Modeling of deformation texture development based on rate independent crystal plasticity
The authors derive constitutive equations for plastic strain and spin rates by using empiric correlations between the dislocation velocity and the shear stress on a slip system, and between the first one and the slip rate Burger's vector (density of mobile dislocation). The theory involves the Cauchy stress and the velocity gradient in a current configuration. A plastic potential is introduced as a function of stresses, and the constitutive equations are expressed through potential derivatives in the stress space. The authors express the yield condition by means of the introduced potential, and compare it with the criterion for stress prescribed by Schmid law. The yield surfaces are presented for different values of governing parameters, and are compared with Schmid and Mises criteria for cubic and orthorhombic lattices. For a critical constant stress the hardening rule contains a complete number of equations, including the equilibrium equation. Thus, the authors are able to predict reorientation paths during the extension of crystals. Some consequences are formulated: 1) in lattice coordinates the procedure is easy to implement; 2) for a material parameter \(n\) greater than 1,5 the results are similar to those based on the Schmid law, which agrees with experimental data for high stacking fault energy; 3) the materials with low s.f.e. can be described by the present model at small values of \(n\); 4) \(n\) can be defined for yield surfaces with rounded vertices. The results may be also extended to models with rolling, of Taylor and brass-copper type.
scientific article; zbMATH DE number 1076928