Constitutive equations of flow stress of magnesium AZ31 under dynamically recrystallizing conditions

Constitutive equations for the relationship between flow stress, strain, strain rate and temperature for magnesium AZ31 alloy under hot working conditions where dynamic recrystallization is prevalent have been developed. Equation development data were obtained using isothermal plane strain compression (PSC) tests carried out at 300-500 °C with strain rates ranging from 0.5 to 50^s-1, to an equivalent strain of 0.7. The predicted flow stress curves show good comparison with the experimental isothermal flow curves in terms of peak, steady state stress and flow softening behaviour but at higher Zener-Hollomon (Z) values (>10¹¹ s^-1) the predicted peak stress deviates from the isothermal value in the range of 14-25 MPa suggesting a breakdown in the hyperbolic sine equation at those Z values. The developed constitutive equations for the valid thermomechanical conditions were adopted in a finite element model to simulate the PSC conditions. The distributions of strain, strain rate and temperature qualitatively suggest higher strain rate at the centre of the sample which agrees well with that of the quantitative analysis of the dynamically recrystallized grain size.