Uncertainty quantification of microstructural properties due to variability in measured pole figures

Abstract

Experimental pole figures are an important input for microstructure homogenization models. In this paper, we derive an exact analytical formulation to quantify the uncertainties in homogenized properties due to uncertainty in the experimentally measured pole figures. The pole figures are acquired from a set of Ti-7Al alloy samples. These samples were obtained from the same process: by compressing a beta forged ingot at room temperature followed by annealing. The samples were taken from different regions of the original ingot, and this created variability in the resulting pole figures. The joint multivariate probability distributions of the computed orientation distribution function (ODF) is then found using the method of characteristic functions based on a Gaussian model of the pole figures. Engineering properties such as elastic modulus can be obtained by volume averaging over the ODF. We also show that uncertainty in elastic properties can be analytically obtained using direct transformation of random variables in the homogenization approach.