesis. The structure of the present work is displayed in Fig. 1.3. Chapter 2 gives a brief discussion of the mechanical, optical, and photoelastic principles which are necessary for this study. Chapter 3 describes glass based on its mechanical and optical properties. It contains the formation of the different residual stress states in tempered glass and their photoelastic behavior. The chapter is concluded with a description of the visual perception of anisotropy effects in tempered glass. Chapter 4 describes known and novel photoelastic measurement methods that can be used to analyze anisotropy effects created by stress differences in the glass. Depending on the method, different physical values can be visualized and measured. Also presented is a self-built device for measuring the polarization of the sky. In Chapter 5, after initial validation experiments, three full-field measurement methods are selected, and a total of 736 tempered glass sheets are photoelastically investigated. Influences of geometrical and furnace parameters on the formation of optical retardation in tempered glass are analyzed qualitatively. The correlation between retardation measurement in the laboratory and its visibility under natural daylight is tested by means of a field study in chapter 6. For this purpose, an outdoor test rig is constructed in which various tempered glass panes are installed

6

1 Introduction

and examined under different viewing and lighting situations. Then, in chapter 7, digital image processing methods are presented to evaluate the acquired retardation images. For this purpose, existing methods are described in detail, and novel methods are extended. For the application of the combined textural feature CCP, a calculation algorithm is developed and presented. Chapter 8 includes the application of all three evaluation methods on the retardation images of 491 tempered glass specimens and their comparison for their possibilities and disadvantages. The collected results are then statistically evaluated, and quantitative relationships are identified that allow classification into anisotropy qualities. In the next step, an evaluation concept is established, which defines requirements for the measurement and evaluation and classifies the tempered glass sheets into a optical quality class based on their evaluation value. In the end, the visual difference between the quality classes and the proportional distribution of the quality classes depending on the glass type will be discussed. Finally, chapter 9 summarizes the main findings of the present work. Based on the observations during this investigation, several topics for further investigation are suggested. Schematic Structure

Motivation 1. Introduction Theory 2.

Theoretical Principles

3.

Glass and their Photoelastic Behaviour

4.

Photoelastic Methods for Measuring Anisotropy Effects Experiments

5.

Photoelastic Measurements on Tempered Flat Glass

6.

Experimental Field Studies on Tempered Flat Glass Evaluation

7.

Methods for evaluating Anisotropy Effects in Glass

8.

Evaluation and Concept Final

9. Figure 1.3

Summary and further Research

Schematic overview of the structure of the present thesis.

1.5 List of own Publications on this Ph.D. Thesis

7

1.4 Achievements of this Work The scientific added value consists of measurement method testing, material characterization, evaluation method development and concept formulation. Photoelastic methods are presented which can be used for full-field measurement of retardation from residual stress differences in tempered glass. Of these, the RGBP is further developed and a measurement system with the novel MWP is co-developed. A method to verify the accuracy of the respective measurement systems (RGBP, MWP, PPSM) is presented and tested. An unprecedented experimental database is being collected for full-field retardation measurements of tempered glass. For this purpose, 736 glass panes are scanned, analyzed, and evaluated with several measuring systems. With the construction of an outdoor test rig and the performance of field tests, the fundamentals for the visibility of anisotropy effects in tempered glass are systematically developed, and the relationship between the reality in the field and the photoelastic measurement in the laboratory is established. An algorithm is developed that applies texture analysis to evaluate the homogeneity and distribution of retardation values across the glass pane in a rapid and size-independent manner. This novel method and other proven methods, such as the quantile value method and the threshold method, are presented and compared, and the advantages and disadvantages are discussed. Based on the retardation measurements and the field study experience, an optical classification of tempered glass into three different quality classes is introduced. The concept provides an objective evaluation of the subjective and varying optical anisotropy effects in tempered architectural glass. By transferring this concept to DIN SPEC 18198 (2022), the work achieves both scientific and economic added value.

1.5 List of own Publications on this Ph.D. Thesis Parts of the results of this study have already been published and thus made available to an international expert audience: • Dix, S., L. Efferz, S. Hiss, C. Schuler, and S. Kolling (2022a). “Spannungsoptische Untersuchungen an polymeren Zwischenschichten in Verbundgläsern”. In: Glasbau 2022. Ed. by B. Weller and S. Tasche. • Dix, S., C. Schuler, and S. Kolling (2022b). “Digital full-field photoelasticity of tempered architectural glass: A review”. In: Optics and Lasers in Engineering 153. • Dix, S., C. Schuler, S. Kolling, and J. Schneider (2022c). “The relation between measurement and visibility of anisotropy effects in tempered glass. A case study.” In: Glass Performance Days 2021. Tampere.

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1 Introduction

• Dix, S., K. Thiele, L. Efferz, C. Schuler, J. Schneider, and S. Kolling (2022d). “Test facilities and concept for the evaluation of optical anisotropy effects in tempered glass”. In: ICSA 2022 - The International Conference on Structures and Architectures. Aalborg. • Dix, S., P. Müller, C. Schuler, S. Kolling, and J. Schneider (2021a). “Digital image processing methods for the evaluation of optical anisotropy effects in tempered architectural glass using photoelastic measurements.” In: Glass Structures & Engineering 11.6, p. 10. • Dix, S., L. Efferz, L. Sperger, C. Schuler, and S. Feirabend (2021b). “Analysis of residual stresses at holes near edges in tempered glass.” In: Engineered Transparency 2021. Ed. by B. Weller, J. Schneider, C. Louter, and S. Tasche, pp. 145–162. • Dix, S. and C. Schuler (2018). “Untersuchungen an thermisch vorgespannten Gläsern mittels spannungsoptischer Methoden.” In: Glas im konstruktiven Ingenieurbau. Ed. by C. Schuler, pp. 165–176. • Feldmann, M., R. Kasper, P. Di Biase, B. Schaaf, C. Schuler, S. Dix, and M. Illguth(2017a). “Flächige und zerstörungsfreie Qualitätskontrolle mittels spannungsoptischer Methoden”. In: Glasbau 2017. Ed. by B. Weller and S. Tasche. Berlin: Ernst Sohn, pp. 327–338. • Feldmann, M., C. Schuler, R. Kasper, P. Di Biase, B. Schaaf, S. Dix, and M. Illguth (2017b). “Methoden zur Erfassung und Analyse von Anisotropien bei thermisch vorgespannten Glasprodukten.” In: Konstruktiver Ingenieurbau – KI 2017.2, pp. 7–15. • Schaaf, B., P. Di Biase, M. Feldmann, C. Schuler, and S. Dix (2017). “Fullsurface and Non-destructive Quality Control and Evaluation by Using Photoelastic Methods”. In: Glass Performing Days. Tampere, pp. 130–134. Standards • Dix, S., B. Schaaf, T. Fiedler, and H. Sonnleitner (2017). “Zerstörungsfreie Qualitätskontrolle - Neues Online-System zur Erfassung von Anisotropien.” In: Glaswelt 7, pp. 86–89.

2 Theoretical Principles This chapter briefly introduces solid mechanics and optics, particularly the nature and origin of polarized light, to reveal the physical processes leading to the visibility of anisotropy effects in glass facades. The chapter concludes by presenting the fundamentals of photoelasticity, which is necessary for reproducing anisotropy effects under laboratory conditions. This chapter is based on several text books (Theocaris and Gdoutos (1979) Können (1985), Coulson (1988), Aben and Guillemet (1993), Ramesh (2000), Fujiwara (2009), Gross et al. (2017)), and papers (Illguth et al. (2015), Dix et al. (2022b)) to which the reader is referred to.

2.1 Basics of Linear Elasticity As part of continuum mechanics, linear elasticity is the simplest case of a material model. It describes how solid objects deform and become internally stressed caused by prescribed loading conditions. For glass, it is known that it behaves almost linearly elastic until fracture. Although stress and strain are interrelated, this section describes the stress state in a material because the following chapters deal with residual stresses without measurable deformation or strain. In a three-dimensional (3D) stress state, nine components of the stress vectors are the components of a second-order Cartesian tensor called the Cauchy stress tensor σ , which completely defines the state of stress at a point and is represented in a 3x3 matrix 

σxx σ = σyx σzx

σxy σyy σzy

  σx σxz σyz  = τxy σzz τxz

τxy σy τyz

 τxz τyz  σz

(2.1)

where σxx , σyy , and σzz are normal stresses, and τxy , τxz , τyx , τyz , τzx , and τzy are shear stresses. The first index x indicates that the stress acts on a plane normal to the x-axis, and the second index y denotes the direction in which the stress acts. If both of them point in positive directions, the stress component is also positive. The shear stress components are not all independent, and a symmetry τxy equals τyx is valid, which can be shown via the law of conservation of angular momentum, c.f. Gross et al. (2017). © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_2

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10

2 Theoretical Principles

Fig. 2.1 (a) displays the stress vectors in a 3D stress state. To simplify this representation and for a better comparison of stress information, the stress tensor from Eq. (2.1) is transformed into principal directions and principal stresses. With the assumption of the characteristic polynomial !

det(σ − λ 1) = 0

(2.2)

and the solution of the eigenvalue problem by the Cayley-Hamilton theorem, with λ3 − I 1 λ 2 + I 2 λ − I 3 = 0

(2.3)

and the invariants I1 = tr(σ) = σx + σy + σz 2 2 2 − τyz I2 = σx σy + σy σz + σx σz − τxy − τzx 2 2 2 − σy τyz I3 = det(σ) = σx σy σz + 2τxy τyz τzx − σx τxy − σz τzx

For the third-degree polynomial of Eq. (2.3) exists three solutions of the eigenvalues λ1 , λ2 , λ3 . They are sorted such that λ1 ≥ λ2 ≥ λ3 . Applying on the stress tensor, its principal stresses are given to 

λ1 σ =0 0

0 λ2 0

  0 σ1 0=0 λ3 0

0 σ2 0

 0 0 σ3

(2.5)

Because of its simplicity and independence from a local coordinate system, the principal coordinate system is proper when considering the state of the elastic medium at a particular point. The principal stress directions are perpendicular to each other. A common geometric representation of these three principal stress vectors is Cauchy’s stress ellipsoids. Starting from a three-dimensional (3D) stress state on a cubic body, the complexity can be reduced to two dimensions (2D) for a plate. This is of particular interest for the photoelasticity of section 2.6 since the simplified case of the plane stress state (2D) is often used there. A solid body is in a 2D or plane stress state when all the stresses act parallel to one plane. The plane stress state is subject to several assumptions. A ‘true’ 2D theory does not exist since the strain in the thickness direction is non-zero. For the case of a symmetric isotropic plate with a negligible thickness, compared to length and width, it can be assumed that the components σz , τxz , τzx , τzy and τyz are zero. At the same time, the other components σx , σy , and τxy are assumed constant over the total thickness, i.e., independent of z. If we now cut an infinitesimal triangular

2.1 Basics of Linear Elasticity

11

Principal Stress State

Figure 2.1 (a) Stress components in Cartesian coordinates. (b) Normal and shear stress components in a triangle element (adapted from Aben and Guillemet (1993) and Wolf (1961)).

element from the xy plane of Fig. 2.1 (a), we obtain Fig. 2.1 (b). By obeying the equilibrium conditions, σ in the perpendicular direction is given as σ = σx cos2 φ + σy sin2 φ + 2τxy sin φ cos φ

(2.6)

and for equilibrium condition parallel to AB τ=

σx − σy sin 2φ − τxy cos 2φ 2

(2.7)

Based on Eq. (2.6) and (2.7), the angle φ on which the plane σ become extreme values can be determined by differentiation to φ and set equal to zero. tan 2φ = φ = arctan

2τxy σx − σy

2τxy π + σx − σy 2

(2.8a) (2.8b)

The two principal stresses together with its orientation, the angle φ completely specify the state of plane stress at a point. For the determination of the principal stresses the values sin 2φ and cos 2φ from Eq. (2.8b) are inserted into Eq. (2.6). This reveals r σx + σy σx − σy  2 σ1,2 = ± + τxy (2.9) 2 2 which is often used for residual stress calculation in glass, see section 4.2.

12

2 Theoretical Principles

2.2 Nature of Polarized Light 2.2.1 Nature of Light Light can be described through three properties: brightness, color, and polarization. The human eye is susceptible to differences in brightness and color changes, but it is almost impossible to detect polarization, c.f. Können (1985). Since the discovery of polarized light by Bartholin (1669) and Huygens (1690), it has been used greatly in laboratory investigations. In the 19th century, Arago, Malus, and Brewster investigated polarization of visible light in the natural environment, so Lord Rayleigh explained the blue color and polarization of the sunlit sky, c.f. Coulson (1988). Huygens (1690) , Young (1804), and Fresnel (1823) introduced the wave theory, which described light as a transversal wave in nature. With Faraday’s demonstration of the relationship of light waves and magnetic fields, Maxwell (1873) ⃗ and magshowed that an electromagnetic light wave consists of electric vector E ⃗ netic vector H . The wave results from a motion of an electric charge in a magnetic field. This electromagnetic theory was an important step in understanding light since these fields can propagate in space without the hypothetical ether used in earlier investigations. Both vectors vibrate perpendicular to each other in the wave’s propagation direction, as shown in Fig. 2.2. However, only one of these two vectors is usually considered, the electric vector, briefly referred to as the light vector ⃗ The velocity of light waves c (electromagnetic waves) is independent of the E. wavelength of light and shows a constant value of c = 2.997 · 108 m/s. More detailed information on the history and the development of the different light theories can be found in Coulson (1988) and Kliger (1990).

Vector Components of an Electromagnetic Wave

⃗ and magnetic vector H ⃗ associated with a plane electromagnetic, wave Figure 2.2 Electric vector E adapted from Aben and Guillemet (1993).

2.2 Nature of Polarized Light

13

The Electromagnetic Spectrum of Light

Figure 2.3 The electromagnetic spectrum with detail on the visible spectrum for the human eye, from Ronan (2021), with the colors: violet (V), blue (B), green (G), yellow (Y), orange (O) and red (R).

At a given point along the direction of propagation, the present magnitude of ⃗ can be expressed according to Ramesh (2000) as the light vector E ⃗ = a cos 2π ct = a cos 2πf t = a cos ωt E λ

(2.10)

where, λ is the wavelength of light, c is the velocity of propagation, t is time, a is amplitude, f is the frequency, and ω is the circular frequency of the light. Instead of a cosine function, a sine function can also be used to represent a plane harmonic wave, i.e., ⃗ = a sin ωt. E (2.11) The electromagnetic theory combines light with all the other for human invisible entities of the electromagnetic spectrum, such as ultraviolet rays (UV) and infrared rays (IR), as shown in Fig. 2.3. The frequency f of a light wave determines that quality which the human eye recognizes as color. The visible spectrum range is a narrow band between a wavelength from approximately 380 nm to 750 nm. The lowest frequency that the human eye can recognize as light is about 3.9 × 1014 Hz, which corresponds to deep red color. The highest frequency is approximately 7.7 × 1014 Hz, corresponding to deep violet. Light from a source that emits a continuous spectrum with nearly identical energy for each wavelength is interpreted as white light. Light with a single wavelength is called monochromatic light. In nature, the light vector is not limited and can be considered to be composed of a series of

14

2 Theoretical Principles

arbitrary transverse oscillations. When the waves of a light beam are constrained to vibrate systematically in planes perpendicular to the direction of propagation, the beam is defined as polarized, c.f. Aben and Guillemet (1993).

2.2.2 Types of Polarized Light The behavior of the light vector describes the form of polarization, see Fig. 2.4. A light stream is unpolarized if the light waves show complete symmetry around the direction of propagation. When the waves in a light beam oscillate in parallel planes so that the orientation of the light vector is constant, the beam is said to be plane or linearly polarized. Suppose the vibration is such that the amplitude remains constant while the orientation of the light vector changes uniformly so that the tip of the vector describes a circle. In that case, the light is called circularly polarized. If both the amplitude and the orientation vary in a related way so that the vector tip describes an ellipse, the light is defined as elliptically polarized, c.f. Aben and Guillemet (1993) and Ramesh (2000). Depending on the direction of rotation, circularly and elliptically polarized light can describe a left-handed L (counter-clockwise) or right-handed R (clockwise) motion, see Können (1985). By ⃗ into the components E⃗x and E⃗y parallel to the x and y splitting the light vector E axes a phase difference ∆ of these vector components is present for circularly and elliptically light, see Fig. 2.4. Coulson (1988) describes that only radiation direct from the sun and thermally emitted radiation from diffuse surfaces is essentially unpolarized. Completely unpolarized light is rare in nature and difficult to generate in the laboratory. Therefore, most light beams exhibit partial polarization of some type. Partial elliptical polarization is the most frequent state, while linear and circular polarization are exceptional cases. The proportion of polarized light Ip in the total intensity I is defined as the degree of polarization p and can simply be expressed as p=

Ip . I

(2.12)

2.2.3 Stokes Parameters A light beam may be characterized entirely by its total intensity I, degree of polarization p, ellipticity ϵ, and the azimuth angle θ, c.f. Coulson (1988). Here, θ describes the angle of the polarization plane relative to the reference axis Ex . This geometrical relationship is illustrated as an ellipse in an (ε, θ) coordinate system, see Fig. 2.5 (a). Fig. 2.5 (b) shows an alternative coordinate system (ψ, ∆) where ψ and ∆ represent the angles of the amplitude ratio (tan ψ = Ex0 \Ey0 ) and phase difference ∆ respectively.

15

2.2 Nature of Polarized Light

Types of Polarized Light

Figure 2.4 Types of polarized light: (a) unpolarized; (b) linear polarized; (c) circularly polarized; (d) elliptically polarized. Phase differences ∆ between the electric fields parallel to the x and y axes are (a,b) 0, (c)π/2, and (d) π4 .

Representation of Polarized Light

Figure 2.5 Representation of the vibration of the electric vector for the case of elliptic polarization in coordination system of ε, θ (a) and ψ, ∆ (b). Illustrations adapted from Fujiwara (2009).

16

2 Theoretical Principles

Poincaré sphere

Point P on the surface of the Poincaré sphere, adapted from Fujiwara (2009).

Figure 2.6

For most analytical work, Stokes parameters are used, consisting of a set of four values, which describe the polarization state of electromagnetic radiation. The method was developed by Stokes (1852) and was nearly forgotten for a century. A major advantage is that the Stokes parameters can also be used to describe unpolarized and partially polarized light. In addition, they are calculated by intensity measurements, and thus, the polarization state can be determined quite easily. The four Stokes parameters are denoted S0 , S1 , S2 and S3 . Depending on the available lightwave information and used coordinate system, Stokes Parameter can be expressed as in Table 2.1.

Table 2.1

Stokes parameters S0,1,2,3 , given by Fujiwara (2009).

Stoke Parameter

S0 S1 S2 S3

Light Intensity

Coordinate System ε, θ

Coordinate System ψ, ∆

Ix + I y Ix − I y I+45◦ − I−45◦ I R − IL

1 cos 2θ cos 2ε sin 2θ cos 2ε sin 2ε

1 − cos 2ψ sin 2ψ cos ∆ − sin 2ψ sin ∆

With the use of the Poincaré sphere, all polarization states can be described as point P on the sphere’s surface by using the (ψ, ∆) coordinate systems as shown in Fig. 2.6. The size of the Poincaré sphere itself displays the total light intensity

17

2.2 Nature of Polarized Light

S0 . In a totally polarized light, the degree of polarization p and the angles ε and θ are given by: q S12 + S22 + S32 p= (2.13) S0 θ=

1 S2 tan−1 2 S1

1 −1 sin (S3 ) 2   S0  S1  ⃗ =  S  S2  S3

ε=

(2.14) (2.15)

(2.16)

Examples for Stokes vectors, which describe the states of polarization of light, are shown in Table 2.2. The Stokes vector itself and in combination with the Jones and Mueller calculus forms the basis for several applications, e.g., in remote sensing, geophysics, ellipsometry, photoelasticity, etc.

18

Table 2.2

2 Theoretical Principles

States of polarization discribed as Stokes vectors adapted from Fujiwara (2009).

Polarization State

Polarization State

Vector

Vector

  Linearly polarized (horizontal)

1 1    0  0

 Linearly polarized (vertical)

  1

0   0

unpolarized

0

(2.25)



1 −1   0 0

  1

(2.27)

0   0

Right-hand circularly polarized

1

  Linearly polarized (+45◦ )

1 0    1  0

 Linearly polarized (-45◦ )



(2.29)

 Elliptical polarized (2.31)

(2.28)



1 0   0 −1

Left-hand circularly polarized



1 0   −1 0

(2.26)

(2.30)



1  − cos 2ψ     sin 2ψ cos ∆  − sin 2ψ sin ∆

(2.32)

2.3 Polarization of Light 2.3.1 General Coulson (1988) describes the generation of polarization by some phase relationship or magnitude difference in the orthogonal components of the vibration of the electric vector. A natural source can produce plane-polarized light via reflection, scattering, use of polarizers, or Nicol’s prism, see Ramesh (2000). The transformation of linearly polarized light into circularly or elliptically polarized light can be achieved by exploiting the property of birefringence of optically anisotropic materials, e.g., a retarder or compensator. A transparent material is birefringent if it shows different refractive indices n depending on light propagation direction in the

2.3 Polarization of Light

19

medium. The refractive index n is an optical material property that describes the ratio of the light propagation speed in vacuum c to that in the material s c n= . s

(2.33)

In transparent media, n determines the propagation of electromagnetic waves completely. According to Fujiwara (2009), a complex refractive index has to be defined for materials with strong light absorption. However, in this work, a simplified assumption of a non-complex refractive index is used. The refraction index of common architectural glass is n ≈ 1.52, see Polyanskiy (2021). To explain the problem of anisotropy effects on facade glazing, polarization by reflection and scattering is of particular interest, c.f. Illguth et al. (2015).

