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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. [ABSTRACT FROM AUTHOR]

Abstract: Epitaxially grown thin films with nominal composition Ni50Mn30Ga20 and thickness 1.5μm were prepared on MgO(100) substrate with a Cr buffer layer by DC magnetron sputtering. The surface layer microstructures of the as-deposited thin films consist of non-modulated (NM) martensite plates with tetragonal structure at ambient temperature, which can be classified into the low and high relative contrast zones of clustered plates (i.e. plate colonies) with parallel or near-parallel inter-plate interface traces in secondary electron images. Orientation analyses by electron backscatter diffraction revealed that individual NM plates are composed of alternately distributed thicker and thinner lamellar variants with (112)Tetr compound twin relationship and coherent interlamellar interfaces. In each plate colony, there are four distinct plates in terms of the crystallographic orientation of the thicker lamellar variants and therefore, in total, eight orientation variants. For the low relative contrast zones, both thicker and thinner lamellar variants in adjacent plates are distributed symmetrically across their inter-plate interfaces (along the substrate edges). At the atomic level, there are no unbalanced interfacial misfits and height misfits, resulting in long and straight inter-plate interfaces with homogeneous contrast. However, in the high relative contrast zones, the thicker and thinner lamellar variants in adjacent plates are oriented asymmetrically across their inter-plate interfaces (at ∼45° to the substrate edges). Significant atomic misfits appear in the vicinity of the inter-plate interfaces and in the film normal direction. The former result in bending of the inter-plate interfaces, and the latter give rise to the high relative contrast between adjacent plates. [Copyright &y& Elsevier]