Dislocation model of localized plastic deformation initiated with a flat punch

We consider a classical contact mechanics problem, namely, the indentation of a ductile half-plane by a rigid flat punch (in plane strain), and revisit it using the dislocation mechanics approach. The dislocation nucleation and dislocation interaction beneath the indenter are examined. The threshold load for dislocation nucleation and the dislocation emission angle are obtained in analytical form. Moreover, based on the consideration of dislocation interaction, we explore the mechanism of contact load evolution (hardening). A triangular “dead zone” beneath the indenter, which could not be thus far accurately explained by traditional continuum models, is predicted in good agreement with the results of careful experiments that are reported in the literature. The proposed model is likely to be useful for the analysis of contacts at both the micro- and macro-scales.