2.3.2 Polarization by Scattering Polarized light is mainly produced through the scattering of sunlight in the atmosphere of the earth. In principle, two different types of scattering phenomena occur while a light ray propagates through the atmosphere. If the light ray hits spherical particles, e.g., raindrops, with a size similar to the wavelength, it is scattered according to the Mie theory. If the size of the scattering particles is much smaller, e.g., molecules of atmospheric gases, so-called Rayleigh-scattering occurred and can be observed as blue sky, c.f. Coulson (1988) and Können (1985). While Mie-scattering is wavelength-independent and has a minimal polarizing effect on the incident light beam, Rayleigh-scattering produces wavelengthdependent strongly polarized light. The intensity of scattering increases strongly at small wavelengths. Therefore, the intensity of scattered blue parts of the sunlight is a maximum, and the sky appears blue. When the light propagates much longer through the atmosphere at sunrise or sunset, the larger wavelengths dominate, and the sky turns orange and red, c.f. Können (1985) and Illguth et al. (2015). The intense polarization of electromagnetic rays caused by Rayleigh-scattering occurs because the gas molecules are vibrated in the plane of the ray. As a result, the molecules emit radiation in a directional characteristic of a Hertzian dipole, which means no radiation in the direction of oscillation of this dipole, and the light is linearly polarized perpendicular in the plane of the beam. In principle, there are two ways to determine the degree of polarization p (DoP) of a clear sky. The first one is by measuring via polarimeter, c.f. section 4.6. The second one is by estimation with the single scattering Rayleigh sky model. Illguth et al. (2015) apply the Rayleigh sky model following Coulson (1988). Using the knowledge of the position of the sun and the viewing direction of the observer, the DoP can be estimated using the angular relations from Fig. 2.7 (a)

20

2 Theoretical Principles

p= with

sin2 γ 1 + cos2 γ

cos γ = sin θs sin θ cos ψ + cos θs cos θ.

(2.34) (2.35)

Fig. 2.7 (a) represents the geometry for the sky model in which, γ is the angular distance between the observed pointing and the sun, Θs is the sun zenith distance (90◦ – solar altitude), Θ is the angular distance between the observed pointing and the zenith (90◦ – observed altitude), and ψ is the angle between the sun direction and the observed pointing at the zenith. Fig 2.7 (b) shows exemplarily the application of the sky model depending on the sun. It can be seen that at sunrise or sunset in the east or west, respectively, a band of highly polarized light stretches from the north - zenith - south. At noon, only the horizon is polarized, c.f. Illguth et al. (2015). To summarize the above, the highest DoP will be found Single Scattering Rayleigh Sky Model

Figure 2.7 (a) Representation of the geometry for the Rayleigh sky model (Courtesy: Illguth et al. (2015). (b) DoP of the sky with north at the top and the yellow dot marks the sun; i) at sunrise Θs = 80◦ and ii) at noon Θs = 10◦ (Courtesy: Illguth et al. (2015)).

in deep blue areas of the sky, see Fig. 2.8. The intensity of the scattered polarized light thus depends on the direction of oscillation of the dipoles. The most polarized regions of the sky are perpendicular to the sunlight propagation when the sun’s altitude is low.

2.3 Polarization of Light

21

Real Skylight Polarization

Figure 2.8 Images of skylight polarization taken by a fisheye-lens camera from Wilkie et al. (2004). (a) Polarisation pattern of a real sky at sunset photographed with a 90◦ linear polarizing filter. (b) Horizontal view 90◦ away from the sun over a lake through a horizontal polarizing filter. (c) Similar to (b) but without a polarizer.

2.3.3 Polarization by Reflection When a unpolarized light beam encounters a dielectric medium, it will be partly reflected and refracted at the point of incidence N , see Fig. 2.9. According to Snell’s laws, the angle of incidence αi is equal to the angle of reflection αR . According to Hecht (2018) the angle of refraction β can be determined sin αi n1 = . sinβ n2

(2.36)

Where n1 is the refractive index of the initial medium through which the light propagates (e.g., air), and n2 is the index of the dielectric medium. Also, Brewster (1815b) discovered that the reflected light beam becomes linear polarized perpendicular to the plane of incidence, termed the s-polarized beam, see Eq. (2.25). This electromagnetic effect can be explained by the directional characteristic of a vibrating dipole: a dipole emits no radiation in the direction of vibration, c.f. Illguth et al. (2015). A dielectric medium shows the phenomenon of dielectric polarization, which separates electric charges in a medium spatially, as detailed described in Fujiwara (2009). In the natural environment, dielectric surfaces are typically non-metallic materials such as glass or water.

22

2 Theoretical Principles

(a) Reflection of unpolarized Light

(b) Reflection of p-polarized Light

Figure 2.9 (a) Polarization of an unpolarized light beam by the reflection of a dielectric medium, adapted from Ramesh (2000). (b) Reflection behavior for a p-polarized Light beam under Brewster’s angle αB . In addition a legend and definition is given.

2.4 Brewster’s Angle As stated above, depending on the angle of the incident light αi , under the Brewster angle αB , unpolarized light becomes completely s-polarized. In addition, a further phenomenon can be observed, namely that if an incident p-polarized light beam impinges at a glass surface under Brewster’s angle, no reflection will occur, see Fig. 2.9 (b). In p-polarized light, the electric field vibrates parallel in the linear vertical direction of the plane of incidence, see Eq. (2.27). The physical mechanism can be explained by how electric dipoles in dielectric media respond to p-polarized light. After p-polarized light hits the surface at the point of refraction N , no light can be reflected because the dipole emits no radiation in the vibration direction (Coulson (1988), Hecht (2018). Using Snells’Law from Eq. (2.36) and geometrically principles, αi + β = 90◦ (2.37)

2.4 Brewster’s Angle

23

and the incident angle αi = αB , at which no light is reflected, n1 sin αi = n2 sin(90◦ − αB ) = n2 cos αB αB can be solved as

αB = tan−1

n1 . n2

(2.38) (2.39)

This equation is known as Brewster’s law, and the angle defined by it is Brewster’s angle αB . For commercial architectural glass (n2 ≈ 1.52) in air (n1 ≈ 1), αB is approximately 56◦ , while for an air-water interface (n2 ≈ 1.33), it is approximately 53◦ , see Polyanskiy (2021). The reflectance R behaves utterly different for a beam polarized perpendicular to the plane of incidence (index s), and a parallel (index p) polarized one. With the Fresnel equations, the intensity of the reflected beam Rs for an ideal dielectric (no light absorption) can be determined according to Hecht (2018). n cos α − n cos β 2 1 i 2 Rs = n1 cos αi + n2 cos β n cos β − n cos α 2 1 2 i Rp = n1 cos β + n2 cos αi

(2.40) (2.41)

and for completeness, the transmittance T Ts = 1 − Rs

(2.42)

T p = 1 − Rp .

(2.43)

Fig. 2.10 shows the alteration of the transmittance T and the reflectance R for the cases of s- and p-polarized light depending on the angle of incidence at the transition from air to glass (a) and vice versa (b). In Fig. 2.10 (a), the intensity of a reflected parallel beam is always lower than that of a perpendicular polarized beam. For the parallel beam, the intensity reduces steadily until αB is reached. At this point, total transmittance and no reflectance are achieved. Fig. 2.10 (b) depicts the reverse case, a light beam from the medium glass hits the medium air, αB = 90◦ − 56◦ = 34◦ . Here a total internal reflection occurs above the so-called critical angle αc of ≈ 41◦ in a glass medium. According to Hecht (2018) αc is defined as n2 αc = sin−1 . (2.44) n1

24

2 Theoretical Principles

(a) Air to Glass

(b) Glass to Air

Figure 2.10 Reflectance R and transmittance T depending on the angle of incidence for s- and ppolarized light. For the cases, air to glass (a) and glass to air (b).

2.5 Passage of Light through Media Depending on the refractive and reflection behavior of a medium, it can be classified into isotropic and anisotropic media. Typical naturally anisotropic media are crystals. The laws governing the passage of light through isotropic media are well known as Snell’s laws of refraction and reflection, presented in section 2.3.3 and illustrated in Fig. 2.9. Ramesh (2000) describes the passage of light through anisotropic media in detail. A single incident light beam entering a crystal medium causes two refracted rays, ordinary ’o’ and extraordinary ’e’, thus exhibiting what is generally known as double refraction, see Fig. 2.11. One ray is extraordinary because it violates Snell’s Law under certain circumstances by no limitation to the plane of incidence. In addition, its velocity alters continuously with the angle of incidence. Only in the direction of an optic axis, the refractive index of ray ’e’ is identical to ’o’, and the behavior is simultaneous to an isotropic medium. While unpolarized light propagates smoothly through an isotropic medium, light traveling through a crystal is always polarized. The ordinary and extraordinary rays are linearly polarized with perpendicular planes of polarization. If the incident rays are perpendicular to the optic axis, the ’e’ ray propagates faster than the "o" ray because of its lower refractive index, but it moves in the same direction. For the general case with an angle between zero and 90 degrees from the optic axis, the ’o’ ray will propagate undeviated and is refracted according to Snell’s law. The ’e’ ray will deviate from the ’o’ ray because of the different direction indices, absent from the optic axis and generally out of the plane of incidence. The following photoelastic phenomenon from section 2.6.2 is based on the incident rays being perpendicular to the optical axis. The principal stress directions

2.6 Basics of Photoelasticity

25

Double Refraction in Anisotropic Media

Figure 2.11

Passage of light through a crystalline medium adapted from Ramesh (2000).

act as polarizing axes at the point of interest and the two rays are polarized perpendicular to each other. The ’o’ and ’e’ rays propagate in the same direction but with different velocities resulting in a relative retardation between the rays, c.f. Ramesh (2000).

2.6 Basics of Photoelasticity 2.6.1 General Photoelasticity is used as a standard experimental method for investigating stress or strain fields in mechanics by analyzing the change of state and velocity of electromagnetic radiation interacting with these bodies, c.f. Theocaris and Gdoutos (1979). The major techniques are examining birefringence by measuring the change of polarized light intensity transmitted or reflected from the body under observation. This method has been applied to architectural glass for several years to investigate residual stresses in quality assurance and research, c.f. Bucak and Schuler (2008), Feldmann et al. (2012b) and Nielsen et al. (2021). To understand the measurement techniques from chapter 4, some fundamentals will be presented here, which can be found in the textbooks from Frocht (1948); Wolf (1961); Föppl and Mönch (1972); Kuske and Robertson (1974); Dally and Riley (1978); Theocaris and Gdoutos (1979); Aben and Guillemet (1993); Ramesh (2000).

26

2 Theoretical Principles

This section contains principles of transmission light photoelasticity, including the creation of artificial birefringence, the stress-optical law and standard arrangements of the polariscope using monochromatic light.

2.6.2 Artificial Birefringence The basis of the photoelastic method is the physical characteristic of certain noncrystalline transparent materials, e.g., glass and some polymers. Similar to crystals, they may become birefringent or doubly refractive, as described in section 2.5. Under normal conditions, these materials are optical isotropic but become anisotropic under stress, see Fig. 2.12. Stress or strain causes intermolecular changes in the structure of the body, altering its optically isotropic character. This phenomenon of temporary or artificial birefringence was first observed by Brewster (1815b). The so-called photoelastic phenomenon typically persists while the stresses are applied. Conversely, it disappears almost immediately or after a certain time, depending on the material and the conditions, when the stresses are released. The relationship between optics and stress state is essential for understanding photoelasticity and was discovered by Neumann (1841) and Maxwell (1873). They connected the principal refractive indices of Fresnel’s birefringence ellipsoid with the principal stresses of Cauchy’s stress ellipsoid, c.f. Theocaris and Gdoutos (1979). Photoelastic Phenomenon in Glass

Figure 2.12 Schematic representation of the photoelastic effect on annealed floatglass under bending stress in a dark-field circular polariscope (see section 2.6.4). (a) Sketch of glass under four-point bending stress. (b) Stress distribution in a glass beam. (c) Isochromatic Image under different load cases using white light, see section 4.3.

According to Mueller’s theory of photoelasticity in amorphous solids, stressbirefringence is caused by the superposition of two effects: a lattice and an atomic effect (Müller (1938)). A lattice effect is negative due to the alteration in the Lorentz force arising from the rearrangement of atoms under the uniaxial strain. The second, an atomic effect is due to a deformation of the neighbouring ions, c.f.

2.6 Basics of Photoelasticity

(a) Unstrained Material

27

(b) Lattice effect

(c) Lattice and Atomic Effect

Figure 2.13 Schematic representation of the different effects unstrained (a) and uniaxial strained (b,c). (b) lattice effect and (c) lattice effect with atomic effect, from Aben and Guillemet (1993).

Aben and Guillemet (1993). A strain creates optical anisotropy of the atoms and their neighboring ions cause positive birefringence. Fig. 2.13 shows schematically the impact of both effects. For most glass, the atomic effect dominates, but for glass with a high refractive index, the lattice effect takes precedence, c.f. Müller (1938). The interested reader can find supplementary models to explain the photoelastic effect in Tashiro (1956), Borelli and Miller (1968), and Matusita et al. (1984). In summary, the photoelastic birefringence results from the change of the electron density distribution caused by elastic strain.

2.6.3 Stress-Optical Law For the explanation of the stress-optical law the basics of elasticity from chapter 2.1 are required. The coaxiality of stress, strain, and birefringence ellipsoids resulting from symmetry considerations for elastic deformations constitutes one part of the stress-optical law. The second part of the stress-optical law are the NeumannMawell’s equations which are transformed for the case of the refractive indices along the principal stress directions by Wertheim (1854) as n1 − n2 = C(σ1 − σ2 )

(2.45a)

n2 − n3 = C(σ2 − σ3 )

(2.45b)

n3 − n1 = C(σ3 − σ1 )

(2.45c)

with n1 , n2 and n3 be the principal refractive indices for waves vibrating parallel to the principal stresses σ1 , σ2 , σ3 , and C is the material dependent photoelastic constant, c.f. Theocaris and Gdoutos (1979). Equations 2.45 express the stressoptic law for material under any general 3D state of stress. The principal axes of the index ellipsoid coincide with the principal stress axes (Fig 2.14). For a 2D

28

2 Theoretical Principles

Relation between Ellipsoid of Stress and Index Ellipsoid

Figure 2.14

Principial axes of the index ellipsoid coincide with the principal stress axes from Eq. 2.1.

stress state with σ3 is zero over the plate’s thickness d, the Equations 2.45 reduce to n1 − n2 = C(σ1 − σ2 )

(2.46a)

n2 − n3 = C(σ2 )

(2.46b)

n3 − n1 = C(σ1 )

(2.46c)

When polarized light is passed through a plate at perpendicular incidence in the direction of the z-axis (Fig. 2.15), the incident wave is split into components oscillating in the y-z and x-z planes. These components emerge with relative retardation of δ = (n1 − n2 )d = C(σ1 − σ2 )d (2.47) and are defined as the Wertheim law, according to Aben and Guillemet (1993). For a non-constant stress state, e.g., for tempered glass, the Wertheim law must be transferred to the integral form for thin slices through the thickness: δ=C

Z

z=d

(σ1 (z) − σ2 (z)) dz

(2.48)

z=0

2.6.4 Plane and Circular Polariscope In a polariscope or polarimeter, stress fields in a birefringent sample can be evaluated by analyzing light information. Typically for known incident light, the emergent ray is analyzed for stress information. The plane polariscope is standardsetting and one of the simplest optical arrangements in photoelasticity, see Fig. 2.15 (a). It consists of a light source, a camera, and a model (sample) placed

2.6 Basics of Photoelasticity

29

(a) Plane Polariscope

(b) Circular Polariscope

Figure 2.15 Scheme of plane (a) and circular (b) polariscope in a dark-field setup. Resulting camera images (left) of a 12 mm tempered glass recorded in the individual polariscopes.

between two linear polarizers, the polarizer and analyzer. Polarizers are optical elements mainly made from a CaCO3 crystal called calcite that transmit light only in the direction parallel to their axis and therefore generates linear polarized light. The axis orientation of the polarizers results in the amount of light intensity captured by the camera. With perpendicular orientation (axes crossed), a dark field is generated, and with parallel orientation, a bright field, c.f. Fig. 2.16 (a). The use of white light, i.e., light consisting of a spectrum of colors (red, green, and

30

2 Theoretical Principles

blue), may be necessary for certain tasks, see chapter 4.3. For the description of the passage of light in a dark-field polariscope, monochromatic light is assumed, i.e., light that has a specific wavelength. In a linearly polarized light field, a birefringent medium, e.g., glass with residual stresses, causes the light vector A to split into the components A1 and A2 in the principal stress directions of σ1 and σ2 . According to the stress-optical law, after passing the birefringent medium, the components experience relative retardation δ contributing to the formation of fringes. The analyzer transmits only the elements in the polarization direction H1 and H2 of these partial waves. H1 and H2 are always equal and opposite. For the case of a homogeneous stress field, σ1 −σ2 equals zero, no retardations occur because the components eliminate each other, and the observer will notice a black screen. Conversely, in a non-homogeneous stress field, the light intensity maximizes if the retardation is precisely a half wavelength. Due to interference, the fringes or isochromatics appear as black lines for the observer. Depending on their level of retardation, they can be classified into fringe order N = 0, 1, 2, etc. The plane polariscope has the major disadvantage that the resulting image changes depending on the orientation of the analyzer (Fig. 2.16 (a)) and sample (Fig. 2.17 (a)). In addition to the isochromatics, so-called isoclinics appear, dark lines or areas that depend on the principal stress direction and the polarization direction. The angle between these directions is the isoclinic angle ψ. If ψ is zero, the light vector of the polarized beam is not split, and no retardation occurs, although a non-homogeneous stress state in the glass may exist. The use of a polariscope with circularly polarized light is recommended to overcome these difficulties, see Fig. 2.15 (b). For this purpose, two quarter-wave plates (QWP) oriented perpendicular to each other are added at a angle of 45°to the existing plane polariscope setup. The QWP or retarder consists of a birefringent material (crystal), which has a fast and a slow axis and generates retardation of a quarter wavelength. The first QWP creates circularly polarized light before impinging the birefringent body. The second QWP retransforms the light into a linear polarization after it. In a circularly polarized light field, the polarization vector rotates. Since no single plane of oscillation exists, no isoclines can occur, and the fringes are independent of the orientation of the glass sample or the principal axes to the polarizers, see Fig. 2.17 (b). The interested reader will find advanced literature with the mathematical description of polarizer and retarder based on the Jones and Mueller Calculus in Theocaris and Gdoutos (1979), Patterson (2002) and Fujiwara (2009).

2.6 Basics of Photoelasticity

31

(a) Plane Polariscope - Dependence on Analyzer Orientation

(b) Circular Polariscope - Independence on Analyzer and QWP Orientation

Figure 2.16 Resulting images of a 12 mm glass sample with residual stresses in plane (a) and circular (b) polariscope using a dark-field setup in monochromatic light with a rotating analyzer.

(a) Plane Polariscope - Dependence on Sample Orientation

(b) Circular Polariscope - Independence on Sample Orientation

Figure 2.17 Resulting images of a clockwise rotating 12 mm tempered glass sample in plane (a) and circular (b) polariscope using a dark-field setup in monochromatic light.

3 Glass and their Photoelastic Behaviour This chapter describes the material glass based on its structural and optical properties. In the beginning, the typical building products are briefly introduced. By describing the manufacturing process of tempered glass, the reader is shown how residual stresses are induced and how glass behaves optically under stress. Here, the photoelastic behavior of glass is examined in detail and the effect of anisotropy on visual perceptibility is shown. Most of the containing information can be found in several textbooks (Bucak and Schuler (2008), Schneider et al. (2016), Feldmann et al. (2012a), Siebert and Maniatis (2009), Le Bourhis (2006), Aben and Guillemet (1993)), papers (Dix et al. (2021a), Dix et al. (2021b), Nielsen et al. (2021), Dix et al. (2022b)) and Ph.D. theses (Laufs (2000), Nielsen (2009), Alter (2019) and Pourmoghaddam (2020)).

3.1 General For over 2000 years, man has shaped the material glass to his imagination. The industrial history of glass tempering began nearly 100 years ago. Nowadays, glass is traditionally used for architecture and automotive glazing, tableware, and glass fibers in telecommunication. In architecture, glass is often processed to insulating or laminated glazing. Formerly used as a filling element, glass is also applied as a structural construction element, see Fig. 3.1. As a building product, mostly soda-lime-silica glass is manufactured using the Float Process. The molten glass mass is distributed onto a tin bath, thus achieving a very smooth glass surface. The glass is slowly cooled to room temperature in a multi-stage process to obtain a product without residual stresses. The fabricated continuous glass sheets are cut to standard dimensions and can be further processed, e.g., coated, tempered, laminated, etc. The chemical composition of the resulting glass material has a significant impact on its physical properties. A typical soda-lime-silica glass consists of 69 to 74 percent silica (SiO2), 12 to 16 percent sodium oxide (Na2O), 5 to 10 percent lime (CaO), and a few percent other materials, such as for tinting. Soda-lime-silicate glass is macroscopically homogeneous and isotropic. The amorphous, non-crystalline structure of the silica (SiO2) provides the material with its © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_3

33

34

3 Glass and their Photoelastic Behaviour

Structural Use of Glass

Figure 3.1 Structural use of tempered glass in a complex glass structure at the building project Tottenham Court Road Station © Christian Schuler.

Float Glass Process

Figure 3.2

Scheme of float glass process adapted from Nielsen (2009).

transparency in the visible wavelength band. Besides the common clear float glass, there exists also especially decolorized white glass (low-iron glass) or tinted (colored) glass. Tinted glass is often colored into gray, blue, green, pink or bronze by adding metal oxides into the glass mass. In the case of white glass, the proportion of iron oxide in the quartz sand, which in the case of normal float glass leads to a slight green coloration, is almost completely removed. This creates particularly clear and neutral in color the float glass. One of the essential optical properties of the glass is its light transmission in the visible spectral range (λ = 380 nm to λ = 750 nm), see section 2.2.1. In the infrared range, the various base glass show different levels of absorption behavior, but from a wavelength of λ = 5000 nm, virtually all silicate glass are opaque. There is an absorption threshold between λ = 250 nm and λ = 150 nm, depending on composition for the ultraviolet range. Below, the glass is not transparent to UV light. When light penetrates glass, a portion of the light is absorbed by the medium. This part of the light interacts with the stimulable components of the medium and is transformed into different forms of energy, e.g., heat, electrical or chemical energy.

3.1 General

35

In order to optimize glass properties and improve physical characteristics, the glass can be coated online during the float glass process or afterward offline. The transparency of the glass is altered by applying thin, transparent metallic or oxide layers in so-called soft- or hard-coating processes. In term of their function, coatings can be divided into thermal insulating (low emissive) coatings and solar control coatings. The interested reader will find further information on manufacturing processes, setups and optical properties of these coatings in Schneider et al. (2016) or Interpane (2019). The mechanical behavior of glass is nearly ideal linear-elastic until fracture, and can easily be described with Young’s modulus E and Poisson’s ratio ν at room temperatures, see Table 3.2. Table 3.1 Properties for glass at room temperature, given by Haldimann et al. (2008) Property

Young’s modulus Poisson’s ratio Density Tensile strength (float glass)a Compressive strengthb Thermal expansion coefficient Specific thermal capacity a b

Symbol

Value

Unit

E ν ρ ft fc α cp

70 0.23 2500 45 >800 9.10 720

GPa kg/ m3 MPa MPa 10−6 K−1 J/ (kg K)

Depends on various parameters and can deviate from the values. Large scattering can be found in the literature.

