Size Effects for Crack Initiation at Blunt Notches or Cavities in Brittle Materials

This work relies on an Irwin-like criterion able to predict brittle crack initiation at corners, v-notches and other situations such as interfaces breaking a free surface (delamination initiation). It is based simultaneously on an energy and a maximum stress criteria. The reason of this dual formulation can be found for instance in Parvizi et al.1 experiments as analysed in a paper by one of the author.2 It is shown that, if the singular exponent of the stress elastic field at the concentration point is not 1/2 (a pure crack), the crack initiation is a brutal process (unstable) at least on a short initiation length l.2,3 This distance being used as a small parameter in matched asymptotics, it leads to the following expansion of the energy release rate G and next to the Irwin-like criterion: $$ G = k{\text{ }}A\ell ^{2\lambda {\text{ - 1}}} + \ldots ;{\text{ }}k \geqslant k_c = \left( {\frac{{G_c }} {A}} \right)^{1 - \lambda } \sigma _c^{2\lambda {\text{ - 1}}} $$ (1) where A is a scaling coefficient, K is the generalised intensity factor of the singularity with exponent λ. Here, G c and σ c are two failure parameters: the toughness and the strength of the material (the use of two parameters is a usual feature in Cohesive Zone Models). The above criterion matches with the Griffith’s one for a crack (λ = 1/2) and with the stress one for a straight edge without stress concentration (λ = 1).