Toughness - curve behavior of structural materials using traditional σ-ϵ diagram

The Neuber-Novozhilov approach is proposed for description of the stress distribution and crack opening in the prefracture zone in the vicinity of rupture cracks when solutions of the classical elasticity theory has a singular component. The stress distribution in the classical Leonov-Panasyuk-Dugdale model is chosen for a approximation. Modification of this model is proposed when the scheme of a fiber bundle is used for the prefracture zone, the fiber bundle occupying a rectangle in the front of the tip of the initial crack. The stress distribution in the prefracture zone and in the front of it is obtained in the first approximation in the case when the standard σ - ε diagram of material has jump discontinuity. The function that describes the stress distribution may also have jump discontinuity. The function that describes a crack opening is a smooth function. For critical lengths of prefracture zones and the critical coefficient of material crack toughness, relations between structural and strength characteristics of the material are obtained.