A finite element method to calculate geometrically necessary dislocation density: Accounting for orientation discontinuities in polycrystals

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Strain gradients have been used to link various microscale deformation phenomena to the mechanical response of a polycrystalline material, revealing sub-crystal deformation structures. The strain gradients are computed in terms of the orientation gradients and then converted to geometrically necessary dislocation densities, a quantity considered important to explain flow stress and strain hardening behaviour. In this study, a unique method has been developed to compute the orientation gradients by finite element method while enforcing orientation continuity inside the grains and allowing sharp gradients at the grain boundaries by a global minimization approach. The method is showcased on an exemplar electron backscatter diffraction datasets of a stainless type of steel. The energy minimization method (Demir et al., 2009) reveals geometrically necessary dislocation densities that are an order of magnitude lower than those calculated using the widely accepted Least-Squares minimization approach (Arsenlis et al., 1999). The proposed approach successfully eliminates sharp orientation gradients at grain boundaries, removing the artificially high dislocation densities near orientation discontinuities that is characteristic to the finite difference-based approaches.