Modified elastic-plastic model: implementation algorithm and comparison of computational efficiency with the elastic-viscoplastic model

Abstract

The most important element of mathematical models of thermomechanical processing of metals and alloys is the constitutive model. In recent decades, multilevel physically-oriented constitutive models (CMs) have found widespread application. The first two-level model was the rigid-plastic theory of J. Taylor,a rigorous mathematical justification of which was developed by J. Bishop and R. Hill (TBH type models). The main disadvantage of this model is the uncertainty of the choice of active slip systems when more than 5 systems are activated. Despite this, the TBH models have become widespread, and its basic provisions have been preserved in many later developments. It seems that limiting the number of active slip systems to 5 has no physical justification and is determined only by the numerical procedure for implementing the model.

Since the 1970s, elastic-viscoplastic models have emerged; it has been shown that as the velocity sensitivity parameter tends to zero, the macroparameters determined in the modeling converge to a solution using an elastic-plastic model. However, the system of equations becomes rigid, requiring the use of implicit schemes and extremely small time steps, which significantly reduces the computational efficiency. The paper proposes a modification of elastic-plastic model of the TBH type, in which a procedure for overcoming the above-mentioned drawback is proposed. To compare the computational efficiency of the elastic-plastic and elastic-viscoplastic models, a series of numerical experiments was carried out.