Constitutive modeling for the flow stress behaviors of alloys based on variable order fractional derivatives

Abstract

During hot working, alloys may experience three kinds of flow stress behaviors, including strain hardening, strain softening, or steady flow, because of the competition of work hardening and thermal softening. Modelling the flow stress behaviors plays an essential role in understanding the mechanical properties of alloys. In this paper, the variable order fractional model is provided to describe the flow stress behaviors of alloys. The variation of the fractional order between 0 and 1 can reflect the mechanical property changing between solids and fluids. By assuming that the fractional order varies linearly with time, the proposed model can describe both the strain softening and strain hardening behaviors of alloys. The model fitting results are compared to the experimental data of A356 alloy for strain softening and Cu-Cr-Mg alloy for strain hardening under different temperatures and strain rates. It is validated that the variable order fractional model can accurately describe the flow stress behaviors of alloys. Furthermore, the rule of the variable order is also discussed to analyze its overall values and the changes before and after the yield point. It is concluded that the variation of the fractional order can intuitively reveal the changes in mechanical properties in the flow stress behaviors of alloys, including both strain softening and strain hardening.