Asymptotic finite fracture mechanics solution for crack onset at elliptical holes in composite plates of finite-width

The onset of cracks at elliptical holes in finite-width laminated plates under uniaxial tension loading is investigated using a finite fracture mechanics approach. A coupled stress and energy criterion is applied in order to determine the effective strength of the notched plate and the size of instantaneously initiating cracks. A semi-analytical approach based on complex potential theory in combination with a two-scale asymptotic analysis is proposed leading to explicit relations for the stress field and energy quantities due to crack formation. This allows for an efficient finite fracture mechanics solution and a significant reduction of the numerical effort compared to a full-numerical treatment. The effect of higher-order terms in the asymptotic procedure and a technique leading to an improved convergence of the expansions are discussed in detail. A thorough comparison with numerical data is performed in order to analyse the validity range of the asymptotic solution. Furthermore, the failure load predictions are compared to experimental data from literature.