On the use of internal variable constitutive equations in transient forming processes

Abstract

Constitutive relations which utilize internal variables to characterize the changing state of a material during a deformation process have been proposed by several investigators in recent years. The internal variable models offer the advantage of extending the range of conditions over which a single material description is applicable at the computational cost of integrating the evolution equations for the internal variables. A method is presented for including a constitutive equation utilizing a single scalar internal variable in a model for transient thermomechanical phenomena. Galerkin's method is used to obtain the finite-element formulation for the time integration of the evolution equation. As an illustration of the technique Hart's model is implemented in a simplified form where the anelastic strain has been neglected leaving only the scalar internal variable. A method for determining material parameters is outlined in the context of a particular material (304 Stainless Steel). The material parameters are determined entirely from data independent of the application. As an application, the process of upset welding is simulated and comparisons of the results are made to experiments and to simulations performed with a viscoplastic material model which neglects strain hardening. Qualitative and quantitative improvements over the strain independent model are noted with only a modest penalty in computational effort for the process modeled.