Investigation of the relationship between work done during indentation and the hardness and Young's modulus obtained by indentation testing

Existing indentation models (both analytical models and numerical analysis) show a linear relation between delta(r)/delta(m) and H/E(r), where delta(r) and delta(m) are the residual depth and maximum depth, and E(r) and H are the reduced Young's modulus and hardness of the test material, respectively. However, in this paper it is shown that the relationship between delta(r)/delta(m) and H/E(r) is actually nonlinear. Based on the analysis by Oliver and Pharr, a new relationship between delta(r)/delta(m) and H/E(r) has been derived in different ways without any additional assumptions and verified by finite element analysis for a range of bulk materials. Further, with the aid of finite element simulation a new relationship between the irreversible work over total work and hardness over Young's modulus for materials with different work hardening behaviour has been derived which shows excellent agreement with experimental observations.