Numerical Analysis of Adhesively Bonded Single Lap Joins Under High Speed Tensile Loading

221 Pages·2015·7.8 MB·English

NUMERICAL ANALYSIS OF
ADHESIVELY BONDED SINGLE LAP JOINTS UNDER
HIGH SPEED TENSILE LOADING

A Thesis by

Sean M. McCann

Bachelor of Science, Southern Illinois University Carbondale, 2011

Submitted to the Department of Aerospace Engineering
and the faculty of the Graduate School of
Wichita State University
in partial fulfillment of
the requirements for the degree of
Master of Science

December 2015
© Copyright 2015 by Sean M. McCann

All Rights Reserved
NUMERICAL ANALYSIS OF ADHESIVELY BONDED SINGLE LAP
JOINTS UNDER HIGH SPEED TENSILE LOADING

The following faculty members have examined the final copy of this thesis for form and
content, and recommend that it be accepted in partial fulfillment of the requirement for the
degree of Master of Science, with a major in Aerospace Engineering.

Suresh Keshavanarayana, Committee Chair

Gerardo Olivares, Committee Member

Anil Mahapatro, Committee Member

Page | iii of 206
ABSTRACT
Adhesively bonded joints pose complex solid mechanics problems through their inherent
variations; material properties dependent on fabrication, stress singularities created by geometry
of bonded structural assembly, and in a non-uniform state of stress when loaded. When testing
adhesives at high strain rates additional variations are observed; particularly in strength. It is
hypothesized that a non-uniform field of constitutive relations exists in an adhesive lap joint,
owing to the strain rate sensitivity of the adhesive material.
This study investigates the non-uniform distribution of strain rate in the overlap region of ASTM
D3165 and D5656 single lap joint (SLJ) specimens, and how the strain rate sensitivity of the
adhesive affects the stress distribution when the joint is subjected to varying tensile loading
speeds. The numerical method of Finite Element Analysis (FEA) has been used to analyze the
joint. Commercially available LS-DYNA implicit dynamics solver and one of its standard material
formulations, *MAT_19_STRAIN_ RATE_DEPENDENT_PLASTICITY, were implemented to model
incremental stiffness as a function of effective strain rate, within the adhesive lap joint.
This thesis reports strain rates at various locations in the adhesive overlap for four test speeds,
from 25.4 mm/s to 1270 mm/s. Results of stress distributions of the joint are presented
comparing the relative effects of using strain rate insensitive and strain rate sensitive material
models. Comparative results show that while the force vs. displacement curves show negligible
change, strain rate levels and stresses at the bondline edge increase significantly with test speed.
As this location is known to be site of failure initiation, these results indicate this may be an
underlying mechanism controlling or at least affecting failure strengths of adhesive joints tested
at high loading rates.
Page | iv of 206
TABLE OF CONTENTS
Chapter Page
Introduction ............................................................................................................................ 1
1.1 Adhesively Bonded Single Lap Joint Testing ................................................................... 6
1.1.1 Synopsis of (available) Quasi-Static Testing................................................................ 7
1.1.2 Dynamic Single Lap Joint Testing and Analyses ........................................................ 10
1.1.3 Single Lap Joint Analysis Detail Considerations ........................................................ 34
1.2 Adhesive Material Characterization ............................................................................. 39
1.2.1 Polymeric Constitutive Modeling.............................................................................. 40
1.2.2 Failure Characterization ............................................................................................ 48
1.3 Summary ....................................................................................................................... 51
1.4 Research Objectives and Approach .............................................................................. 54
MATERIAL LEVEL ANALYSIS ................................................................................................... 56
2.1 Material Properties ....................................................................................................... 56
2.1.1 Adherend – 2024-T351 Aluminum – Material Properties ........................................ 56
2.1.2 Adhesive – PR-520 Epoxy – Material Properties ...................................................... 58
2.2 Material Formulations .................................................................................................. 64
2.2.1 Adherend – 2024-T351 Aluminum – Material Formulation ..................................... 65
2.2.2 Adhesive – PR-520 Epoxy – Material Formulations .................................................. 66
