Semi-analytical approaches to assess the crack driving force in periodically heterogeneous elastic materials

When a crack propagates in a heterogeneous elastic material, its crack driving force depends strongly on the distribution of the local stiffness near the crack tip. In materials with periodic spatial variations of the Young's modulus, shielding and anti-shielding effects appear, i.e. the crack driving force is reduced or enhanced, compared to a homogeneous material. The effect is of great practical relevance, since it may lead to a strong increase of the fracture resistance. The concept of configurational forces (CCF) offers an established procedure for calculating the crack driving force. A very general relation for the periodic variation of Young's modulus is applied, allowing the description of both harmonically varying and layered microstructures. Numerical results are presented. Two semi-analytical approximation concepts, based on either the CCF or the moduli perturbation concept, are introduced and discussed. Comparisons are provided and recommendations given.