Structural Mechanics Behavior of Transparent Thin Glass Polymer Laminates for High-performance Light Weight Glazing Applications

September 2014

Yuki Shitanoki

A Thesis for the Degree of Ph.D. in Engineering

Structural Mechanics Behavior of Transparent Thin Glass Polymer Laminates for High-performance Light Weight Glazing Applications

September 2014

Graduate School of Science and Technology Keio University

Yuki Shitanoki

Structural Mechanics Behavior of Transparent Thin Glass Polymer Laminates for High-performance Light Weight Glazing Applications

September 2014

A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering

Keio University Graduate School of Science and Technology School of Integrated Design Engineering

Yuki Shitanoki

ABSTRACT

Recent commercial availability of thin glass has raised the possibility of fabricating laminates with higher interlayer / glass thickness ratio. Because its major component is polymer, the thin glass laminates demonstrate significant strength / weight ratio advantages over monolithic glass or laminated glass made using conventional structures. However, structural behavior and weight reduction benefit of such unusual composite structures hasn’t been studied thoroughly. In this dissertation, structural behavior of transparent thin glass polymer laminates has been studied and design approaches for lightweight and structurally efficient thin glass laminates for various glazing applications have been provided. Chapter 1 reviews background of polymer glass laminates technology and recent trend for thin glass laminates. Chapter 2 introduces basic theories that describe flexure and fracture properties of glass laminates. Chapter 3 summaries chemistry and properties of component materials for glass laminates. Chapter 4 describes experimental methodology and detail setups used in this dissertation. Chapter 5 provides suitable mechanical models for glass laminates that treat the bending and stress concentration of the thin glass laminates. Chapter 6 demonstrates a simpler and non-destructive characterization method of time and temperature dependent shear relaxation modulus of polymeric interlayers. Chapter 7 provides rational and systematic approaches to predict fractural properties of glass laminates used for double-glass type photovoltaic modules. Chapter 8 quantitatively clarifies the potential and limits of weight reduction with thin glass laminates. The analysis also provides the methodology to design a thin glass laminate with target strength and light weightiness. Chapter 9 summarizes key findings in this dissertation and provides conclusions. The analysis and methodology presented in this dissertation provide a holistic process to predict mechanical behavior of thin glass laminate glazing and an approach to optimize its layer structures.

TABLE OF CONTENTS

List of Figures ................................................................................................................ vi List of Tables ................................................................................................................ xii Acknowledgements ..................................................................................................... xiv

Chapter 1 :

Introduction ................................................................................................1

References ............................................................................................................................... 5

Chapter 2 : 2.1

Theoretical Models for Glass Laminates ...................................................7

Preface ............................................................................................................................ 7

2.2 Viscoelastic Models for Interlayers ................................................................................ 8 2.3

Effective Thickness : Expression for Strength and Stiffness of Glass Laminates ........ 10

2.3.1 The Effective Thickness Concept ......................................................................... 10 2.3.2

Effective Thickness Experimentally Obtained by Four Point Bend Test .............. 10

2.3.3

Effective Thickness by Wölfel-Bennison Model .................................................. 14

2.3.4 The Enhanced Effective Thickness by Galuppi and Royer ................................... 16 2.3.5 2.4

Effective Thickness Delivered by the Composite Beam Model ........................... 17

Stress and Deflection of Plates Subjected to Lateral Load ........................................... 19

2.4.1 The Differential Equation for Plates ..................................................................... 20 2.4.2

Navier’s Solution for Four-side Simply-supported Plates .................................... 21

2.4.3 Two-side Simply-supported Plates ........................................................................ 23 2.4.4

Four-side Simply-supported Plate Subjected to Transverse Tension .................... 24

2.5

Glass Fracture: Statistical Approach to Treat Glass Breakage ..................................... 28

2.6

Conclusions .................................................................................................................. 29 i

References ............................................................................................................................. 30

Chapter 3:

Interlayer Materials and Sheet Glass ........................................................33

3.1

Preface .......................................................................................................................... 33

3.2

Poly-vinyl Butyral ........................................................................................................ 33

3.3

Ethylene Vinyl Acetate Copolymer (EVA)

3.4

Ethylene Methacrylic Acid Copolymer Based Ionomer .............................................. 35

................................................................ 34

3.4.1

Polymer Structures ................................................................................................ 35

3.4.2

Mechanical Properties ........................................................................................... 38

3.5

Float Glass .................................................................................................................... 41

3.5.1

Raw Materials for Float Glass (Soda-lime Glass) ............................................... . 41

3.5.2

Float Process ......................................................................................................... 42

3.5.3

Air Tempering ....................................................................................................... 42

3.6

Conclusions .................................................................................................................. 42

References ............................................................................................................................. 44