Glass is fragile and breaks under tensile stress depending on the load duration, ambient conditions, and residual stress distribution caused by microcracks at the surface (Griffith (1921), Shand (1965), Beason and Morgan (1984), Meyland et al. (2021)). In order to strengthen glass, flaws on the surface have to be subjected to compressive stress. This can be achieved via chemical strengthening or thermal tempering. Chemically strengthened glass (CSG) typically has compressive stresses at the surface of > 565 MPa down to a maximum depth of 300 µm, cf. Karlsson et al. (2010) and Varshneya (2010). Due to the vulnerability to scratches, CSG is currently used less as architectural glass than in special applications, c.f. Laurs et al. (2019). Tempered glass is ideally suited for load-bearing structures where a high degree of transparency of the building envelope is desired, cf. Marchewka (2010), O’Callaghan and Bostick (2012), Feirabend et al. (2020). Therefore, the horizontal tempering of flat glass is an established pre-stressing process and will be examined in more detail, see Fig 3.3. Mechanical treatments of the glass sheet, such as cutting, seaming, and drilling, are usually performed before. After cleaning, the glass plate moves in the furnace on ceramic rollers. In the oven, the glass is heated to

3 Glass and their Photoelastic Behaviour

36

Glass Tempering Process

Figure 3.3 Scheme of the common process for tempering flat glass, adapted from Pourmoghaddam (2020).

about 100 K above the glass transition temperature Tg and then further transferred on rollers wrapped with Kevlar straps. Reaching the quench area, the glass plate is rapidly cooled by quenching with air, rolling back and forth in order to minimize disturbance effects from the rollers. The tempered glass leaves the quenching area with surface temperatures close to room temperature. This procedure creates a residual stress state in the glass to protectively subject the surface to compressive stress, increasing the strength compared to annealed glass, see section 3.2. Depending on the cooling rate during quenching, two different building products are manufactured, known as heat-strengthened glass (HSG) and fully tempered glass (FTG). HSG which is slower cooled, consists of a lower pre-stress level and a breakage pattern similar to annealed glass, including longer, jagged fragments. Conversely, FTG is cooled rapidly to achieve a higher pre-stress level and strength. During breakage, the induced elastic strain energy is released resulting in a smallfragmented fracture pattern. In dependence of the quality of the tempering process, the following optical effects can occur: • local distortions, so called roller waves, • local unevenness of the edges, known as edge lift, edge kink or frame effect, • white haze, • and optical anisotropy effects, see Fig. 3.9. More Information about distortion effects and white haze are stated in Henriksen and Leosson (2009), Neugebauer (2014), Vogel (2017). Anisotropy effects in tempered glass can become visible under polarized light resulting from a non-uniform heat exposure and transfer during tempering. From chapter 2 it is known that glass can become artificial or stress birefringent. In the case of tempered glass, this results from a residual stress state that is not in equilibrium, i.e., σ1 is not equal to σ2 over the glass thickness.

3.2 Residual Stresses

37

3.2 Residual Stresses Stress Distribution in Tempered Glass

Figure 3.4 A schematic illustration of the residual stresses and their stress distribution in tempered glass based on the classification of prestressing zones according to Laufs (2000), adapted from Dix et al. (2022b).

In every glass exist residual stresses resulting from the annealing process after forming (float glass) or from a tempering process (tempered glass). With successful tempering, the glass receives protective compressive stress on the surface, which compresses surface flaws and increases the bending strength. During the thermal treatment, the glass changes its material properties from elastic to viscoelastic after exceeding the glass transition temperature Tg . Due to the quenching with air, initial tensile stresses on the glass surfaces can be relieved within a few seconds. While the glass surface continues to cool below Tg , resulting in an increase in viscosity, there is still a temperature gradient between the surface and the core of the glass. The outer cooler surface hinders the inner warmer glass contraction, resulting in a residual stress state. Furthermore, corners, edges, and holes cool more quickly because three-dimensional cooling creates a temperature gradient to the exposed edges.

3 Glass and their Photoelastic Behaviour

38

The generation of residual stresses during thermal tempering is complex. Several authors, Laufs (2000), Schneider (2001), Nielsen et al. (2010a), Pourmoghaddam et al. (2016), Aronen and Karvinen (2018), Dix et al. (2021b) investigated the formation of these residual stresses in their experimental and numerical works. Therefore, rheological models are applied to calculate the residual stresses in the thermal prestressing process to investigate the effects of stress relaxation due to viscoelasticity and structural relaxation. Depending on geometric boundary conditions, residual stresses in glass develop differently and produce different stress states across the glass thickness, see Fig. 3.4. The stress profile across the thickness divides residual stresses into thickness and membrane stress, c.f. Aben and Guillemet (1993). Membrane stresses are nearly constant, and thickness stresses are parabolically distributed through the glass thickness. Laufs (2000) classifies four zones with different residual stress properties, suitable and sufficient to describe the entire plate. In zone 1, the plate area far from edges, the principal stresses σ1 and σ2 are nearly equal while σ3 , is zero. Nielsen et al. (2010b) shows that this assumption is only accurate with a probability of 60%. In addition, when approaching the corners, the likelihood of a plane hydrostatic stress state decreased. However, the stress profile is assumed parabolically distributed and consists of compressive stresses σC at the surface and tensile stresses σT at the core, see Fig. 3.5 (a). The depth of the compression zone is about 20% of the total thickness t, c.f. Nielsen et al. (2021). The residual stress distribution σz across the thickness can be approximately calculated as σ(z) = σT · (1 − 3 · ξ)

(3.1)

2·z σC , σT = − t 2

(3.2)

where ξ=

(a) Parabolic Stress Distribution

(b) Membrane Stress Distribution

Figure 3.5 Schematic illustration of the residual stress distribution of a tempered glass in prestress zone 1 (a) and in prestress zone 2 (b) across the glass thickness.

3.2 Residual Stresses

39

According to ASTM C1048 (2018), typical surface compressive stresses σC in undisturbed zone 1 are between −24 MPa to −52 MPa for HSG and greater than −69 MPa for FTG. As Mognato et al. (2018) indicates, the minimum limits for HSG and FTG according to ASTM C1048 (2018) are too low and not generally valid for each tempered glass. In zone 2, 3, and 4, different residual stress states are created in the form of membrane stresses, see Fig. 3.4. They result from the geometry and thus from the area to the free edge changing heat transfer coefficients in the tempering process. Approaching the edge of the plate (zone 2) and hole (zone 4), the perpendicular principal stress to the edge becomes zero. Zone 3, the plate corner, occupies a unique position by bending the membrane stresses around the corner. Fig. 3.5 (b) shows exemplarily the profile of the membrane stress σC,edge for zone 2. Laufs (2000) showed that the glass thickness and the cooling rate affect the curve’s formation, varying from nearly constant to parabolic. Therefore, the mean edge membrane stress is usually measured and compared, c.f. Dix and Schuler (2018). In general, residual stresses are strongly process-related and vary under different boundary conditions. Pourmoghaddam (2020) lists essential parameters: the cooling rate, the nozzle arrangement and diameter, the distance between the nozzles and the glass surface, and the roller distances. The initial temperature before quenching and the cooling rate significantly influence the development of residual stresses, see Aronen and Karvinen (2018). Fig. 3.6 shows the arrangement of a conventional quenching area consisting of an upper and lower cooling device. An inhomogeneous cooling of the glass pane results partially from the disturbance of the cooling air-jet and different heat transfer at the contact of the Kevlar strips.

(a) Upper Cooling

(b) Lower Cooling

Figure 3.6 Quenching area in a tempering oven of the company Semcoglas Holding GmbH. Arrangement of the upper cooling device (a), and the rollers and nozzles (b), from Pourmoghaddam (2020).

3 Glass and their Photoelastic Behaviour

40

3.3 Photoelastic Behaviour Under external or internal stress, glass changes its optical properties and becomes birefringent. Photoelasticity exploits this phenomenon in principle and allows one to visualize and measure principal stress differences and orientations. From chapter 2, the behavior of light in birefringent bodies and Wertheim’s law is known from Eq. (2.48). The components characterizing the optical retardation δ, are the integral of the principal stresses differences over the glass thickness and the photoelastic constant C or S. Both constants are material coefficients that characterize the photoelastic behavior. While S is related to the wavelength of the used light, C is wavelength-independent and more frequently applied in practice. S and C can be derived by experimental tests, see Nielsen et al. (2010a), Vivek and Ramesh (2016), Kirsch (2017), and Laurs et al. (2019). Table 3.2 gives a current overview of photoelastic constants C, which have been experimentally determined for different types of glass. Table 3.2

Photoelastic constant in soda-lime-silica glass for architectural use.

Glass type

Annealed Float Glass Float Glass Float Glass Float Glassb Float Glass HSGb FTGb Tempered Glass CSG a b

C

TPa 2.61 2.71 2.70 2.73 2.75 2.80 2.85 3.01 3.03

Type of Test

Measuring methoda

Bending Bending N/A Bending Bending Bending Bending Bending Bending

Carrier Carrier N/A Scalp BSC Scalp Scalp Scalp Scalp

Reference

Vivek and Ramesh (2016) Scalp Manual (2013) Kirsch (2017) Nielsen et al. (2010a) Laurs et al. (2019)

Methods are explained in the reference or in chapter 4. Mean Values at surface.

Factors influencing C are the chemical composition of the material, the temperature, the dispersion of light, and the electron density distribution across the thickness, c.f. Aben and Guillemet (1993). The chemical composition in architectural glass is quite homogeneous, and the influence of temperature is negligible at standard test temperatures of 20◦ C to 80◦ C for glass. Zee and Noritake (1958) show in their investigations on container glass that C increases significantly in the range of the glass transition temperature Tg . In the visible light range, a relative variation of C from ≈ 8% can be produced by dispersion, see Pindera (1971). Tempered glass exhibits a frozen residual stress state. Consequently, a variation of the electron density distribution results, which causes a change of the photoelastic

3.3 Photoelastic Behaviour

41

Residual Stress States visualized in Circular Polariscope

Figure 3.7 Dark-field isochromatics in the respective prestress zone of a tempered architectural glass pane recorded using RGB photoelasticity. Areas with low or high retardations are created, see Dix et al. (2022b).

constant, c.f. Aben and Guillemet (1993). Nielsen et al. (2010b) and Kirsch (2017) determine up to eleven percent higher C values for tempered glass in their experiments. Consequently, the surface compressive stress measurement values deviate by eleven percent when applying the incorrect C value. This factor is neglected for retardation measurement of residual stress differences because only tempered glass is investigated in this work. The second aspect that determines the photoelastic behavior of tempered glass is the effect of the residual stress state on the integral of the principal stress differences over the glass thickness. Depending on geometrical constraints of the prestress zone, various photoelastic images are obtained, which differ strongly from each other. Fig. 3.7 shows the dark-field isochromatics in the respective prestress zone of a tempered glass pane recorded using RGB photoelasticity from chapter 4. In Fig. 3.4, it was shown that in zone 1, for standard tempered architectural flat glass, σ1 is assumed to be approximately σ2 . For the optimal case, σ1 = σ2 , the optical retardation is zero, and the photoelastic image shows a black screen. Typically, only minor optical retardations smaller than 500 nm are expected for monolithic glass panels in this region. The variation of retardations with different magnitudes over the glass area can result in a heterogeneous color pattern. On the contrary, high retardations greater than 500 nm occur in zones 2 to 4. These result from the decrease of the perpendicular principal stress and simultaneously increase nonlinearly in the direction of the free edge. The development of the residual stress states of zones 2 to 4 is very homogeneous if there is sufficient distance between these zones. The observable interference colors in the polariscope of Fig. 3.7 can also occur under naturally polarized light and are widely referred to as anisotropy effects.

42

3 Glass and their Photoelastic Behaviour

3.4 Visual Perception of Anisotropy Effects The principles for the formation of polarized daylight and stress-birefringence are given in chapter 2. In this work, the term optical anisotropy effect refers to the optical retardations occurring in the prestress zone 1, which vary across the glass sheet and create a heterogeneous color pattern. The cause of anisotropy effects is to be found in the formation of principal stress differences of the parabolic residual stress resulting from the thermal toughening process. These lead to artificial birefringence, which, following Eq. (2.48), cause an optical retardation δ and can become visible under naturally polarized daylight as Michel-Lévy interference colors. The anisotropy effects in zone 2 to 4 will be mainly generated by the geometrical boundary conditions and can only be slightly influenced in the tempering process. In contrast, Dehner and Schweitzer (2015), Pasetto (2014), and Illguth et al. (2015) show that the prestress process of zone 1 can be monitored via photoelastic measurements, and anisotropies can be reduced. Fig. 3.8 shows an example of an internal tempering furnace optimization performed by a leading glass supplier to minimize the visibility of anisotropy. Although optical anisotropy effects are now undesirable (Pasetto (2014)), they are not considered defects or deficiencies according to the current standards (EN 12150 (2015), EN 1863 (2012), ASTM C1048 (2018)). Fig. 3.9 (a) illustrates the diversity of typical anisotropy patterns in tempered architectural glass. The patterns often appear as dots or stripes, with only black and white or rainbow color changes, depending on the level of anisotropy and the magnitude of the retardations. Fig. 3.9 (b) shows the analytically calculated interference chart according to Sørensen (2013), also known as Michel-Lévy-chart, suitable for estimating retardation with the human eye. Effect of a non-homogeneous tempering process.

Figure 3.8 Dark-field isochromatic images of two similar tempered architectural glass panes recorded using RGB photoelasticity. (a) High retardations (red arrow) indicate a heterogeneous tempering process with heat disturbance in the furnace. (b) Improved furnace configuration produces a more homogeneous pattern and lower retardations. (Images in Courtesy of Pasetto (2015)).

3.4 Visual Perception of Anisotropy Effects

43

(a) Different Anisotropy Pattern

(b) Michel-Lévy Chart

Figure 3.9 (a) Facades with tempered glass panes and various anisotropy patterns. Stripe- (arrows 1, 6), point- (arrow 2), cross-stripe- (arrow 3) and mixed pattern (arrow 4, 5). (1 and 2 (Courtesy: Illguth et al. (2015)), 3 (Courtesy: Henriksen and Leosson (2009)), 4 (Courtesy: Feldmann et al. (2017a)), 5 and 6 (Ref: Dix et al. (2021a)) . (b) Interference color scale according to Michel-Lévy analytically calculated in Illguth et al. (2015).

44

3 Glass and their Photoelastic Behaviour

Due to variations in the amount of polarized light in natural daylight and the influence of the angle of observation, a visual-only evaluation of anisotropy effects in a model or glazing in-situ is not recommended. Instead, with the introduction of photoelastic methods for quality control, a tool for quantitative measurement of retardation in tempered glass was established. The aim is to identify a reliable objective measurement and evaluation method considering human perception.

4 Photoelastic Methods for Measuring Anisotropy Effects This chapter describes known and novel photoelastic measurement methods that can be used to analyze anisotropy effects created from stress differences in the glass. Depending on the method, different physical values can be visualized and measured. They are appropriate either locally for detecting the 3D stress state or for the 2D full-field analysis of optical retardations from stress differences. The author has also published the methods described herein in his publication: Dix et al. (2022b). At the end of the chapter, a device is introduced that can measure skylight polarization which bases on phase-shifting methods.

4.1 General Recent reviews by Ramesh and Sasikumar (2020), Solaguren-Beascoa Fernández et al. (2010), and Ajovalasit et al. (2015b) show that photoelasticity is mainly used to analyze stress concentrations in complex components under external load. Residual stresses in glass are also considered in reviews by Ramesh and Vivek (2016), Aben et al. (2008), and Scafidi et al. (2015). However, all these reviews focused on small measurement areas of maximum 500 mm by 500 mm. With recent developments of known methods (Illguth et al. (2015), Dehner and Schweitzer (2015), Feldmann et al. (2017b), Vogel (2017), Moreau (2019), Dix et al. (2021a)) and the application of new technologies (Dix et al. (2017b), Hidalgo and Elstner (2018), Katte and Saur (2018)), in-situ characterization of large-scale areas on the square-meter scale are possible. A revolution in the quality control of tempered architectural glass has started. This thesis, therefore, deals specifically with digital full-field photoelastic methods and their application on tempered architectural glass, where measurement areas range from 0.5 m2 up to 60 m2 .

4.2 Scattered Light Method The scattered light method (SLM) is a three-dimensional photoelastic technique that, like the surface-guided wave method, is already widely used to measure resid© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_4

45

46

4 Photoelastic Methods for Measuring Anisotropy Effects

Scheme of Scattered Light Polariscope

Figure 4.1 Illustration of optical measuring scheme of scattering light polariscope with description (a) side view, (b) front view, (c) top view, (d) exemplary distribution of measured retardation and calculated stress for a 8 mm tempered glass (Courtesy from Dix et al. (2022b)).

ual stress at discrete points in glass quality control, c.f. (ASTM C1279 (2013), Feldmann et al. (2012b), Mognato et al. (2018), Zaccaria and Overend (2020), Nielsen et al. (2021)). However, surface-guided wave methods that use the Mirage Effect can only determine residual stresses near the surface on the tin-side of a thin float glass sheet, c.f. Gardon (1980). SLM was introduced by R. Weller (1941) and was the first technique used to measure stresses in glass by Bateson et al. (1964). Reviews of this method are presented in Ascough (1981), Aben and Guillemet (1993), Hundhammer et al. (2002) and Ramesh and Vivek (2016). The method is based on Rayleigh and Mie scattering of light passing through transparent materials (Menges (1940), Aben and Guillemet (1993). This allows one to observe changes in polarization of the incoming light from the side and to measure the retardation while the light passes through a birefringent medium. The alteration of polarization is visible to the observer, e.g., a camera, as a change in the intensity of scattered light and depends on the stress distribution in the glass as described in chapter 3. Since the scattered light is only faintly detectable, intense laser light has mainly been used as a light source since Bateson et al. (1964).

4.2 Scattered Light Method

47

A mobile measuring device, which is also suitable for industrial applications due to its compactness and robustness, is the Polariscope SCALP, developed by GlasStress Ltd. (Anton and Aben (2003), Aben et al. (2008), Lochegnies et al. (2005) and Scalp Manual (2013)). Fig. 4.1 (a) to (c) illustrate the working principle of SCALP with a description of the axes and the optical elements. Using a cartesian coordinate system with the axes x and y in the center of the glass pane, and the axis z perpendicular to them. The optical axes η and ξ are perpendicular to each other and defined by the angle of incidence α. Depending on the device version, stress can be determined over the entire glass pane thickness at an angle of incidence α of 45◦ or up to a depth of approx. 5.77 mm at α of 70◦ . Anton and Aben (2003) describe the approach to determine the thickness stress σ in ’MPa’ from the relative retardation of the laser beam δη (nm) in the glass, mathematically expressed as: δη = C

η

Z

(σx − σy cos2 α)dη

(4.1)

η0

Where C is the photoelastic constant in ’TPa-1’, λ is the wavelength in ’nm’, and ηo is the coordinate in ’mm’ where the laser beam enters the panel. σx and σy are normal stresses in perpendicular directions. In the middle of the glass plate, with an early isotropic residual stress state in zone 1 (σx ≈ σy ≈ σ1 ≈ σ2 ), a measurement of residual stress is sufficient and given according to Scalp Manual (2013): σ=

1 δη′ C sin2 α

(4.2)

′ Here δη is the relative retardation in ’nm’ and δeta is the derivative of δη along η. For a simple non-uniform stress state, a minimum of two perpendicular measurements has to be performed. The axis perpendicular to η is ξ, after which retardation δξ is calculated:

δξ = C

Z

ξ

(σy − σx cos2 α)dξ

(4.3)

ξ0

Fig. 4.1 (d) shows a diagram demonstrating the determination of the stress σ across the thickness from the measurement data δ. C must be known for the determination of the stress state and can be used from Table 3.2. In order to measure the surface compressive stress and record the scatter of the prestress quality, five measuring points per pane are required, according to EN 1863 (2012) and EN 12150 (2015). Four of them are neither in the center of the pane nor in an axis of symmetry. For this reason, three or four individual stress measurements in 45◦ directions (x, x1 , y and y1 ) per measuring point are recommended for determining

48

4 Photoelastic Methods for Measuring Anisotropy Effects

Stress Field Measurement via SCALP

Figure 4.2 (a) Tempered 8 mm glass pane produced under stationary cooling in a dark-field plane polariscope (RGBP). (b) Measured stress by SCALP in the dashed line area of (a) (Courtesy: Ref.Karvinen and Aronen (2019)).

the principal residual stresses σ1 , σ2 according to Anton and Aben (2003), Scalp Manual (2013) and ASTM C1279 (2013). The accuracy and precision of the scattered light polariscope were investigated by Zaccaria and Overend (2020) for different photoelastic constants. For C =3.01 TPa−1 in tempered glass, they determined an accuracy of ±4.7 MPa and precision of ±3.9 MPa. Unfortunately, it is not mentioned which version of the instrument and which fitting method were used. Most authors use the scattered light polariscope to measure residual surface stresses in flat (Nielsen et al. (2010a), Pourmoghaddam and Schneider (2018), Dix et al. (2021b), Thiele et al. (2022)) or curved tempered glass locally at discrete points. In principle, it is unsuitable as a full-field method due to the punctual light source and the associated high number of measurement points. Nevertheless, Y. Chen et al. (2013) investigated the residual stress state in tempered glass due to non-uniform cooling at point distances of 4 mm over an area of 28 mm x 56 mm using SCALP and compared these with the results of numerical finite element calculations. In similar studies, Karvinen and Aronen (2019) examined the formation of the anisotropy pattern Fig. 4.2 (a) and the residual stress state on different cooled tempered glass sheets using plane dark field polariscope and SCALP. They use glass plates of 500 mm x 500 mm and extend the measuring field to 190 mm x 200 mm. To increase the spatial resolution of the measurements, both authors used a scanning CNC coordinate device. As shown in Fig. 4.2 (b), a full-field evaluation of the stress state is, therefore, possible by means of a Scattered Light Polariscope but is time-consuming and not recommended for evaluating large-scale anisotropy effects.

