Development of multilevel models based on crystal plasticity: Description of grain boundary sliding and evolution of grain structure

In recent decades, multilevel constitutive models of polycrystalline metals and alloys have been developed intensively. These models consider the structure of the material and physical mechanisms of deformation at the crystallite level explicitly and allow the description of changes in the internal structure and of physical and mechanical properties of the material during thermomechanical processing that depend on the state of the material. Models of micro- and nanomechanics (for example, elements of molecular dynamics, dislocation dynamics) can be used either as submodels in a multilevel model of materials or can be used for clarification of its parameters. In the present paper, we present a modification of multilevel models, which was previously developed by a team of authors, by taking into account the mechanism of grain boundary sliding and changes of the grain structure as a result of breaking and fragmentation of grains. The earlier proposed two-level model of inelastic deformation of polycrystalline metals is used as a reference model. In describing the grain boundary sliding, viscoplastic shears at grain boundaries are explicitly considered with account for changes in the critical shear stresses: an increase due to intrusion as a result of intercrystalline slip, and a decrease due to increasing in energy as a result of inflow of the intragranular dislocations and diffusion processes. In order to describe the fragmentation associated with changes in mutual orientations of crystallite parts, the couple stresses that cause the fragment rotation due to nonsimultaneous dislocation sliding in it and in the neighboring fragments, are considered. The process of crystallite breaking is described by analogy with the ductile fracture. For finding the most probable plane, an optimization problem is formulated: the plane and the direction where the largest shears are accumulated are determined with account for grain elongation in the direction perpendicular to the plane. The proposed model allows the description of “regular” inelastic deformation of polycrystalline materials and deformation under the conditions of structural superplasticity (with specific effects and the state of grain structure), the transitions between these conditions of deformation (including grain structure refinement on preparation of material to superplastic deformation). The test calculation results illustrating the capacities of the proposed model are presented. © 2015 by Begell House, Inc.