Stress Distributions in Soft Metals Due to Static and Dynamic Loading by a Steel Sphere

The quasi-static and dynamic indentation of a hard steel sphere into a massive lead block, considered to represent a rigid perfectly-plastic half-space, has been investigated experimentally. The technique of visioplasticity was employed to calculate the stress pattern from which an empirical relation delineating the variation of hydrostatic pressure with depth of indentation was constructed. This expression was utilized in conjunction with a model of the surface-deformation process to describe the growth of the crater analytically. The force-indentation relation obtained in this manner agrees with that determined by direct observation to within 6 percent, while the predicted permanent crater depth was found to be 10.8 percent lower than that measured under dynamic conditions. The results of the present investigation have also been compared with solutions based upon the Haar-Karman criterion of yielding and upon the hypothesis of a constant flow pressure.