Simulation of the flow behavior of AZ91 magnesium alloys at high deformation temperatures using a piecewise function of constitutive equations

The hot deformation behavior of AZ91 magnesium alloy was studied using single-pass compression experiments within a temperature range of 473-623 K and strain rate of 0.001-1 s−1. The flow stress first increases to a peak value with the work hardening, and then decreases slowly during dynamic softening. New piecewise function models were proposed to describe the constitutive equations of AZ91 magnesium alloy of stress-strain curves. Meanwhile, new methods to obtain the material constants k, C1 and C2 were proposed to predict accurately the flow stress corresponding within the range of strain from peak values to end based on the phenomenological representation of stress-strain curves in the second stage. Furthermore, the strain-compensated Arrhenius equation model was also used to describe the constitutive equations of plastic stage. The results predicted by these models are in good agreement with the measured data in the second stage, and the maximum average relative error of the predicted results is less than 10%. The strain-compensated Arrhenius equation model shows good capability under certain conditions, but it has lower fitting precision and also needs consume much time to obtain more material constants compared with piecewise function models. The piecewise function models show higher precision; the average relative error of the predicted results is less than 3% when the stress-strain curves in the second stage are described as nonlinear functions. These proposed methods for obtaining material constants k, C1 and C2 are valid and the piecewise function models are significant for establishing constitutive equations of metal alloys in hot deformation processes.