Chapter 4:

Experimental and Simulation Methods ................................................................ 45

4.1

Preface .......................................................................................................................... 45

4.2

Sample Preparation ...................................................................................................... 43

4.3

Four Point Bend Test .................................................................................................... 46

4.3.1 Testing Setups ....................................................................................................... 46 4.3.2

Electric Resistance Strain Gages ........................................................................... 48

4.3.3

Plane Stress and Rossete Analysis ........................................................................ 50

4.3.4

Linear Variable Differential Transformer (LVDT) ............................................... 53

4.3.5

Finite Element Model to Replicate the Four Point Bend Test .............................. 54

4.4

Sand Bag Load Test ..................................................................................................... 55 ii

4.5

Ring on Ring Test ........................................................................................................ 55

4.5.1

Basic Test Scheme ................................................................................................ 55

4.5.2

Correction for Thin Glass ...................................................................................... 56

4.6

Dynamic Mechanical Analysis ..................................................................................... 60

4.7

Conclusions .................................................................................................................. 60

References ............................................................................................................................. 61

Chapter 5:

Applicable Limit of Wölfel-Bennison Model to Thin Glass Laminates ....... 63

5.1

Preface .......................................................................................................................... 63

5.2

Experimental and Simulation ....................................................................................... 63

5.2.1

Optimization of Four Point Test Geometry ........................................................... 63

5.2.2

Experiment with Thin Glass and Thick Polymer Interlayer Laminates ................ 66

5.2.3

FEA of Thin Glass and Thick Glass Laminates .................................................... 67

5.3

Results .......................................................................................................................... 67

5.3.1

Four Point Bend Test Results ................................................................................ 67

5.3.2

Comparison of Effective Thickness by the Two Model by FEA .......................... 69

5.4

Discussion .................................................................................................................... 75

5.4.1

Connection from Wölfel-Bennison Model to Composite Beam Model ................ 75

5.4.2

Applicable Limits of Wölfel-Bennison Model ...................................................... 75

5.5

Conclusions .................................................................................................................. 77

References ............................................................................................................................. 78

Chapter 6: 6.1

Characterization of Shear Relaxation Modulus of Viscoelastic Interlayers ......... 79

Preface .......................................................................................................................... 79

6.2 Theory .......................................................................................................................... 81 6.2.1

Inverse Calculation of Effective Thickness Equations .......................................... 81 iii

6.2.2 6.3

Selecting Optimum Laminate Structures for Target Shear Modulus .................... 84

Experimental ................................................................................................................ 87

6.3.1

Characterization of Time and Temperature Dependent Shear Moduli by DMA .. 87

6.3.2

Four Point Bend Creep Test .................................................................................. 87

6.3.3

500mm × 500mm Size Uniform Load Test ........................................................ 88

6.4

Results and Discussion ................................................................................................. 89

6.4.1

Shear Relaxation Modulus Obtained by DMA Analysis ...................................... 89

6.4.2

Shear Relaxation Modulus Obtained by Four Point Creep Test ........................... 89

6.5

Conclusions .................................................................................................................. 95

References ....................................................................................................................... 96

Chapter 7: 7.1

Application to Structural Designing for Photovoltaic Modules ........................... 97

Preface .......................................................................................................................... 97

7.2 The Approach to Design PV Modules with the Required Load Resistance ................. 99 7.2.1

Step 1: Calculation of Effective Thickness of Modules ........................................ 99

7.2.2

Step 2: Parameterization of Installation Factors and Calculation of the Largest Maximum Principal Stress .................................................................................. 101

7.2.3 7.3

Step 3: Evaluating Glass Breakage Probability ................................................... 103

Calculation and Experiment ....................................................................................... 104

7.3.1

Load Test of Monolithic Glass to Obtain Ci of the Frame and Mounts .............. 104

7.3.2

Ring-on-ring Test of Monolithic Glass and Calculation of Allowable Stress ..... 104

7.3.3

Load Test of the Actual Module to Validate the Calculated Stress Values ........ 105

7.4

Results and Discussion ............................................................................................... 105

7.4.1

Ci Parameter Obtained from the Experiment ...................................................... 105

7.4.2 The Experiment to Obtain Allowable Stress of t1.1mm Glass ........................... 106 7.4.3

Determining Effective Area for Breakage Probability ........................................ 106 iv

7.4.3 Validation of the Calculation Scheme by Experiments of Actual Modules ........ 111 7.4.4 7.5

Estimation of Breakage Probability .................................................................... 111

Conclusions ................................................................................................................ 113

References ..................................................................................................................... 114

Chapter 8:

Weight Reduction Limits and Light Weight Designing ..................................... 115

8.1

Preface ........................................................................................................................ 115

