Semi-inverse method for predicting stress–strain relationship from cone indentations

A method for determining the stress–strain relationship of a material from hardness values H obtained from cone indentation tests with various apical angles is presented. The materials studied were assumed to exhibit power-law hardening. As a result, the properties of importance are the Young's modulus E, yield strength Y, and the work-hardening exponent n. Previous work [W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992)] showed that E can be determined from initial force–displacement data collected while unloading the indenter from the material. Consequently, the properties that need to be determined are Y and n. Dimensional analysis was used to generalize H/E so that it was a function of Y/E and n [Y-T. Cheng and C-M. Cheng, J. Appl. Phys. 84, 1284 (1999); Philos. Mag. Lett. 77, 39 (1998)]. A parametric study of Y/E and n was conducted using the finite element method to model material behavior. Regression analysis was used to correlate the H/E findings from the simulations to Y/E and n. With the a priori knowledge of E, this correlation was used to estimate Y and n.