Bounds on the electrical resistance between contacting elastic rough bodies

Abstract

A method is developed for placing bounds on the electrical contact conductance between contacting elastic bodies with rough surfaces. An analogy is rst established between contact conductance and the incremental sti¬ness in the mechanical contact problem. Results from contact mechanics and the reciprocal theorem are then used to bracket the mechanical load{displacement curve between those for two related smooth contact problems. This enable bounds to be placed on the incremental sti¬ness and hence on the electrical conductance for the rough contact problem. The method is illustrated by two simple examples, but its greatest potential probably lies in establishing the maximum e¬ect of neglected microscales of roughness in a solution of the contact problem for bodies with multiscale or fractal roughness.

Contact conductance of rough surfaces composed of modified RMD patches

“…if the surface is fractal in the Weierstrass-Mandelbrot sense), there must nonetheless exist a largest length dimension representing the finite size of the nominal contact area. Since the coarser features of the surface profile are known to dominate the contact conductance [13,15], the length scales defining these two processes are important parameters in the problem description. Here we shall characterize the long wavelength cut-off by the length parameter D and the finite dimensions of the nominal contact area by L. We therefore propose the following functional dependence for the incremental stiffness per unit area: dp dd ¼ dp dd…”

“…The specific contact conductance of rough surfaces, or conductance per unit area C, can be correlated to the the derivative of the force-indentation curve, i.e., the incremental stiffness, according to the electrical-mechanical analogy established in [13]. In formulae:…”

“…More specifically, the random midpoint displacement (RMD) generation algorithm is modified in order to generate surfaces with minimized waviness effects. This issue is particularly important for the contact conductance, which is primarily governed by the coarse scale topological features of the rough surface [13]. Applying the electric-mechanical analogy derived in [13], the specific contact conductance is determined via the derivative of the pressure vs. separation curve (incremental contact stiffness).…”

“…This issue is particularly important for the contact conductance, which is primarily governed by the coarse scale topological features of the rough surface [13]. Applying the electric-mechanical analogy derived in [13], the specific contact conductance is determined via the derivative of the pressure vs. separation curve (incremental contact stiffness). Detailed numerical results will show the effect of the principal dimensionless numbers on the power-law exponent b.…”

A Thermo-mechanical cohesive zone model

“…Obviously, such models require detailed information about the surface characteristics in order to be used for qualitative predictions. The work of Barber [16], addressing the electrical resistance of contacting elastic rough surfaces, provided lower and upper bounds for electrical contact resistance as a function of surface roughness. Based on a theorem of contact mechanics and assuming that the contacting bodies can be modeled as half spaces, it is proved that there exists a simple relation between the electrical resistance and the incremental elastic compliance of the contacting bodies.…”