Diffused interface Crystal Plasticity Finite Element Method: Biased mesh generation and accuracy

Diffused interface Crystal Plasticity Finite Element Method (CPFEM) can allow incorporation of grain boundary constitutive models, seamless connection to phase-field based microstructures, and negate the issue of poor elements typical of sharp interface and grain geometry conformal CPFEM. However, the use of uniformly structured mesh in diffused interface CPFEM reduces the utility of this approach by increasing the computational cost exorbitantly. Since the gradients of stress, strain, etc. in the grain interiors are much smaller than at the interfaces, biased mesh can be employed in diffused interface CPFEM to reduce the computational cost significantly. Furthermore, the use of non-conformal elements in the mesh size transiting regions does not alter the structured mesh and provide accurate results. All these factors have been incorporated in this work to develop a diffused interface CPFEM framework. A biased mesh generation algorithm for polycrystalline domains have been developed and a sensitivity study has been performed to identify the critical parameters that control the mesh. Taylor's model has been implemented to capture the constitutive response of the grain boundary regions. The accuracy of the framework has then been evaluated by comparing the global and local responses from the diffused interface CPFEM simulations with sharp and stepped interface results. The comparisons show that the proposed framework can be successfully applied to perform diffused interface CPFEM simulations of polycrystalline microstructures.