Elastoplastic interaction of grains in polycrystalline materials

Abstract

A new method is developed for solving boundary value problems of elastoplastic deformation of polycrystalline materials based on the field-theoretical approach. The boundary value problem for inhomogeneous global strain fields in differential form is transformed into a system of integral equations for mesostrain tensors in grains. In this approach, strain at any point of any grain represented as a superposition of homogeneous macrostrain and contributions of interactions with strain in given grain and all another grains of polycrystalline body . It is shown that the effects of the interaction of strains in polycrystal grains can be described using tensors of the fourth rank. This tensor has 36 independent components. The interactions are additive in nature, that drastically simplifies the solution of some problems, for example, search for extreme microstructures of a polycrystal in which critical localized phenomena arise, such as nucleation of the first plastic slips occur. Constitutive equations of deformation type are used for whole body and separate grains. A model of elastoplastic deformation of single crystals of grains is constructed. The physical mechanisms of plastic deformation are shifts in slip systems of crystals. General expressions are obtained for calculating the secant modules of single crystals for any multiaxial deformation. To solve systems of integral equations for mesostrains in grains the perturbation theory upon intergrains interaction used. Nonlinear systems of equations for plastic strains are solved by the iteration method. The features of the elastoplastic interaction of grains are theoretically investigated. The intensity of the elastoplastic interaction depends on the deformed state of the grains. For two identical grains, the elastoplastic interaction of the pair is several times more intense than the elastic one. In this case, the effect of plastically deformed grain on elastically deformed grain is much higher than the inverse effect. An increase in the intensity of interaction with the development of plastic deformations leads to the effect of homogenization of mesodeformations. Computational experiments were performed using polycrystalline titanium as an example.