Transverse failure of carbon fiber composites: Analytical sensitivity to the distribution of fiber/matrix interface properties

An analytic differentiation method is presented to calculate the sensitivity of the transverse failure response of carbon fiber composite laminates to the distribution parameters of the fiber/matrix interface properties. The method starts with the evaluation of the sensitivities of the transverse failure response with respect to the interface properties of each fiber, ie, the cohesive failure strength and the critical displacement jump. These individual sensitivities are then used to calculate the sensitivities with respect to the mean and standard deviation of the interface properties. The derived sensitivities are implemented in a nonlinear interface-enriched generalized finite element method solver specially developed for this application. The interface-enriched generalized finite element method solver combines a cohesive modeling of the fiber/matrix interface failure with finite element meshes that do not conform to the composite microstructure. The approach is first demonstrated on a model material involving a one-dimensional domain containing N cohesive interfaces described by randomly selected cohesive failure properties. The method is then applied to the more complex problem of a composite laminate involving a large number of fibers.