Constitutive relations and their application to the description of microstructure evolution

The paper considers an approach to the development of a crystal plasticity model comprising constitutive equations, equations of evolution and closure equations. The approach is based on the hypothesis that there exists a finite set of internal tensor variables and physical mechanical parameters fully representative of the “here-and-now” state of material. This makes possible physical equations in the form of simple relations (tensor-algebraic or differential), while not discarding the loading history; its “carriers” are introduced internal variables. Consideration is given to a possible structure type of the constitutive model. The derivation of constitutive relations is exemplified with a 2D plastic strain problem for single crystals. Algorithms are presented for determination of active slip systems under force and kinematic loading. The behavioral peculiarities of crystals in lattice rotation are studied for different loading conditions. The evolution of the orientation distribution function for the crystallographic coordinate system of grains under kinematic loading is determined.