Comparison of CPFEM and spectral solution methods in prediction of strains near grain boundaries in a uniaxially loaded oligocrystalline tensile specimen

In this work, we have built upon the work done by Lim et al 2014, to determine whether the discrepancy in experimentally observed grain boundary strains and those calculated by Crystal Plasticity Finite Element Method (C.P.F.E.M.) is a result of inherent shortcomings of Finite Element Method (FEM). We also determine if a spectral solution method would prove helpful and relatively more accurate at predicting strains near these grain boundaries. In the work done by Lim et al 2014, a rather highly resolved C.P.F.E.M. simulation of an oligocrystalline uniaxially loaded tantalum tension sample captured most of the experimentally observed features but markedly underestimated the grain boundary strain concentrations when the results of the simulation were compared with experimental results. Simulations were performed for the same oligocrystalline uniaxially loaded tension sample using Dusseldorf Advanced Materials Simulation Kit (DAMASK) and used the built in finite element and spectral solvers to calculate strains both inside the grains and near the grain boundaries. Varying resolutions comparable to those used by Lim et al 2014, were used in these simulations. Investigation has been done on whether the inability of using finer resolutions with FEM as it is computationally prohibitive, and more importantly an inherent stiffness in the FE solution method, was the reason or the discrepancies observed as compared to experimental data. The spectral solvers use a Polarisation solution method which converges rapidly and allows us to use even finer resolutions without being too computationally expensive. It also has much lower stiffness as regards the solution strategy. The resulting strain maps of the Spectral Solution method were observed and compared with results from FEM. The distribution of equivalent strain as a function of grain boundary distance was plotted. Comparisons and equivalencies with the results from finite element solutions were done and established to ascertain whether or not the observed discrepancies in the case of finite element simulation were inherent in the method itself.