Macroscopic behavior, field fluctuations and texture evolution in viscoplastic polycrystals

This study focuses on two fundamental aspects of polycrystalline plasticity, i.e. accurate homogenization models for the macroscopic behavior and field fluctuations in viscoplastic polycrystals, and simulation of the texture evolution of polycrystalline materials in forming processes.; The second-order nonlinear homogenization method (SOE) of Ponte Castañeda (2002a) is extended to viscoplastic polycrystals, incorporating the averages and fluctuations of the stress field in an optimally chosen linear comparison polycrystal. Applications of this method have been carried out to investigate the effective behavior and field fluctuations in model two-dimensional, cubic (FCC and ionic) and HCP (Ti- and ice-type) polycrystals. This model is found to be superior to the previous micromechanics models, such as the incremental and tangent self-consistent models, by satisfying all available bounds for the effective flow stress, even for strongly nonlinear/highly anisotropic cases where the other methods are known to fail. The SOE predictions are also in good overall agreement with the full-field FFT simulations for the 2-D polycrystals. Finally, the second-order method allows computation of the statistical moments up to second order of the local stress and strain-rate fields, which are also found to compare favorably with corresponding FFT results for the 2-D polycrystals.; Application of the new second-order model and its simplified version, the variational self-consistent model, have been made to simulate texture evolution in polycrystals undergoing finite deformations. With the variational self-consistent model, simulations have been carried on tension/compression and plane-strain compression forming processes of highly anisotropic titanium metal. In comparisons with the experimental measurements and FEM direct simulations, the model shows its advantages in predicting closer stress-strain relation and deformation textures to the corresponding FEM results, than the Taylor and tangent models.; Application of the second-order method has been attempted for the texture evolution of initially isotropic halite in extrusion, which features strongly nonlinear and highly anisotropic crystal properties. The overall stress-strain relations and the deformation textures are studied in detail. Comparisons are given with the other micromechanics simulations, the “hybrid element polycrystal” numerical results and the corresponding experimental measurements.