2.3 Adhesive Material Model Validation ............................................................................ 79
2.3.1 Modeling Issues ........................................................................................................ 79
2.3.2 Material Verification Results .................................................................................... 83
2.3.3 Final Observations Carried Over to Joint-Level Analyses ......................................... 91
JOINT-LEVEL ANALYSIS .......................................................................................................... 92
3.1 Single Lap Joint Specimens ........................................................................................... 92
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TABLE OF CONTENTS (continued)
Chapter Page
3.2 Finite Element Model .................................................................................................... 95
3.3 Analysis Summary ....................................................................................................... 101
3.4 Test Speed Selection ................................................................................................... 102
3.5 Failure Load Estimation .............................................................................................. 102
3.6 Dynamic Oscillations ................................................................................................... 105
3.7 Output Locations ......................................................................................................... 109
3.8 Filtering ....................................................................................................................... 114
NUMERICAL ANALYSIS RESULTS ......................................................................................... 116
4.1 Strain Rates ................................................................................................................. 117
4.2 D3165 Results ............................................................................................................. 127
4.2.1 Force vs. Displacement ........................................................................................... 127
4.2.2 Static Stress Distributions ....................................................................................... 134
4.2.3 Static Adhesive Simple Failure Criteria Check ........................................................ 138
4.2.4 Dynamic Stress Distributions .................................................................................. 139
4.2.5 Discrete Point Stress Components ......................................................................... 148
4.2.6 Pressure Dependence ............................................................................................. 150
4.3 D5656 Results ............................................................................................................. 152
4.3.1 Force vs. Displacement ........................................................................................... 153
4.3.2 Static Stress Distributions ....................................................................................... 156
4.3.3 Dynamic Stress Distributions .................................................................................. 159
4.3.4 Discrete Point Stress Components ......................................................................... 167
CONCLUSION ....................................................................................................................... 173
5.1 Strain Rates ................................................................................................................. 174
5.2 Stresses ....................................................................................................................... 177
Page | vi of 206
TABLE OF CONTENTS (continued)
Chapter Page
5.3 Summary and Inferences ............................................................................................ 182
5.4 Recommendations for Future Analysis and Testing ................................................... 183
REFERENCES ............................................................................................................................... 185
APPENDIXES ............................................................................................................................... 195
A - LS-DYNA Keywords ........................................................................................................... 196
B - PR-520 Material Data ........................................................................................................ 202
C - FE Model Energy Balance Check ....................................................................................... 203
D - Element Results ................................................................................................................ 205

