On frictional effects at inelastic contact between spherical bodies
Normal inelastic contact between spherical bodies in examined theoretically and numerically. The analysis is focused on viscoplastic material behaviour. In particular, the effect of Coulomb friction is analyzed 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 can be reduced to 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 solution as outlined in a previous study by \textit{B. Storåkers}, \textit{S. Biwa} and \textit{P.-L. Larsson} [Int. J. Solids Struct. 34, No. 24, 3061-3083 (1997; Zbl 0939.74573)]. The results show that frictional effects can be of importance only when global properties such as the contact area and the mean contact pressure are close to perfectly-plastic material properties. Even under 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 such features as crack initiation and crack growth.
scientific article; zbMATH DE number 1421745