Collective Behavior of Asperities As a Model for Friction and Adhesion

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Collective Behavior of Asperities As a Model for Friction and Adhesion 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) ii 5/3/2015 Try Google Input Tools online – Google Input Tools ಸಂೕಹೕಕೃಲ ಂದಲ ಇಂ ನಂ ಂಂಂದಲ ಂ ೕದಂದದ ಮನಂ ಇಂೕ ಮತತ ಮಂಮ ­ c 2015 Srivatsan Hulikal All Rights Reserved data:text/html;charset=utf-8,%3Cspan%20style%3D%22color%3A%20rgb(0%2C%200%2C%200)%3B%20font-family%3A%20arial%2C%20sans-serif%3B%20fo… 1/1 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 v 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. Looking back, I realize I had an idyllic childhood, one that could have been straight 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. vi Contents Acknowledgments iv Abstract xi 1 Introduction1 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 vii 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 viii 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 energyγ ¯ < 1.............. 90 5.2.2 Nondimensional surface energyγ ¯ > 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 ix 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 x Appendices 129 A Rough surface generation 130 A.1 Gaussian autocorrelation......................... 133 A.2 Exponential autocorrelation....................... 135 Bibliography 137 xi Abstract Understanding friction and adhesion in static and sliding contact of
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