Effect of Wear on the Evolution of Contact Pressure at a Bimaterial Sliding Interface

The eigenfunction method pioneered by Galin (J Appl Math Mech 40: 981–986, 1976) is extended to provide a general solution to the transient evolution of contact pressure and wear of two sliding elastic half-planes, under the assumption that there is full contact and that the Archard–Reye wear law applies. The governing equations are first developed for sinusoidal profiles with exponential growth rates. The contact condition and the wear law lead to a characteristic equation for the growth rate and more general solutions are developed by superposition. The case of general initial profiles can then be written down as a Fourier integral. Decay rates increase with wavenumber, so fine-scale features are worn away early in the process. Qualitative features of the problem are governed by two dimensionless wear coefficients, which for many material combinations are small compared with unity. If one of the bodies does not wear and is non-plane, the system evolves to a non-trivial steady state in which the wearing body acquires a profile which migrates over its surface.