Contact Mechanics Modeling of Homogeneous and Layered Elastic-Plastic Media: Surface Roughness and Adhesion Effects By Zhichao Song A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering – Mechanical Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Kyriakos Komvopoulos, Chair Professor David Bogy Professor Robert Ritchie Fall 2012 Contact Mechanics Modeling of Homogeneous and Layered Elastic-Plastic Media: Surface Roughness and Adhesion Effects Copyright © 2012 By Zhichao Song Abstract Contact Mechanics Modeling of Homogeneous and Layered Elastic-Plastic Media: Surface Roughness and Adhesion Effects by Zhichao Song Doctor of Philosophy in Engineering-Mechanical Engineering University of California, Berkeley Professor Kyriakos Komvopoulos, Chair The main objective of this dissertation was to analyze surface contact interaction at different length scales and to elucidate the effects of material properties (e.g., adhesion and mechanical properties), normal and shear (friction) surface tractions, and topography parameters (e.g., roughness) on contact deformation. To accomplish this objective, a surface adhesion model based on an interatomic potential was incorporated into finite element contact models of rough surfaces exhibiting multi-scale roughness described by statistical and fractal geometry models. The problem of a rigid sphere in contact with an elastic-plastic half-space was first examined in the light of finite element simulations. Four post-yield deformation regimes were identified and the boundaries of neighboring regimes were obtained by curve-fitting of finite element results. Material hardness was shown to significantly deviate from the similarity solution with decreasing elastic modulus-to-yield strength ratio and the logarithmic dependence of the mean contact pressure on the indentation depth was found to hold only when the plastic zone was completely surrounded by elastic material. Constitutive equations were first derived for elastic- perfectly plastic half-spaces from curve-fitting finite element results and were then extended to isotropic, power-law hardening half-spaces, using the concept of the effective strain, which correlates the indentation depth with the indenter size. Finite element simulations of unloading process and repetitive normal contact were used to correlate the residual indentation depth and the dissipated plastic energy with the maximum indentation depth. Elastic shakedown, plastic shakedown, and ratcheting were identified by tracking the accumulation of plasticity for different values of maximum contact load and elastic modulus-to-yield strength ratio. The semi-infinite half-space was characterized by three different regions, named ratcheting region, shakedown region and elastic region, as the distance to contact surface increases. The obtained results have direct implication in material property measurements obtained with indentation method, particularly for materials exhibiting strain hardening behavior, and provide insight into the accumulation of plasticity due to repetitive contact loading, which is important in the understanding of the contact fatigue life of contact-mode devices. 1 Sliding contact between a rigid fractal surface exhibiting multi-scale roughness and an elastic-plastic half-space was examined to elucidate rough-surface deformation due to small- amplitude reciprocating sliding (fretting). Stick-slip at the asperity scale was analyzed based on Mindlin’s theory and a friction model that accounts for both adhesion and plowing effects. Numerical results yield insight into the effects of surface roughness, contact pressure, oscillation amplitude, elastic modulus-to-yield strength ratio, and interfacial adhesion on the friction force, slip index, and energy dissipation. The results of this study illustrate the important role of the contact load and surface topography on the energy dissipation and fretting wear of small- amplitude oscillatory contacts. Surface adhesion modeled as surface traction obeying the Lennard-Jones (LJ) potential was incorporated into the contact analysis of a rigid sphere indenting an elastic half-space to study contact instabilities associated with instantaneous surface contact (jump-in) and detachment (jump-out). This surface traction was introduced into a finite element contact model in the form of nonlinear spring elements and the jump-in/jump-out condition obtained analytically was confirmed by finite element results. Then, adhesive contact between a rigid sphere and an elastic-plastic half-space was analyzed and the effect of plasticity on the pull-off force and the commencement of contact instabilities was interpreted in terms of a modified Tabor parameter. The developed finite element model with nonlinear spring elements representing adhesive surface interaction provides a physics-based, computationally-efficient technique for studying adhesive contacts. The obtained results provide explanation for the contact instabilities encountered during surface probing with microprobe tips and stiction (permanent adhesion) in contact-mode microdevices. Adhesive contact between a rigid sphere and a layered medium analyzed with the finite element method shed light into adhesion-induced contact deformation. Two modes of surface detachment were observed for perfect bonding of the film to the substrate – brittle- and ductile- like surface detachment. Simulation results illustrate the effects of the maximum surface separation, film thickness, film-to-substrate elastic property mismatch, and substrate yield strength on the mode of surface detachment and residual deformation. Introducing a cohesive model that allows for crack formation and growth along the film/substrate interface in the previous finite element model, a residual cohesive zone was found at the crack tip after complete unloading. Contact instabilities and interface delamination were interpreted by the competing effects of surface adhesion and interfacial cohesion. Crack closure and crack-tip opening displacement (CTOD) were studied by performing a parametric study of the cohesive strength, interfacial energy, surface energy, surface adhesive strength, substrate yield strength, and initial defect size. The obtained results can be used to explain thin-film failure in contact systems due to the effect of adhesion and to improve the endurance of thin-film media subjected to surface tractions. Adhesive contact of two elastic rough surfaces was analyzed by integrating asperity-scale constitutive equations into the model of Greenwood and Williamson (1966) to account for the effect of contact instabilities at asperity level on the macroscopic contact response. The strength of adhesion was found to be mostly affected by the Tabor parameter and the surface roughness. The widely used adhesion parameter of Fuller and Tabor (1977) was shown to be appropriate only for contact systems characterized by a high Tabor parameter. Therefore, a new adhesion 2 parameter that governs the strength of adhesion of contact systems with a low Tabor parameter was introduced. Finally, a generalized adhesion parameter was derived by using the concept of the effective interatomic separation, defined as the ratio of the elastic stretch due to adhesion and the equilibrium interatomic distance. The research carried out in this dissertation provides fundamental understanding of the evolution of the stress and strain fields in contacting surfaces, the evolution of plasticity in indentation, the development of friction and dissipation of energy in fretting contacts, the occurrence of adhesion-induced contact instabilities and interfacial delamination, and the factors affecting the strength of adhesion for rough surfaces in normal contact. The results of this thesis have direct implications in various technologies, including high-efficiency gas turbines, magnetic storage devices, and microelectromechanical systems. 3 Dedications To my father, mother and girlfriend for their support, encouragement and unselfish love i Table of Contents List of Figures................................................................................................................................v List of Tables...............................................................................................................................xiv Acknowledgements......................................................................................................................xv Chapter 1 Introduction.................................................................................................................1 Chapter 2 Elastic-plastic spherical indentation: deformation regimes, evolution of plasticity and hardening effect...................................................................................................6 2.1 Introduction...................................................................................................................6 2.2 Method of analysis........................................................................................................8 2.2.1 Problem definition...............................................................................................8 2.2.2 Finite element model...........................................................................................8 2.2.3 Constitutive material model...............................................................................10