Electron backscatter diffraction (EBSD) scans are an important experimental input for microstructure generation and homogenization. Multiple EBSD scans can be used to sample the uncertainty in orientation distribution function (ODF), 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 ODF to predict properties and the stochastic information is lost. In this work, we develop analytical methods to account for the uncertainty in the EBSD data during property analysis. To this end, we develop a linear smoothing scheme in the Rodrigues fundamental region to compute the ODF from the EBSD data. The joint multivariate probability distributions of the ODF are then modeled using a Gaussian assumption. We also compute the uncertainty in engineering properties that are obtained by homogenization. We show that uncertainty in non-linear properties can be analytically obtained using direct transformation of random variables in the homogenization approach.
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