Estimation of anisotropic elastic moduli from high energy X-Ray data and finite element simulations

Abstract

A suite of finite element simulations was executed to find optimal values for high-temperature single crystal elastic moduli of low solvus high refractory (LSHR) nickel super alloy from high energy x-ray diffraction microscopy (HEDM) measurements. In the experiment, a polycrystalline specimen was scanned in an unloaded state to determine a three-dimensional spatial map of lattice orientations in the gauge volume. The specimen was then heated and loaded while performing in situ X-ray measurements to determine grain-averaged elastic strain tensors at several macroscopic loads. The finite element simulations, utilizing three meshes of increasing resolution, mimicked the experimental loading. Initial simulations were conducted to find a box containing the optimal moduli, from which a finer grid of trial moduli was created. A suite of simulations was then executed using these meshes and moduli. For each simulation, an error was determined by comparing the simulated strain field to the measured one, with the resulting data set providing rich information about this fitting process. Anisotropy of the optimal moduli was studied relative to the level of mesh refinement, and a tendency for the anisotropy to decrease as the mesh refinement increases was found. Optimal values of anisotropic moduli and isotropic moduli were determined using the presented optimization methodology; the anisotropic moduli gave appreciably better results. Furthermore, we examined the sensitivity of the error to changes in the moduli; the takeaway was that size of the modulus had a primary effect on the sensitivity, with larger moduli being harder to fit.