A new constitutive strain dependent Garofalo equation to describe the high-temperature processing of materials-application to the AZ31 magnesium alloy

Abstract

A new strain-dependent equation derived from that of Garofalo is developed in this work. This equation describes mathematically the deformation behavior of materials as a function of strain, strain rate, and temperature and is valid over a wide range of strain with good statistical accuracy. An explicit expression σ(ε)=f(ε,T,ε˙) is introduced that reproduces stress-strain curves. Statistical tools for determining the validity of the equation have been applied. Predictions from this expression were compared with torsion data obtained in AZ31 magnesium alloy that was deformed at various temperatures and strain rates. Analysis of the strain dependence of the Garofalo parameters allowed us to establish a steady state at strains of about 0.6. It also allows drawing conclusions about the microstructural changes that occur during deformation of the alloy. In addition, the characteristic points in the evolution with strain of the parameters of the equation are related to the most significant values that characterize the microstructural processes occurring during deformation of the AZ31 alloy. The observed decrease of Q and n as a function of strain is attributed first to a softening process due to dynamic recrystallization and grain size refinement and finally to flow localization. The predicted values obtained with the new constitutive equation and the experimental values for the AZ31 alloy are in good agreement with an average relative error of about 6.5 pct.