A meshless multiscale approach to modeling severe plastic deformation of metals: Application to ECAE of pure copper

Severe plastic deformation (SPD), occurring ubiquitously across metal forming processes, has been utilized to significantly improve bulk material properties such as the strength of metals. The latter is achieved by ultra-fine grain refinement at the polycrystalline mesoscale via the application of large plastic strains on the macroscale. We here present a multiscale framework that aims at efficiently modeling SPD processes while effectively capturing the underlying physics across all relevant scales. At the level of the macroscale boundary value problem, an enhanced maximum-entropy (max-ent) meshless method is employed. Compared to finite elements and other meshless techniques, this method offers a stabilized finite-strain updated-Lagrangian setting for improved robustness with respect to mesh distortion arising from large plastic strains. At each material point on the macroscale, we describe the polycrystalline material response via a Taylor model at the mesoscale, which captures discontinuous dynamic recrystallization through the nucleation and growth/shrinkage of grains. Each grain, in turn, is modeled by a finite-strain crystal plasticity model at the microscale. We focus on equal-channel angular extrusion (ECAE) of polycrystalline pure copper as an application, in which severe strains are generated by extruding the specimen around a 90°-corner. Our framework describes not only the evolution of strain and stress distributions during the process but also grain refinement and texture evolution, while offering a computationally feasible treatment of the macroscale mechanical boundary value problem. Though we here focus on ECAE of copper, the numerical setup is sufficiently general for other applications including SPD and thermo-mechanical processes (e.g., rolling, high-pressure torsion, etc.) as well as other materials systems.