Uncertainty Quantification of Microstructural Properties due to Experimental Variations

Abstract

Electron backscatter diffraction scans are an important experimental input for microstructure generation and homogenization. Multiple electron backscatter diffraction scans can be used to sample the uncertainty in orientation distribution function: both point to point within a specimen as well as across multiple specimens that originate from the same manufacturing process. However, microstructure analysis methods typically employ only the mean values of the orientation distribution function to predict properties, and the stochastic information is lost. In this work, analytical methods are developed to account for the uncertainty in the electron backscatter diffraction data during property analysis. To this end, a linear smoothing scheme is developed in the Rodrigues fundamental region to compute the orientation distribution function from the electron backscatter diffraction data. The joint multivariate probability distributions of the orientation distribution function are then modeled using a Gaussian assumption. The uncertainty in engineering properties that are obtained by homogenization are also computed. It is shown that the uncertainty in nonlinear properties can be analytically obtained using direct transformation of random variables in the homogenization approach.