UC Berkeley

The principal objective of this dissertation was to develop numerical and analytical mechanics models accounting for nano-/micro-scale solid surface interaction. This was accomplished by developing finite element models of an asperity in adhesive sliding contact with a homogenous half-space and asperity micro-fracture due to normal and sliding contact of homogenous or layered half-spaces, and analytical models of nanoscale surface polishing and nanoparticle embedment on rough surfaces using a probabilistic approach.

Adhesive interaction of a rigid asperity moving over a homogeneous elastic-plastic half-space was modeled by nonlinear springs obeying a constitutive law derived from the Lennard-Jones potential. The evolution of the normal and friction forces, subsurface stresses, and plastic deformation at steady-state sliding was examined in terms of the work of adhesion, interaction distance (interfacial gap), Maugis parameter, and plasticity parameter, using the finite element method (FEM). The deformation behavior of homogeneous elastic-perfectly plastic (EPP) and elastic-linear kinematic hardening plastic (ELKP) half-spaces subjected to repeated adhesive sliding contacts was also the objective of this analysis. Numerical results provided insight into the effects of the aforementioned parameters on the friction and normal forces, stress-strain response, and evolution of subsurface plasticity with the accumulation of sliding cycles. The steady-state mode of deformation due to repeated adhesive sliding contacts was examined for both EPP and ELKP material behavior.

Subsurface cracking in a layered medium consisting of an elastic hard layer and an elastic-plastic substrate due to adhesive sliding against a rigid asperity was analyzed using linear elastic fracture mechanics (LEFM) and FEM model. The dominance of shear and tensile mode of crack propagation was examined in terms of the interaction depth, layer thickness, crack location, crack length, work of adhesion, and mechanical properties of the thin layer and substrate materials. The effect of adhesion on asperity failure due to normal contact was also studied. The crack growth direction, dominant fracture mode, and crack growth rate were predicted as functions of the initial crack position, asperity interaction distance, interfacial properties, and mechanical properties. FEM results showed the occurrence of different crack mechanisms, such as of crack-face opening, slip, and stick.

The evolution of the surface topography during nanoscale surface polishing was studied with a three-dimensional stochastic model that accounts for a multi-scale (fractal) surface roughness and elastic, elastic-plastic, and fully-plastic deformation of the asperities on the polished surface caused by hard abrasive nanoparticles embedded in the soft surface layer of a rigid polishing countersurface. Numerical results of the steady-state roughness of the polished surface, material removal rate, and wear coefficient were determined in terms of the apparent contact pressure, polishing speed, original topography and mechanical properties of the polished surface, average size and density of the nanoparticles, and surface roughness of the polishing plate. The density of hard abrasive nanoparticles embedded in the soft countersurface was predicted by a probabilistic-hydrodynamic model in terms of the surface topographies, particle size distribution, applied forces, macroscopic geometry of the moving surfaces, surface kinematics, and fluid properties.

The findings of this dissertation yield new insight into the deformation behavior of adhesive contacts involving homogeneous and layered half-spaces, from the single asperity level to surfaces with multi-asperity topographies. The significance of the interfacial properties and material properties on adhesive asperity sliding contact, the effects of interfacial adhesion and crack properties on asperity cracking and subsurface cracking, and the dependence of the surface topography evolution during nanoscale polishing on the surface topographies, material properties, and abrasive nanoparticle size were examined in the context of numerical and analytical results. The results of this thesis elucidate the mechanical aspects of surface contact interaction in nano/microscale engineering components and surfacing processes, such as hard-disk drives, micro-electro-mechanical systems, and nanoscale surface polishing, and provide insight into the underlying reasons leading to mechanical failure of homogeneous and layered half-spaces subjected to surface tractions. Solutions and FEM results for single-asperity contacts obtained in this work can be integrated into probabilistic analyses of contacting rough surfaces to advance the current state of contact mechanics of surfaces exhibiting multi-asperity topographies.