On normal and oblique inelastic contact

by Larsson, Joachim

In this thesis normal and oblique inelastic contact is analysed in four papers. Analysis of normal contact is of major concern in hardness testing and in numerous practical applications. In traditional hardness testing, plastic material properties are determined by pressing an indenter into a solid material of current interest. In Paper A spherical impact has been analysed and dynamic hardness and its relation to constitutive parameters, corresponding to strain-hardening and strain-rate sensitivity, studied in detail. A consistent three-dimensional contact theory has been laid down and based on detailed finite element computations, universal relations between hardness, impression velocity and depth together with resulting contact regions have been determined. Paper B concentrates on normal flattening of rough surfaces. A micro-mechanical analysis is carried out for general viscoplastic contact between single asperities. Probabilistic models are used to determine the macrobehaviour for relations between resulting force, approach and true contact area between surfaces. Features such as volume conservation, strain-hardening effects and topographic scale dependence are discussed. Many practical applications in contact mechanics comprise oblique contact. In these applications, such as compaction of powder aggregates, relations between normal and shear forces, contact region and impression depth are of major interest. In Papers C and D proportional oblique contact has been analysed for power-law creeping solids in two and three dimensions, respectively, with perfect plasticity as an asymptotic case. A solution strategy based on a self-similar transformation resulting in a reduced problem, corresponding to flat die indentation of a nonlinear elastic solid, was developed. A three-dimensional finite element procedure was worked out to explicitly solve the problem. An invariant relation between contact area and indentation depth was found to depend only on four parameters, i.e. the creep exponent, the indenter profile, the level of obliquity and the coefficient of friction, the influence of the latter two shown to be weak. Detailed results were given for the location and shape of contact regions as well as micro-slip contours and resulting deformation fields. Although surface displacements proved to be severely asymmetric at increasing creep exponent and angle of impression, ? ? ??3,in the spherical case reduced normal and tangential forces proved to be remarkably independent in contrast to the plane strain case.