Micromechanics of fabric reinforced composites with periodic microstructure

A model to predict the effective stiffness of woven fabric composite materials is presented. Taking advantage of the inherent periodicity of woven fabric architecture, periodic microstructure theory is used at the mesoscale for the case of a two-phase heterogeneous material with multiple periodic inclusions. For plain weave fabrics, the representative volume element (RVE) is discretized into fiber/matrix bundles and the pure matrix regions that surround them. The surfaces of the fiber/matrix bundles are fit with sinusoidal equations using two approaches. The first is based on measurements taken from photomicrographs of composite specimens and the second is based on an idealized representation of the plain weave structure. Three-dimensional sinusoidal surfaces are generated from the face equations and weave shape for the real and idealized cases in order to mathematically describe the fiber/matrix bundle regions, which are treated as unidirectional composites. Model results from the idealized geometry are compared to experimental data from the literature and show good agreement, including interlaminar material properties. From a comparison of the real and idealized geometry results for similar material RVE dimensions, it is seen that the model is capable of predicting significant changes in the in-plane material properties from slight mismatch in the fiber/matrix bundle shape and crimp, which can be captured using the geometric surfaces generated from photomicrograph measurements.