Grain boundary sliding is an important deformation mechanism, and therefore its description is essential for modeling different technological processes of thermomechanical treatment, in particular the superplasticity forming of metallic materials. For this purpose, we have developed a three-level statistical crystal plasticity constitutive model of polycrystalline metals and alloys, which takes into account intragranular dislocation sliding, crystallite lattice rotation and grain boundary sliding. A key advantage of our model over the classical Taylor-type models is that it also includes a consideration of grain boundaries and possible changes in their mutual arrangement. The constitutive relations are defined in rate form and in current configuration, which makes it possible to use additive contributions of intragranular sliding and grain boundary sliding to the strain rate at the macrolevel. In describing grain boundary sliding, displacements along the grain boundaries are considered explicitly, and changes in the neighboring grains are taken into account. In addition, the transition from displacements to deformation (shear) characteristics is done for the macrolevel representative volume via averaging, and the grain boundary sliding submodel is attributed to a separate structural level. We have also analyzed the interaction between grain boundary sliding and intragranular inelastic deformation. The influx of intragranular dislocations into the boundary increases the number of defects in it and the boundary energy, and promotes grain boundary sliding. The constitutive equation for grain boundary sliding describes boundary smoothing caused by diffusion effects. The results of the numerical experiments are in good agreement with the known experimental data. The numerical simulation demonstrates that analysis of grain boundary sliding has a significant impact on the results, and the multilevel constitutive model proposed in this study can be used to describe different inelastic deformation regimes, including superplasticity and transitions between conventional plasticity and superplasticity.
Evaluation of local stress state due to grain-boundary sliding during creep within a crystal plasticity finite element multi-scale framework
