Characterising the rate dependent response of adhesively bonded structures

211 Pages·2008·42.68 MB·English

Contents
Summary i
Copyright ii
Acknowledgements iii
Declaration iv
Table of contents v
List of figures ix
List of tables xvii
Chapter 1: Introduction 1
1.1 Background 1
1.2 Methodology 2
1.3 Overview of the content 3
Chapter 2: Literature review 5
2.1 Introduction 5
2.2 Material behaviour 6
2.2.1 Experimental work 6
2.2.2 Material models 14
2.2.3 Concluding remarks 19
2.3 Joint data 20
2.3.1 Experimental work-Creep 20
2.3.2 Experimental work-Monotonic loading at various rates. 22
2.3.3 Experimental work- Effect of geometry and surface conditions 24
2.3.4 Numerical modelling 25
2.3.5 Concluding remarks 37
2.4 Failure criteria 38
2.4.1 Failure criteria for creep 39
2.4.2 Failure criteria for monotonic loading 40
I.Maximum stress/strain criterion 40
II.Stress/strain/strain-energy and a distance criteria 41
III.Ultimate tensile stress (UTS) over a zone 42
IV.Fracture mechanics approach 42
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Contents
V. Bi-material stress intensity 43
2.4.3 Concluding remarks 43
2.5 Conclusions 44
Chapter 3: Specimen manufacture 45
3.1 Introduction 45
3.2 Flat tensile specimens 45
3.3 Thick adherend shear test (TAST) joints 51
3.4 Single lap joints 54
3.5 Concluding remarks 56
Chapter 4: Experimental material data 58
4.1 Introduction 58
4.2 Bulk material tests 58
4.2.1 Test variables 58
4.2.2 Test apparatus and procedure 58
4.2.3 Test results 64
4.2.4 Discussion of results 65
4.3 Thick adherend shear test (TAST) 69
4.3.1 Test variables ............................................................ 69
4.3.2 Test apparatus and procedure 69
4.3.3 Test results 77
4.3.4 Discussion of results 77
4.4 Substrate tension tests 80
4.4.1 Test variables ............................................................ 81
4.4.2 Test apparatus and procedure 81
4.4.3 Test results 82
4.5 Conclusions 83
Chapter 5: Experimental joint testing 84
5.1 Introduction 84
5.2 Test variables 84
5.3 Test apparatus and procedure 85
5.4 Test results 88
5.4.1 Video microscopy 88
5.4.2 Strain rate test results 90
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Contents
5.5 Discussion of results 93
5.6 Conclusions 99
Chapter 6: Material models for finite element analysis 101
6.1 Introduction 101
6.2 Processing bulk tensile data 101
6.2.1 Initial development 102
6.2.2 Generated material data 106
6.3 Rate dependent von Mises model 108
6.3.1 Bulk FEA 108
6.3.2 TAST FEA 110
6.4 Generalised plane strain problem 115
6.4.1 Beam problem 116
6.4.2 TAST joint 118
6.4.3 3D TAST joint ............................................................ 119
6.5 Hydrostatic stress sensitive material model 123
6.5.1 Determination of material parameters 124
6.5.2 Bulk FEA 125
6.5.3 TAST FEA 127
6.6 User defined model 130
6.6.1 Mathematical formulation 130
6.6.2 Determination of material parameters .............................. 131
6.6.3 Implementation of the user model into ABAQUS ................ 132
6.6.4 Bulk FEA 132
6.6.5 TAST FEA 133
6.7 Concluding remarks 134
Chapter 7: Analysis of single lap joint 136
7.1 Introduction 136
7.2 Material model for the substrate 137
7.3 Finite element models for single lap joints 138
7.4 User defined material model-Configuration A 139
7.5 Rate dependent von Mises model- Configuration A 142
7.6 von Mises material model-Configuration B 149
7.7 von Mises material model-Configuration C 152
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Contents
7.8 von Mises material model-Configuration D 157
7.9 Joint strength prediction 161
7.10 Concluding remarks 163
Chapter 8: Conclusions and future work .................................... 165
8.1 Introduction 165
8.2 Concluding remarks 165
8.3 Future work 167
References 169
Appendix I: ABAQUS input file — von Mises rate dependent — bulk .... 181
Appendix II: ABAQUS input file — von Mises rate dependent — TAST..... 184
Appendix Ill: ABAQUS input file — Raghava rate dependent — bulk .... 188
Appendix IV: ABAQUS input file — User Defined material model — bulk... 191
Pge viii
List of figures
Figure 2.1: Logarithmic dependence of shear stress on strain rate for a

