A flow stress for the deformation under varying condition-internal and state variable models

This paper presents development and validation of internal and state variable models of flow stress to predict the impact of the varying processing conditions on the mechanical behavior of hot-deformed material. Constitutive equations basing on Taylor's dislocation theory [1] and describing the mechanical behavior of f.c.c. structures present a new internal variable model. This model is multiplicative and considers three factors. The first one is normalized dislocation density, which depends strongly on the strain and weakly on the temperature and strain rate. The second factor introduces the deformation conditions: temperature and strain rate. Its main feature is the consideration of varying conditions, the effect of which is not instantaneous, but with some delay. The third factor takes into account an influence of recrystallization. To verify the proposed solution for varying condition considerations, not only the internal variable model, but also the state variable model is tested. The model developed by Davenport et al. [2] and based on the concept of Sellars and Tegart [3] was chosen as an example and modified then. Results obtained by both internal and state variable models confirm the high accuracy and efficiency of the proposed multiplicative approach for analysis and prediction of the flow stress under the varying deformation conditions for the material of f.c.c. structure.