A Multiscale Theoretical Analysis of the Mechanical, Thermal, and Electrical Characteristics of Rough Contact Interfaces Demonstrating Fractal Behavior

Abstract

The highly complex contact interface phenomena require analysis at different length scales ranging from nanometer up to nearly centimeter scales. When two nominally smooth surfaces are brought into contact, solid-solid interaction across their contact interface is confined at multiple protrusions (asperities) of various shapes, sizes, and heights. The deformation mechanisms encountered at the asperity level control the surface conformity, which, in turn, influences the transmission of traction, heat, and electric current across the contact interface. Thus, the multiscale roughness of real surfaces necessitates the advance of methodologies and contact models that bridge the spectrum of relevant length scales. Rough surfaces have been traditionally charac¬terized by statistical parameters, which cannot be uniquely deter-mined because they depend on the sampling interval and the resolution of the mea¬sur¬ing device. On the contrary, the scale-invariant parameters employed in fractal geometry provide an unbiased representa¬tion of the surface topography. This article provides an appraisal of the multiscale mechanical, thermal, and electrical characteristics of rough contact interfaces demonstrating fractal behavior. Theoretical treatments of elastic, elastic-plastic, and fully plastic deformation, heat conduction, temperature rise, and electrical contact resistance are presented for contact interfaces characterized by fractal geometry, providing a fundamental basis for developing multiscale thermo-electro-mechanics analytical treatments for contacting solid bodies.