The electrical/thermal conductance of rough surfaces––the Weierstrass–Archard multiscale model

Abstract

Rough surfaces show a load-dependent electrical constriction resistance. Here, using a recent analogy due to Barber [Proc. R. Soc. London A 459 (2003) 53] between the incremental stiffness and the conductance in the elastic regime, and the Archard hypothesis to solve the multiscale contact problem, the conductance is found for the profile defined by the Weierstrass series. The analysis is also approximately valid, neglecting thermal effects on the contact area, for the thermal conductance.

A Genetic-Algorithm-Optimized Fractal Model to Predict the Constriction Resistance From Surface Roughness Measurements

“…The first term, known as electrical constriction resistance (ECR), is due to the roughness of the contacting surfaces since the electrical current has to flow through the geometric constriction. The second term, known as film resistance, is attributed to poorly conductive films or oxides formed at the contacts' interface [5]. In this work this latter term is almost removed by applying a previous chemical cleaning of the interface so that the main term of the contact resistance is the constriction resistance.…”

“…Early studies were pioneered by Holm [7] and Greenwood [8], who proposed analytical formulas to calculate the ECR due to round shaped clusters [5]. Different approaches to model the contact resistance of rough surfaces are found in the technical literature, including statistical, multiscale and fractal models [9].…”

“…Surface measurements have revealed that peaks and valleys associated to rough surfaces show a multiscale pattern [5], [11] with no evident smallest scale [10]. Fractal-based models are good candidates to reproduce constrictive effects taking into account such different scales [5], since most of the statistical models do not consider this phenomenon [9].…”

“…Fractal-based models are good candidates to reproduce constrictive effects taking into account such different scales [5], since most of the statistical models do not consider this phenomenon [9]. It is expected that when increasing the number of scales, the ECR approaches a limit value even under the elastic approach in which the real contact area is assumed to be proportional to the mechanical load intensity [5]. However, when considering a perfect fractal surface with infinite scales, the true area of contact comprises an infinite number of infinitely small contact spots, which are subjected to an infinite contact pressure [12].…”

“…Due to its random and multiscale nature, an accurate prediction of the ECR of rough surfaces is still a challenging problem [5]. Kogut and Kompoupoulos [13] developed a model to determine the contact resistance of conductive rough surfaces, assuming a fractal geometry, elastic-plastic asperities and sizedependent micro-contacts.…”