Transverse failure has long been considered as a key failure mode in fiber-reinforced composite laminates, as it is often a precursor to inter-ply delamination and fiber breakage. The initiation and propagation of transverse cracks are affected by a variety of random microstructural quantities including fiber placement, fiber radii, constitutive properties of the fibers and the matrix, and failure properties of the fiber/matrix interfaces.
We present a gradient-based method to calculate the sensitivity of the transverse failure response with respect to the distribution characteristics (mean and standard deviation) of (i) the cohesive failure properties of the fiber/matrix interface and (ii) the geometrical features (placement and radius) of the fibers. The computational model of the transverse failure event combines a nonlinear Interface-enriched Generalized Finite Element Method (IGFEM) solver specially developed for this application, and a cohesive model of interfacial debonding, which has been shown in experiments to be the primary mode of transverse crack propagation in high-volume-fraction carbon-epoxy composites. The sensitivity analysis relies on an analytic computation (using the direct method) of the sensitivities of the failure response with respect to the cohesive properties of each interface and the geometrical parameters defining every fiber present in the virtual model of the composite.