Failure initiation at V-notch tips in quasi-brittle materials

Under the assumption that the damaged zone and the virtual crack extension are small, matched asymptotic expansions are used. It is shown that the damaged zone grows first, proportionally to the square of the applied load and then, above a threshold, a virtual crack of a given length simultaneously satisfies the energy and stress criteria, and failure occurs. The approach allows taking into account varying tensile strength and material toughness in the damaged zone, as may reasonably be expected. Moreover, it is shown that the same coupled stress-energy criterion can directly be applied to quasi-brittle materials by appropriately using the actual material toughness as measured on a cracked specimen.