Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si

Abstract

A method is proposed to determine the variance of an arbitrary material property based on the statistics of the texture of polycrystalline materials for a specified volume. This method is applied to determine the variance of the Taylor factor (i.e., measure of plastic deformation in crystal plasticity) and is compared to a random sampling method. The results from the random sampling method correlated well with the statistical variance relationship when the magnitude of the variance was greater than that of the numerical errors observed in the statistical calculation. An empirical relation was also shown to model the results, and the constants for this relationship were determined for pseudo-three-dimensional Fe-3%Si. Implementation of the statistical variance relationship in true three-dimensional microstructures is not limited by material opacity, since it depends only on the two-point pair correlation functions. The connection between the variance of the R-value and variance of the Taylor factor is considered. Although only a weak connection was found, it was observed that relatively small variations in the Taylor factor yield large variances in the R-value.