Some Issues of Rough Surface Contact Plasticity at Micro- and Nano-Scales
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Some Issues of Rough Surface Contact Plasticity at Micro- and Nano-Scales Y. F. Gao, A. F. Bower and K.-S. Kim Division of Engineering, Brown University, Providence, RI 02912, U.S.A. ABSTRACT Rough surface contact plasticity at microscale and nanoscale is of crucial importance in many new applications and technologies, such as nano-imprinting and nano-welding. This paper summarizes our recent progress in understanding contact plasticity from a multiscale point of view, and also presents our perspectives. We first discuss a contact model based on fractal roughness and continuum plasticity theory. Interestingly, our simple, elastic-plastic contact model of the Weierstrass-Archard type gives rise to many practical scaling relations of contact pressure, contact compliance etc. The usefulness of those predictions is discussed for experimental measurements of the thermal/electrical contact resistance. A material length scale can be introduced by a nonlocal plasticity theory, or implicitly by dislocation mechanics modeling. The recent work on micro-plasticity of surface steps gives a variety of surface yielding and hardening behaviors, depending on interface adhesion, roughness features and slip systems. As a consequence, a rough surface contact at mesoscale can lead to the formation of a boundary layer with sub-layer dislocation structures, which cannot be predicted by existing strain gradient plasticity theories. The micromechanical analysis of surface plasticity could serve as the connection between microscale bulk dislocation plasticity and nanoscale atomistic simulations. INTRODUCTION Many important mechanical properties and failure problems are governed by rough surface contact at microscale and nanoscale. Recent technological advancements, such as nanoscale imprinting and cold-welding [1], require fundamental understandings of rough surface contact plasticity, adhesion and friction at small length scales. Rough surface contact plasticity is intrinsically a multiscale problem because of the multiscale nature of surface roughness, the structure- and size-sensitive material deformation behavior, and the importance of surface forces and other physical interactions. The surface roughness is usually characterized by the power spectral density function (PSDF), which is the Fourier transform of the spatial autocorrelation function of the roughness profile. For an ideally self-affine fractal surface, the PSDF is a straight line and the slope tells the fractal dimension. A real rough surface might be piece-wise fractal (i.e. different fractal dimensions at different scale ranges), or not fractal at all. For example, a cleaved surface of LiF is very flat elsewhere except some widely separated surface steps. For large scale contacts, even if we restrict our attention to the use of classic plasticity theory, there is no agreement on the prediction of contact pressure distribution, contact compliance and other properties [2,3]. Motivated by the recent work in [4], we have carried out an elastic-plastic contact analysis of
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