The variance of the Taylor factor due to variations in the microstructure and window size is explored using both a random sampling method and a previously developed statistical relationship. 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 developed 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 3D microstructures is not limited by material opacity, since it depends only upon the 2-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.
College and Department
Ira A. Fulton College of Engineering and Technology; Mechanical Engineering
BYU ScholarsArchive Citation
Przybyla, Craig P., "Methodology for Determining the Variance of the Taylor Factor: Application in Fe-3%Si" (2005). Theses and Dissertations. 687.
plasticity, polycrystalline materials, property variance, two-point correlation functions, Taylor theory