Some aspects of post-yield contact problems

Abstract

The mechanics of contact between a frictionless ball and a semi-infinite block of material are well known when the resulting deformation is wholly elastic. If a sufficiently heavy load is imposed, some material will enter the plastic regime and there will be a redistribution of the contact pressure. The nature of the resulting and residual stress field after both single and repeated loadings is discussed. It is shown that in each case a residual tensile stress develops normal to the surface and a residual compressive stress lies parallel to the plane of the surface. A comparison is made between the form of the residual stresses calculated on the basis of rigid plastic behaviour (using the slip line field theory) and on the basis of incremental plasticity (under the assumption that the extended elastic stress field dominates the problem). An extension to the problem is considered involving the repeated random indentation of a block: this models approximately the shot-peening process, and enables the resulting residual stresses to be quantified.