Using the ratio of loading slope and elastic stiffness to predict pile-up and constraint factor during indentation

In recent literature, the ratio of the residual depth of indentation to the total depth, h(f)/h(max), has been shown to be a useful parameter in predicting constraint factor and pile-up during indentation in hulk materials. In this work h(f)/h(max) is shown to have a simple one-to-one relationship to S-l/S, or the ratio of the slope of the load vs. displacement curve when loading to the elastic stiffness of the contact. Experimentally, the parameter S-l/S is attractive because-unlike h(f)/h(max) it can be determined continuously during loading, using only data near the depth of interest. The elastic stiffness, S, is measured using a forced-oscillation technique, thus allowing S-l/S to be determined as a function of depth. Previous predictions for constraint factor and pile-up are recast in terms of S-l/S.