A critical evaluation and extension of internal state variables consititutive models

This study provides a critical comparison of the internal state variables constitutive model sproposed recently in the literature for metals at elevated temperatures and deformed over a wide range of strain rates. As a result of the observations from this comparative evaluation, a set of modified constitutive relations is also presented. The experimental data available in the literature for 1100 aluminum and a fully dense high purity aluminumm were used along with a nonlinear least squares fitting procedure to estimate the material constants. A nonlinear functional dependence of the effective stress with respect to the internal state variable in the evolution relationship was determined to model more effectively, compared to previous models, the case that a material may exhibit both hardening and softening behaviors, respectively, corresponding to different applied strain rates at the same temperature. The modified relations presented here propose a simple form of this nonlinear function, which accurately models the material response and which allows a more robust implementation in numerical simulations. The deformation of an aluminium gradient specimen was studied for further comparison of the three constitutive models considered and for a demonstration of the validity of this model.