2-part, cold cured epoxy
7
Figure 2.2: The KGR-1 extensometer. LVDT: linear variable differential
transformer..
8
Figure 2.3: Normalised shear and peel stress versus normalised

distance in the thick adherend test specimen.
9

Figure 2.4: Strain/time plot for crosshead control.. 9
Figure 2.5: Logarithmic dependence of shear stress on strain rate for
FM73.
10
Figure 2.6: losipescu test specimen. 11
Figure 2.7: losipescu test specimen under combined loading. 11
Figure 2.8: Geometry of a loaded beam in 2-point bending. 11
Figure 2.9: Comparison of stress/strain curves for the 1-part epoxy
obtainedby different test methods...................................................
13

Figure 2.10: Yield parameters calculated for LMD 1142 at 23°c 17
Figure 2.11: Plot of peel strength versus log (peel rate) at different test
temperatures for adhesive with 20 phr silica filler.
22
Figure 2.12: Specimen geometry for cleavage tests. 24
Figure 2.13: Adhesive material models for FE analysis......................... 26
Figure 2.14: Piecewise linear fit of creep experimental data.................. 28
Figure 2.15: Peel and shear stress in adhesive layer. 30
Figure 2.16: Single lap joint spew geometries..................................... 37
Figure 3.1 Bulk material specimens. 45
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List of figures
Figure 3.2: Adhesive's thickness control. 46
Figure 3.3: Mould for producing uniform thickness slabs 47
Figure 3.4: Bulk material slab 48
Figure 3.5: Clamp for full size flat Tensile specimens 50
Figure 3.6: LMD1142 Tensile specimens. 50
Figure 3.7: Clamp for reduced size flat Tensile specimens. 50
Figure 3.8: Substrate for TAST joints. 51
Figure 3.9: The making up of a TAST joint. 53
Figure 3.10: Clamp for TAST joints. 54
Figure 3.11: TAST joint: end product. 54
Figure 3.12: Single lap joint. 55
Figure 3.13: Preparing single lap joints 55
Figure 4.1: Instron 6025 test machine and extensorneter...................... 59
Figure 4.2: Instron 6025 console's display. 61
Figure 4.3: MiniPOD data logging card 62
Figure 4.4: Amplifier unit circuit. 63
Figure 4.5: Tensile constitutive data 65
Figure 4.6: Constitutive data for full and reduced size specimens. 66
Figure 4.7 Strain-time plots for bulk tensile specimens. 67
Figure 4.8 Definition of knee stress 68
Figure 4.9: Gripping forks for TAST joints. 70
Figure 4.10: Schematic drawing of KGR-1 extensometers...... ..... 71
Figure 4.11: Detailed drawing of KGR-1 extensometers...... ........ 71
Figure 4.12: Actual and average shear stress in the bond line 72
Figure 4.13: Electric circuit layout of control module. 73
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List of figures
Krieger extensometers.................................................. 73
Figure4.14:
Figure 4.15: Calibration micrometer for KGR-1 extensometers 74
Figure 4.16: Calibration curve for KGR-1 extensometers. 74
Figure 4.17: Shadowgraph 76
Figure 4.18: Shear stress-strain curve for the TAST specimens 78
Figure 4.19: Knee stress in shear versus test temperature 79
Figure 4.20: Shear strain-time plots for TAST joints. 79
Figure 4.21: Strain rate response from bulk specimens and TAST joints.. 81
Figure 4.22: Substrates constitutive data 82
Figure 5.1: Single lap joint test variables. 84
Figure 5.2: Modified clip extensometer. 85
Figure 5.3: Calibration of modified extensometer. 86
Figure 5.4: Line scribed across the bond layer in a single lap joint. 86
Figure 5.5: Experimental setup for the video microscopy...... ....... 88
Figure 5.6: Captured images during a high crosshead speed test 89
Figure 5.7: Captured images showing deformation of the scribed line in
the bond layer
89
Figure 5.8: Measurement of shear angle in single lap joints 90
Figure 5.9: Force-shear angle response for single lap joints. 91
Figure 5.10: Response curves for configuration A of single lap joints 91
Figure 5.11: Response curves for configuration B of single lap joints 92
Figure 5.12: Response curves for configuration C of single lap joints 92
Figure 5.13: Response curves for configuration D of single lap joints 93
Figure 5.14: Force and joint displacement for all tested single lap joints 94
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List of figures
Figure 5.15: Shear stress, shear strain/shear angle response from TAST 96
and lap joints.
Figure 5.16: Normalised deflection-time plots for configuration A 97
Figure 5.17: Normalised deflection-time plots for configuration B 97
Figure 5.18: Normalised deflection-time plots for configuration C...... 98
Figure 5.19: Normalised deflection-time plots for configuration D 98
Figure 6.1: Representative true stress-strain curves for bulk material