4.3 RGB Photoelasticity

49

4.3 RGB Photoelasticity RGB Photoelasticity (RGBP) or Three Fringe Photoelasticity was first introduced by Ajovalasit et al. (1995b). Since then, various authors (Ramesh and Deshmukh (1996), Yoneyama et al. (1998), Umezaki (1999), Ramesh et al. (2015), Illguth et al. (2015), Decourcelle et al. (2017), Dix et al. (2021a)) have adapted the method and further developed it. RGBP offers the opportunity to estimate retardation with a single image in a stationary, calibrated polariscope under white light typical in a circular dark-field arrangement. Circular RGBP is applied on local edge membrane stress measurement in zone 2 (Ajovalasit et al. (2015a), Schaaf et al. (2017)), as well as on full-field retardation measurement to evaluate anisotropy effects in zone 1 of tempered glass plates, c.f. Illguth et al. (2015), Schaaf et al. (2017), Decourcelle et al. (2017), Dix and Schuler (2018), Hidalgo and Elstner (2018), FKG (2019). In this work, the polariscope setup of Fig. 4.3 was used for the photoelastic investigations of small samples up to 1.0 m x 1.1 m. It consists of a conventional digital camera with a left circular polarizing filter and a white light source equipped with a right circular polarizing filter. The white light source1 is made of a twodimensional illuminating box with high-frequency daylight and a color temperature of 6500 K. By replacing the analyzer, isochromatic images in the bright and dark Used Setup for Small Scale Samples in RGBP

Figure 4.3 RGB polariscope setup for small scale specimen with the dimension 1.0 m x 1.1 m, adapted from Dix et al. (2021a). 1 WRG

Light Box; http://www.wrg-roentgen.de/

4 Photoelastic Methods for Measuring Anisotropy Effects

50

field can be acquired in this setup, see Fig. 4.4. The circular polarizing filter 2 was chosen because of its high transmission in the direction of polarization and a good blocking of the other directions for large spectral bandwidth. The resulting isochromatic images provide an image resolution of 1.0 mm/px. (a) Dark-Field Isochromatic Image

(b) Bright-Field Isochromatic Image

Figure 4.4 Resulting isochromatic image of a 1.0 m2 tempered glass pane in a dark-field arrangement with polarizer and QWP crossed (a) and a bright-field arrangement with polarizer parallel and QWP crossed (b) under white light.

The calibration of a polariscope and the creation of a calibration table, called lookup table (LUT), is usually performed using calibration beams, c.f. Ajovalasit et al. (2015b), Illguth et al. (2015). In Feldmann et al. (2017b), Schaaf et al. (2017), Dix et al. (2021a), the authors show alternative methods for generating the calibration table. Here, the use of a Babinet-Soleil Compensator (BSC) as a calibration tool described in Dix et al. (2021a) should be mentioned due to its simplicity. Fig. 4.5 (a) shows the used BSC with the corresponding images taken at different retardation values resulting in a LUT and a calibration chart, see Fig. 4.5 (b). By comparing the color components (Ri , Gi , Bi ) pixel by pixel in the source image with the color components (Rp , Gp , Bp ) from the previously created LUT, a new image is generated with the relative retardation δ in ’nm’ as an intensity value. Fig. 4.6 visualizes the so-called retardation image as false-color plots in 2D and 3D. The five-color scale in ’nm’ allows the observer quickly to locate areas with high retardations in detail. The used search algorithm is based on the minimization of the least-squares error sum E according to Ajovalasit et al. (1995b): 2 Edmund

optics (formerly Itos): Circular Polarization Filter CP42HE

4.3 RGB Photoelasticity

51

(a) BSC and Calibration Images

(b) Calibration Chart

Figure 4.5 Babinet-Soleil Compensator and exemplary source images (a) transferred in an calibration chart(b), adapted from Dix et al. (2021a).

E = (Ri − Rp )2 + (Gi − Gp )2 + (Bi − Bp )2

(4.4)

Calibration and examination must use the same optical components (light source, filter, sensor, glass type) and photometric settings (exposure time, depth of field) to achieve reproducible results. In circularly polarized light, the relative retardation δ can be determined independently of the direction of the glass sample in the polariscope. RGBP is a powerful method to visualize and measure optical retardation in glass from zero to 1500 nm. However, quarter-wave plates are set to a single wavelength, thus producing an error when using white light. The error can be minimized using high-quality circular broadband filters and following the procedures given by Ajovalasit et al. (1995a), Ajovalasit et al. (2010). Visualization of Retardation Image

Figure 4.6

Visualization of an exemplary retardation image in 2D and 3D false color plots.

52

4 Photoelastic Methods for Measuring Anisotropy Effects

4.4 Half-Wavelength and Multi-Wavelength Photoelasticity A simpler way than RGBP is to use monochromatic light in a circular polariscope to calculate optical retardations via the intensity of an image directly. Aben and Guillemet (1993) give the relation in Eq. 4.5 in a dark-field or Eq. 4.6 in a brightfield arrangement with I is the measured light intensity, I0 is the intensity of incident light, and ∆ is the phase difference (∆ = δ2π/λ) in ’rad’. I = I0 sin2

∆ 2

(4.5)

∆ (4.6) 2 One of the first automated approaches is the half-fringe or half-wavelength photoelasticity (HWP) method, introduced by Voloshin and Burger (1983). As the name implies, HWP methods can only detect retardation between 0 to 0.5 of a wavelength. According to Voloshin and Burger (1983), half a wavelength of a monochromatic light source is proper for determining the optical retardation in materials with low birefringence behavior such as glass. However, as Aben and Guillemet (1993) indicate, HWP methods do not consider isoclines and consequently do not allow the calculation of isocline parameters. Nevertheless, they are widely accepted and used due to their simplicity and ease of implementation (Voloshin and Burger (1984), Miskioglu et al. (1987), Wang and Chen (1989) and Burger (1988)). For instance, also for full-field measurement of retardation in tempered glass, see Vogel (2017) and Vogel (2019). I = I0 cos2

Used Measuring Device based on MWP

Figure 4.7 Used device for measuring full-field retardation in tempered glass panes with the maximum dimension 2.3 m x 3.5 m (width x length). The glass panes are moved horizontally through the scanner for image acquisition.

4.4 Half-Wavelength and Multi-Wavelength Photoelasticity

53

The extension of HWP to multiple monochromatic wavelengths (MWP) presented in Dix et al. (2017b), Hidalgo and Elstner (2018) can be considered as a further development of the HWP method. Advances in semiconductor technology, as well as image and signal processing, enable the nearly simultaneous acquisition of multiple, high-resolution monochromatic isochromatic images. On the one hand, substituting the standard fluorescent lamp with light-emitting diodes (LEDs) allows monochromatic LEDs of any color to be installed in the light sources. On the other hand, these can be triggered separately precisely and quickly, opening up new possibilities in digital photoelasticity. When using MWP, like RGBP methods from section 4.3, it is essential to use high-quality quarter-wave plates to minimize these errors. The advantage of the MWP method over RGBP is that only the wavelength with the minor error to the bandwidth of the quarter-wave plate can be applied to calculate the difference in retardation, and the other wavelengths are used only to determine the fringe order N . Hidalgo and Elstner (2018) introduced an error function E, minimized by iterating the difference between the theoretical light transmission IT,i and the measured ′′ transmission Ii for each wavelength λi in ’nm’: E=

i X

′′

|IT,i − Ii | =

1

i  h 1 δ i2  ′′ X −Ii IT,i sin 2 λi

(4.7)

1

MWP extends the fringe order from N = 0.5 to at least 1 and is applied in the commercial measuring system3 (Dix et al. (2017b)), see Fig. 4.7. This device measures full-field relative retardation of a tempered glass pane in a bright-field polariscope and can calculate edge membrane stress along the whole glass edge due to the high spatial resolution of 200 dpi and the telecentric light technique, c.f. Hidalgo and Elstner (2018), Dix and Schuler (2018), Moreau (2019). Fig. 4.8 shows for a 10 mm thick tempered glass pane the simultaneous acquired isochromatic images (a and b), the transmission under infrared light (c), and the resulting retardation image (d). In (d) two strips with retardations up to 150 nm can be observed which result from a standard tempering process, c.f. Dix et al. (2022b).

3 Linescanner

(2021), GlassIQ

54

4 Photoelastic Methods for Measuring Anisotropy Effects

Resulting Images acquired via MWP

Figure 4.8 Tempered 10mm glass pane (HSG), 750 mm x 1500 mm produced in a standard tempering furnace measured via MWP: (a) Isochromatic bright-field image under blue light with λ = 455 nm. (b) Isochromatic bright-field image under green light with λ = 505 nm. (c) Transmission image without polarization under infrared light with λ = 940 nm. (d) The false-color plot was determined from (a) and (b) in relative retardation δ, from Dix et al. (2022b).

4.5 Phase-Shifting Methods In the methods presented so far, simple optical polariscope arrangements are used that provide retardation. A high degree of flexibility in using the intensity information to calculate additional parameters, such as the direction of the principal stresses, is possible when the optical elements are placed at specific positions. A rotation of the optical elements around the optical axis of the polariscope results in phase shifts or phase steps of the observed fringe pattern. The occurring intensity variations in the digitally captured images can be measured to determine the desired phase information, retardation δ and isoclinic (azimuthal) angle φ, c.f. Carré (1966), Hecker and Morche (1986), Carazo-Alvarez et al. (1994), Ajovalasit et al. (1998), Patterson (2002), Aben et al. (1999), Zhang et al. (2007) and Ramesh and Vivek (2016). A variety of phase-shifting methods (PSM) can be chosen from a minimum of four steps (Patterson (2002)) to up to ten steps (Vivek and Ramesh (2016)). Due to the rotating parts and the resulting time delay, the first PSMs were applied only locally for point-by-point analysis, as in the anisotropy measurement system of Dehner and Schweitzer (2015). Recently, two promising methods have been developed: PSM with beam splitting optical elements and pixelated phase-shifting with micro polarizers (PPSM), c.f. Dix et al. (2022b). Patterson and Wang (1998) were the first to achieve simul-

4.5 Phase-Shifting Methods

55

Nanowire Grid for PPSM

Figure 4.9 a) Photograph of a nanowire grid, made of metal, and processed to have a 150-nm fine pitch, with 50-nm width and 100-nm spacing (Courtesy: Ref. Yamazaki et al. (2016)). (b) Schematic wire grid structure with the polarization of the transmitted light indicated, from Dix et al. (2022b).

taneous observation and acquisition of phase-stepped images in a novel photoelastic instrument. By using beam-splitting optical elements (cube beam splitters) in a reflective setup, full-field maps of isochromatic and isoclinic parameters are generated in real-time. This is achieved by splitting the incoming light and detecting it with four CCD cameras with different orientations of the quarter-wave plate and the analyzers. Based on the measured intensity data from four phase shifting images, the isochromatic fringe order and the isoclinic angle can be determined using the Mueller matrix and the knowledge about the orientation of the optical components (Patterson and Wang (1998) and Patterson (2002). Lesniak et al. (2004) follow a similar approach with the development of the Poleidoscope (Polariscope plus Kaleidoscope), commercially available as GFP 2000. The splitting of the light beam is achieved by the Kaleidoscope optics instead of cube beam splitters. Here, the light beam splits into parallel beams, thus, making the recombination of the images easier (Patterson (2002)). The camera sensor can be designed as an area sensor or as a line-scan sensor depending on the application. This allows an application for local measurement of edge membrane stress or for full-field measurement of retardation from principal stress differences in prestressing zone 1. One approach that is currently causing great interest in photoelasticity is the pixelated phase-shifting method (PPSM), c.f. Ramesh and Sasikumar (2020). Instead of using rotating or optical beam splitting elements, the multi-channel (-pixels) of the usual image sensors are adapted, and the well-established phase-shifting algorithms are applied. The adaptation is implemented by micro polarizer arrays, which are placed directly on the image array sensor and generate different polarization states. A pixelated polarizer array can consist of a multilayer thin polymer film (Gruev et al. (2007), Gruev et al. (2010)) or a nanowire grid (Novak et al. (2005), Millerd et al. (2006),

4 Photoelastic Methods for Measuring Anisotropy Effects

56

Yamazaki et al. (2016) and Freitas Carvalho et al. (2020)). The nanowire grid, see Fig. 4.9 transmits only polarized light perpendicular to the grid direction. Depending on the required type of polarization state, the sensors ’structure and the polarizers’ orientation differ. An early method from Yoneyama (2006) involved micro retarders and a large polarizer array for simultaneous observation of phase distribution in quartz glass disk under compression load. Shibata et al. (2012), Onuma and Otani (2014), and Yoneyama and Arikawa (2016) used a sensor array whose basic structure consists of four polarizers whose principal axes differ by 45◦ and are attached to a 2-by-2 pixel matrix. From the four individual light intensities I1 , I2 , I3 , I4 detected after the light has passed the four polarizers of the sensor, the azimuthal angle φ in ’◦ ’ and the phase difference ∆ in ’rad’ can be calculated and are expressed as I0 =

I1 + I2 + I3 + I4 2

1 I3 − I1 tan−1 2 I2 − I4 p (I3 − I1 )2 + (I2 − I4 )2 −1 ∆ = sin I0 φ=

(4.8) (4.9) (4.10)

The pixelated phase-shifting technique for the analysis of residual stress states in tempered glass is applied on a small scale (less than 0.4 m by 0.4 m) in Lohr and Weller (2019), Glaser et al. (2019) and Dix et al. (2022a), and on a large scale (up to 3.0 m by 6.0 m) in Katte and Saur (2018) based on the commercially available devices of ilis GmbH. For some experimental investigations in chapter 5, the same full-field measuring system4 was used, see Fig. 4.10. The system determines the retardation in ’nm’, the azimuthal angle in ’ ◦ ’, and predicts an anisotropy image as shown in Fig. 4.11. This prediction is calculated by a global threshold method considering φ and indicating the orientation of the installed pane, c.f. Dehner and Schweitzer (2015), Dix et al. (2021a) and Dix et al. (2022c). The used PPSM system has a measurement range from 0 to 120 nm with a image resolution of 2 mm per pixel.

4 strainscanner

(2021), ilis GmbH

4.5 Phase-Shifting Methods

57

Used PPSM Setup

Figure 4.10 (a) Scheme of used PPSM setup and components (b): 1. Glass sample; 2. matic light source with circular polarizer; 3. Polarization camera as analyzer.4. Computer ling the camera and light source, as well as for image processing and evaluation. (2 and 3 nents of the strainscanner from ilis GmbH Erlangen). Illustration adapted from Dix et al.

Monochrofor controlare compo(2022c).

Resulting Images acquired via PPSM

Figure 4.11 Punctual spatial distribution of retardation in 8 mm tempered glass pane, 750 mm x 1500 mm produced in a common tempering furnace measured via PPSM: (a) False-color plot of the retardation δ in nm. (b) Azimuthal angle φ in ◦ . (c) Predicted anisotropy image (white area) presented as a b-w image with a threshold of 75 nm and considering the observation angle, adapted from Dix et al. (2022b).

58

4 Photoelastic Methods for Measuring Anisotropy Effects

4.6 PSM for Skylight Observation This section differs from the previous sections 4.3 to 4.5, because the polarimeter presented here is not applied to measure retardation in the glass. Instead, the phase-shifting method is used to analyze the incident daylight of the sky in the field study of chapter 6. Several authors (Lee (1998), Horváth et al. (2002), Pust and Shaw (2006), Dehner and Schweitzer (2015)), applied PSM for observation of skylight and determination of degree of polarization p. The techniques can also be divided into two-dimensional ’all-sky’ and point methods. To perform the field experiments in chapter 6, a device for the point-by-point measurement of p of the incident skylight was constructed following Abayaratne et al. (2016) and Abayaratne and Bandara (2017). This technique is based on the phase-shifting method with rotatable optical analyzers. Polarimeter for measuring skylight polarization

Figure 4.12 Polarimeter to determine skylight polarization with: 1) Lightray, 2) Polarizer, 3) Collimator, 4) Light sensor 5) step motors. Red arrow 180◦ for polarizer rotation κ and blue arrow, angular solar distance ξ from zero to 90◦ , adapted from Dix et al. (2022c).

Fig. 4.12 displays polarimeter and the associated components. The incoming light ray will be retarded at the linear polarizer, and the altered light intensity is measured by a calibrated light sensor. Here, the collimator and polarizer can be automatically rotated around the optical axis κ in steps of 11◦ to achieve nearly 180◦ rotation. To observe a greater area of the sky along the angle of the solar distance ξ, the incident light intensities are automatically measured in 6◦ increments, from zero to ≈ 90◦ . The measured light intensity along κ results in a sinusoidal curve. Fig. 4.13 (a) shows for each step ξ the measured light intensity curve and the positions in κ where Ix , Iy , I45 , I−45 , Imin and Imax are output. From these light intensities the Stokes parameters S0 , S1 , S2 as well as the linear degree of

4.6 PSM for Skylight Observation

59

polarization p (LDoP) and the angle θ can be calculated according to Table 2.1 and Eq. (2.14). P can be determined either by Eq. (2.13) or p=

Imax − Imin . Imax + Imin

(4.11)

Fig. 4.13 illustrates step-by-step the determination of p for an typical measurement sequence. While (a) and (c) represent the measured intensity over κ and ξ, (b) shows the extreme values Imin and Imax from which p displayed in (d), distributed over ξ, can be calculated. The corresponding image of the sky to the measurement values is presented in (e).

60

4 Photoelastic Methods for Measuring Anisotropy Effects

(a) 2D Intensity Distribution

(b) Intensity Extreme values

(c) 3D Intensity Distribution

(d) Distribution of p

(e) Image of Sky with Polarimeter Axis ξ

Figure 4.13 Exemplary intensity curves (a and c) used for calculation of Stokes Parameter and extreme values (b) to determine p (d). (e) Simultaneously captured image of the sky on 9 September 2020 at 10:46 (CET).

5 Photoelastic Measurements on Tempered Flat Glass In order to analyze the origin and distribution of optical anisotropy effects from residual stress differences, a large number of full-field photoelastic measurements had to be performed on tempered glass panes. The photoelastic experiments conducted in this chapter form the basis for the usability of the full-field methods from chapter 4. They aim to identify factors that qualitatively influence the retardation pattern of tempered architectural glass, see sections 5.3 to 5.5. The experiments with its retardation images also provide the database for the correlation of anisotropy effects in the field study of chapter 6 and the application of various digital evaluation methods in chapter 8.

5.1 Validation Experiments The novel photoelastic full-field methods are examined for factors that may influence the measurement results. The validation investigations aim to confirm the generated measured values and demonstrate their reliability. A transferability of the results to other devices is not recommended.

5.1.1 Accuracy and Precision Accurate and precise measurements of the optical retardation in glass are essential for validating the non-destructive methods used in this work. According to ISO 5725 (1994), accuracy is the difference between the measured and actual values and is evaluated here using absolute error AE. Precision is the difference between the measured value and the average measured value and, in the present case, is described by the mean x ¯ and the standard deviation σsd of AE. Following the recently introduced ASTM C1901 (2021) and DIN SPEC 18198 (2022), the used photoelastic measurement setups, M11 , M22 , M33 , were verified for accuracy and precision using retarders. 1 Circular

polariscope based on RGBP method, see test setup in Fig. 4.3. method from Linescanner (2021), see test setup in Fig. 4.7. 3 PPSM method from strainscanner (2021), see Fig. 4.10. 2 MWP

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_5

61

5 Photoelastic Measurements on Tempered Flat Glass

62

(a) Arrangement of the Retarder

(b) Exempl. Measurement Result for δm

Figure 5.1 Drawings of the used validation plate with five specific retarders and an inspection hole. (a) Sketch to illustrate rotation and arrangement. (b) Sketch with exemplary measurement results from M1 displayed as false-color plot.

The plastic retarders are birefringent and possess defined retardation δ independent of the device’s light source. Retarders with δa of 0, 50, 75, 100, and 150 nm were chosen and mounted in a plastic plate, measured similarly to the tempered glass samples. The accuracy of the retarder is ±1 nm according to the manufacturer4 . Fig. 5.1 (a) shows the arrangement of the retarders and the rotation directions of the plastic plate during the tests. A total of five validation plates were used. Fig. 5.1 (b) shows exemplary retardation images generated from method M1 in false-colors. From the homogeneous retardation images, the measured retardation δm of the individual retarders was determined by averaging. The absolute error AE is calculated: AE = δa − δm

(5.1)

The evaluation is carried out per measuring series, consisting of five retarders with equal δa , shown in the diagram in Fig. 5.2 and the statistical parameters of all measured values per measuring system in Table 5.1. In the holistic analysis in Table 5.1, it becomes apparent that the error is negative for all apparatuses, hence the measured values are higher than the actual values. Thus the measured values are overestimated, i.e., they are on the safe side. The mean values x ¯ and standard deviations σsd show that M3 is the most accurate and precise but can only detect retardations smaller than 120 nm doubtlessly. M1 is the least accurate with x ¯ of -10.1 nm and the least precise with σsd of 8.0 nm. M2 lies in the middle of M1 and M3. 4 Sharples

Ltd.

5.1 Validation Experiments

Table 5.1

63

Statistical evaluation of the absolute error AE based on all measured values (0 to 150nm).

No. of samples n Mean x ¯ Standard deviation σsd Minimum Maximum a b

M1a

abs. error AE M2

M3b

50 -10.1 8.0 -27.5 2.6

74 -5.2 5.3 -14.8 6.4

56 0.01 1.8 -4.8 3.2

Only in 0◦ and 90◦ orientation. Without retarders with δa 150 nm.

Measurement Accuracy

Figure 5.2 Absolute error AE of the used measurement systems M1 (RGBP), M2 (MWP) and M3 (PPSM) as a function of the orientation and the magnitude of retardation.

Fig. 5.2 provides detailed information. It clearly illustrates the accuracy of M3 independent of rotation and retardation level. M1 exhibits high deviations from the actual value in the range of low retardations, zero to 75 nm, and for retarders with 150 nm, the results varied strongly by orientation. M2 also shows minor error deviations depending on the orientation of the validation plate. For both methods,

5 Photoelastic Measurements on Tempered Flat Glass

64

(a) Setup Heating

(b) Cooling Curve of Sample

Figure 5.3 Drawings of the used validation plate with five specific retarders and an inspection hole. (a) Sketch to illustrate rotation and arrangement. (b) Sketch with exemplary measurement results from M1 displayed as false-color plot.

the cause is assumed in the use of multiple light sources (RGBP or MWP) and their error sensitivity due to the wavelength dependence of the quarter-wave plate. M3, with its monochromatic light, does not exhibit this rotation problem. A correction factor for M1 and M2 cannot be recommended at present. Therefore, for the following experiments, it is noted which measuring system was used.

