Computation of substructural strengthening by the integration of metallurgical models into the finite element code

Several physical models based on the three internal state variables: dislocation density, subgrain size and misorientation across subgrain boundaries, have been proposed to study the mechanism of substructural strengthening. In this paper, the model developed by Sellars and Zhu has been applied to study a hot rolling process by integrating the models into a commercial FEM code. The predicted subgrain size throughout the thickness at the exit fits well with some experimental measurements. The computed dislocation density also shows reasonably agreement with experimental observations. Finally, the flow stress is computed and compared with those calculated by the use of other empirical constitutive equations: the hyperbolic sine function and the Hensel and Spittel equation. Through tuning the constants in the physical model, a good agreement between the empirical formulae and the physical model in the roll gap has been achieved. The problems and difficulties of the application of this model are discussed.