8.2

Weight Reduction Ratio ............................................................................................. 115

8.3

Experimental .............................................................................................................. 117

8.4

Results ........................................................................................................................ 118

8.5

Discussion .................................................................................................................. 122

8.5.1 Theoretical Weight Reduction Limit..................................................................... 122 8.5.2 8.6

Design Approach for Light Weight Glass Laminates ......................................... 126

Conclusions ................................................................................................................ 134

Chapter 9:

Conclusions ........................................................................................................ 135

v

LIST OF FIGURES

Fig. 1-1

Implication of higher specific strength / stiffness with thin glass and stiff

interlayer laminate combinations. The stiff interlayer assumes SentryGlas® under 1 min load at 24 oC. .........................................................................................................................4

Fig. 2-1 Testing geometry of four point bend test. Specific testing equipment is shown in Fig. 4-2. At the left side supported point (x=0), both horizontal and vertical displacement are not allowed, but rotation is allowed. At the right side supported point (x= L2), vertical displacement is not allowed, but horizontal displacement and rotation are allowed. .............................................12

Fig. 2-2 Three ways of supporting edges of rectangular plates. ...........................................26

Fig. 3-1

Chemical structure of poly-vinyl butyral. ..............................................................34

Fig. 3-2

Chemical structure of poly-ethylene vinyl acetate copolymer. ................................35

Fig. 3-3

Synthesis of ethylene acrylic / methacrylic acid copolymer based ionomer. (a)

Polymerization of ethylene methacrylic acid compolymer, (b) Neutralization of carboxyl acid and formation of ionic cross-link. (Cited from ref.[3-4] .........................................................37 Fig. 3-4

Comparison of crystalline structure of ethylene acrylic / methacrylic acid copolymer

and ethylene acrylic / methacrylic copolymer acid copolymer based ionomer. (Cited from ref.[3-4]) ...............................................................................................................................37

Fig. 3-5

Relationship between coefficient of restitution and shore D hardness. (Cited from

ref.[3-4]) ...............................................................................................................................39

Fig. 3-6

Stress-strain curve of ethylene methacylic acid copolymer ionomer with different

neutralization. (Cited from ref.[3-4]) .....................................................................................40 vi

Fig. 3-7

DSC charts of various ethylene methacylic acid ionomer resins.

(Cited from

ref.[3-4]) .............................................................................................................................40

Fig. 3-8

Neutralization metal types vs. coordination geometries and mechanical properties.

(Cited from ref.[3-4]) ............................................................................................................41

Fig. 3-9

Schematic of cross sectional stress distribution of tempered glass. (Cite from

ref.[3-7]) .................................................................................................................................43

Fig. 4-1

Schematic of a vacuum laminator. .........................................................................47

Fig. 4-2

A Four point bend equipment. The loading equipment is connected to the loading arm

and the supporting equipment is mounted on the universal testing machine. The loading arm of universal testing machine moves vertically in programmed speeds and directions. The displacements of arm and the resistance forces to the arm were measured during the loading process. .................................................................................................................................49

Fig. 4-3

Sketches of uniaxial and three-directional strain gages. (Cited from ref.[4-5]) .......52

Fig. 4-4

Schematic of Wheatstone Bridges for strain gages. (Cited from ref.[4-6]) ..............52

Fig. 4-5

Schematic of Linear Variable Differential Transformer (LVDT). Electromagnetic

induction from a primary coil to the two secondary coils is evaluated. Transmitted electric signal are different for each core position, so that displacement of the core is calculated from the difference in signals. (Cited from ref.[4-7]) ...........................................................................53

Fig. 4-6

Finite-element model for four point bend test. The half-length of the laminate plate

was replicated and x-symmetry was used. u3 was fixed at 0 as a boundary condition along the supporting bar in the real experiment. Load was applied as uniform pressure to a rubber strip (3 mm × 38.1 mm × t1 mm) attached to the upper glass ply. .................................................54

vii

Fig. 4-7

Schematic representation of ring-on-ring test. .......................................................57

Fig. 4-8

Comparison of displacement-stress line calculated by Eq. (4-14) and the ones actually

measured by strain gages. ......................................................................................................58

Fig. 4-9 Testing geometry of shear mode of dynamic mechanical analysis (DMA). .............60

Fig. 5-1 Errors between W-B and EET for each laminate glass structure. tx / ty (D or S) denotes “ x mm glass / y mm interlayer / x mm glass,” error rate for rate for effective thickness for deflection or stress. ..........................................................................................................65

Fig. 5-2 Comparison of experimental results and the theoretical effective thickness. Calculated shear transfer coefficient and effective thickness assuming shear coefficient = 1 is also plotted for comparison. .....................................................................................................................68