Page | vii of 206
LIST OF FIGURES
Figure Page
1. Standard Single Lap Joint Specimens [8, 9, 73] ......................................................................................................... 3
2. Typical Primary Stress Plots of a Thin Adherend SLJ [33] .......................................................................................... 4
3. Adhesive Failure Modes [32] .................................................................................................................................... 9
4. Dynamic SLJ Force vs. Time for Two Joint Materials as reported by Harris and Adams [37] ................................. 13
5. SLJ Force vs. displacement for Increasing Test Speeds as reported by Jacob [20] ................................................. 14
6. Failure Strength Dependence of SLJ Strength as reported by Jacob [20] ................................................................ 15
7. Double Lap Joint (DLJ) specimens as reported by Essersi [19] ............................................................................... 16
8. DLJ Force vs. displacement for Increasing Speeds (Composite Adherends) reported by Essersi [19] .................... 17
9. DLJ Force vs. displacement for Increasing Speeds (Aluminum Adherends) reported by Essersi [19] .................... 18
10. Summary of Joint Strengths for Increasing Test Speeds reported by Essersi [19] ................................................ 18
11. Stress-Strain for Bulk Tensile (left) and TAST (right) for Increasing Speeds as reported by Zgoul [26] ................ 20
12. Bulk Tensile and TAST Converted (τ𝟑) Effective Knee (Yield Parameter) Stress vs. Strain Rate reported by Zgoul
[26] ..................................................................................................................................................................... 20
13. Experimental vs FEA Correlation – SLJ Configurations reported by Zgoul [26] .................................................... 21
14. Comparison of Stress and Strain for Two SLJ Test Speeds as Zgoul [26] .............................................................. 22
15. Shear Strain Rate vs. Path Length for Two Test Speeds reported by Zgoul [26] (Note: it is believed there is a
typo in (b) – rate should be 100 mm/min instead of 20) .................................................................................... 23
16. Peak Force vs. Test Speed [11] ............................................................................................................................. 24
17. Sensitivity of Parameters for Fully Plastic (left) and Unbalanced (right) Adherend Configurations [11] ............. 25
18. Adhesive Tensile Stress-Strain Dynamic Response for Varying Speeds as reported by Yang [10] ....................... 26
19. Single Lap Joint Force vs. Displacement – Test Speed: 6.67 m/s as reported by Yang [10] ................................. 28
20. Adhesive Lap Joint Specimens for SHPB Application reported by Srivastava [45] ............................................... 29
21. Adhesive Lap Joint Shear Strength vs. Test Speed as reported by Srivastava [45] ............................................... 30
22. Adhesive Lap Joint Shear Strength vs. Aspect Ratio as reported by Srivastava [45] ............................................ 30
23. SLJ Shear Stress vs. Temperature and Stresses vs. Overlap Length as reported by Chen and Li [24] .................. 31
24. SLJ SHPB Test Force vs. Displacement as reported by Haugouet [17] .................................................................. 32
25. 2024-T3 – Strain Rate Dependency to Yield Stress as reported by Lesuer [60] .................................................... 34
26. Adherend Fillet Parametric Study [28] ................................................................................................................. 35
27. Principal Stress vs. Overlap Distance – Adherend Fillet Study as reported by Silva [28] ...................................... 35
28. Adhesive Spew Parametric Study reported by Silva [28] ...................................................................................... 36
29. Effect of Spew Fillets – Joint Force vs. Displacement as reported by Doruet [31] ............................................... 37
30. Single Lap Joint Bondline Analysis – Principal Stress Vector Plots [30] ................................................................ 38
Page | viii of 206
LIST OF FIGURES (continued)
Figure Page
31. Tensile Stress-Strain Curves of Two Polymers [12] & [1] ...................................................................................... 42
32. CT Force vs. displacements and KIC vs. Cross Head Speed [31] ........................................................................... 44
33. *MAT_89 von Mises Flow Rule and Yield Surface Equation [42] ......................................................................... 46
34. 2024-T351 Raw and Processed Tensile Stress-Strain Curves ................................................................................ 58
35. Shear and Tensile Specimens reported by Gilat [1] .............................................................................................. 60
36.“Raw Data” | Shear Stress – Shear Strain Digitized Curves [1] ............................................................................... 61
37.“Raw Data” | Tensile Stress – Tensile Strain Digitized Curves [1] .......................................................................... 61
38. PR-520 Effective Stress – Effective Strain from Tension and Shear ...................................................................... 64
39. Typical Polymeric Strain Rate Sensitivities............................................................................................................ 68
40. PR-520 True Effective Stress-Strain Curve – Yield Stress Determination ............................................................. 73
41. Plot of Reduced Input Data – *MAT_19 ............................................................................................................... 74
42. Strain Rate Sensitivities of PR-520 ........................................................................................................................ 76
43. Arbitrary Stress-Strain Input Curves – *MAT_89 .................................................................................................. 78
44. Bulk Specimen Meshes (tensile and shear) .......................................................................................................... 80
45. *MAT_89 Error Response – Explicit – 1st Output Time Step (not scaled) ............................................................. 81
46. “Resonance” Response of *MAT_19 with VP=0 in an Explicit Simulation ............................................................ 82
