Interpreting Dynamic Hardness: Separating Roles of Speed, Strain Rate and Shock

Abstract

Mechanical hardness is classically defined as force divided by indented area. Hardness (dynamic) is alternately sometimes defined based on indentation energy absorbed normalized by displaced volume. This elementary study compares static and dynamic hardness using standard definitions. Hardness is often observed to increase with strain rate and this is commonly interpreted as strain-rate hardening by mechanisms such as dislocation drag. This analysis considers the simplest situation – ballistic indentation of an elastic-perfectly plastic material without rate dependence. Results from both Coupled Eulerian-Lagrangian (CEL) and Smoothed Particle Hydrodynamics (SPH) show a linear correlation between indenter impact speed and dynamic hardness. Extrapolating to an impact speed of 0 m/s converges to static hardness. Neither approach demonstrates indenter size dependence. High impact speeds also can introduce shock. It is suggested that speed and shock hardening effects can account for the increase in dynamic hardness with increased indenter speed without strain-rate-hardening.