Fig. 5-3

Effective thickness for deflection and stress of 5 mm glass / 1 mm interlayer / 5 mm

glass laminate as a function of interlayer shear modulus. .......................................................70

Fig. 5-4

Effective thickness for deflection and stress of 1 mm glass / 1 mm interlayer / 1 mm

glass laminate as a function of interlayer shear modulus. .......................................................71

Fig. 5-5

Effective thickness for deflection and stress of 1 mm glass / 5 mm interlayer / 1 mm

glass laminate as a function of interlayer shear modulus. .......................................................72

Fig. 5-6

Effective thickness for deflection and stress of 1 µm glass / 1 mm interlayer / 1 µm

glass laminate as a function of interlayer shear modulus. .......................................................73

Fig. 5-7

Cross sectional maximum principal stress plot of 1 mm glass / 1 mm interlayer / 1

mm glass. The four point bend test model has been used and the cross section at the center of the beam is shown. ................................................................................................................74

viii

Fig. 6-1 Shear transition curve of 5.0 mm glass / 0.76 mm interlayer / 5.0 mm glass structure. The effective thickness for deflection is plotted as a function of the shear modulus of the interlayer. The effective thickness was calculated by the W-B model, assuming a four point bend test in which the supporting span is 180 mm. The loading span is 40 mm, and the sample size is 200 mm × 38.1 mm. ..............................................................................................................83

Fig. 6-2

Shear modulus of polymer interlayer vs. error rates of shear relaxation modulus

measured by the inverse calculation method, assuming thickness of glass and interlayer, effective thickness have 0.15%, 1.7% and 3.0% errors, respectively. The effective thickness value is also presented. The solid arrows indicate which vertical axis each line corresponds to. ...............................................................................................................................................85

Fig. 6-3

Schematic representation of 500 mm × 500 mm load test. .....................................88

Fig. 6-4

Shear relaxation modulus master curve (time scale) for PVB, Butacite® at 20.5 oC.

...............................................................................................................................................91

Fig. 6-5 Deflection as a function of load duration measured by four point bend creep test. ...............................................................................................................................................91

Fig. 6-6

Comparison of shear relaxation modulus at 23.0 oC, obtained by DMA and the four

point bend creep test. ............................................................................................................92 Fig. 6-7

Shear modulus of polymer interlayer vs. error rates of shear relaxation modulus

measurement by the inverse calculation method, assuming thickness of glass and interlayer, effective thickness have 0.15%, 1.7% and 3.0% errors, respectively. Laminate glass structure is 2.0 mm glass / 0.76 mm interlayer / 2.0 mm glass (500 mm × 500 mm size). The solid arrows indicate which vertical axis each line corresponds to. ............................................................94 Fig. 7-1 The approach for designing load resistant modules. ................................................ 99

ix

Fig. 7-2 The load test to obtain

. A monolithic glass plate is attached to aluminum frame

with butyl rubber sealant. The frame is attached to the mount with screws and nuts 2 points for each side. Three axis strain gage is attached at the center of the bottom side of glass to measure principal stress. Then, uniform pressure is applied with sand bags. ....................................... 103

Fig. 7-3 The module structure for experiments. The module size is 995mm × 995mm. Two pieces of t1.1mm glass are normal anneal glass. 36 pieces of 6 inches c-Si cells are embedded in the module. DuPontTMPV5300 is ionomer encapsulant. Two t0.9mm sheets are used to cover cells. The module was laminated by normal vacuum laminator for photovoltaic. Aluminum frame is attached to with butyle rubber sealant. ...................................................................... 104

Fig. 7-4 The applied load versus maximum principal stress at the center in the bottom side of glass and installation factor

. The installation factor

shows stress mitigation by the way of

installation from four side simple support. .............................................................................. 109

Fig. 7-5 The Weibull plot of nominal t3.0 mm glass (actual t2.76mm). The approximation line is drawn along the middle slope and m and

are obtained. .................................................110

Fig. 7-6 The Weibull plot of t1.1mm glass. The approximation line is drawn along all plots except for the three plots from the lowest stresses. From the slope the line, m and

are

obtained. ...................................................................................................................................110

Fig.7-7

Comparison of predicted stress concentration calculated by the scheme and the one

obtained from actual experiment. Though the calculation contains some simplifications, the results agree well with the actual experiment. ......................................................................... 111

Fig. 8-1

Interlayer thickness vs. weight reduction maintaining stress resistance. ................ 120

Fig. 8-2

Interlayer thickness vs. weight reduction maintaining bending stiffness. .............. 121

Fig. 8-3

Intelayer / glass thickness ratio s vs. weight reduction ratio. ................................. 122

x

Fig. 8-4

Relationship between glass laminates Interlayer / glass thickness ratio and thickness

increase by replacing monolithic glass with equivalent bending stiffness (Tw) or stress resistance (Tσ).