5.1.2 Temperature Dependency The experimental photoelastic investigations in this chapter were performed at a room temperature of 20°C ± 3°C in the laboratories of the Labor für Stahl- und Leichtmetallbau GmbH in Kissing, Germany. The influence of the temperature difference between specimen and ambient temperature on the results of the retardation measurements is investigated on an annealed glass specimen. For this purpose, a glass pane with a width w of 0.36 m, a length l of 1.1 m, and a thickness t of 12 mm was selected. The glass was heated uniformly over the entire surface from both sides for three hours using heating mats5 for the experiments and cooled slowly at room temperature. The surface temperature of the glass pane was recorded using a data logger6 . Therefore, three thermocouples type K were applied to the upper surface, as shown schematically in Fig. 5.3. Starting from room temperature (∆T = 0 K), temperature differences ∆T of 10 K, 20 K, 30 K and 40 K were investigated. When the respective test temperature (TT) was reached, the sample was subjected to retardation measurements by method M3 (PPSM). The results are shown as false-color plots summarized in Fig. 5.4 (a). A considerable increase in retardation can be recognized with rising 5 Freek 6 HBM

HTSD Pro 387 C.001. Quantum MX1609B.

5.1 Validation Experiments

65

temperature differences. Here, higher retardations are observed at the edge of the glass than at the glass center. While at ∆T equals 10 K the retardations are mainly below 20 nm, they increase rapidly up to 139 nm in the peak at ∆T equals 40 K, see Fig. 5.4 (b). The cause is assumed to be the present temperature gradient, whereby cooling induces stresses in the glass that diminish as the temperature difference decays. The investigation shows that for comparability of measurements, the surface temperature of the specimen and the room temperatures must be similar. Temperature deviation ±3° C should be acceptable within the error tolerance given in section 5.1.1. Retardation due to temperature differences ∆T

Figure 5.4 Experimental results of the influence of different temperature differences ∆T on retardation measurements using M3. (a) Shown as 2D retardation images in false colors. (b) Distribution of retardation in horizontal section 1.

5 Photoelastic Measurements on Tempered Flat Glass

66

5.2 Specimen For the purpose of this work, 736 tempered glass panes of different sizes (length l, width w), thickness t, glass type, and prestressing level were selected, cleaned, and measured. The author collected these measurement data within the last six years as part of different research projectsa, b, c , see Table 5.2. The different batches of specimens are divided into groups. Within the groups, the raw float glass originates from the same manufacturer. Besides clear soda-lime-silica glass (SLS-CF), SLS with low iron (LI) content, with a low-E coating (LE7 ), with a solar control coating (SC8 ), were used. They were further processed into a heat-strengthened (HSG) or fully-tempered glass (FTG) by different glass processors (tempering facilities) to obtain various anisotropy patterns. Information of the samples are summarized in Table 5.2. The dimensions given are nominal values. The designation of the samples in this thesis, e.g., G5_TF7_134_6-FTG-SC, was determined in the order: Group_facility_number_thickness - level - glass. The used measuring systems M1 (RGBP), M2 (MWP), and M3 (PPSM) are presented in chapter 4. Table 5.2

Summary of specimens measured at the university of applied Sciences Munich.

Prod. Year Temp. Facility Dim. [m] Thick. [mm] Sample No. Glass type Temp. Level Measuring Method

Group 1a,d

Group 2b,d

Group 3b

Group 4c

Group 5c

Group 6c

2016

2017

2019

2019

2020

2020

T1

T2, T3, T4, T5

T3, T4, T6

T5, T7

T1, T5, T7

T1, T5, T7

1.0 x 1.0

1.0 x 3.0

1.0 x 1.0

0.75 x 1.5

1.0 x 3.0

6, 12

6, 12

6, 15

6, 8, 10, 12

62

43

46, 71

CF

CF, LI

CF

CF

FTG

HSG, FTG

HSG, FTG

FTG

6, 8, 10, 12, 15 30, 120, 139 CF, LI, LE, SC FTG, HSG

M1

M1

M1, M2

M2

M2, M3

M2, M3

0.3 x 0.3, 0.36 x 1.1 4, 5, 6, 8, 10, 12, 15 74, 84, 24e

a

Samples from BMWi-AiF-ZIM: Gläsernes Glas (Funding code: ZF4051701GM5). Samples from Fachverband konstruktiver Glasbau e.V. c Samples from BMWi-WIPANO: BENAF (Funding Code: 03TNH011F). d Not used for evaluation in chapter 8. e Samples 0.36m x 1.1m with holes and notches. b

7 Interpane 8 Interpane

- iplus 1.1T, see Table 5.3. - Stopray Vision-50T, see Table 5.3.

38 CF, LI, LE, SC FTG, HSG

5.3 Influence from Geometry Parameters

67

5.3 Influence from Geometry Parameters Based on the following glass-specific parameters, influencing factors could be determined qualitatively.

5.3.1 Thickness Tempered architectural glass is commonly processed in nominal thicknesses from 3 to 15 mm, depending on the level of tempering (HSG up to 12 mm). The stressoptical law from Eq. 2.47 and Eq. 2.48 describes a constant relationship between thickness and optical retardation. This also becomes evident from observing the isochromatic and retardation images recorded in M1. The influence of the thickness on the measurable retardation values is presented using the glass specimen from group 1. Fig. 5.5 demonstrates the alteration of the isochromatic images with rising glass thickness. The magnitude of the retardation values increases obviously. While Isochromatic Images of Tempered Glass with Different Thicknesses

Figure 5.5 Effect of thickness on optical retardation in tempered glass. Isochromatic images of samples (0.36 x 1.1 m) from group 1 recorded in M1 (RGBP). Red frames are displayed in Fig. 5.6.

retardations of 0 to 250 nm are observed in the glass area (zone 1), retardations exceeding 1000 nm are detectable at the edge (zone 2) and corner (zone 3). These regions with high retardation values must be excluded from a subsequent evaluation

5 Photoelastic Measurements on Tempered Flat Glass

68

(a) Retardation Images in 2D

(b) Retardation Distribution in 3D

Figure 5.6 Effect of thickness on optical retardation in tempered glass. Detailed view of the red areas from Fig. 5.5 in the 2D false-color plot (a) and 3D surface plot (b).

of anisotropy effects, c.f. section 7.1. Therefore, only retardations in the glass area (zone 1) are considered in further consideration. Below a thickness of 8 mm, low retardations with black-grayish interference colors are to be expected. Above a thickness of 8 mm, white interference colors appear in increasing intensity and thus retardation with increasing thickness, see Fig. 5.6 (a). In addition to the punctual level of retardation, the distribution of interference colors over the glass surface is also of interest for subsequent evaluation of anisotropy phenomena. In the 2D isochromatic image, frequent changes between black and white interference colors can be observed. Examining this spatial distribution in detail in the 3D plot of Fig. 5.6 (b), wave-shaped surfaces with more or less prominent minima and maxima can be identified as a function of the glass thickness.

5.3.2 Size Conventional tempered architectural glass varies in size from 1 m2 to 50 m2 for specific facade projects, c.f. Feirabend et al. (2020). For the geometries studied in table 5.2, it was concluded that for the analysis of optical retardations resulting from the tempering process, a minimum size of 1 m2 should be given. Smaller geometries, such as the smallest geometry (Fig 5.7 (a)) or also the standard geometry (Fig. 5.7 (b)) for specimens from EN 1863 (2012); EN 12150 (2015) are unsuitable. First, a larger glass area (zone 1) is not available for analysis because this area

5.3 Influence from Geometry Parameters

69

Size Dependency

Figure 5.7 Effect of sample size on optical retardation in 12 mm fully tempered glass panes. Isochromatic images of different sample sizes (a to d) recorded in M1 (RGBP). Sample (a) and (b) from group 1. Sample (c) from group 2 and (d) from group 3, both tempered in T3.

of relatively homogeneous residual stress state cannot develop undisturbed by the other zones 2 and 3. Second, the vast majority of tempering furnaces are optimized for producing large-scale component geometries. Consequently, the quality of small samples cannot be compared to the quality of samples of large-scale components. Therefore, only specimens with a minimum size of 1 m2 were measured from group 2 onwards in the present work, see Fig. 5.7 (c) and (d).

5.3.3 Holes and Cut Outs Point-fixed glazings of tempered glass are popular in facade and roof constructions. For this purpose, the glass is drilled or cut out to install it afterwards to a substructure. Depending on the edge distances, the hole diameter, and the glass thickness, residual stress states can overlay and possibly reduce the strength, see Dix et al. (2021b). When analyzing the glass specimens with holes and cut-outs

5 Photoelastic Measurements on Tempered Flat Glass

70

Effect of Holes and Cut Outs in Tempered Glass

Figure 5.8 Effect of holes and cut outs on optical retardation in 12 mm tempered glass. (a to c) Isochromatic images of samples without holes (a), with different hole diameter (b) and with cut-outs (c), recorded in M1. Detail (d) shows high retardation areas created from superposition (black arrow). Detail (e) reveals low (white arrow) and high retardation regions (blue arrow) depending on corner design.

(Group 1), higher optical retardations were observed than for unaltered samples. In Fig. 5.8 (a to c), the effects are exemplarily shown for 12 mm thick glass sheets. For evaluating anisotropy effects where the focus is on the glass surface, it is interesting to note that increased retardations occur in the vicinity of holes. These retardations increase in case of multiple hole arrangement (Fig. 5.8 (d)). Cut-outs cause more or less retardation depending on whether the corners are sharp-edged (blue arrow) or rounded (white arrow), see Fig. 5.8 (e). However, both geometry effects have to be considered during the design process.

5.4 Influence from Glass-Specific Parameters 5.4.1 Type of Glass As described in Chapter 3, the raw glass in the architectural application is clear soda-lime-silicate glass (SLS-CF) or, in highly transparent applications, SLS with reduced iron content (SLS-LI). Due to rising energy prices and the associated increase in building physics requirements for glass, it is often coated. Two temperable coatings, Low Emissive (LE) and Sun Control (SC), are tested in this work. The advantage of a temperable coating is that the glass can be stored directly at the

5.4 Influence from Glass-Specific Parameters

Table 5.3

71

Luminous and solar characteristics of used glass types according to Interpane (2019). Single Glassa

SLS-CF SLS-LI SLS-LE SLS-SC a b

Insulating Glassb,c

τe [%]

ρe [%]

αe [%]

T [%]

ρv [%]

αv [%]

81 90 -

7 8 -

12 2 -

81 b 50 b

12 b 17 b

10 b 39 b

Monolithic glass pane 6 mm. Insulating glazing: Glass 6 mm - 16 mm Argon - Glass 6 or 4 mm.

Effect from Glass Type

Figure 5.9 Effect of glass type on optical retardation in 6 mm fully tempered glass panes from Group 5, TF 5, measured in M2.

glass processor and produced as required. Further processing, e.g., insulating glass, can subsequently be carried out without an intermediate step, i.e., shipment to the coating plant. The typical luminous and solar characteristics according to EN 410, such as the solar transmittance τe (τv ), solar reflectance ρe (ρv ), solar absorptance αe are summarized in Table 5.3. The qualitative observation reveals that differences in retardation images can result from the type of glass, c.f. figure 5.9. While SLS-LI glass sheets do not differ substantially from conventional clear float glass (SLS-CF), the examined glass panes with temperable coatings exhibit recognizable (LE) to markedly (SC) higher retardation values. The reason can be assumed to be the strongly altered solar characteristics of the unilaterally coated glass panes. The heating and cooling of these glass sheets are more difficult to control via the tempering furnaces. Detailed evaluation can be found in Appendix A, Table A.3.

5 Photoelastic Measurements on Tempered Flat Glass

72

5.4.2 Tempering Level Heat-strengthened glass (HSG) and fully-tempered glass (FTG) are popular building products that differ in residual stress, strength, and fracture pattern, c.f. section 3.2. One would be wrong if expecting HSG to create lower optical retardations due to a slower cooling process and a lower pre-stress level. As much as the products FTG and HSG differ in the listed properties, they are very similar in forming optical retardations. The cause can be found in Eq. 2.48. Here, the integral of the principal stress differences is decisive. Subjectively, it appears that the lower prestressed heat-strengthened glass often produces slightly higher retardations. However, tendencies to higher or lower retardation formation cannot be clearly attributed to the tempering level and is predominantly dependent on the manufacturer or the used furnace. Variations can be recognized in the distribution of retardation values over the glass surface, the pattern. For example, thick HSG tends to have higher retardations in the edge and corner areas than FTG. A cross pattern is often evident in HSG and a kind of blurred cross or dot pattern in FTG, see Fig. 5.10. Further investigations and detailed quantitative evaluations are examined in section 8.2 on this aspect. Influence from Tempering Level

Figure 5.10 Effect of tempering level on optical retardation in 10 mm SLS-CF glass panes: FTG (a) and HSG (b) from Group 5, TF 7, measured in M2.

5.5 Influence from Furnace Parameter

73

5.5 Influence from Furnace Parameter The tempering furnace, its loading, and control system represent the part in which the manufacturer can partly intervene and influence the retardation pattern. A distinction can be made here between fixed and variable setting parameters. Furnacespecific parameters that can only be changed to a limited extent are, for example, the type of heating (radiation, partial or full convection), transport roller and air nozzle distances, arrangement of heating elements and center supports. Variable settings for individual furnace control are, for example, the heating and cooling durations, quenching pressure of the air cooling, and oscillation velocity. However, even these parameters are limited since the critical settings for fulfilling the product quality (strength, fracture pattern, and tolerances) must not be influenced. In this work, therefore, the effect of the furnace loading with position and orientation of the glass panes is examined.

5.5.1 Glass Position In a standard tempering furnace, a glass sheet of 2.8 m x 6.0 m can be processed into HSG and FTG. Currently, the largest flat glass geometry that can be tempered is 3.6 m x 20.0 m9 . For an energy-efficient and economical usage of the tempering furnace, often several sheets are tempered simultaneously. The impact of furnace loading on the retardation pattern was investigated as a parameter variation in specimen group 4. Glass sheets in a multiple-surface arrangement, Fig. 5.11 (a), and a single-line arrangement, Fig. 5.11 (b), were tempered and measured using the M2 measuring system. Examining different furnace loadings and the resulting retardation images, it becomes evident that they differ in pattern and level of retardation. The front and rear glass panes (PL1, PR1, PL3, PR3, PM1, PM3) tend to show higher retardation values than the glass panes in the middle. The reason is assumed to be the different temperature distribution in the heating and cooling process. In addition, the patterns vary depending on the type of furnace loading, position A or position B. In B, a stripe forms in the center, and in A, rather a retardation plateau. In the future, there is a high potential for data-driven solutions (AI) in the optimization of furnace loading. The detailed evaluation results are displayed in Appendix A.

5.5.2 Glass Orientation The glass orientation in the tempering furnace is typically dictated by the geometry of the glass and the furnace, as well as the effort to reduce optical distortions, 9 sedak

GmbH & Co. KG.

74

5 Photoelastic Measurements on Tempered Flat Glass

Influence from different Glass Position

Figure 5.11 Effect of different glass positions in the furnace on the optical retardation pattern in 15 mm SLS-CF glass panes (FTG): six glass sheets (a) and three glass sheets (b) from Group 4, TF 7, measured in M2.

like roller waves. In Group 3, the influence of orientation was tested on rectangular glass sheets arranged orthogonally or longitudinally in the furnace. Passage perpendicular to the direction of transport is impossible for glass larger than 3 m and is increasingly rare. However, it is frequently applied to smaller glass panes to efficiently and economically utilize the furnace. Fig. 5.12 shows an example of the typical retardation images of a furnace load with identical glass panes that are tempered in two orientations. A difference between the distribution of high retardation values, the retardation pattern, is significantly visible. While longitudinally transported glass sheets exhibit a stripe with high retardation in the middle of the glass pane. Orthogonally moved glass panes have an irregular pattern in areas without glass behind it. It is assumed that a non-homogeneous temperature distribution has caused the formation of these retardations.

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The elongated stripes at samples with Position PL, PM and probably already result from the unavoidable temperature gradient surface to edge. Again, similar to section 5.5.1, the location of the sample affects their retardation values, as the outer glass panes subjectively show higher retardations than the middle pane PM. The experimental investigations indicate that many factors cause optical retardations and influence the retardation pattern. Influence from Glass Orientation

Figure 5.12 Effect of glass orientation in the furnace on the optical retardation pattern in 6 mm SLS-CF glass panes from Group 3, T3, measured in M1.

Apart from the presented factors, the optimization to a homogeneous and low retardation pattern has to be conducted oven-individually. The methods introduced in chapter 7, can be used to evaluate the retardation images and are intended to assist in assessing the anisotropy quality. Results are detailed in Appendix A.

6 Experimental Field Studies on Tempered Flat Glass Optical anisotropy effects in tempered glass are described as partially disturbing since they only become visible to the human observer under specific environmental influences and viewing conditions, c.f. section 3.4. To correlate the subjectively perceived optical effects with the results of the photoelastic measurements and thus objectify the problem, a test facility in the form of a facade is being designed based on the state of knowledge, see Fig 6.1. A series of observational studies on the visibility of anisotropy effects in tempered glass are performed at the outdoor test rig.

6.1 Design and Construction the Test Facility The test facility was designed and finally erected in 2020 at the Labor fuer Stahlund Leichtmetallbau GmbH in Kissing (Bavaria), Germany. It was located on-site that surrounding objects do not cast shadows, and the reflection image in the glass facade is minimally disturbed. The stationary test rig consists of a self-constructed facade that allows a simple installation of the test panes mounted on a re-used pillar jib crane. The crane can be rotated 360° to aim different facade orientations, see Fig. 6.2. The facade is made of a steel frame with movable mullions and transoms, allowing flexible arrangement of different sized tempered glass panes, see Fig. 6.1 (b). For this purpose, mounting rails1 and set-on-top profiles2 were welded on the steel substructure, c.f. Fig. 6.1 (c). The dead weight of the glass is transferred via bearing blocks and wind loads are transferred by means of a pressure plate system into the substructure. The facade area covers a total of 20 m2, with a width of 4 m and a height of 5 m. A black light-absorbing background can be added inside the facade using a lifting system to investigate background scenario effects. Simultaneously, sky polarization measurements will be conducted using the polarimeter from section 4.6. 1 HM

40/22, HALFEN GmbH. SI, RAICO GmbH.

2 Therm+

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_6

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Design of Outdoor Test Facility

Figure 6.1 (a) 3D scheme of the test rig with its main components. (b) Drawing of the test rig in front view with various glass arrangements. (c) Horizontal section with facade connection detail. Sketches adapted from Dix et al. (2022d).

Test facility for Observation of Anisotropy Effects in Tempered Glass

Figure 6.2 Test facility in front (a) and top view (b) in west (c), south (d), and east (e) facade orientation.

6.2 Setup and Specimen

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6.2 Setup and Specimen (a) Facade View from Right

(b) Facade View from Left

Figure 6.3 3D scheme with observation grid, frequently used positions P1, P2 and P3 as well as the angle of sun to facade orientation γ.

From 20 July 2020 to 24 February 2021, observation studies were carried out for twelve days on two series with tempered glass sheets installed in the outdoor test stand. The observations were accompanied by measurements of the incoming partially polarized daylight via polarimeter. A digital camera3 with 17 mm wideangle lens.The camera was mounted on a tripod to capture different exposure scenarios under identical viewing conditions. Fig. 6.3 shows how the glass samples were observed, and images were recorded in a fixed grid and from specific positions (P1, P2, and P3). The observations made by the author with the naked eye were simultaneously documented. From the specimens already photoelastically measured in Chapter 5, six uncoated clear glass panes from Specimen Group 5, Tempering Facility 1 (Table 5.2), were selected and installed for the first series of observations. The panes of glass located in the facade below specimens 5 and 6 are not considered in this thesis. The analyzed samples have different thicknesses (8 mm and 10 mm) and tempering levels (Fully tempered (FTG) and heat-strengthened (HSG)). The monolithic glass panes are 750 mm wide, and 1500 mm long and were measured with method M3 (PPSM). The results of the photoelastic measurements are collected and displayed in Fig. 6.4 (a) and (b) as false-color plots with respective scales. The arrangement of the samples is simultaneous to the installation situation in the test rig. The 3 Nikon

D5500 with Sigma lens

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glass sheets differ significantly in the amount of retardation and their spatial arrangement (pattern), c.f. Fig. 6.4 (a). The azimuthal images of Fig. 6.4 (b) give additional information about the direction of the principal stresses. (a) Retardation Images - CF

(b) Azimuthal Images - CF

Figure 6.4 Results of photoelastic measurements (M3) of clear tempered glass samples. (a) Retardation images and azimuthal images (b) in false color 2D plots.

(a) Retardation Images - SG

(b) Azimuthal Images - SG

Figure 6.5 Results of photoelastic measurements (M3) of tempered glass samples with coatings or made of low iron glass. (a) Retardation images and azimuthal images (b) in false color 2D plots.

A second observation series investigated whether findings from clear glass can be transferred to special glasses (SG). For this purpose, the six clear glass panes

6.3 Influence from the Building Environment and Use

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(CF) were replaced by two samples with low E coating (LE), two with solar control coating (SC), and two samples of low iron glass (LI). The tempered glass plates of the second observation series are from sample group 5, tempering facility T5. The dimensions differ from the first series only in the glass thickness, here thicknesses of 10 mm and 12 mm were used for the investigation. The retardation (a) and azimuthal images (b) shown in Fig. 6.5 were recorded in advance in the laboratory using the M3 measuring system. The tempering levels are heat-strengthened for samples 1, 2, 5, and 6 and fully tempered for samples 3 and 4. The level of retardation present in the samples are nearly similar for all glass panes. To analyze the effect of the coating, samples were installed with coating facing the inside (1 and 3) and outside (2 and 4) of the facade. The evaluation of the samples according to the methods defined in chapter 7 is shown in Appendix B.

