Analytical relations between hardness and strain for cold formed parts

Our objective in this study is to establish an analytical relation between hardness and effective strain induced in a metal during cold working. In this way, its hardness can be determined from numerically obtained plastic strains without producing the part and taking measurements. For each of the two most commonly used measures of indentation hardness, Vickers’ and Brinell's, a separate analytical relation was proposed relying on the previous empirical and numerical studies. The results of the analytical models compared well with the data obtained from the experiments that we conducted. The models were also verified by comparing its predictions with the experimentally determined hardness values reported by previous researchers. The results showed that both of the analytical models can reliably be used to determine hardness distribution within a cold formed part.