....................................................................................................................................... 124

Fig. 8-5

s vs. Γ for stress and deflection matching weight reduction for k = 1.0 ................. 129

Fig. 8-6

s vs. Γ for stress and deflection matching weight reduction for k = 1.5. ................ 130

Fig. 8-7

s vs. Γ for stress and deflection matching weight reduction for k = 2.0. ................ 132

xi

LIST OF TABLES

Table 1-1

Comparison of interlayer materials. ......................................................................5

Table 2-1

α and β for four-side simply supported plate for each aspect ratios (a > b). .........27

Table 2-2

α and β for two-side simply supported and two-side free plates for each aspect ratio.

a and b donate free edges and simply supported edges, respectively. ......................................27

Table 3-1 Standard composition of glass for float process. (cited from ref.[3-6]) ................43

Table 5-1

Laminate glass structures for the four point bend experiment. .............................66

Table 5-2

Laminate glass structures examined by FEA. ......................................................67

Table 5-3

Young’s modulus of the interlayer when the composite beam model deviates from

the effective thickness model is 1%. ......................................................................................77

Table 6-1

Coefficients for the generalized Maxwell series of PVB (Butacite ®). ................90

Table 6-2 Comparison of experimental results of 500 mm × 500 mm load test to calculation results with shear relaxation modulus obtained by four point bend creep. ...............................92

Table 7-1

Shear moduli of DuPontTMPV5300 at each temperature and load duration. ....... 101

Table 7-2

Conditions of ring-on-ring test and the Weibull parameters m and coefficient σo.

................................................................................................................................. 105

xii

Table 7-3

βc and RS;ef for the four side simply supported monolithic glass (m = 7.2, n = 0.23)

calculated from the plate theory and Eq. (7-9). ....................................................................... 108

Table 7-4

Allowable stress of t3.0mm and t1.1mm monolithic glass. ................................109

Table 7-5

Calculation results of stress concentrations and allowable stress for the module

represented in Fig. 7-3 against 3940 Pa for 3s and 1313 Pa for 1 h. ...................................... 112

Table 8-1

Laminate glass structures for the four point bend experiment.. .......................... 118

Table 8-2

Comparison of experiments and calculation. ..................................................... 119

xiii

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to my advisor, Prof. Yasuhiro Koike for insightful advisory to my Ph.D research and for his generosity to support me to pursue research themes beyond photonics polymers as an extension of functional transparent polymers. I’ve learnt universal basis as a scientist through lots of discussion with him. I would also like to express my appreciation to the rest of the thesis committees, Prof. Tetsuya Suzuki, Prof. Koji Suzuki and Prof. Eisuke Nihei for their insightful comments, fruitful discussions and encouragement. I would especially like to express my appreciation to Dr. Stephen J. Bennison, Technical Fellow of Glass Laminating Solutions & Vinyls, Kuraray America, Inc.* for his knowledgeable comments and advisory as a world-leading specialist of glass laminates and for guiding me to successful research work. I would like to express my appreciation to Dr. Ryuichi Hayashi, Executive Operating Officer and Director of Technology and Innovation of DuPont Kabushiki Kaisha and Dr. Rutger Puts, Global Technology Manager of Glass Laminating Solutions & Vinyls, Kuraray America, Inc.* for continuous support to my Ph.D research as an extension of my project work. I would also like to express my appreciation to Mr. Jun Koishikawa, Development Manager and Mr. Hitoshi Akabane Country Manager of Glass Laminating Solutions, Kuraray Co. Ltd.* for giving me such a wonderful opportunity to work on the high-performance glass laminates. Lastly, I would like to thank to all of my colleagues around world in New Business Development Japan, Packaging & Industrial Polymers of DuPont and Glass Laminating Solutions of Kuraray* for lots of support and advisory to my research work.

* Glass Laminating Solutions & Vinyls of Kuraray America, Inc. and Kuraray Co. Ltd. were Glass Laminating Solutions of E.I. DuPont du Nemors and Company, Inc. and DuPont Kabushiki Kaisha until business sale on June 1st, 2014. xiv

