Collective behavior of asperities as a model for friction and adhesion

160 Pages·2015·12.98 MB·English

Collective behavior of asperities as a model for
friction and adhesion
Thesis by
Srivatsan Hulikal
In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
California Institute of Technology
Pasadena, California
2015
(Defended 14th April 2015)
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Srivatsan Hulikal
All Rights Reserved
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iii
To my parents and my sister for giving me an idyllic childhood
iv
Acknowledgments
It gives me great pleasure to thank the many people who have made this thesis
possible.
First, I would like to thank my advisors Prof. Nadia Lapusta and Prof. Kaushik
Bhattacharya. One is lucky to find one good advisor, I consider myself doubly fortu-
nate to have been able to work with two wonderful people. I was given all the freedom
in the world to pursue anything that interested me. It is nice when you can just say
“why?”, and there is someone who is willing, patient, and even happy to answer your
questions. Kaushik has been that person for me the last few years. His ability to
distill a problem to its essence is remarkable, and I hope I have developed some of it
over the years. A PhD is not without its hard times, and on many occasions when I
have been despondent, meeting Nadia has helped me look at the situation in a more
positive light. I hope I can carry the attitude for the rest of my life. I should also
thank Nadia for asking me to smile more. Nadia, I promise to try.
I would like to thank Prof. Guruswami Ravichandran and Prof. Jose Andrade for
serving on my committee and their suggestions with respect to this work. In spite
of his busy schedule, Ravi has always found time to meet with me any time I asked.
Thank you Ravi for your invaluable advice.
My life at Caltech has also given some of the best friendships which I hope will
last the rest of my life. Ninja, B, Teja, Maha, Batuk, and Gopi, your friendship is
one of the most valuable things I take away from Caltech, thank you guys. I will
forever cherish the time I have spent with Jeff, Aubrie, Ellie, Cindy, Theva, Mythili,
Navaneet, and Swetha. Most of the C++ and parallel programming I know, I learnt
in a few sessions with Jeff. I cannot thank him enough for his patience and helpful
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nature. Mauri, Gal, Zubaer, thank you guys for being amazing friends and sharing
your experience and advice with me, I miss walking periodically to your office and
disturbing you. I would also like to thank all members of Kaushik’s and Nadia’s
groups for being great colleagues. To Ashish, Subbu, Phanish, Naresh, Bharat, Piya,
Mike Mello, Aaron, Gerry, Asghar, and many other friends who made my stay at
Caltech enjoyable, thank you. I also want to thank Shalva, Shashi, Sanju, Sonu,
Venkatesh, Prabha, Neha, Sahana, Raghunandan, Kiran, and Nishita for all their
warmth and being my family in this country. I also thank Carolina, Leslie, Lynn,
Cheryl, Chris, and Maria for all their help over the years.
Lookingback,IrealizeIhadanidyllicchildhood,onethatcouldhavebeenstraight
out of an RK Narayan book. I find it hard to even imagine how it could have been
better. For this and their unwavering love and support, I am very grateful to my
parents, Sampath Kumaran and Sumithra, and my sister, Srilatha.
