Uncorrelated volume element for stochastic modeling of microstructures based on local fiber volume fraction variation

One source of microstructural variability in fiber reinforced polymers is variability in fiber volume fraction. Despite large scatter in fiber volume fraction, an average value is usually reported without any consideration regarding the variability. Significant variation in fiber volume fraction across the sample reveals that homogeneity throughout the sample is a poor assumption and the commonly employed representative volume element is a poor representation of real microstructures. In this work, the distributions of fiber volume fraction at different length scales are investigated. The variation in distributions suggests that a length scale-dependent distribution must be selected in probabilistic analysis. A cross-correlation between fiber volume fractions of nearest neighbors was computed and an uncorrelated volume element (UVE) is introduced for the length scale at which fiber volume fractions become uncorrelated. The concept of a UVE enables random attribution of properties in stochastic modeling.