A numerical elastic-plastic contact model for rough surfaces

Elastic-plastic contacts were analyzed by means of a three-dimensional numerical model based on minimization of complementary energy, in which the effect of plastic deformation is included by superimposing the plastic residual displacement on the geometry of contacting surface. The plastic strain increments are determined through the radial return method and J₂ flow theory, which are integrated with the conjugate gradient method (CGM) algorithm and the fast Fourier transform (FFT) technique for improving numerical efficiency. The results from the present numerical model were compared to those from finite element method (FEM) for three typical contacts-i.e., those of a smooth elastic-plastic 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-which showed persistent good agreement between our model and FEM. Then, three-dimensional elastic-plastic contacts of real engineering surfaces produced by a grinding process were analyzed. Due to roughness effect, the maximum von Mises stress and plastic region were found at the locations closer to the surface. In elastic-plastic contacts, the pressure decreases at the peaks and increases at the valleys if compared to the results from purely elastic model. Moreover, plastic flow makes the rough surface flatten or become less fluctuating.