Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium

This work aims at studying the stress relaxation behavior of a nominally flat (rough) surface of a viscoelastic material in contact with a rigid half space. The effect of temperature will be included through the concept of activation energy using Arrhenius's equation. A synthesized Cantor–Borodich (CB) profile is used to construct the rough surface. CB profile has two scaling parameters, a and b, and different heights hi for each generation of asperities. This simple model is applicable for fractal surfaces in which a single exponent (the fractal dimension) is enough to describe their quality.The surfaces in contact are viscoelastic, and they are assumed to behave according to the linear Maxwell model. An asymptotic power law is obtained, which relates the force and the bulk temperature acted on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-viscoelastic. The obtained model shows a good agreement when compared with the experimental results obtained by Handzel-Powierza et al. [Handzel-Powierza Z, Klimczak T, Polijaniuk A. On the experimental verification of the Greenwood–Williamson model for the contact of rough surfaces. Wear 1992;154:115–24].