A new reverse analysis to determine the constitutive response of plastically graded case hardened bearing steels

A new reverse analysis is presented that determines the plastic response of both nongraded and plastically graded materials (PGMs) without the need for traditional tension or compression tests. The method utilizes the concepts of expanding cavity model for strain hardening materials, Tabor’s rule of converting Vickers hardness to flow stress, representative plastic strain induced by indentation, and finite element modeling of the macro indentation process. A unique flow curve is determined when the experimentally measured increase in micro Vickers hardness matches that predicted by the proposed method within the plastic zone of a macro Vickers indent. The method is validated for a nongraded stainless steel first and then extended to determine the gradient in flow curves of plastically graded, case-hardened M50 NiL material, a widely used bearing steel. Such knowledge of the plastic response of the case hardened region will help optimize the design of case hardened bearings with longer rolling contact fatigue life and higher thrust load capabilities.