Modeling of Polycrystalline Materials Deformation with Dislocation Structure Evolution and Transition to Fracture

Abstract

Computing experiments on simulation of deformation and destruction processes of polycrystalline materials is a relevant and efficient research method. This approach suggests building a mathematical model of the material and its exploitation for numerical experiments. The development of the physically based mathematical model for the description of the material behavior during deformation will allow optimizing the properties of constructions without conducting numerous natural experiments. It has been established that when solving similar tasks, it is necessary to take into account the evolution of the meso- and microstructure, including nucleation and development of defects at various structural and scale levels. Consideration of the dislocation structure evolution enables establishing the regions of dislocation accumulation and, as a consequence, simulating the nucleation and subsequent development of microcracks. The purpose of the present study is to develop and realize the dislocation-oriented direct elasto-visco-plastic model, taking into account the processes of microcrack nucleation. The structure and the algorithm of the numerical implementation of the direct model have been presented; the structural levels of the description of elasto-plastic deformation have been identified; a system of evolution equations for the description of dislocation motions and dislocation substructures formation on slip systems with subsequent transition to destruction has been presented. Using the parameters, characterising the dislocation structure, a criterion of the transition into the destructed state has been suggested, in which the material element of the appropriate scale level loses an ability to resist external impacts. The description of the application software package intended for the implementation of multilevel models of the representative volume of polycrystalline solids has been given. The submodel of the description of the dislocation density evolution of the crystallite has been realised; the influence of the mechanisms of nucleation and annihilation of dislocations on their total density has been analysed.