On frictional effects at inelastic contact between spherical bodies

Abstract

Normal inelastic contact between spherical bodies is examined theoretically and numerically. The analysis is focused on viscoplastic material behaviour. In particular the effect of Coulomb friction is analysed in some detail, both regarding global and field variables. It is shown that the solution to the problem of contact between two deformable spherical bodies is provided by the solution of the fundamental problem of indentation of a viscoplastic half-space by a rigid sphere. The indentation analysis is based on self-similarity and cumulative superposition of intermediate flat die solutions as outlined in detail in a previous study by Storåkers et al. (International Journal of Solids and Structures 1997;34:3061–83). The results show that frictional effects, when global properties such as the contact area and the mean contact pressure are at issue, will only be of importance at close to perfectly plastic material behaviour. Even in such circumstances the difference between values given by the solutions for frictionless and for full adhesive contact is no more than approximately 10%. Accordingly, it can be concluded that frictional effects are essentially negligible, when, for example, material characterization of viscoplastic solids by Brinell indentation is of interest. The situation is, however, quite different when field variables are at issue. In this case, stress and strain fields can be substantially influenced by friction with possible implications for features such as crack initiation and crack growth.