Predicting variability in transverse effective elastic moduli and failure initiation strengths in UD composite microstructures due to randomness in fiber location and morphology

In this study, variability in transverse mechanical properties of unidirectional (UD) composites arising from the randomness present in the geometrical descriptors of the fibers, specifically fiber location and morphology was quantified via finite element analysis of an ensemble of computer-generated microstructures. These microstructures were produced based on geometrical descriptors evaluated from the image analysis of an actual microstructure. To ensure consistency, all synthetic microstructures were modified to match both the short-range and long-range statistics of the actual microstructure. This technique enabled generation of microstructures that are statistically similar but morphologically different, i.e. they have the same statistics but different configurations. Image-based three-dimensional finite element models were developed for the microstructures based on pixel and morphology-based meshing strategies and subsequently analyzed for elastic and strength properties, respectively. Cohesive zone modeling and extended finite element method were employed to predict failure initiation strengths of the stochastic microstructures under two transverse biaxial loading scenarios: (i) transverse tension – transverse tension and (ii) transverse tension – transverse shear loading. Seven load ratio cases were investigated for each scenario, namely 0/1, 0.2679/1, 1/3, 1/1, 3/1, 3.7321/1, and 1/0. To demonstrate the variability existing in the investigated biaxial strengths of the UD composite microstructures, stochastic failure envelopes showing contours of three different reliability levels were developed. The results indicated that microstructural variability has little to no influence on transverse elastic moduli; however, it significantly influences transverse strengths. It was also found that the hexagonal packing microstructure provides a good estimation for the average effective elastic moduli, however, it overpredicts the strengths by a large margin.