Dislocation-Based Constitutive Model: Description of the Influence of Grain Boundaries on the Deformation of Metals

A modification of the dislocation-based constitutive model is proposed to describe the deformation of polycrystalline materials taking into account intragranular and grain boundary strengthening. The developed model is based on the introduction of internal variables, physical elastoviscoplasticity theory, and multilevel approach; it is considered at three (macro, meso-1, and meso-2) hierarchically related structural and scale levels. At the upper level (of a representative macrovolume), the response of the material (a measure of the stress state) to thermomechanical effects (given changes in the measure of deformation and temperature) is determined. Elements of the meso-1 and meso-2 levels have the same scales, differing in the way they are described. The meso-1 elements are considered in terms of mechanical variables (stress measures, residual and critical shear stresses, and shear rates in slip systems). At the meso-2 level, the description is carried out in terms of densities and velocities of dislocations. Particular attention is paid to the interaction of dislocations with grain boundaries, which have a significant effect on the behavior of polycrystalline materials. Grain boundaries determine the local stress-strain state and are barriers to dislocation slip, which can lead to dislocation pile-ups in the near-boundary regions. The submodel taking into account the dislocation flow in the vicinity of grain and subgrain boundaries within the dislocation-based model is described in detail. Examples of the model application to the study of loading of bicrystal specimens are given. It is shown that the developed model allows describing dislocation fluxes through the boundary and takes qualitative account of grain-boundary strengthening.