6.3 Influence from the Building Environment and Use 6.3.1 Background Lighting The lighting situation in the interior of a building, here background illumination, varies depending on its use. In principle, a distinction can be made between bright and dark illuminated backgrounds. If a building is less used or in a state of construction, the background lighting is usually off, i.e., dark. On the contrary, if the building is used frequently and the interior is well lit, e.g., office use, the lighting situation is bright. In order to simulate the two lighting situations, observations were performed in the field study with maximum (bright) and minimum (dark) background lighting. Maximum means without and minimum with a curtain 4 which absorbs most of the light transmitted through the glazing, see Fig. 6.6. Both images (a) and (b) were captured at minor time intervals under similar environmental conditions. The comparison of the two images shows a significant difference depending on the background. In the reflection image without a curtain, Fig. 6.6 (a), the observer does not recognize any anisotropy effects in the tempered glass panes with the naked eye. In contrast, interference colors are visible in sample 2 when adding the curtain in Fig. 6.6 (b). The diagonal stripe pattern shines in the colors graywhite with blue turbidity. In Fig. 6.6 (b), this is marked with a red arrow. In all observations performed by the author, no anisotropy effects could be perceived with the naked eye and bright background. Conversely, prominent interference colors could be perceived with a dark background, depending on the existing retardation in the glass. 4 Black

Molleton curtain, company allbuyone.

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(a) Bright Background

(b) Dark Background

Figure 6.6 Reflection image from observation point P3 in south facade orientation with bright (a) and dark (b) background. The white frame enclosing sample 2 shows clear differences in the visibility of the anisotropy effects, see also red arrows in (b).

6.3.2 Reflection Disturbances When viewing a facade made of glass, the visibility of anisotropy effects can be disturbed in the reflection image. In the field study, these disturbances were clouds or surrounding buildings and objects. Assuming a clear blue sky that is reflected in a glass facade, cloudiness in the reflection causes anisotropy effects to be more challenging to perceive. Fig. 6.7 compares two reflectance images taken on September 09th, 2020, from observation point P2, with the facade oriented to the west. In the region of the clouds, the interference colors from Fig. 6.7 (a) can not be perceived by the observer in Fig. 6.7 (b). The naked eye cannot distinguish between the grayish-white cloud color and the whitish interference colors. Comparable is the case with buildings or objects when they appear in the reflection image. While cloud cover depends on the weather and varies with time, reflections from surrounding buildings or solid objects are invariant. Fig. 6.8 shows the typical interfering reflections that occurred in the respective facade orientations of the test facility. The disturbing reflections were primarily

6.3 Influence from the Building Environment and Use

(a) Cloudless Sky Reflection

Figure 6.7 sky(b).

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(b) Cloudy Sky Reflection

Reflection image of sample 6 in west facade orientation, with cloudless (a) and cloudy

Reflection Images with Disturbance from Surroundings

Figure 6.8

Reflection disturbance in west (a), east (b) and south (c) facade orientation.

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located in the lower samples 7 and 8. Therefore the upper specimen 1 to 6 could be observed without restrictions. The facade orientation to the north was not investigated because of the interfering reflections of the adjacent test hall.

6.4 Influence from Viewing 6.4.1 Viewing Angle (a) Brewster Angle

(b) Perpendicular View

Figure 6.9 (a) Reflection image in south facade orientation from observation point P3 near Brewster’s Angle. (b) Reflection image in south facade orientation from observation point P3 in perpendicular view. Red arrows marks visible retardations and yellow arrow slightly visible retardations.

A facade can be observed from a wide variety of viewing situations. In this field study, the facade was observed from different positions and angles from the outside. From state of the art in section 2.4, it is known that incident parallel polarized light (p-polarized) is not reflected at the outer glass surface under Brewster’s angle. Thus, according to theory, anisotropy effects resulting from optical retardation in the glass sheets are most clearly perceptible to observers standing at the Brewster angle. The extreme cases, perpendicular viewing, and viewing from

6.4 Influence from Viewing

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the Brewster angle were tested in the investigations. Fig. 6.9 exemplifies the reflectance image’s alteration when changing the viewing angle. Comparing the images (a) and (b) in detail, striking differences are visible, especially for the glass samples 2 and 7. When viewed perpendicular, no interference colors are visible. Only when the angle in the viewing plane approaches the Brewster angle again do very slight interference colors in gray-blue become perceptible in sample 2. Observing almost simultaneously from the lateral Brewster angle, intense interference color patterns in light gray and white-blue grow visible in samples 2 and 7.

6.4.2 Viewing Position In this section, the influence of changing the viewing position is examined. The viewing position includes the variables, front and side distance to the facade. Suppose one keeps the angle to the facade and only varies the viewing position along a given grid. In that case, each glass pane can be examined holistically for anisotropy effects from the Brewster angle. This was investigated for the whole day on September 04, 2020, in the south facade orientation. From 4:45 p.m. onwards, interference colors became partly visible in the glass panes, depending on the present retardation levels. Fig. 6.10 demonstrates the alteration of the reflection image when the observer’s position is changed. The individual images are labeled with the axis names from Fig. 6.3. Detailed observation reveals that with increasing distance along axis 2 and 3, anisotropy effects become more perceptible. When shifting the camera from axis A to C, the retardation corresponding to the Brewster angle can be observed in the form of interference color patterns. At intersection A3, close to observation point P3, almost all visible anisotropy effects at the facade were recognizable in the reflection image. Therefore, observation points P3 and P2 are suitable for observing maximum visual anisotropy effects.

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Alteration of Viewing Position

Figure 6.10 Reflection image in south facade orientation from various grid intersections, captured on 04. September 2020, at 17:15.

6.4 Influence from Viewing

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6.4.3 Viewing Direction and Sun Position The different facade orientations allow a variety of viewing and observation scenarios of the glass panes. Factors that could be examined for the first time are considering the influence of the viewing direction and the position of the sun on the interference image. The sun’s course and its position depend on the time of day and location. On-site, in the Northern Hemisphere, it typically rises in the east, peaks at midday, and sets in the west. Depending on the season, the course of the sun and its height varies. In this section, the glass facade has been observed from the left (P3) or from the right (P2) in the Brewster angle for anisotropy effects. During the field study, various phenomena were identified at different times of day and facade orientations. No visible interference colors occur when the sun is in the direct reflection of the facade. Consequently, visual assessment of anisotropy effects is practicable only in the shadow of the facade or with the sun behind the viewer. As illustrated in Fig. 6.11, depending on the position of the sun and the viewing direction, either dark-field or bright-field retardation patterns are generated. The kind of patterns are known from section 2.6 and Fig. 4.4. Therefore, the polarization direction of the incident light beam and the viewing direction are assumed to be the causative factors. Interference colors from retardation in a bright field were much more difficult to detect than in a dark field. The intensity of these dark-field and bright-field patterns vary throughout the day. In the shadow of the facade, both types of patterns can be observed simultaneously from different viewpoints, as displayed in Fig. 6.12. However, due to its (a) Bright-Field Pattern

(b) Dark-Field Pattern

Figure 6.11 (a) Reflection image in west facade orientation from (a) observation point P3 (left view) and (b) P2 (right view).

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whitish interference colors, the dark field pattern (a) is more perceptible than the dark color pattern from the bright field (b). Fig. 6.13 shows exemplary for the south facade orientation that a dark field pattern can appear in the morning and in the evening depending on the position of the sun and the viewing direction. (a) Dark-Field Pattern

(b) Bright-Field Pattern

Figure 6.12 Reflection image of sample 6 in east facade orientation from (a) grid intersection C2 (left view) and (b) F2 (right view).

(a) Dark-Field Pattern (Right View)

(b) Dark-Field Pattern (Left View)

Figure 6.13 Reflection image in south facade orientation with similar pattern from (a) observation point P2 (right view) at 09:00 and (b) from P3 (left view) at 17:30.

6.5 Influence from Skylight Polarization

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6.5 Influence from Skylight Polarization In section 2.2.3, the Stokes parameters S0 , S1 , and S2 were presented, which are measured by the constructed polarimeter of section 4.6 and whose values can describe the state of linearly polarized light. They also allow the evaluation of the linear degree of polarization p (LDoP) and the angle θ, which describe the orientation of the polarization. In the study, reflection images were taken from the same observation points at the Brewster angle for two to four hours on several days, and simultaneous polarization measurements were performed. The sky polarimeter was aligned in the light incidence direction of the reflection image. Thus, when viewed at the Brewster angle, the polarimeter was positioned at a light incidence angle of about 56° to the facade. Per measurement time point, sky polarization measurements were then performed in six-degree rotations along the polarimeter tilt direction ξ. Fig. 6.14 shows exemplary reflectance images (a), the individual Stokes parameters S0 , S1 , and S2 (c to e) as well as LDoP (b) and θ (f) obtained for the examinations on 12 February 2021 in the period from 10 to 12 o’clock. Fig. 6.14 (a) demonstrates how clearly the perceptibility of the anisotropy effects in the reflection image differs from the time of day and the sun’s angle to the facade orientation γ. While at γ = 127◦ the interference colors are only slightly visible, at γ = 90◦ they become clearly visible. The 3D curves of the polarization measurements (Fig. 6.14 b to f) provide a graphical overview of how the values change with time and as a function of the measurement direction ξ. For further evaluation, the measurement direction of ξ equals 57◦ (red circle in Fig. 6.14 (b) to (f)) is applied. This direction was chosen based on the law of reflection and the corresponding observation in the Brewster angle. Evaluating these measurement points, it is noticeable that p decreases slightly towards noon, while θ clearly approaches the value 45◦ . This results from the decrease in S1 and the increase in S2 over the same period. It indicates that not only the degree of polarization p but especially the direction of the linear polarization θ with its Stoke parameters S1 and S2 play a role in the evaluation of the perceptibility of anisotropy effects. Therefore, for future investigations, it is recommended to evaluate the described parameter and collect data over a more extended period.

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(a) Reflection Images

(b) LDoP p [−]

(c) S0 [−]

(d) S1 [−]

(e) S2 [−]

(f) θ [◦ ]

Figure 6.14 (a) Reflection image from sample 2 in west orientation from 12 February 2021 with low (10:10 o’clock) and high intense anisotropy effects (11:40 o’clock). Results of sky polarization measurement in 3D false color plots (b to f).

6.6 Visual Intensity of Anisotropy Effects

91

6.6 Visual Intensity of Anisotropy Effects Most of the factors that led to a maximum intensity of anisotropy effects from retardation in single tempered glass have been already presented in the individual sections. Table 6.1 summarizes these findings for observation with the naked eye. In addition, further examples of minimum and maximum visual intensity of anisotropy effects in clear and coated glass panes are shown with the results of polarization measurements. Fig. 6.15 displays the different intensities of the anisotropy effects in sample 2 (clear float) during the observation from the fixed observation points P2 or P3 at different times of the day under a cloudless sky. It is noticeable that the pattern of the interference colors does not change, whereas their intensity varies strongly. At perpendicular orientation of the facade to the sun, γ ≈ 90◦ the most intense, i.e., maximum, anisotropy effects could be observed in Fig. 6.15 (f). Various Anisotropy Intensities in Dependency on Observation Time

Figure 6.15 Reflection images with corresponding sun orientation and measured polarization values. Images captured in east facade orientation from P3 on 11 February 2021 at 12:35 (a) and 15:15 (b). In south facade orientation from P3 on 11 February 2021 at 16:05 (c) and 17:05 (d). And in west facade orientation from P2 on 12 February 2021 at 10:10 (e) and 11:40 (f).

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Table 6.1

Factors leading to minimum and maximum visual intensity of anisotropy effects.

Minimal Intensity

Maximum Intensity

-

-

Reflection disturbances or cloudy sky Bright illuminated background Perpendicular observation angle Bright-field pattern Direct sun light on the facade or γ > 120◦ - p|S2 | and θ ≈ 0◦

Clear blue sky in the reflection Dark background Observation in Brewster’s angle Dark-field pattern Facade lies in the shade and γ = 90 to 100◦ - with p>0.2, |S1 |«|S2 | and θ ≈ 45◦

In the diagrams of the polarization measurements of Fig. 6.16, the Stokes parameters, p, and the polarization direction θ can be found. These results are consistent with the findings of section 6.5 and Table 6.1. The Stoke parameters change significantly depending on the time and the sun’s position. This is most evident in the orientation θ of the incident polarized light. The maximum intensity of the interference colors in the reflection image prevails at θ ≈ 45◦ and a negligible fraction of S1 compared to S2 . Results of Sky Polarization Measurements - Clear Glass

Figure 6.16

Results of different parameters depending on facade orientations and daytime.

Next, the findings from the observation of coated and low iron glass panes, here termed special glasses, are presented. Fig. 6.17 shows that the conditions under which anisotropy effects become visible in the facade’s reflection image can also be

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6.6 Visual Intensity of Anisotropy Effects

applied to special glasses. However, the intensity of the anisotropy effects appears to be strongly influenced by the solar characteristics of the coating, c.f. Table 5.3. Strong Intensity - Special Glass

Low Intensity - Special Glass

Figure 6.17 Reflection images from coated and low iron glass captured in east facade orientation from P3 on 22 February 2021 at 12:25 (a) and 15:00 (b). More Information of installed samples are shown in Fig. 6.5.

Results of Sky Polarization Measurements - Special Glass

Figure 6.18

Results of different parameters depending on facade orientations and daytime.

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Glass panes with solar control coatings have high absorbing and reflecting properties, and these seem to change the reflection color, which also influences the interference colors, i.e., the anisotropy effects. Nevertheless, for coatings that have high transmittances in the visible range, such as sample 2 (SLS-LE) in Fig. 6.17, the differences between (a) and (b) are clearly perceptible to the human eye in the intensity of the anisotropy effects. The simultaneously recorded measured values (a) of the incident partially polarized daylight and another measured value with facade orientation west (b) are presented in Fig. 6.18. Here, the findings from section 6.5 and table 6.1 can also be confirmed

6.7 Correlation between Measurement and Observation The previous investigations prove that the visibility of anisotropy effects varies significantly and can be perceived differently. A measuring method that detects the optical retardation independent of all these factors already in the tempering facility is essential for evaluating the anisotropy effects. The correlation between the results of the photoelastic measurements and the maximum visible anisotropy effects from the observation series reflection images is now followed in this section. First, clear glass (SLS-CF) without coating is analyzed. Fig. 6.19 compares the known retardation images (a) with the reflection images (c). In samples 1, 3, and 5, almost no anisotropy effects (orange arrows), i.e., different interference colors, become perceptible to the observer in (c). The extensive color patterns in sample 2 and sample 6 (red frame) are much more striking. The retardation images from (a) confirm these findings. Areas with high retardation values correlate with grayish or white interference colors. The excellent correlation becomes even more evident when comparing the black and white patterns from the threshold images (c) with the reflection images (a). In the images in (c), the white areas represent retardations equal to or above the selected threshold T = 75 nm, and conversely, the black areas are below T. That the threshold level of 75 nm is well chosen as a kind of human perceptibility threshold is also indicated by the retardation paths from diagram Fig. 6.19 (d). These paths run horizontally in samples 3 and 4, and the locations are marked in (a) by a white dash-dot line. The analysis of the paths reveals that in sample 3, the threshold in the center of the glass plate is only slightly exceeded by 78 nm. In contrast, in sample 4, the retardation values often exceed or approach the threshold of 75 nm. This circumstance affects the visible interference colors, which are much more dominant in sample 4 than in sample 3.

6.7 Correlation between Measurement and Observation

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Thus, for clear glass, it can be stated: An excellent correlation between the maximum intensity of anisotropy effects in the field study and the retardation images is present. Therefore, photoelastic measurements on tempered glass can be recommended to simulate anisotropy effects in real installation situations. Correlation with Clear Float Glass

Figure 6.19 Retardation images (a), azimuthal images (b) and reflection images (c) of the installed SLS-CF samples. (d) Comparison of retardation values of sample 3 and sample 4 along horizontal section (see (a)).

Next, special glass panes with coating or low-iron glass are analyzed in Fig. 6.20. Identical to Fig. 6.19, retardation and threshold images are compared with the reflection image (c). Here it is shown that in sample 4, the sample with the solar control coating on the outside, no anisotropy effects could be perceived when observing the facade, although high retardation values were measured in the sample.

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Here it is shown that in sample 4, the sample with the solar control coating (SLS-SC) on the outside, no anisotropy effects could be perceived when looking at the facade, although high retardation values were measured in the sample. The reason is likely the position and type of coating. Because the thin silver layer is outside the glass pane, most of the polarized light is directly reflected or absorbed. The proportion of transmitted light was assumed to be insufficient for perceiving interference colors. Sample 3, on the other hand, with solar control coating on the inside of the facade, shows deviations in the reflection color. These correlate with the areas of high retardation values in figure (a). However, the reflectance image of sample 3 still differs significantly from samples 1, 2, 5, and 6. These samples, here SLS-LI and SLS-LE, which have similar solar properties to clear float glass (SLS-CF), also achieve a good correlation between retardation (a), threshold (c), and reflection images (b). Correlation with Special Glass

Figure 6.20 Retardation images (a), azimuthal images (b) and reflection images (c) of the installed SLS-LI, SLS-LE and SLS-SC samples. (d) Comparison of retardation values of sample 1 and sample 2 along horizontal section (see (a)).

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In addition, the evaluation of the paths (Fig. 6.20(d)) shows that the faintly perceptible interference colors in sample 1 (orange arrow) only slightly exceed the selected perception threshold of T = 75 nm in contrast to sample 2. The anisotropy effects in sample 2 (red arrows) are clearly visible to the observer. In the case of glass panes made of SLS-LI, samples 5 and 6, it even appears that due to the 9 % higher transmittance compared to SLS-CF, see Table 5.3, retardation from 70 nm already becomes perceptible. For coated glass, it can thus be stated that the solar characteristics have a significant influence on the perceptibility of interference colors from anisotropy effects. However, for glass with comparable solar properties to clear glass, there was a very good correlation between photoelastic measurement and observation in the field study. Glass with solar control coatings or coatings that strongly influence the solar characteristics need to be investigated in more detail in future field studies.

7 Methods for evaluating Anisotropy Effects in Glass In this chapter, digital image processing methods (DIPM) for evaluating optical anisotropy effects in tempered glass are presented. The author has partly published the methods described here in his publication: Dix et al. (2021a). Finally, a continuation of the texture analysis to the combinate feature CCP from Contrast C and Cluster Prominence CP is presented in section 7.5.

7.1 Evaluation Zone For the evaluation of the retardation images, evaluation zones are introduced according to Fig. 7.1. These are necessary because, as discussed in section 3.3, very high optical retardations can occur near edges, corners, and holes in contrast to the glass surface. These unavoidable retardation values must be excluded so that they do not distort and falsify the evaluation, see Dix et al. (2021a). Therefore, three evaluation zones were applied to the retardation images in this thesis. The individual glass panes is divided into the areas edge zone (E), hole zone (H) and main zone (M). The edge zone E and the hole zone H are completely excluded from the evaluation. Apart from high retardation values in this area, they are also often hidden in the installation state, e.g., by cover strips. Fig. 7.1 shows exemplary the division of the evaluation zones represented as an isochromatic image (M1) with high retardation near the edges. The inner dimension of the edge zone is defined as approximately 20 % of the respective clear width and height of the glass. For specific glass sizes, e.g., particularly large or very narrow panes, extreme values have been defined to limit the percentage value. For glass thicknesses equal or less than 8 mm, width wa and length wa are set to a minimum of 50 mm and a maximum of 200 mm. Respectively, for thicknesses greater of 8 mm, the maximum value is set to 350 mm. With increasing glass thickness, higher maximum values wa and length la are required because higher retardations propagate near the edges, c.f. Fig. 5.5. Since only glass panes without holes were evaluated, no dimension for zone H is given here. Therefore, only the remaining ’main’ zone M is used for the evaluation in section 8. © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_7

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7 Methods for evaluating Anisotropy Effects in Glass

Evaluation Zones

Figure 7.1 HSG-SC.

Classification of the evaluation zones with dimensions for the sample G6_TF1_16_10-

7.2 Statistical Method - Quantile Value Statistical methods are the first step in evaluating quantitative information. The information, in this case, retardation values per pixel, can be processed in grey values of 8 or 16 bit (0-255, or 0- 65,535 numerical values), see Fig. 7.2 (a). To ensure that higher retardation values are not cropped at 255, the data acquisition in the used measuring systems (see section 5.1) is performed in a 16-bit data format. As displayed in Fig. 7.2 (b), with the help of histograms, the frequency distribution of the grey value intensities occurring in the image can be easily visualized. Since no values above 255 nm were found in the samples from section 5.2, data processing in MATLAB® was carried out in the 8-bit format. First-order statistical methods are effective for quick and simple determination of comparable characteristic values from the empirical distribution of intensity values of the retardation image. The empirical cumulative distribution function ECDF depicts these values in a diagram which is the basis for our statistical analysis, see Fig. 7.2 (c). All values of the image are listed from zero to the largest retardation value along the x-axis. The y-axis shows the sum of the relative frequencies of the

7.2 Statistical Method - Quantile Value

101

individual values. In engineering, α-quantiles, such as the 5% fractile value, are often used and well known for evaluating test series. (a) Grey-Value Image

(b) Histogram

(c) Statistical Values from ECDF

Figure 7.2

Evaluation via statistical methods of first order.

An α-quantile splits data into the parts α ∗ 100% and (1 − α) ∗ 100%. Assuming that the 60% quantile is being searched for, the characteristic xα can be found in which at least 60% of the characteristic values are smaller than or equal to xα and at least 40% of the characteristic values are larger than xα . In this investigation the 95% quantile x95 was used under the assumption of normal distribution. The calculation of the quantile values can be expressed mathematically for k = n · α in integers and n number of occurring pixels as: 1 xα = (x(k) + x(k+1) ) 2

(7.1)

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7 Methods for evaluating Anisotropy Effects in Glass

An ideal glass without residual stress differences and optical retardations would have x95 =0 nm. A lower value thus represents a higher glass quality with less optical retardation, which can lead to undesirable interference colors.

