Polycrystals multilevel models using crystal plasticity: consistency of constitutive equations at different scale levels

Abstract

Abstract. Two-level models of different polycrystalline metal's inelastic deformation based on crystal plasticity and describing viscoplastic intragranular dislocations slip, lattice rotation with an explicit consider of dislocation slip incompatibility in neighboring grains, and fragmentation of crystallites are developed. The homogenization of constitutive equations at various scale levels is used, which allows to connect the same type of characteristics of different scale levels and leads to an unambiguous description of geometric nonlinearity on the macro level by specifying the corotational derivative of Cauchy stress tensor. An algorithm for solving boundary value problems in FEM package Abaqus with using proposed models to describe the behavior of the material is developed, corresponding computational modules are created. Numerical investigation of different loading of samples from various polycrystalline metals with a description of the evolving internal structure is done. IntroductionNumerous theoretical and experimental studies show that the performance of the internal material structure determines the behavior of the material at the macro level and its performance characteristics. During intensive plastic deformation the internal structure of the material is significantly restructured: the grain and dislocation structures are changing, crystallites lattice is rotated; it is widely used to produce materials with unique properties: submicrocrystalline, nanocrystalline, textured materials and materials, which are capable of superplastic deformation.At the time, the construction of models capable of describing the change of the internal structure of polycrystalline materials, a growing acceptance of the approach based on an explicit introduction to the structure of the constitutive relations parameters reflecting the state and evolution of meso-and microstructure evolution and the kinetic equations for these parameters (so-called internal variables) [1]. In particular, recent decades, a very wide development of crystal plasticity based models, which built in the framework of this approach and explicitly describing the material structure and the mechanisms of inelastic deformation at the crystallite level, is observed; this models allows a natural way to describe the structure evolution at deep plastic strain.Based on the crystal plasticity models can be divided into three classes [2,3]: statistics, selfconsistent and direct. Models of the last two classes require inaccessible currently computing resources, so for modeling of real processes statistical constitutive model are more popular.The paper briefly discusses the general structure of the two-level models of polycrystalline metals inelastic deformation developed by the authors, explains how to homogenize the constitutive equations