Piecewise Model with Two Overlapped Stages for Structure Formation and Hardening upon High-Pressure Torsion

The evolution of micro/nanostructure in metals subjected to high-pressure torsion (HPT) still need to be explained theoretically although experimental datasets are growing persistently. A major problem associated with the understanding of HPT is the synergetic effect of several competing processes that alter the material structure. In this study, we propose a piecewise model to analyze material hardness and true strain data during the HPT procedure. The model is built on two postulates: (a) the hardness vs true strain dependence is a sum of two piecewise power-law functions (each of these functions describes an unique micro/nanostructural stage of the deformation) and (b) each piecewise function has free-fitting strain breakpoints, which limit the strain range in which one mechanism predominantly determines the micro/nanostructure. The model was applied to analyze the HPT data for pure polycrystalline iron, AISI 1020 steel, and AISI 13B20 steel to reveal the distinctive strain breakpoints and power-law exponents. In the result, we found that deduced power-law exponents for AISI 1020 and AISI 13B20 steels are remarkably close to each other within full strain range.