UC Berkeley

The main objective of this dissertation was to develop both finite element and analytical models of contact, friction, and wear phenomena encountered at the nanoscale. This was achieved by the development of continuum mechanics and discrete dislocation models of the deforming homogeneous or layered media and the use of self-affine (fractal) geometry for the representation of the interface topography. The specific accomplishments of this work are as follows.

The contact problem of a rigid flat indenting an elastic-plastic semi-infinite medium with a sinusoidal surface profile was examined in light of a two-dimensional plane-strain finite element analysis. Numerical results of the dimensionless contact pressure, normal approach, average surface rise, center-line-average roughness, peak-to-valley roughness, cavity volume, and ratio of truncated-to-real contact area versus fractional contact area obtained for relatively compliant and stiff elastic-perfectly plastic half-spaces were compared with results obtained from a slip-line plasticity analysis. These results have direct application to metal working processes, such as rolling, and provide insight into the evolution of surface and subsurface contact deformation and asperity interaction of contacting surfaces exhibiting periodic waviness.

Mechanical failure of patterned alternating phase-shift mask (APSM) nanostructures due to dynamic pressure loadings caused by megasonic cleaning was examined in the context of simulation results obtained from a two-dimensional plane-strain finite element analysis. A parametric study of the effects of microstructure geometry and loading frequency on the subsurface stress state and mask structural integrity was performed for two typical chromium-quartz APSM patterns. Numerical results elucidate possible failure modes and effect of microstructure dimensions on pattern damage during megasonic cleaning, and have direct implications to the design of extreme ultraviolet lithography masks and optimization of the megasonic cleaning process.

Analytical models were developed to study the friction, wear, energy dissipation, and plastic flow of surfaces exhibiting multi-scale roughness in both sliding and normal contacts. A contact mechanics study of friction, energy dissipation, and abrasive wear of a hard and rough (fractal) surface sliding against a soft and smooth substrate was developed based on the slip-line theory of plasticity. The slip-line model yields relationships of the deformation behavior and coefficient of friction of a fully plastic asperity microcontact in terms of the applied normal load and interfacial adhesion. The analysis of the rough surface contact provides insight into the dependence of global friction coefficient, energy dissipated during sliding contact, and abrasive wear rate and wear coefficient on the global interference (total normal load effect), interfacial friction conditions (adhesion effect), fractal parameters (roughness effect), and elastic-plastic material properties (deformation mode effect). Numerical results for representative contact systems illustrate the effects of interfacial adhesion, global interference (total normal load), topography parameters, and material properties on friction coefficient, dissipated frictional energy, and wear rate/coefficient.

The dependence of plastic deformation at asperity contacts and wear rate (coefficient) on global interference (total normal load), elastic-plastic material properties, topography (roughness), and work of adhesion of contacting surfaces was examined in a contact mechanics analysis of adhesive wear of rough (fractal) surfaces in normal contact. Loss of materials (wear) was presumed to originate from plastic contacting asperities, accounting for the contribution of interfacial adhesion to the normal load at each asperity microcontact. The effects of material properties, roughness, surface compatibility, and environmental conditions on the adhesive wear rate and wear coefficient were discussed in the context of numerical results for representative contact systems.

Plane-strain indentation of a single-crystal semi-infinite medium by a rigid indenter was analyzed by discrete dislocation plasticity. The profile of the rigid indenter was characterized by either a smooth (cylindrical) or a rough (fractal) surface. This is the first contact analysis based on discrete dislocations derived for crystalline materials indented by a surface exhibiting multi-scale roughness. Short-range dislocation interactions were modeled in accord to dislocation constitutive rules, while long-range dislocation interactions were modeled by the elastic stress fields of edge dislocations. Simulation results provided insight into the effects of contact load, dislocation source and obstacle densities, slip-plane orientation and distribution, indenter radius, topography (roughness) of fractal surface, and multi-scale asperity interactions on damage at the onset of yielding (emission of first dislocation dipole) and plasticity evolution represented by the development of dislocation structures. Plastic deformation under the theoretical strength of the material was related to contact size effects.

The findings in this dissertation provide fundamental understanding of surface deformation behavior, evolution of subsurface stress field due to contact traction, and tribological characteristics of elastic-plastic media with patterned and rough surface profiles subject to contact and/or surface loadings. The obtained results have direct implications in various industry fields, such as metal working, semiconductor electronics packaging, magnetic storage recording, and microelectromechanical devices.