Influence of Equi-Biaxial Residual Stress on Spherical Indentation of Strain Hardening Materials

Residual stress plays an important role in the mechanical performance of engineering structures. In this paper, the indentation of pre-stressed strain hardening materials by a rigid sphere is simulated through the finite element method. It is shown that the mean contact pressure in the post-yield regime keeps continuously increasing with the indentation proceeding. Compared to the case without residual stress, compressive residual stress tends to increase the mean contact pressure at a given indentation depth, while tensile stress has an inverse effect. To quantitatively indicate the influence of residual stress, a nominal contact pressure is defined, which obtains its maximum value at a critical depth. The dependences of the maximum nominal pressure and the critical indentation depth on the residual stress and the material properties are determined explicitly through large numbers of simulations. Inspired by the nominal pressure deviation stemmed from residual stress, a new approach is proposed for measuring residual stress through spherical indentation tests.