The local approach (LA) to fracture has been considerably developed over the past two decades, not only to provide a better understanding of the frac- ture behavior of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional global fracture mechanics. However, recent findings have demonstrated limitation of both the predictive capabilities and fundamental assumptions of conventional versions of LA to fracture. The main reason of the problems lies in empirical nature of existing versions of LA to cleavage fracture because all of them are based on empirical Weibull distribution which was obtained for very brittle materials, such as ceramics, so, it can’t account for specific features of cleavage fracture of metal. This appears, specifically, in the fact that Weibull distribution parameters, aren’t material’s constants but depend on the temperature, notch radius and plastic strain value.
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