Prefracture model of a layer with a hole based on the interaction arc concept

For an elastic symmetric body in the form of a layer weakened by a hole and loaded in mode 1, the concept of an interaction arc (IA) is introduced. The IA forms a small neighborhood of the point of maximum specific free energy in the middle section of the layer. The free energy flow through IA is represented by the energy product (EP) - the product of the specific free energy and a linear parameter. Using the well-known asymptotic expressions for the stress field in the neighborhood of the hole apex, a relationship is obtained between the linear parameter and the radius of curvature of the hole apex, which ensures the independence of the EP from the radius of curvature and the linear parameter. When the radius of curvature is zero, the hole degenerates into a mathematical cut. In this case, the EP is reduced to the Irwin formula. Thus, if any hole degenerates into a mathematical cut, then regardless of the geometry of the cut edges, in the limit, we must come to the same stress intensity factor (SIF). In particular, we use a semi-elliptical hole. A technique for determining the SIF-1 is proposed, based on the representation of the approximating SIF in terms of dimensionless free energy flows that take a stationary value as the radius of curvature tends to zero. The values of the SIF obtained by this method coincide with their values given in other sources based on the analysis of the disclosure of the mathematical cut. In particular, a rectangular layer subjected to a distributed load is considered. The solutions were obtained by the FEM using the CAE Fidesys software package. The difference with the known results was less than one percent.