Stochastic Multiscale Modeling of Dynamic Recrystallization

Materials by design is a core driver in enhancing sustainability and improving efficiency in a broad spectrum of industries. To this end, thermo-mechanical processes and many of the underlying phenomena were studied extensively in the context of specific cases. The goal of this thesis is threefold: First, we aim to establish a novel numerical model on the micro- and mesoscale that captures dynamic recrystallization in a generalized framework. Based on the inheritance of the idea of state switches, we term this scheme Field-Monte-Carlo Potts method. We employ a finite deformation framework in conjunction with a continuum-scale crystal plasticity formulation and extend the idea of state switches to cover both grain migration and nucleation. We introduce physically-motivated state-switch rules, based on which we achieve a natural marriage between the deterministic nature of crystal plasticity and the stochastic nature of dynamic recrystallization. Using a novel approach to undertake the states-switches in a transient manner, the new scheme benefits from enhanced stability and can, therefore, handle arbitrary levels of anisotropy. We demonstrate this functionality at the example of pure Mg at room temperature, which experiences strong anisotropy through the different hardening behavior on the 〈c+a〉-pyramidal and prismatic slip systems as opposed to the basal slip systems as well as through the presence of twinning as an alternative strain accommodating mechanisms. Building on this generalized approach, we demonstrate spatial convergence of the scheme along with the ability to capture the transformation from single- to multi-peak stress-strain behavior. Second, motivated by the lack of transparency concerning the benefits of high-fidelity approaches in the modeling of dynamic recrystallization, we present two derivative models of the Field-Monte-Carlo Potts method, both of which afford reduced computational expense. One model preserves the spatial interpretation of grains, but imposes a Taylor assumption regarding the distribution of strain; the other reduces the spatial notion of a grain to a volume fraction in the idea of a Taylor model. In order to concentrate on the differences in accuracy between the various approaches, we fit all three schemes to experimental data for pure copper, which allows us to employ a well-understood crystal plasticity-based constitutive model and to simultaneously provide sufficient data for the analysis of the texture, stress and grain-size evolution. Owing to the large strains attained in these simulations, using the FFT-based scheme, we achieve capturing a precursor of continuous dynamic recrystallization. For low temperatures, the Taylor model fails to replicate the nucleation-dominated recrystallization process, whereas, at high temperatures, it shows compelling agreement with experiments and the two higher-fidelity models both in terms of the homogenized stress-evolution and the microstructural evolution. Finally, we present a novel multiscale analysis of thermo-mechanical processes through coupling of the computationally efficient Taylor model for modeling dynamic recrystallization on the mesoscale to a max-ent based meshfree approach on the macroscale in the idea of vertical homogenization. We analyze the severe plastic deformation-based process of equal channel angular extrusion, which is intriguing from a numerical perspective due to the heavily localized zone of extensive shear deformation. By employing novel tools on the microscale regarding the stable update of internal variables as well as a careful interpretation of macroscale boundary conditions, we present the first multiscale analysis of a severe plastic deformation process informing simultaneously about the evolution of stress, texture and grain refinement. We attain convincing qualitative agreements for the evolution of the plunger force and texture. As an outlook on future investigations, we analyze multiple passes of the same billet in the form of route C with emphasis on the texture evolution after the second pass.