Nonlinear multivariate constitutive equations for modeling hot deformation behavior

Abstract

Nonlinear constitutive equations are proposed to model variations in flow stress as a function of strain rate and temperature during hot deformation. Modified constitutive are applied to seventy data sets about hot deformation of alloys. Two modifications to conventional constitutive models are introduced, viz. (1) nonlinear and (2) multivariate models with the fitting of flow stress simultaneously with two variables. The predictive accuracy of constitutive equations was evaluated using three statistical parameters and compared with a conventional Arrhenius-like model. It is shown that nonlinear constitutive equations have improved predictive accuracy for variations in flow stress during hot deformation. The advantages of multivariate models include less computation and material parameters that are constants independent of temperature or strain rate. In another type of multivariate model, flow stress is expressed as linear and nonlinear polynomial functions of the Zener-Holloman parameter. This approach gives a single value of the activation energy of hot deformation. The results have indicated that a generalized second-order multivariate constitutive equation can be used to better predict flow stress, as a function strain rate and temperature, during hot deformation.