Modelling crack nucleation in composite materials: a semi-analytical two-scale approach

The objective of this work is to provide an efficient semi-analytical approach for predicting crack onset at sharp notches, bi-material junctions and openings in fibre-reinforced laminates. On the one hand, this is achieved employing a complex potential approach that accurately captures stress concentrations and enables a precise calculation of generalised stress intensity factors. On the other hand, the method of matched asymptotic expansions is applied interpreting a newly nucleated crack as a small perturbation parameter within a singular perturbation problem. This methodology enables an efficient evaluation of the coupled stress and energy criterion forming a necessary and sufficient condition for fracture. Predictions relying on the asymptotic approach are validated against fully numerical reference data as well as experimental findings from literature.