Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere—II. Results

Abstract

The title problem is considered within the theory of incremental elastoplasticity and results of an earlier finite element analysis (Part I) processed to furnish: the indentation response with increasing pressure, contact and interior stresses on loading and unloading, yield region growth, strain distributions, and surface displacement profiles. The more significant findings stemming from these results may be summarized as being: theoretical confirmation of Tabor's simple experimental correlations for work-hardening materials, demonstration of an improved finite element capability, over that reported previously in terms of accuracy and ability to track the indentation processes to higher load levels, an appreciation of some of the inadequacies of slip-line analysis in dealing with problems of this type, generally good agreement between theory and the physical evidence whenever comparison possible, nearly self-similar response to increasing load in the fully plastic regime, and some quantification of the residual tensile stresses that can occur.