A Mechanics Analysis of Cumulative Damage Leading to Material Loss at Fractal Contact Interfaces Subjected to Fretting

Abstract

Basic understanding of the removal of material in oscillatory contacts subjected to small-amplitude oscillatory sliding, known as fretting, requires comprehensive mechanics analysis accounting for the effects of interfacial topography, surface traction, and oscillation cycles on the evolution of plasticity-induced damage. For that reason, an elastic–plastic contact mechanics analysis of an isotropic strain hardening half-space in oscillatory contact with a rigid surface exhibiting multi-scale roughness characterized by fractal geometry was performed with the finite element method. Cumulative damage was modeled with a dimensionless damage variable given by an integral equation of the equivalent plastic strain. Material degradation was tracked by a dimensionless parameter depending on the fracture energy for creating a crack of unit area, the effective stress at the initiation of material degradation, the equivalent plastic strain, and a characteristic length determined by the size of the smallest finite elements. Numerical results of the subsurface stress and plastic strain fields and the material removal rate obtained for a range of fractal parameters, normal load, and oscillation cycles illuminated the effect of the progression of plasticity-induced damage on the loss of material. Contrary to the classical wear law, the material removal (wear) rate demonstrated a nonlinear dependence on normal load, attributed to the dependence of relative slip at the contact interface on mechanical interlocking, resulting from the increase of surface conformity with the normal load and loss of material. From a fundamental perspective, this study provides a computational mechanics framework for performing parametric studies of the material removal rate in mechanical devices operating in reciprocating sliding contact mode.