Identification of the 3D crystallographic orientation using 2D deformations

Polycrystalline materials consist of grains (crystals) oriented at different angles resulting in a heterogeneous and anisotropic mechanical behavior at that micro-length scale. In this study, a novel method is proposed for the first time to determine the 3 D crystal orientations of grains in a 2 D domain, using solely 2 D deformation fields. The grain boundaries are assumed to be unknown and delineated from the reconstructed changes in the crystallographic orientation. Further, the constitutive equations that describe the mechanical behavior of the domain in 2 D under plane stress conditions are derived, assuming that the material is transversely isotropic in 3D. Finite element based algorithms are utilized to discretize the inverse problem. The in-house written inverse problem solver is coupled with Matlab-based optimization scripts to solve for the mechanical property distributions. The performance of this method is tested at different noise levels with synthetic displacements that were used as measured data. The reconstructions deteriorate as the noise level is increased. This work presents a first milestone in the verification of this novel technology with synthetic data.