Role of the mesoscopic rotation modes of deformation in formation of macroscopic stress–strain curves

Abstract

In the framework of the asymmetric theory of the elastic-plastic Cosserat continuum in a two-dimensional formulation for plane strain, the simulation of inelastic localized deformation was performed for homogeneous samples and the mesoscale volumes of the polycrystalline material. It is assumed that the development of rotational deformation modes in loaded materials is associated with the development of localized plastic deformation in them and the formation of curvatures of the crystal lattice in the material at the micro and nanoscales. For this reason, the parameters of the Cosserat model are considered as functions of inelastic strain for each local volume of the medium. It is shown that the couple stress forming at the mesoscale makes a significant contribution to the hardening of macroscopic stress-strain curves. The simulation results show that if the rotation modes of deformation are blocked in the loaded material, the accommodation capacity of the material decreases, the local and macroscopic degree of inelastic strain sharply increases and fracture patterns are formed much faster. Conversely, the creation of meso- and nanosized substructures with a high curvature of the crystal lattice in materials contributes to the activation of rotational deformation modes, reducing the degree of localized strain and relaxation of dangerous stress concentrators.In the framework of the asymmetric theory of the elastic-plastic Cosserat continuum in a two-dimensional formulation for plane strain, the simulation of inelastic localized deformation was performed for homogeneous samples and the mesoscale volumes of the polycrystalline material. It is assumed that the development of rotational deformation modes in loaded materials is associated with the development of localized plastic deformation in them and the formation of curvatures of the crystal lattice in the material at the micro and nanoscales. For this reason, the parameters of the Cosserat model are considered as functions of inelastic strain for each local volume of the medium. It is shown that the couple stress forming at the mesoscale makes a significant contribution to the hardening of macroscopic stress-strain curves. The simulation results show that if the rotation modes of deformation are blocked in the loaded material, the accommodation capacity of the material decreases, the local and macroscopic deg...