Chapter 1: Introduction

1

Chapter 1

Introduction

Laminated safety glass has been used in many varied applications such as architectural facades, partitions, doors and enclosures and automotive glazing. Traditionally, the polymer functions as a safety component reducing the risk of cutting injuries in case of accidental breakage from human impact. This traditional safety function has expanded to include barrier and laminate retention properties in the case of breakage from a severe mechanical event. Laminated glass can be designed to resist both natural threats, such as hurricanes, typhoons and earthquakes, and man-made threats, such as a bomb blasts, physical and ballistic attacks. Laminated glass consists of a periodic structure of polymer and glass sheets. In the most common and simplest case, one polymer interlayer is sandwiched by two glass sheets. Standard interlayers are summarized in Table 1-1. The most widely, and historically longest used polymer interlayer is poly-vinyl butyral (PVB) [1-1], which is a compliant (rubbery) interlayer originally developed for automobile windshields (human impact safety). Indeed, glass is excellent material. It is low cost, hard, stiff, transparent and chemically stable against various environmental stresses such as heat, humidity and UV, but it has one detriment: brittleness. This brittleness is intrinsic trade off of ceramic materials against these extraordinary advantages. Laminate glass is based on the idea to compensate the brittleness of glass materials with viscoelasticity of polymeric materials. The viscoelasticity of interlayer absorbs impact of human head in car accident and prevent human from being thrown away out of vehicles. PVB has been selected because of its viscoelasticity due to its softness, good adhesion to glass and its transparency. Now laminated safety glass is mandated in many countries by law for windshield of automobiles. However, though a PVB interlayer surely prevents glass from scattering around on breakage, the glass laminate cannot maintain its structural consistency after the breakage and doesn’t have

2

Chapter 1: Introduction

stiffness to withstand external mechanical forces anymore. As a solution for this, DuPont™ developed a new structural interlayer called “SentryGlas®” based on an ethylene copolymer ionomer resin, long after PVB commercialization [1-2]. Since the ionomer has an ionic cross-linked structure, it can be repeatedly melted during laminate processing at elevated temperatures. On cooling, the interlayer reforms its ionic cross linked structure with associated high stiffness and toughness as compared to PVB interlayers. Because of the flexibility of ionic assembly in cross linking structure [1-3], ionoplast resin generally has good balance of viscoelasticity and high modulus. For this reason, ionoplast resin “Surlyn®” has been used long year for the surface coating of golf balls. The stiffness of the ionoplast interlayer enables the design and implementation of strong laminates that have been used in applications such as high performance impact facades, structural glass fins, frameless glazing, canopies. Because of the stiffness of ionomer, multi-periodic structure of glass and SentryGlas® provides enough stiffness to support human on the laminates after breakage, which enables glass floors for walkaways [1-4] and stairs. Most laminated glass used to date has been comprised of glass components that are typically 2 mm to 25 mm in thickness. Common polymer interlayer thicknesses fall into the range of 0.38 mm to 2.5 mm, so the ratio of glass / polymer thickness is typically 3 to 10. In recent years we have seen the commercial availability of thin glass (0.4 to 1 mm) increase significantly due to use in display and mobile device applications. This raises the possibility of fabricating laminates where the glass polymer thickness ratio can be reduced readily in to the range of 0.1 to 1. Laminates consisting of thin glass and a thick ionoplast interlayer have recently been shown to exhibit strength equivalent to 3 mm to 5 mm monolithic glass [1-5]. For example, as shown in Fig. 1-1, “5 mm glass / 0.9 mm SentryGlas® / 5mm glass” structure has equivalent stiffness (flexure property) to about 10 mm monolithic glass (assuming 1 min load at 24 oC), which means there is almost no difference in weight between the two. On the other hand, “1.1 mm glass / 0.9 mm SentryGlas® / 1.1 mm glass” structure has equivalent stiffness to 3 mm monolithic glass, which means there is about 16 % difference in weight. In other words, 3 mm monolithic glass can be substituted by the 16 % weight reduced glass laminate. Thus, because the major component of the laminate is now polymer, thin-glass ionomer (TGIO) laminates demonstrate significant strength / weight ratio advantages over monolithic glass or laminated glass made using conventional structures. However, because of

Chapter 1: Introduction

3

the uncommon glass / polymer thickness ratio in such high-performance laminates there is a need to investigate the structural behavior of TGIO laminates and develop a rationale design methodology to establish optimum laminate structures. In this dissertation, a mechanical design approach for such thin glass laminates is presented, with which glass laminate structures which have target stiffness, strength and weight reduction percentages can be predicted systematically. From Chapter 2 to Chapter 4, basic mechanical models for beam and glass laminate, characteristics of major components of laminated glass and experimental methods used in this study are summarized. In Chapter 5, mechanical behavior of the thin glass laminates is clarified, and applicable mechanical models to calculate strength and stiffness thin glass and polymer laminates are presented. However, to obtain precise strength and stiffness prediction from theoretical calculation and numerical simulation by finite element analysis, proper shear modulus of interlayer needs to be obtained. Because of viscoelasticity of an interlayer material, its shear relaxation modulus depends on temperature and load duration. Though the most accurate method to characterize shear relaxation modulus of interlayer is the Dynamic Mechanical Analysis (DMA), the method requires skills to obtain precise storage moduli and complex calculation to transform them to time scales. Therefore, in Chapter 6, a simpler method to measure the interlayer time and temperature dependent shear relaxation modulus characteristics using a four point bending test in combination with a laminate effective thickness theory is presented. Once strength and stiffness of glass laminates are calculated, stress and deflection in actual gazing system should be delivered as the final step of the design approach. As an example, structure optimization method for photovoltaic module with glass laminate is presented in Chapter 7. In this field, recent diversification of module structure has raised necessity of simple but rational design approach. Major interlayer used for photovoltaic module, ethylene vinyl acetate (EVA), presents viscoelastic behavior explained in the same model as glass laminates especially for double glass type modules. In Chapter 8, the significant strength / weight ratio advantage of thin glass and stiff interlayer laminates is discussed. There, weight reduction limit with thin glass and stiff polymer laminate combination has been demonstrated theoretically and experimentally. Based on the finding, the approach to design glass laminates which can substitute target monolithic glazing with lighter weight structure maintaining its strength or stiffness is presented.

