Local strain energy density near sharp v-notches in plates

Conditions of fracture of the local strain energy density, which were first formulated by Sih for a sharp V-notch with an arbitrary tip angle, are proposed. The edges of the considered V-notch are free from loading. If loading schemes of type I and type II are used, it is shown that the known brittle fracture conditions proposed by Sih contradict one of the basic postulates in fracture mechanics: the greater the intensity of stresses or elastic energy near the V-notch tip, the greater the probability of crack propagation. The proposed new conditions of fracture (in a polar coordinate system) are obtained as a result of independent determination of the energy densities of changes in volume and shape. In this case, the above-mentioned contradiction is eliminated.