Microstructure-Sensitive Stochastic Design of Polycrystalline Materials for Quasi-Isotropic Properties

Abstract

The present study addresses a multiscale and stochastic design approach for polycrystalline microstructures to achieve a zone of isotropic elastic properties to improve the predictability of the performance of aerospace components. The microstructures are modeled with Orientation Distribution Function (ODF), which is related to the volume densities of crystallographic orientations in a microstructure. The microstructures can have inherent uncertainty due to the variations arising from thermomechanical processing that can alter the component performance. Example design problems are solved for titanium (Ti), aluminum (Al), and galfenol, which are either widely used or have potential applications in the aerospace industry. The level of isotropy for the materials is measured using the available anisotropy index formulas. The optimum microstructure designs are found to provide equivalent stiffness and Young’s modulus values in different directions. Next, property closures for stiffness parameters are generated to demonstrate the ranges of their anisotropy. The closures show that multiple microstructure designs can provide quasi-isotropic elastic properties and the range of material anisotropy is larger for galfenol compared to Ti and Al. Additionally, the stochastic analysis is performed using Gaussian process regression, which is validated with Monte Carlo Simulation. The results show that 10% uncertainty in the ODFs, due to variations in the thermomechanical processing steps, can cause 1.44, 0.44, and 1.02 GPa of standard deviations from the mean values of Young’s modulus for Ti, Al, and galfenol, respectively. However, the effects of the uncertainty are found to be negligibly small for the anisotropy ratio.