47. “Dummy” Input Curves - Material Verification Analyses ...................................................................................... 83
48. Bulk Specimen Material Verification – Tension .................................................................................................... 85
49. Bulk Specimen Material Verification – Shear ....................................................................................................... 85
50. Implicit Dynamics – Bulk Tensile – *MAT_89 – Gauge Section Elem Response ................................................... 86
51. Bulk Tensile Run 2 – Stress vs. Time and Strain Rate vs. Time – *MAT_89 .......................................................... 86
52. Single Element Results – Tensile – Material Verification Analyses ....................................................................... 88
53. Single Element Results – Shear – Material Verification Analyses ......................................................................... 88
54. Single Element Test – *MAT_89 Stresses and Strains vs. Time ............................................................................ 89
55. Final *MAT_19 PR-520 Material Input Curves – Single Element Test .................................................................. 90
56. Single Lap Joint Specimen Geometry .................................................................................................................... 95
57. Joint Boundary Conditions .................................................................................................................................... 96
58. Joint-Level Analysis Mesh (Only +X half is modeled) (D3165) .............................................................................. 97
59. Mesh Side View (D3165) ....................................................................................................................................... 98
60. Mesh Bondline Detail – 1 (D3165) ........................................................................................................................ 98
61. Mesh Bondline Detail – 2 (D3165) ........................................................................................................................ 99
Page | ix of 206
LIST OF FIGURES (continued)
Figure Page
62. D5656 Mesh ........................................................................................................................................................ 100
63. Comparing EA9394 and PR-520 Shear Stress-Strain ........................................................................................... 103
64. D3165 Inertial Effects on Force vs. displacement ............................................................................................... 106
65. Dynamic Effects on Max and Average Shear Stress Values (D3165) .................................................................. 107
66. Dynamic Effects on Max and Average Peel Stress Values (D3165) ..................................................................... 108
67. Surface and Point Results Z-Direction Locations ................................................................................................ 109
68. Output Point Locations ....................................................................................................................................... 110
69. Z-Stress Across Bondline (X=0 to X= 12.7 mm, Y=6.30 mm, Z=0.025 mm) ......................................................... 111
70. Z-Stress Across Thickness (X=0.370 mm, Y= 6.30 mm, Z= -0.075 to Z= +0.075 mm) .......................................... 112
71. Candidate Shear Stress Elements – “Point 1” (X=0.370 mm, Y=0.053 mm) – All Stress Components .............. 113
72. Candidate Peel Stress Element – “Point 2” – All Stress Components ................................................................. 113
73. Filtering Example ................................................................................................................................................ 114
74. YZ-Strain Rates for Multiple Time Steps – Elastic/Dynamic – v = 762 mm/s ...................................................... 118
75. Shear Strain Rate Maximum and Minimum vs. Time – Elastic/Dynamic – v = 762 mm/s ................................. 119
76. Delta YZ-Strain Rate (SR/D minus E/D) – v = 762 mm/s – 5 kN .......................................................................... 120
77. Delta ZZ-Strain Rate (SR/D minus E/D) – v = 762 mm/s – 5 kN........................................................................... 120
78. Peel (Z-Strain) Strain Rate vs. Specimen Displacement – Point 2 ....................................................................... 121
79. Peel Strain Rate vs. Specimen Displacement – ................................................................................................... 122
80. Peel Strain Rates – Both Specimens – Point 2 – MAX prior to d = 0.05 mm ....................................................... 123
81. Shear Strain Rates – Both Specimens – Point 1 – MAX prior to d = 0.05 mm .................................................... 123
82. Peel Strain Rates – Both Specimens – Point 2 – MAX prior to d = 0.10 mm ....................................................... 124
83. Shear Strain Rates – Both Specimens – Point 1 – MAX prior to d = 0.10 mm .................................................... 125
84. Final Peel Strain Rates – Both Specimens – Absolute Average ........................................................................... 126
85. Final Shear Strain Rates – Both Specimens – Absolute Average......................................................................... 126
86. D3165 Joint Force vs. Displacement – All Cases – All Speeds ............................................................................. 128
87. D3165 Force vs. Displacement – v = 25.4 mm/s ................................................................................................. 129
88. D3165 Force vs. Displacement – v = 254 mm/s .................................................................................................. 129
89. D3165 Force vs. Displacement – v = 762 mm/s .................................................................................................. 130
90. D3165 Force vs. Displacement – v = 1270 mm/s ................................................................................................ 130
91. ΔF – Static vs. Dynamic Cases ............................................................................................................................. 133
92. ΔF – Elastic vs. SR Mat’l Cases............................................................................................................................. 133
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