Application of Invariant Set Theory to Dynamic Recrystallization Constitutive Behavior

Abstract

This article presents a method to predict the material state and process conditions sufficient to cause a peak in flow stress associated with dynamic recrystallization. The method uses an in- ternal variable approach to material modeling and the local invariant set theorem to establish a criterion for the peak stress. The criterion is an analytic expression of material structure and imposed conditions that guarantee asymptotic stability. The criterion shows an interaction be- tween dislocation density, volume fraction recrystallized, temperature, and strain rate for the material to avoid the first peak in stress. Strain does not appear in the criterion. The criterion is partially validated by comparison with dynamic recrystallization data for isothermal, constant strain-rate conditions. A computer simulation of the model and criterion for oxygen-free high conductivity (OFHC) copper correlate well with experimental data. A diagram based on a sim- plified version of the criterion is presented that describes a region in strain rate, temperature, and strain space within which the first peak in stress is avoided as structure is evolving. The method may be applicable to other material kinetic processes. The first peak in flow stress resulting from dynamic recrystallization is an example phenomenon for application of the method.