tensile tests.
102
Figure 6.2: Typical true stress-strain curve for bulk material showing key
points.
103
Figure 6.3: Strain rate-Stress plots at various points....................... ..... 105
Figure 6.4: Experimental and generated data for bulk tensile tests 107
Figure 6.5: Generated data for bulk tensile at various crosshead speeds. 108
Figure 6.6: Mesh used for bulk material finite element analysis......... ..... 109
Figure 6.7: Rate dependent model compared to experimental data

(original input data)
109
Figure 6.8: Rate dependent model compared to experimental data
(modified input data).
110
Figure 6.9: FEA model for TAST joint.. 111
Figure 6.10: Location of extensometer's pins 112
Figure 6.11: Displacement and rotation of TAST joint. 113
Figure 6.12: Predicted and experimental data for TAST joint at various
crosshead speeds.
113

Figure 6.13: Modified predicted data for TAST joint... 114

Figure 6.14: Generalised plane strain model. 115
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List of figures
Figure 6.15: Beam model for generalised plane strain problem.............. 117
Figure 6.16: FEA results for 1 extra set of nodes. 117
Figure 6.17: FEA results for 2 extra set of nodes. 118
Figure 6.18: FEA results for 4 extra set of nodes. 118
Figure 6.19: Z-strain distribution across mid plane of the adhesive layer

(2D TAST joint model)
120
Figure 6.20: Shear Stress distribution across mid plane of the adhesive

layer (2D TAST joint model)
120
Figure 6.21: 3D TAST joint model 121
Figure 6.22: Z-strain distribution across mid plane of the adhesive layer
in the 3D joint model.
121
Figure 6.23: Shear stress distribution across mid plane of the adhesive
layer in the 3D joint model.
122
Figure 6.24: Compliance of the 2D and 3D joint models along the
adhesive layer.
123
Figure 6.25: Schematic diagram of hardening for the general exponent

model in the p-q plane
124
Figure 6.26: Mesh used for Raghava model in bulk material FEA 126
Figure 6.27: Raghava rate dependent model response compared to 126
experimental data.
Figure 6.28: Comparison between von Mises and Raghava rate
dependent models.
127
Figure 6.29: Predicted and experimental data for TAST joint using

Raghava material model at the lowest strain rate
128
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List of figures
Figure 6.30: Predicted and experimental data for TAST joint using
Raghava material model..
129
Figure6.31: Validation of user model................................................ 132
Figure 6.32: User model compared to experimental data 133
Figure 6.33: User model prediction for shear stress and shear strain in
TAST joints.
134
Figure 7.1: Rotation of single lap joint. 136
Figure 7.2: Material data for substrates. 138
Figure7.3: FEA model for single lap joint.......................................... 139
Figure 7.4: Location of extensometer points on single lap joints 140
Figure 7.5: Predicted response of configuration A-rate1 using user-
defined model.
140
Figure 7.6: Extensometer and end displacement for the single lap joint... 141
Figure 7.7: Variable strain rate displacement predictions for the single
142
Figure 7.8: Variable strain rate results using user-defined model............ 143
Figure 7.9: Predicted response of configuration A-rate1 using von Mises
model..
144
Figure 7.10: Predicted response of configuration A. 144
Figure 7.11: von Mises stress across adhesive path length for
configuration A.
145
Figure 7.12: von Mises strain across adhesive path length for
configuration A.
146
Figure 7.13: Strain rate (shear) variation for configuration A.................. 147
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