7.3 Threshold Method - Isotropy value

103

7.3 Threshold Method - Isotropy value Threshold methods are common image processing tools and belong to a group of algorithms that are mainly used for segmentation of digital images. Using thresholding, the source image (grey-value image) is converted into a binary image, returned as an m-by-n logical matrix, see Gonzalez et al. (2011). Threshold methods can be implemented quickly due to their simplicity and segmentation results can be calculated with little effort. Furthermore, they offer the possibility to integrate human-subjective perception thresholds into the evaluation. Threshold methods can be divided into global, local and hybrid threshold techniques. The more complex techniques are mainly used for medical image segmentation or document image analysis, c.f. Gatos (2014), Drass et al. (2021). The simplest thresholding method replace each pixel in an image with a black pixel if the image intensity is less than some fixed constant T , or a white pixel if the image intensity is greater or equal than that constant. If I(x, y) is the original greyscale image, then the resulting binary image B(x, y) is defined as: ( B(x, y) =

1, if I(x, y) ≥ T 0, if I(x, y) < T

(7.2)

Fig. 7.3 (c) shows the resulting binary image for applying a threshold of T = 75 nm on an exemplary retardation image Fig. 7.3 (a). From the binary image, Fig. 7.3(c), the ratio of white pixels NI,white to the sum of NI,black and NI,white pixels can be calculated. This ratio value in percentage is called isotropy value IsoT and can be described as: IsoT = 100 −

NI,white NI,black + NI,white

(7.3)

The intention of the isotropy value by Dehner and Schweitzer (2015) was to introduce a method that considers a threshold where anisotropy effects from retardation become visible to the observer. With increasing isotropy value, the optical anisotropy quality should improve. Section 6.7 has already revealed that a perceptibility threshold of T = 75 nm is well chosen. In Dehner and Schweitzer (2015) the orientation of the principal stress directions is also considered when determining the isotropy value. Hereby, the azimuthal image A(x, y) (Fig. 7.3 (b)) is used to calculate a new threshold image with: ( 1, if I(x, y) ≥ T, andA(x, y)[−90 : −75], [−15 : 15]or[75 : 90] BA (x, y) = (7.4) 0, if I(x, y) < T, orA(x, y)[−74 : −16]or[16 : 74]

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104

Determination of Threshold Images and Isotropy Value

Figure 7.3 (a) Retardation image with evaluation zone M (inside of white dotted rectangle) and azimuthal image (b) of an exemplary 10 mm tempered glass pane (sample G5_TF5_86_10-T-LE) as false color plots measured in M3 (PPSM). Threshold image without (c) and with consideration of azimuthal image (d).

Fig. 7.3 (d) shows the resulting threshold image with consideration of the stress orientation (azimuthal image). When comparing Fig. 7.3 (c) and (d), only a difference in the corners and at the edge of the glass pane can be seen for this example. From Fig. 7.3 (d), the isotropy value IsoT,A can be determined as before using Eq. 7.3. By excluding the evaluation zone E, the difference between B and BA is minimized to the isotropy value, see Fig. 7.3 (a). The Orientation of the principal stresses was not considered for further evaluation in this thesis as the azimuthal image can only be recorded with method M3, see Fig. 4.10.

7.4 Texture Analysis Texture analysis with the determination of textural features according to Haralick et al. (1973) is a method for recognizing and evaluating striking objects and regions of interest in images. This technique has been used successfully for years to evaluate medical images or remote sensing images (Soh and Tsatsoulis (1999); Aborisade et al. (2014)) and also in the building industry, e.g., for the evaluation of pummel-test images, c.f. Schuster et al. (2020). Hidalgo and Elstner (2018) applied these methods for the first time on retardation images from sample Group 2 (Ta-

7.4 Texture Analysis

105

(a) Grey Value Image with Intensities

(b) Direction ζ and Distance ds

Figure 7.4 (a) Exemplary grey-value image with corresponding intensities for an image with Ng = 8. (b) Exemplary application of direction ζ and distance ds for a symmetric (GLCM).

ble 5.2), acquired with measuring method M1 at the University of Applied Sciences Munich. The aim is to develop an evaluation criterion that, in addition to firstorder statistical methods, can also consider the distribution of retardation values of the image over the area. Texture analysis starts here, and since this first study was promising, the applicability of these methods was further investigated in Dix et al. (2021a). Texture analysis is also called the second-order statistical method because it includes intensities of pixels and the spatial relationship of pixels for statistical analysis. The integration of the spatial component can be realized with different methods, c.f. Soh and Tsatsoulis (1999); Gonzalez et al. (2011). The Grey Level Co-occurrence Matrix (GLCM) is a proven method to relate pixel intensities with neighboring pixel intensities. When creating such matrices, parameters must be defined in advance, influencing the evaluation of the textural features. Parameters required to create a GLCM are the direction ζ, the step size or distance ds , and the number of the grey levels Ng . Fig. 7.4 (a) represents an exemplary grey-value image with its corresponding pixel intensities for a (GLCM) with eight grey levels, i.e., Ng = 8. I(p, q) is the intensity level of the analyzed pixel and I(p + ∆x, q + ∆y) is the intensity level of the neighbour pixel separated by a spatial distance ds = max(|∆x|, |∆y|) in a given direction ζ. Mathematically, Hidalgo and Elstner (2018) define the GLCM as: P (i, j) =

( n X m X 1 if I(p, q) =

i and I(p + ∆x, q + ∆y) = j

p=1 q=1

0 otherwise

(7.5)

In this thesis, rotationally invariant symmetric (GLCM) matrices with directions of ζ is 0◦ , 45◦ , 90◦ and 135◦ are calculated and then normalized for texture feature extraction. Fig. 7.4 (b) displays the application of ζ, the effect of symmetry, and the distance ds for calculating the GLCM. Haralick et al. (1973) has introduced 14 features, of which Hidalgo and Elstner (2018) applied two to grey value images with

7 Methods for evaluating Anisotropy Effects in Glass

106

stored retardation values. While the feature Contrast (C) represents the amount of local grey level intensity variation in an image, the feature Cluster Prominence (CP) defines areas of constant intensity deviating from GLCM mean values. For a “constant” image with no variation, C is zero. C=

Ng −1 Ng −1 X X i=0

(i − j)2 P (i, j)

(7.6)

j=0

Ng −1 Ng −1

CP =

X X i=0

(i − µi + j − µj )4 P (i, j)

(7.7)

j=0

with Ng −1 Ng −1

µi =

X X i=0

i P (i, j)

(7.8a)

j P (i, j)

(7.8b)

j=0

Ng −1 Ng −1

µj =

X X i=0

j=0

Further texture features were examined in Dix et al. (2021a), according to Haralick et al. (1973), Albregtsen (2008), and Aborisade et al. (2014). These investigations have shown that other texture features, such as dissimilarity, entropy, and cluster shade, are not superior alternatives to the proven C and CP features proposed by Hidalgo and Elstner (2018).

7.5 Method and Combined Textural Feature CCP In Dix et al. (2021a), a method was presented and tested to rapidly compute the textural features Contrast C and Cluster Prominence CP from different format retardation images in a uniform and size-independent approach. For this purpose, the first step is a size normalization of the evaluated image area M to a reference image area Iref and introducing geometry factors fr and fI,ref . Iref was defined as 10.000 px2 . The scaling to the normalized image area Iref is performed in Matlab® using the function "imresize," the interpolation method "nearest neighbor", and a scaling factor which is defined here as the image scale factor fI,ref . For the calculation of fI,ref the ratio factor fr is determined first, which considers the ratio length

107

7.5 Method and Combined Textural Feature CCP

lM,O to width wM,O of the original retardation image, see Fig. 7.1. Both factors are mathematically expressed as fr =

lM,O , wM,O q

fI,ref =

Aref fr

wM,O

(7.9)

(7.10)

.

The second step, the calculation of the symmetric GLCM in Matlab® , contains the implementation of Ng = 8 and the so-called offset size, which includes the distance d and the four directions of ζ. To create comparable GLCM, d has to be normalized to ds via the offset size factor fof f,ref , which can be described as q fof f,ref =

Aref fr

wM

(7.11)

.

Here wM is the true width of evaluation zone M in ’mm’, which has to be captured during the acquisition of the retardation images. Multiplying fof f,ref and the true distance dtrue in ’mm’ gives ds for the formation of the GLCM. As dtrue equals 100 mm were chosen from Dix et al. (2021a). ds = fof f,ref · dtrue

(7.12)

After forming the rotationally invariant and averaged GLCM, the third step is to determine the textural features C and CP, as shown in Eq. 7.6 and Eq. 7.7. In Hidalgo and Elstner (2018) and Dix et al. (2021a), it was shown that the features Contrast C and Cluster Prominence CP generate additional knowledge about the homogeneity and spatial clustering of high retardation values. In the last step, a combination criterion CCP of the two individual features is introduced by normalization. Here, the two single feature results Ca and CPa are mathematically added due to the respective non-linear relationship and the normalization to the maximum measured individual values1 . CCP =

√  √  4 1 C CPa √ a +√ 4 2 Cmax CPmax

(7.13)

The normalization leads to CCP values between 0 and 1. A low CCP value represents a good optical quality with low retardation values in the glass sheet and a homogeneous spatial distribution of retardation values. As the value rises, 1 Worst

Sample: G6_TF1_16_10-HSG-SC;

√

Cmax =2.0 (1.96);

√ 4

CPmax =3.0 (2.99).

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7 Methods for evaluating Anisotropy Effects in Glass

the level of retardation values generally increases, as well as the heterogeneity and spatial accumulation of higher retardation values. Finally, the flow chart in Fig. 7.5 represents the scheme by which textural features can be extracted step by step from the original retardation image, independent of the glass format. The normalization of the reference area, the calculation of the geometry factors, the formation of the GLCM, and the determination of C, CP, and CCP are accomplished in a calculation algorithm written in the program Matlab® . Flow Chart of Calculation Algorithm

Figure 7.5

Flow chart of the calculation algorithm used in Matlab® .

8 Evaluation and Concept This chapter introduces a concept that evaluates the homogeneity and quality of the tempering process with respect to the interference colors and patterns (anisotropies) perceivable by the human observer based on retardation images of tempered architectural glass. First, the evaluation methods presented in Chapter 7 are compared to determine commonalities, deviations, advantages, and weaknesses. Subsequently, the final evaluation of the retardation images, acquired with measuring system M2, is performed on glass samples of groups 3 to 6. This includes the identification and verification of the influencing factors of chapter 5 and the classification of the glass panes into quality classes. Finally, a concept is presented and discussed with which anisotropy effects on the perception of facades can be reduced in the future.

8.1 Assessment of Evaluation Methods For this purpose, the isotropy values Iso75 , the quantile values x95 and the texture feature CCP are calculated from the retardation images of the specimens from Groups 3, 4, 5, and 6 (Table 5.2), which were all acquired with the validated measuring system M2. The individual correlation charts in Fig. 8.1 show the single results of all samples, the correlations to each other using the respective regression fit function, as well as the scatter band in which the values vary. In addition, via the square of the correlation coefficient R2 , the scatter of the data to the fitting function is described, c.f. Hedderich and Sachs (2016). R2 ranges from zero to one, with one being a ideal approximation. The analysis illustrates which values the individual evaluation methods achieve for the 491 specimens in the photoelastic tests. Here: • Iso75 values range between 51 % to 100 % • x95 values vary between 31 nm and 160 nm • CCP values range from 0.16 to 1.0 When looking at the diagrams in Fig. 8.1, it becomes apparent how clearly the results of the isotropy values differ from those of the x95 and the CCP values. © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_8

109

110

8 Evaluation and Concept

Correlation of the different Evaluation Methods

Figure 8.1 Comparison of photoelastic measurement results on samples of groups 3, 4, 5, and 6 (M2) evaluated by Iso75 versus x95 (a), Iso75 versus CCP (b), and CCP versus x95 (c).

8.1 Assessment of Evaluation Methods

111

On the Scattering of Isotropy Value

Figure 8.2 Comparison of the horizontal and vertical scattering of the isotropy value based on the retardation images (a to d). ECDF of the four retardation images with the individual intersections for the threshold of 75 nm (e). Table with characteristic values for the different samples (f).

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8 Evaluation and Concept

On the contrary, with R2 = 0.97, there is a good correlation between the CCP and the x95 values. Below an Iso75 value of 90 %, the scatter band increasingly widens. The cause of the broadband scattering is analyzed here, using four selected specimens (marked in blue in Fig. 8.1), representing the outer edges of the scatter band. For these samples, Fig. 8.2 (a-d) displays the respective retardation images, in (e) the empirical cumulative distribution functions (ECDF), and in (f) the results of the evaluation methods. The retardation images of sample Fig. 8.2 (a) were compared to sample (b) to investigate the horizontal scattering, similar isotropy values at different quantile and CCP values. While sample (a) has a larger area of retardation values slightly above the threshold T=75 nm, sample (b) shows a strong clustering of retardation values above 100 nm in the center of the glass sheet. Iso75 incorrectly rates sample (b) as better due to the proportionally smaller area above the threshold, neglecting the high retardations and clustering, see Fig. 8.2 (f). In contrast, the x95 and CCP detect the high retardation values and correctly classify sample (a) as better glass quality. The reason for the underestimation of the high retardation values can be found in the ECDF of the individual samples. There it can be seen that while sample (a) has a constant slope, sample (b) bends and flattens out with increasing retardation. The isotropy value cannot capture this phenomenon, which explains the high horizontal scatter in Fig. 8.2 (a) and (b). The analysis of the scatter in the vertical direction, different isotropy values at similar quantile and CCP values, is performed on retardation images of samples in Fig. 8.2 (c) and (d). While sample (c) has a much larger area with retardations of about 100 nm to 125 nm, sample (d) shows a stripe with retardation of 125 to a maximum of 150 nm only in the center of the glass pane. Iso75 evaluates, due to the proportionally larger area, sample (c) by 39 % worse than the sample (d). Compared to the other two methods, the difference ∆d−c is significantly higher. Thus, the x95 value of sample (c) classifies a recognizably worse quality. However, the CCP value evaluates sample (c) only minimally worse than (d) since CCP considers the apparent accumulation of high retardations in the center of the pane. The ECDF in Fig. 8.2 (e) shows the cause for the significant deviation (cross marks). There, it can be seen that sample (c) has constantly higher retardations than sample (d). Sample (d) contains mostly low retardations and only kinks significantly at about 90 %. Due to the definition of the threshold at 125 nm, the isotropy value has no possibility of considering this phenomenon and incorrectly evaluates sample (d) overly positively. Fig. 8.1 (c) demonstrates the strong correlation between x 95 and CCP. However, a small scatter is evident in the horizontal direction, with similar CCP values at different x95 values. The cause is assumed to be the consideration of the spatial arrangement of the retardation and its influence on the textural features. The quantile method can not consider these effects, which results in a

8.1 Assessment of Evaluation Methods

113

Consideration of Retardation Accumulations

Figure 8.3 Comparison of two exemplary retardation images (a and b) to illustrate the impact of the accumulation of high retardation values on the different evaluation methods (c).

difference ∆d−c of -18 nm. In the vertical direction, identical x95 values at different CCP values, a slight scatter is evident. Based on two selected retardation images in Fig. 8.3 (a) and (b), it is demonstrated how the spatial arrangement of the retardation values is included in the evaluation of CCP. Thus CCP evaluates the strip-shaped arranged retardations in (b), which amount to approx. 110 nm, worse than the finely distributed retardations in (a), which amount to approx. 90 nm. Finally, the advantages and disadvantages of each evaluation method are listed and summarized in a recommendation. Iso75 + Consideration of a threshold T that includes the visual perception of anisotropy effects, here T=75 nm from chapter 6. + Threshold image pattern simplifies the representation of the false color retardation image. + Short algorithm with simple implementation in commercial anisotropy scanners. − For thin glass, no or only marginal differentiation between good or low quality is possible, as the value is often above 95 % or reaches 100 %.

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114

− For values below 85 %, obvious scatter in the retardation images occurs for identical isotropy values since the method does not distinguish whether the included retardation value is slightly or significantly above the threshold. − The method does not consider the spatial distribution of the retardation values over the glass pane. x95 + The statistical method is fundamentally known in the construction industry and is commonly applied for the strength characterization of building products. + Short algorithm with easy implementation in commercial anisotropy scanners. + In the evaluation, high retardation values are considered more appropriately than in Iso75 . + The results showed a good correlation with the CCP value. − Single, punctual retardation peaks above 95 % of the pixel set are not considered in the evaluation. − The method also does not consider the spatial distribution of the retardation values over the glass pane. CCP + The texture analysis method considers the spatial distribution of retardation values over the glass sheet. + The evaluation is performed in respect of homogeneity and accumulation of high retardation values in the image. + All retardation values are included in the evaluation, regardless of their level. + Fast algorithm that can be implemented in commercial anisotropy scanners. − For comparable results, the algorithm must be applied according to the specifications of this thesis. − The robustness of the method in different online anisotropy scanners during production remains to be tested.

8.2 Anisotropy Quality of Tempered Flat Glass

115

8.2 Anisotropy Quality of Tempered Flat Glass In this section, the anisotropy quality refers to the evaluation of the measured retardation images of the glass samples and not to the optical interference colors in the facade. Here, it was shown in section 6.7 that further investigations are necessary due to the complex color interaction for glass panes with solar control coating. Nevertheless, the retardation images represent the uniformity of the tempering process and the existing optical retardation in the glass. Therefore, determining the optical quality based on retardation images is correct and reasonable at this point. The presentation of the evaluation results of the retardation images is preferably based on the x95 value since it is currently widely applied in the industry, and thus the results can be compared more easily. Fig. 8.4, Fig. 8.5, and Table 8.1 show the evaluations on the basis of which the quality classes are defined in section 8.3. The results of all individual test specimens sorted by manufacturer are illustrated in Fig. 8.5. Fig. 8.4 illustrates the statistical evaluation of the results of Table 8.1. There, the individual results of the specimens are evaluated independently of the specimen group and manufacturer and are recombined depending on the glass type, thickness, and tempering level. The simplified representation of the mean values (black marker), standard deviations (whisker), and extreme values (red marker) can quickly provide conclusions for the viewer. The following findings can be derived: • As the thickness of the glass increases, the x95 value and the level of anisotropy also rise while the optical quality decreases. However, the large scatter of the extreme values shows that equally low x95 values can be obtained with thick glass. • The choice of the glass type influences the x95 value. While there is no significant deviation between clear glass CF and low iron glass LI for the test series (n>8), a slight deviation can be seen between CF and LE and a significant deviation between CF and SC. Here, coated glass generated higher x95 values for the same thickness, i.e., lower quality. Fig. 8.6 (a) demonstrates this by the difference of the respective glass type xLI,LE,SC with xCF and its division by xCF .

8 Evaluation and Concept

116

Comparison of Evaluation Results

Figure 8.4 Diagram representing the results of Table 8.1 of different glass types, glass thicknesses and tempering levels.

• The tempering level, i.e., the type of tempering process, also influences the anisotropy quality. On average, HSG samples have consistently higher x 95 values than fully tempered glass samples. Fig. 8.6 (b) shows this, based on the deviation and in relation to the mean values ((xHSG − xF T )/xF T ) of the respective glass thickness and glass type. This influence is clearly visible for series with a number of samples greater than three. However, Fig. 8.5 shows that depending on the tempering facility, the opposite could also be observed for samples of TF 3 and 4. There is no generality, and it is recommended to consult the manufacturer in advance. For understanding what effect a certain x95 value has on the retardation image is shown in Fig. 8.7. Here, as an example for samples from group 5, the alteration of the retardation image with increasing x95 value is displayed. From the sample with a minimum value of 31 nm (a) to the sample with a maximum value of 146 nm (l).

8.2 Anisotropy Quality of Tempered Flat Glass

117

Representation of all individual Results of x95

Figure 8.5 Representation of all evaluated samples, acquired with M2, sorted by tempering facility, glass thickness, glass type and temper level. The evaluation is based on the x95 value.

8 Evaluation and Concept

118

Table 8.1

Statistical evaluation of x95 values from sample Group 3 to 6, see Table 5.2. CF FTG

t [mm] n min. [nm] max. [nm] ¯ x [nm]

σsd [nm]

HSG

6

8

10

12

15

6

8

10

12

81 32 80 44 10.1

19 44 91 58 11.2

20 59 95 69 8.4

27 73 143 97 18.5

64 88 155 114 14.0

32 33 85 57 12.2

18 53 110 72 15.4

20 58 122 94 18.1

25 69 152 103 23.6

LI FTG

t [mm] n min. [nm] max. [nm] ¯ x [nm]

σsd [nm]

HSG

6

8

10

12

6

8

10

12

14 31 74 47 13.1

2 66 114 90 24.0

1

15 73 110 93 11.1

14 50 72 60 7.9

2 69 81 75 6.0

1

15 69 139 108 21.9

91 LE

SC

FTG

t [mm] n min. [nm] max. [nm] ¯ x [nm]

σsd [nm]

HSG

FTG

HSG

6

10

6

10

6

10

6

10

16 38 83 60 12.0

8 54 101 78 15.0

16 46 89 77 10.6

23 63 109 87 10.1

13 54 114 83 20.9

22 71 130 88 11.3

15 66 114 84 12.8

9 99 173 123 21.0

(a) Influence from Glass Type

Figure 8.6

121

(b) Influence from Tempering Level

Difference between mean values for glass type (a) and tempering level (b).

8.2 Anisotropy Quality of Tempered Flat Glass

119

Retardation Image depending on the Evaluation Result

Figure 8.7

Arrangement of different retardation images with increasing x95 value, from (a) to (l).

8 Evaluation and Concept

120

8.3 Evaluation Concept 8.3.1 General The results obtained from the previous investigations are transferred into a concept for measuring and evaluating optical anisotropy effects in tempered flat glass. First, manual classification defines three categories of anisotropy quality based on photoelastic measurement. Then, requirements for the measurement and the procedure of the evaluation concept are presented. Finally, a short discussion is given on the benefits and disadvantages of the concept.

8.3.2 Definition of the Quality Classes The three classes, A, B, and C, were determined for categorizing the anisotropy quality of monolithic, flat, tempered glass sheets. Individual limit values for the examined thicknesses from 6 to 15 mm are given in Table 8.2. It also provides limit values for glass sheets evaluated either by the x95 or CCP methods. Limit values for the isotropy value method are not specified here. Table 8.2

Quality classes depending on evaluation method

Glass t

A

Quality Class x95 B

Ca

A

Quality Class CCP B

Ca

[mm]

[nm]

[nm]

[nm]

[-]

[-]

[-]

≤ 70 ≤ 80 ≤ 95 ≤ 115 ≤ 130

> 70 & ≤ 95 > 80 & ≤ 120 > 95 & ≤ 140 > 115 & ≤ 155b > 130 & ≤ 165b

> 95 > 120 > 140 > 155b > 165b

> 0.43 & ≤ 0.57 > 0.49 & ≤ 0.71 > 0.57 & ≤ 0.82 > 0.68 & ≤ 0.90b > 0.76 & ≤ 0.96b

> 0.57 > 0.71 > 0.82 > 0.90b > 0.96b

≤6 8 10 12 15 a b

≤ ≤ ≤ ≤ ≤

0.43 0.49 0.57 0.68 0.76

For limit values higher than the specified values and for glass without measurement. Limit values deviating from DIN SPEC 18198.

