General energetic analysis of fracture instabilities in elastic media and the elastic field rupture

The singular integral equations method makes it possible to determine a general analytical solution to the problem of a crack subjected to any stresses, including singular ones. The singularity of stresses means that they tend to infinity in the concentration point. In exponential functions describing this relationship, the exponent characterizes the stress curvature growth. Also the energy released by crack opening can be described by a simple analytical formula. The problem is solvable for an exponent greater than −1. The class of all the cracks subject to stresses that exponentially grow to one of the crack ends is divided into three sub-classes. One of these embraces most of crack types, also Griffith’s. The remaining two are a source of microcracks in an elastic medium. The onset of such a stress concentration gives rise to a microcrack which cancels the stress singularity up to that with the exponent of −1/2, ensuring a strong stability of the medium. An analysis of the nucleation of such cracks brought about a concept of elastic field rupture without destruction of interatomic bonds, which has implications relating to the conductivity of metals. A general formula for the crack energy singles out a special crack of unit length, whose energy is constant and independent of stress concentration.