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Contents
Acknowledgments iv
Abstract xi
1 Introduction 1
1.1 Motivation and background . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Overview of historical studies of friction . . . . . . . . . . . . 2
1.1.3 Rate and state effects . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.1 Point of view . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . 13
2 Collective behavior of independent viscoelastic asperities interacting
through a mean field 15
2.1 Basic ingredients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Single asperity . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Rough surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3 Local friction law . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Static friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . 22
2.2.3 Static friction evolution . . . . . . . . . . . . . . . . . . . . . 23
2.3 Kinetic friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
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2.3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.2 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . 27
2.3.3 From one to many . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.4 The case of pure white noise . . . . . . . . . . . . . . . . . . . 29
2.3.5 Monte Carlo method . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.6 Test of Monte Carlo method . . . . . . . . . . . . . . . . . . . 30
2.3.7 Velocity jump test . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.8 Velocity strengthening vs. velocity weakening . . . . . . . . . 35
2.3.9 Distribution of forces on asperities . . . . . . . . . . . . . . . 36
2.3.10 Characteristic slip distance . . . . . . . . . . . . . . . . . . . . 36
2.3.11 Parametric study . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.12 Comparison with rate and state formulations . . . . . . . . . . 38
2.3.13 State variable . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.14 Moment as a state variable . . . . . . . . . . . . . . . . . . . . 40
2.4 Nonlinear contact model . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.5 Multiple timescales . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 Static and sliding contact of rough surfaces: effect of surface rough-
ness, material properties, and long-range elastic interactions 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . 49
3.2.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.3 Computational Memory and Complexity considerations . . . . 52
3.2.4 Rough surface generation . . . . . . . . . . . . . . . . . . . . . 52
3.3 Validation using Hertzian contact . . . . . . . . . . . . . . . . . . . . 54
3.4 Static contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4.1 Evolution of contact and force distribution . . . . . . . . . . . 56
3.4.2 Dilatation, area, and friction evolution . . . . . . . . . . . . . 57
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3.4.3 Dependence on normal pressure and system size . . . . . . . . 60
3.4.4 Dependence on surface roughness . . . . . . . . . . . . . . . . 61
3.4.5 Dependence on viscoelastic properties . . . . . . . . . . . . . . 63
3.5 Sliding contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.5.1 Evolution of contacts . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.2 Velocity jump test . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5.3 Dependence on velocity and viscoelasticity . . . . . . . . . . . 69
3.5.4 Magnitude of the direct effect . . . . . . . . . . . . . . . . . . 72
3.5.5 Normal stress jump and pulse tests . . . . . . . . . . . . . . . 72
3.5.6 Dependence of characteristic slip on roughness and viscoelasticity 74
3.5.7 Convergence with increasing spatial frequency . . . . . . . . . 76
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 Static and sliding contact of viscoplastic rough surfaces 79
4.1 Elastic-viscoplastic model . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Static Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Sliding contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Dependence on temperature . . . . . . . . . . . . . . . . . . . . . . . 83
4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 Inclusion of adhesive interactions 86
5.1 Previous studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 A single degree-of-freedom (DOF) system . . . . . . . . . . . . . . . . 88
5.2.1 Nondimensional surface energy γ¯ < 1 . . . . . . . . . . . . . . 90
5.2.2 Nondimensional surface energy γ¯ > 1 . . . . . . . . . . . . . . 91
5.3 Ensemble of independent adhesive elements . . . . . . . . . . . . . . . 96
5.3.1 Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.2 Unloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.3 Energy dissipation . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.4 Force evolution . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.5 Depth-dependence of adhesive strength . . . . . . . . . . . . . 100
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5.3.6 Dependence of adhesive strength on roughness . . . . . . . . . 100
5.3.7 Depth-dependent energy dissipation . . . . . . . . . . . . . . . 101
5.3.8 Dependence of energy dissipation on surface roughness and sur-
face energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4 Extension to three dimensions . . . . . . . . . . . . . . . . . . . . . . 103
5.4.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.4.2 Numerical implementation . . . . . . . . . . . . . . . . . . . . 105
5.4.3 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . 107
5.4.4 Indentation of an elastic spherical surface . . . . . . . . . . . . 107
5.4.5 Effect of adhesion on rough surface friction . . . . . . . . . . . 109
5.4.6 Viscoelastic adhesive contact . . . . . . . . . . . . . . . . . . . 109
5.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6 A force threshold model for adhesion and mode I interfacial cracks111
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 Indentation of a spherical surface . . . . . . . . . . . . . . . . . . . . 116
6.5 Dependence on discretization size . . . . . . . . . . . . . . . . . . . . 117
6.6 Scaling of critical force with discretization size . . . . . . . . . . . . . 118
6.7 Is 0.75 the magic number? . . . . . . . . . . . . . . . . . . . . . . . . 119
6.8 The case with no elastic interactions . . . . . . . . . . . . . . . . . . 122
6.9 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7 Conclusion 125
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.2.1 Effects of shear forces at the contacts . . . . . . . . . . . . . . 126
7.2.2 Effects of temperature . . . . . . . . . . . . . . . . . . . . . . 127
7.2.3 Sliding stability . . . . . . . . . . . . . . . . . . . . . . . . . . 127
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Appendices 129
A Rough surface generation 130
A.1 Gaussian autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.2 Exponential autocorrelation . . . . . . . . . . . . . . . . . . . . . . . 135
Bibliography 137