Quality class A is defined as the class with the highest quality and the lowest risk of visible anisotropy effects. Class B combines a higher standard and shall avoid anisotropy effects resulting from an unnatural disturbance in the tempering process, e.g., failure of a heating element or blocked cooling nozzles. Class C has been defined as glass with lower limit values than class B. It also includes the case where glass manufacturers cannot measure and thus classify their glass panes using photoelastic methods. These glass panes then automatically fall into quality class C.

8.3 Evaluation Concept

121

Boxplot Distributions of the Test Results with Limit Values

Figure 8.8 Boxplots of the summarized test data subdivided according to glass thickness and with indication of the limit values of the respective quality class A, B or C. Evaluated according to x 95 method (a) and CCP method (b).

As a basis for defining the limits of the individual classes, the test results from Fig. 8.4 were used and presented in a simplified boxplot diagram (Hedderich and Sachs (2016)) only as a function of thickness. In Fig. 8.8, the boxplots of the test data are superimposed with the individual limit values of the quality classes, represented as colored areas and red dashed outlines. The 75 % quartile, the upper part of the box, was chosen as the upper limit for quality class A. The upper limit for quality class B was defined so that all the clear glass panes examined (CF, LI) could be included. This is based on the assumption that the investigated glass panes were not exposed to unnatural disturbances in the tempering process. The characteristic values exceeding the upper limits of quality class B are categorized in quality class C. The quality classes presented in this thesis have been integrated into DIN SPEC 18198 (2022). The limit values essentially correlate except for the values marked with footnote ’b’. The deviation results from considering additional measurement results of the participating industry partners.

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8 Evaluation and Concept

8.3.3 Requirements for the Measurement In order to generate reproducible measured values and results, the following requirements are specified for the measurement: • The measurement has to be conducted on flat monolithic glass panes under constant temperature. • Use of circularly polarized light in the measuring instrument. • The measurand is retardation in ’nm’ and optional azimuthal angle in ’

◦

’.

• Image resolution of at least 0.5 px/mm (M2 was 1.96 px/mm) for the evaluation of the characteristic values. A lower image resolution leads to a smoothing of retardation peaks and thus to a distorted evaluation. • Measurement range should cover 0 nm to 300 nm (till glass thickness of 15 mm). For measuring systems with a lower measuring range, the detectable glass thickness must be limited, or redundant measures must be taken to ensure that the retardations of the specimens do not exceed the measuring range. • Measurement accuracy shall be verified at several retardation levels (e.g., 0, 50, 75, 100, 125, 150 nm) and different specimen orientations as specified by the manufacturer. • Measurement protocol must include the characteristic values and the retardation image in false colors. Further details on accuracy and calibration as well as restrictions have been defined collaboratively in ASTM C1901 (2021) and DIN SPEC 18198 (2022).

8.3.4 Procedure of the Evaluation Concept Several steps are required to accomplish the concept for measuring and evaluating anisotropy effects in tempered flat glass. It starts with the retardation measurement of the individual glass sheet directly after production in the tempering furnace, considering the requirement from section 8.3.3. The captured retardation image is digitally processed, zone E and H are excluded, and evaluation zone M is evaluated according to the methods described in chapter 7. Finally, with the output of the characteristic values x 95 , and CCP, the quality class of the glass is determined. Fig. 8.9 illustrates the presented concept for the different anisotropy qualities of three 10 mm thick tempered glass sheets. A significant dissimilarity is evident to the observer from the retardation images, which are also present in the quality classes.

8.4 Discussion

123

Evaluation Concept

Figure 8.9

Schematic representation of the evaluation concept.

8.4 Discussion By introducing the objective concept, it will be possible to reduce visible anisotropy effects in glass constructions in the future, simply by selecting the highest quality class A. This minimization is exemplified by Fig. 8.10, with tempered glass panes in quality class A (left) and class B (right). The reflection images are captured at the outdoor test rig (Fig. 6.19) under worst-case conditions at the Brewster angle. With identical glass thickness of 10 mm and identical environmental and viewing conditions, fewer to almost no interference colors are visible in higher quality A (left). In the glass sheet with quality class B (right), the higher retardation values cause white interference colors resulting in an irregular pattern. As the level of retardation values increases in category C, more intense and colorful interference colors can be expected according to the Michel-Levy chart, c.f. Fig. 3.9. Different anisotropy qualities can be observed in the investigated glass sheets (Group 3 to Group 6). The distribution of the quality classes with respect to all glass specimen, and as a function of the level of tempering and the glass type, can be analyzed in the diagrams in Fig. 8.11. It is evident from these graphs that the majority of all the glass panes examined, 76 percent, achieve quality class A.

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8 Evaluation and Concept

Visual Difference between Quality Classes

Figure 8.10 Comparison of the visual impact of quality classes A (left) and B (right) under the same viewing and environmental conditions. Single reflection images of the glass panes are extracted from Fig. 6.19..

Quality class C represents a negligible proportion of two percent of all samples. The proportion of class A glass is even higher, 90 percent, if only fully tempered glass is considered. Conversely, the proportion of glass with quality class A decreases to 58 percent for a heat-strengthened glass. Fully tempered glass panes made of CF, LI, as well as those with LE coating, can achieve high optical quality. However, when solar control coating SC is applied, the proportion of glass with quality class A drops to 69 percent, with 17 percent classified as class B and 14 percent as class C. The heat-strengthened samples have worse characteristic values, resulting in a higher proportion of class B glass. For LI and LE glass, the proportion of class B is already close to 50 percent, which increases to 75 percent for heat-strengthened glass with SC coating. Quality class A could only be achieved for four percent of the glass panes, i.e., for one sample. As a result, it becomes apparent that tempered glass sheets in quality class A may not be delivered or only by many scraps, depending on the glass type or the tempering level. An increased reject rate then logically leads to higher unit costs. However, a quality class B could also be sufficient for solar control coated glass because, as the initial field studies in section 6.7 demonstrated, anisotropy effects became less visible to the observer compared to clear glass.

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Further research on a variety of monolithic glass panes with different coatings is necessary to complete the previous findings. The extension of the knowledge base to insulating and laminated glass needs to be investigated in the future. Distribution of the Quality Classes

Figure 8.11 Diagrams with division into quality classes A to C with indication of the respective number of samples (n). Starting from all glass sheets (top left), then depending on the tempering level FTG or HSG (top, middle and right), and finally subdivided depending on the glass type.

9 Summary and further Research This work presents a concept for evaluating optical anisotropy effects in tempered architectural glass. The strength-increasing manufacturing process of tempered glass is achieved by creating a residual stress state with compressive stresses at the surfaces and tensile stresses in the core. Unnatural and natural disturbances in the tempering process create residual stress differences, which cause artificial birefringence. Under partially polarized daylight, it can lead to perceptible interference color patterns (anisotropy effects) after installation in the building envelope. For this purpose, a common basis of necessary fundamentals from mechanics, optics, and photoelasticity is first prepared to present the primary relationships. In particular, in photoelasticity, which is essential here, the differences between linear and circular polariscopes and their effects on direction-independent measurement are illustrated and discussed. Motivated by the possibility of fully visualizing and measuring the optical retardation responsible for these interference colors, several photoelastic methods were presented in Chapter 4 and tested afterward. Also, a self-built polarimeter is presented to measure the sky polarization during the field study. Methods that are generally recommended for measuring optical retardation from residual stress differences are the RGB (RGBP), the Half-Wavelength (HWP), the MultipleWavelength Photoelasticity (MWP), the PSM with beam splitter optics, and the Pixelated Phase-Shifting method (PPSM). The RGBP, the MWP, and the PPSM were applied in measuring systems in the experimental laboratory investigations in Chapter 5. The accuracy of the novel photoelastic measuring systems was verified by measuring retarder plates with various retardation levels and in different orientations. M1 using RGBP, which was available at the beginning of the study, has a very high measurement range from zero to 1000 nm but achieved the highest deviations from the nominal values at retardations smaller than 75 nm. M3 applying PPSM showed very high accuracy regardless of orientation. However, it is limited due to the measuring range, which only resolves up to 120 nm. Higher retardation values in the glass pane lead to © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1_9

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misinterpretation. For specific tests, M1 was used due to its extensive measuring range, and M3 was required to determine low retardations and the azimuthal angle. Mainly the measuring system M2 (MWP) is used due to the acceptable accuracy and the high measuring range. In the experimental laboratory investigations, an unprecedented amount of retardation measurements were performed on tempered flat glass. Differentiated by manufacturing group, tempering facility, glass dimensions, glass type, tempering level, and measuring system, 736 specimens were examined. Before determining an evaluation criterion, a qualitative examination of the measurement results was done using isochromatic images and false-color retardation plots. Influences from the geometry, first of all, the glass thickness, are recognizable to the observer. The cause can be determined in the Wertheim Law in Eq. 2.48, where the thickness is included as a constant variable in the formation of the retardation value. Thus, in principle, higher retardations are observed in thicker glass. Influences from the choice of glass-specific parameters became apparent in a qualitative examination. In particular, the type of glass, clear or coated glass. In the retardation images of SLS-SC glass, significantly higher retardations were observed. The choice of tempering level, HSG or FTG, initially showed no distinctive differences in the amount of retardation but in the formation of the retardation pattern. HSG tended to have cross-shaped patterns, and FTG often showed a sort of blurred cross or dot pattern. The influence of furnace-specific parameters is diverse but is limited by fixed settings and the fulfillment of technical requirements, such as the product’s strength. A parameter that could be studied was the furnace loading, with different positioning and orientation of the glass in the furnace. Glass sheets positioned at the edge of the furnace and the batch showed qualitatively higher retardations. Different retardation patterns were also observed in the laboratory measurements depending on the transport direction, longitudinal or transverse. The experimental investigations were complemented by systematically conducted field studies and accompanying polarization measurements of the sky in Chapter 6. With the help of a rotatable facade test rig, optical anisotropy effects in tempered glass could be observed under different environmental and viewing conditions, thus expanding the state of knowledge. It was known that anisotropies in the reflection of the blue skylight, under the Brewster angle and a high degree of polarization, should be particularly visible. The investigations showed that the maximum intensity of the contained retardations, and interference colors, depend on further factors. Thus, visibility was increased when a dark background was introduced into the facade and when the viewing standpoint and the incident polarized light

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created a dark-field pattern. Furthermore, it is not the maximum degree of polarization but a polarization angle θ close to 45° that produces the maximum visible anisotropy effects. These correlate with an angle γ, sun to facade orientation, equal to 90° till 100° in an unclouded sky. Comparing the results of the field study and the laboratory tests show a correlation between the retardation measurement and the maximum visible anisotropy effects in the facade for the glass types CF, LI, and LE. A color deviation could be detected for glass panes with SC coating. The optical interference colors were not comparable to those of the clear glass and were subjectively less prominent for the same retardation values. Based on the maximum visible anisotropy effects and the analysis of individual samples, a perception threshold of the interference colors of T = 75 nm was determined in the field study. Chapter 7 presents known and novel digital processing methods for the evaluation of retardation images. Before application, the original measurement data were cropped to the evaluation zone M and extreme values at the edge and around boreholes were excluded. Then the 95% quantile value x95 was determined from the ECDF, the isotropy value Iso75 from the threshold image, and the CCP value via texture analysis. Whereas the first two methods are known, a new calculation algorithm was developed to form the new combined textural feature CCP. This algorithm determines the textural features C and CP from a GLCM rapidly and independently of size and combines them under normalization to CCP. In chapter 8, 491 samples, and thus retardation images, were analyzed and evaluated according to the previously described methods. First, the particular evaluation methods were compared and evaluated in correlation charts based on all samples. Then, the benefits and disadvantages of each method were presented. While the Iso75 , value is subject to a large scatter, the CCP and the x95 value correlate. The CCP value additionally considers the spatial distribution of the retardation values. In a subsequent detailed quantitative evaluation, the influencing variables of the qualitative analysis from the laboratory measurement could be confirmed. The glass thickness, glass type, and tempering level have the most significant effect on the resulting retardations in the glass samples. Based on the collected findings, limit values were defined for the classification into three different quality classes, A, B, and C, depending on the glass thickness and the evaluation method. The novel concept for evaluating optical anisotropy effects in tempered glass includes measurement, evaluation, and classification into quality classes. Since most anisotropy scanners are used in the online process at the end of the furnace, an immediate evaluation of the tempered glass pane is performed

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during production. With the choice of glass panes in quality class A, anisotropy effects in the glass building envelope can be reduced in the future. Further Research In the present work, open questions for improvement and extension have arisen in several research areas. The measurement techniques are very advanced due to the rapid developments in the last five years. The accuracy of the novel PPSM and the ability to record stress orientation in tempered glass enables new areas of interest. However, for a reliable measurement in architectural glass, the measurement range must be extended to 300 nm. Furthermore, no measurement system currently exists to inspect anisotropy effects in curved glass panes. Glass panes in the building industry often consist of several glass sheets in series, e.g., laminated glass and insulating glass. Their measurement with respect to anisotropy effects using photoelasticity is currently not provided for in the process chain. A superposition of the interference colors of each tempered glass is to be expected, and an increase, as well as a change of the effects, is likely. This superposition effect and the influence of highly reflective coatings on the visibility behind glass will be investigated. Therefore, the field study experience has to be extended with respect to test specimens with different solar control coatings in laminated and insulating glass. In addition, parameters leading to maximum visibility of anisotropy effects have to be developed when viewed from the inside out. The realistic simulation of the retardation superpositions considering the orientation of the principal stress and the solar characteristics of the glass, may become attractive for some prestige projects. The robustness of the CCP value method needs to be tested by implementing it in commercial anisotropy scanners. The perceptibility in terms of which anisotropy patterns are more disturbing to the observer needs to be widely investigated. For this, collecting more data and retardation patterns directly during production and using data-driven models will be of interest in the future. The further optimization of the individual tempered glass in connection with the furnace control could also be a step toward an intelligent furnace with the help of photoelasticity.

References Own Publications Dix, S., L. Efferz, S. Hiss, C. Schuler, and S. Kolling (2022a). “Spannungsoptische Untersuchungen an polymeren Zwischenschichten in Verbundgläsern”. In: Glasbau 2022. Ed. by B. Weller and S. Tasche. Dix, S., P. Müller, C. Schuler, S. Kolling, and J. Schneider (2021a). “Digital image processing methods for the evaluation of optical anisotropy effects in tempered architectural glass using photoelastic measurements”. In: Glass Structures & Engineering 11.6, p. 10. Dix, S., C. Schuler, and S. Kolling (2022b). “Digital full-field photoelasticity of tempered architectural glass: A review”. In: Optics and Lasers in Engineering 153. Dix, S., P. Di Biase, C. Schuler, and M. Feldmann (2017a). “Flächige und zerstörungsfreie Qualitätskontrolle mittels spannungsoptischer Methoden”. In: Glas im konstruktiven Ingenieurbau. Ed. by C. Schuler, pp. 150–159. Dix, S., L. Efferz, L. Sperger, C. Schuler, and S. Feirabend (2021b). “Analysis of residual stresses at holes near edges in tempered glass”. In: Engineered Transparency 2021. Ed. by B. Weller, J. Schneider, C. Louter, and S. Tasche, pp. 145– 162. Dix, S., B. Schaaf, T. Fiedler, and H. Sonnleitner (2017b). “Zerstörungsfreie Qualitätskontrolle - Neues Online-System zur Erfassung von Anisotropien”. In: Glaswelt 7, pp. 86–89. Dix, S. and C. Schuler (2018). “Untersuchungen an thermisch vorgespannten Gläsern mittels spannungsoptischer Methoden”. In: Glas im konstruktiven Ingenieurbau. Ed. by C. Schuler, pp. 165–176. Dix, S., C. Schuler, S. Kolling, and J. Schneider (2022c). “The relation between measurement and visibility of anisotropy effects in tempered glass. A case study.” In: Glass Performance Days. Tampere. Dix, S., K. Thiele, L. Efferz, C. Schuler, J. Schneider, and S. Kolling (2022d). “Test facilities and concept for the evaluation of optical anisotropy effects in tempered glass”. In: ICSA 2022 - The International Conference on Structures and Architectures. Aalborg. © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1

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Feldmann, M., R. Kasper, P. Di Biase, B. Schaaf, C. Schuler, S. Dix, and M. Illguth (2017a). “Flächige und zerstörungsfreie Qualitätskontrolle mittels spannungsoptischer Methoden”. In: Glasbau 2017. Ed. by B. Weller and S. Tasche. Berlin: Ernst & Sohn, pp. 327–338. Feldmann, M., C. Schuler, R. Kasper, P. Di Biase, B. Schaaf, S. Dix, and M. Illguth (2017b). “Methoden zur Erfassung und Analyse von Anisotropien bei thermisch vorgespannten Glasprodukten”. In: Konstruktiver Ingenieurbau - KI 2017.2, pp. 7–15. Schaaf, B., P. Di Biase, M. Feldmann, C. Schuler, and S. Dix (2017). “Full-surface and Non-destructive Quality Control and Evaluation by Using Photoelastic Methods”. In: Glass Performing Days. Tampere, pp. 130–134.

Standards ASTM C1048 (2018). Standard Specification for Heat-Strengthened and Fully Tempered Flat Glass. ASTM C1279 (2013). Standard Test Method for Non-Destructive Photoelastic Measurement of Edge and Surface Stresses in Annealed, Heat-Strengthened, and Fully Tempered Flat Glass. ASTM C1901 (2021). Standard Test Method for Measuring Optical Retardation in Flat Architectural Glass. Bundesverband Flachglas (2009). Guideline to Assess the Visible Quality of Glass in Buildings. DIN SPEC 18198 (2022). Measurement and evaluation of optical anisotropy effects in thermally toughened glass. EN 12150 (2015). Glass in building - Thermally toughened soda lime silicate safety glass - Part 1: Definition and description. EN 1863 (2012). Glass in buildings - Heat strengthened soda lime silicate glass Part 1: Definition and description. FKG (2019). Technical Note FKG 01/2019 -The visual quality of glass in building anisotropies in heat treated flat glass. Ed. by Fachverband konstruktiver Glasbau e.V. ISO 5725 (1994). Accuracy (trueness and precision) of measurement methods and results.

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Appendix A Experiments Results The quantitative evaluation results in the following tables complement the individual qualitative investigations in chapter 5. Table A.1 with M2).

Evaluation results of Fig. 5.9, comparison glass type, all Group 5 from TF 5 measured Sample

Results

Fig.

No.

x95 [nm]

(a) CF (b) LI (c) LE (d) SC

G5_TF5_04-6-FTG-CF-PR2 G5_TF5_16-6-FTG-LI-PR2 G5_TF5_98-6-FTG-LE-PR1 G5_TF5_120-6-FTG-SC-PR3

46 51 68 114

Iso75 [%]

CCP [-]

100 100 98 67

0.30 0.32 0.44 0.64

Quality A A A A

Table A.2 Evaluation results of Fig. 5.11, comparison glass position, all Group 4 from TF 7 measured with M2 (MWP). Sample

Results

Pos.

No.

x95 [nm]

Iso75 [%]

CCP [-]

PL1 PR1 PL2 PR2 PL3 PR3

G4_TF7_63-15-FTG-CF-PL1 G4_TF7_62-15-FTG-CF-PR1 G4_TF7_61-15-FTG-CF-PL2 G4_TF7_60-15-FTG-CF-PR2 G4_TF7_59-15-FTG-CF-PL3 G4_TF7_58-15-FTG-CF-PR3

106 121 97 98 109 123

73 69 81 82 74 66

0.58 0.75 0.53 0.57 0.61 0.73

A A A A A A

PM1 PM2 PM3

G4_TF7_57-15-FTG-CF-PM1 G4_TF7_56-15-FTG-CF-PM2 G4_TF7_55-15-FTG-CF-PM3

118 116 134

61 65 51

0.65 0.63 0.75

A A B

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1

Quality

145

146

A Experiments Results

Table A.3 Evaluation results of Fig. 5.12, comparison glass orientation, all Group 3 from TF 3 measured with M1 (RGBP). Sample

Pos.

No.

PO PR PM PL

G3_TF3_01-6-FTG-CF-PO G3_TF3_02-6-FTG-CF-PR G3_TF3_03-6-FTG-CF-PM G3_TF3_04-6-FTG-CF-PL

Results

x95 [nm]

Iso75 [%]

CCP [-]

69 74 62 82

96 94 97 92

0.35 0.43 0.37 0.56

Quality A B A B

The evaluation methods applied to these retardation images are presented in detail in chapter 7.

Appendix B Field Study Test Results In chapter 6 the field study results are presented. The samples and measurements included there have been analyzed in more detail here. The evaluation of these retardation images using the methods from chapter 7 are summarized in the following tables. Table B.1 Evaluation results of Fig. 6.4, clear glass samples measured with M2 (MWP) and M3 (PPSM), for observation in the outdoor test rig. (RGBP). Evaluation results from M2. Sample

Results

Fig.

No.

x95 [nm]

1 2 3 4 5 6

G5_TF1_29-10-FTG-CF-PM1 G5_TF1_31-10-HSG-CF-PM1 G5_TF1_18-8-FTG–CF-PM2 G5_TF1_21-8-HSG-CF-PM2 G5_TF1_30-10-FTG–CF-PM2 G5_TF1_36-10-HSG-CF-PM2

61 101 52 65 61 122

Iso75 [%]

CCP [-]

99 77 100 98 99 60

0.39 0.58 0.34 0.41 0.38 0.68

Quality A B A A A B

Table B.2 Evaluation results of Fig. 6.5, special glass samples measured with M2 (MWP) and M3 (PPSM) for observation in the outdoor test rig. (RGBP). Evaluation results from M2. Sample

Fig.

No.

1 2 3 4 5 6

G5_TF5_88-10-HSG-LE-PR2 G5_TF5_86-10-HSG-LE-PR1 G5_TF5_75-10-FT-SC-PL2 G5_TF5_76-10-FT-SC-PR2 G5_TF5_72-12-HSG-LI_PR3 G5_TF5_71-12-HSG-LI_PL3

Results

x95 [nm]

Iso75 [%]

CCP [-]

63 90 87 90 80 93

99 92 89 87 92 85

0.39 0.59 0.50 0.53 0.46 0.54

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2024 S. Dix, A Concept for Measuring and Evaluating Optical Anisotropy Effects in Tempered Architectural Glass, Mechanik, Werkstoffe und Konstruktion im Bauwesen 70, https://doi.org/10.1007/978-3-658-42029-1

Quality A A A A A A

147