Three-dimensional deformation process simulation with explicit use of polycrystal plasticity models

In this work, a comprehensive engineering methodology is developed for including the effects of anisotropy in metal forming analyses. A finite element formulation for viscoplastic flow is developed to analyze macroscopic inelastic deformations. Following from this formulation, an iterative solution procedure which balances the physically-motivated constraint of incompressibility with considerations of computational efficiency is implemented on a data parallel architecture. Anisotropic material properties are derived from a microscopic description based on polycrystal plasticity theory. Efficient computation of the microscopic variables is achieved through massive data parallel computations. A procedure is set forth for initialization of the microscopic state variables from experimental measurement of texture. A parametric study examining the effects of spatial variations in the specification of the initial texture demonstrates the development of locally non-uniform velocity variations within an approximately homogeneous macroscopic deformation. These variations in the velocity field yield improvement in predicted texture when compared to experimental measurements. The feasibility of initializing (from experimental data) and evolving (through massive computations) a detailed microscopic description for a complex deformation process is demonstrated through a predictive simulation. The predicted location and height of ears developed in the hydroforming of aluminum sheet are found to be in good agreement with experiment.; A hybrid formulation is developed in which microscopic deviatoric stresses for individual crystals are included explicitly as primal variables. Spatial interpolation of the microscopic stress using piecewise discontinuous shape functions which enforce equilibrium a priori insures that equilibrium is maintained at the microscopic scale. Elimination of the microscopic deviatoric stresses at the elemental level leads to efficient implementation in the data parallel environment. Superior numerical performance is demonstrated, as compared to kinematic based formulations, when there exists considerable spatial variation in the constitutive response. This improvement is most notable in the limiting case for which each element represents a single crystal. As an application, a "polycrystal" is constructed using 1000 single crystal elements embedded in a test problem with boundary conditions representing plane strain. Components of plane strain texture, which occur in practice due to localized microscopic shearing, are naturally developed in this hypothetical polycrystal.