4

Chapter 1: Introduction

Table 1-1

Comparison of interlayer materials. Ethylene copolymer

Poly-vinyl butyral (PVB)

base ionomer

(e.g. Butacite®*)

Advantages




Lower cost




Impact energy absorption due to its softness

(e.g. SentryGlas®*)


Higher modulus




Lower moisture pick up




Chemically stable




Higher adhesion to glass


Higher moisture pickup
Lower modulus Disadvantages


Degradation by potential


Higher cost

bleed out of plasticizer
Lower adhesion to glass * DuPont Glass Laminating Solution business has been sold to Kuraray as of June 1st of 2014, along with interlayer products, Butacite® and SentryGlass®. Base resin of SentryGlass®, Surlyn® remains as a product of DuPont Packaging & Industrial Polymers.

Fig. 1-1 Implication of higher specific strength / stiffness with thin glass and stiff interlayer laminate combinations. The stiff interlayer assumes SentryGlas® under 1 min load at 24 oC.

Chapter 1: Introduction

5

References [1-1]

S.J. Bennison, A. Jagota and C.A. Smith, “Fracture of glass / poly-vinyl butyral / Butacite® / laminates in biaxial flexure,” Journal of American Ceramic Society, Vol.82, pp.1761–1770 (1999)

[1-2]

S.J. Bennison, P.S. Davies, W. Gao, F.F. Zhu and T. Amos, “Glazing Solutions with Laminated Glass Beyond the PVB Limit: the Use of a Structural Interlayer,” Proceedings of Glass Performance Days, Beijing, April, pp.224-226 (2009)

[1-3]

Yano, S, Hirasawa, E, Aionomer, Ion-sei Koubunshi Zairyo (Ionomer and ionic polymeric materials), popular ed., CMC Publishing, Tokyo (2003)

[1-4]

S.J. Bennison and F. Serruys, “Designing the Grand Canyon’s new laminated glass walkway,” Proceedings of Glass Performance Days, Tampere, June, pp.333-335 (2007)

[1-5]

Y. Shitanoki, “Rigid and light laminate glass with high modulus ionomer (In Japanese),” Proceedings of Ionomer Symposium, Kobe, November pp.19-23 (2013)

Chapter 2: Theoretical Models for Glass Laminates

7

Chapter 2

Theoretical Models for Glass Laminates

2.1

Preface In this chapter, physical models for glass laminate are explained and the concept effective

thickness is introduced. Prior to it, polymer viscoelastic model is introduced so that time and temperature dependency of viscoelasticity of interlayer is reflected to the glass laminate mechanical behavior. Once effective thickness is calculated, it can be used as thickness of plate in the plate equations. When evaluating breakage probability of glass laminate, stress concentration is associated with breakage probability of glass. A statistic model called Weibull analysis to express the glass breakage and calculation method of allowable stress is introduced.

2.2

Viscoelastic Models for Interlayers Laminated glass can be designed to meet various structural loads using several methods.

These methods range from the relatively simple, such as the effective thickness method, through the relatively complex, based on finite element methodology incorporating details of the geometry and the various materials used in the structure. In all methods, the polymer and glass shear modulus (or Young’s modulus) are required to obtain accurate predictions of laminate behavior. Glass behaves in a linear elastic fashion up to rupture and the deformation behavior is determined by well-studied elastic materials characteristics. However, polymer interlayer behavior is more complex because of its viscoelastic nature. Proper characterization of polymer shear relaxation modulus behavior is not simple because of the complex time and temperature dependency. Though Young’s modulus obtained from standard stress-strain chart depends on loading rate, proper selection of tensile loading rate to replicate shear rate in a glass laminate cannot be measured or calculated readily. The most common approach for characterizing

