A Simplified Numerical Elastic-Plastic Contact Model for Rough Surfaces

Abstract

Elastic-plastic contacts have been analyzed by means of a three-dimensional numerical model based on minimization of complementary energy and the fast Fourier Transform (FFT). The effect of plastic deformation is included in solutions by superimposing the plastic residual displacement on the geometry of contacting surface. A plastic factor, α, is introduced to address the effects of residual stress, and the radial return method and J2 flow theory with isotropic hardening law are used for determining plastic strain increment. The results from the present numerical model are compared to those from finite element method (FEM) for three typical contacts: i.e., a smooth elastic ball in contact with a rigid body of different geometry: a smooth plane, a plane superposed with a single asperity, and a sinusoidal wave on the plane. The comparisons show good agreements between our model and FEM. Then, three-dimensional elastic-plastic contacts of real engineering surfaces produced by grinding process are analyzed. Due to roughness effect, the maximum von Mises stress and plastic region are found at the locations closer to the surface. In elastic-plastic contacts, the pressure decrease at the peaks and increase at the valleys if compared to the results from purely elastic model. Moreover, plastic flow makes the roughness surface flatten.