Polycrystal plasticity modeling of bulk forming with finite elements over orientation space

Abstract

Conventional polycrystal modeling is based primarily upon the association of a material element with a representative aggregate of crystals. In this work we focus on an alternate class of polycrystal schemes developed by applying the finite element method to represent and compute the crystal orientation distribution function over an explicit discretization of orientation space. In particular, we extend the methodology applied previously to planar polycrystals, to the modeling of three dimensional polycrystals. Neo-Eulerian axis angle spaces, and specifically Rodrigues' parameter space, are preferred over the conventional Euler angle spaces for this purpose. Various Eulerian and Lagrangian finite element schemes are considered for the ODF conservation equation, stabilized with appropriate combinations of streamline and artificial diffusion to accommodate its hyperbolic nature. One such stabilized scheme, the incremental Lagrangian is applied to simulate the texturing of FCC crystals under monotonic deformations. Next, the finite element polycrystal scheme is employed to capture the development of spatial texture gradients in a bulk forming process. This involves coupled finite element analyses at two length scales: at the macroscopic scale of the deformation process, over a spatial discretization, and at the microstructural level over the discretized orientation space.