8

Chapter 2: Theoretical Models for Glass Laminates

polymer viscoelasticity is through dynamic mechanical analysis (DMA) in combination with a determination of the shear relaxation master curve using data treatments such as the Williams– Landell–Ferry (WLF) method [2-1]. Bennison et al. presented practical examples to characterize viscoelastic performance using DMA and time-temperature superposition [2-1]. Whereas the Young’s modulus of PVB was first obtained and then transformed into the shear modulus in their study, the shear modulus was directly measured by shear mode of DMA in this study. The shear relaxation modulus is represented by a generalized Maxwell series:

=

+

/

where n relaxation modes are expressed by relaxation strength

2 − 1

and relaxation time τi.

is

the long-time plateau modulus, assumed to be 0 at this time. The relationship between the reduced time τ and the actual time t is given by the following Williams–Landell–Ferry (WLF) equation: τ= ⁄

2 − 2

where the shift function aT is given by log

= −

− + −

2 − 3

where C1 and C2 are the material constants, T is the temperature and To is a reference temperature. With DMA of interlayers , the data for G’ was plotted as a function of frequency for different temperatures. Frequencies for each data set are shifted with regards to a reference temperature to obtain a continuous superimposed plot. Then, the shift parameter aT required to superimpose these data are found by sequentially shifting two data sets at a time. Here, a common polynomial can be used to fit these combined data, using the shift parameter to minimize the rms error. Considering the case of shift parameter between two temperatures,

Chapter 2: Theoretical Models for Glass Laminates

9

indexed i and i + 1, each with G’ measured at nf of different frequencies, this is achieved by minimizing,

log

−

log ω

+

log

−

log

,

ω

2−4

with respect to the shift parameter ai + 1,i (between temperatures i + 1 and i) and the polynomial coefficients, ck, where np is the polynomial order ( < 2 (nf − 1)). The relative shift factors are computed by applying this procedure sequentially to the entire set of temperatures. These are then converted to absolute shift factors, aT, relative to a reference temperature. The same set of shift parameters are then used to superimpose the loss modulus data. The transformation from frequency scale to time scale is derived by the methodology proposed by Baumgärtel and Winter [2-2~2-4]. In their method, Gi and τi in Eq. (2-1) are calculated by curve fitting of measured data to the discrete spectrum of the relation between the deformation and stress:

=

+

=

+

1+

τ

2 − 5 2 − 6

1+

For the transformation from frequency scale to time scale, gi and τi are determined by minimizing, ω

where

and

−1

+

ω

−1

2 − 7

are measured data, and m is the total numbers of frequency mode.

10

Chapter 2: Theoretical Models for Glass Laminates

2.3

Effective Thickness : Expression for Strength and Stiffness of Glass Laminates

2.3.1

The Effective Thickness Concept

Many previous studies of glass-polymer laminate glass that have been published since the first commercialization of PVB have attempted to address the large modulus discrepancy between the glass and soft interlayer [2-1, 2-7~2-21]. Due to the softness of polymer interlayers, the strain distribution in the cross section of the interlayer is not continuously linear; therefore, a standard composite beam model based on its linearity is not applicable. Among various analytical approaches, the concept of the “effective thickness” of laminate glass was proposed [2-18] as a rational and practical design method and has been widely used in the design community for general, thicker glass-polymer laminates. In this section, two types of effective thickness approaches are reviewed and corresponding expressions via a traditional composite beam model are delivered. The analysis proposes analytic equations that provide a method to calculate the thickness of a monolithic beam with bending properties equivalent to those of a laminated beam. This thickness can then be used in place of the actual thickness in analytic equations for the deformation of beams and a simplified finite element analysis.

2.3.2

Effective Thickness Experimentally Obtained by Four Point Bend Test

Considering its definition, effective thickness expresses the thickness of equivalent monolithic glass which has the same flexural or fractural properties, namely, “load vs. deflection” or “load vs. stress” lines, in specific load test. The simplest way of evaluating the effective thickness is conducting actual load tests whose deflection and stress in monolithic beam can be calculated analytically. In this study, four point bend test has been selected as a major test to experimentally evaluate effective thickness because of its preciseness and consistency with theories. As we can find in the basic mechanical engineering text books [2-5], stress concentration, when load is applied to a two-side simply-supported beam, is expressed by, = where

2 − 8

is the compressive stress above the neutral axis and tensile stress below the neutral

Chapter 2: Theoretical Models for Glass Laminates

11

axis, M is the moment applied by the load I is the second moment of inertia and z is the distance from neutral axis of the cross section. For deflection w, differential equation is given by, =−



2 − 9

where E is the young modulus of the beam material. The geometry of the four point bend test is shown in Fig. 2-1. Moment by external force along the beam is given by,

=

2

2

0 < − 2