Comparison of general regularities inherent to structures of surface cracks and stresses near the tips of spatial cracks

The paper compares the results of numerical simulation of surface cracks with the aim to find a possible relationship between the parameters of singular behavior of stresses near the common tip of several cracks of different configurations and the frequency of occurrence of such configurations in real patterns of surface crack networks. A finite element method is used to build a numerical model of spatial cracks, which takes into account the intersection of two, three and four wedge-shaped cracks with an opening angle of 90°. The nature of the stress singularity in the vicinity of singular points in three-dimensional bodies is estimated by making use of the developed numerical algorithm that extracts the asymptotics of stresses near singular points from the numerical solution. The proposed algorithm has been tested for different types of singular points in two-dimensional and three-dimensional problems, associated with the assessment of the behavior of stresses at the tip of a single spatial crack that has reached the body surface. It is demonstrated that the developed algorithm makes it possible to calculate the stress singularity index at the common tip of spatial cracks. The results of calculations are discussed. To make an additional comparison between different model configurations of intersecting cracks in terms of the mean strain energy densities, a small sphere with the center situated at the common crack tip is introduced. The dependences of the mean strain energy density on the angles that determine the geometry of intersecting spatial cracks are plotted. General signs of the patterns of surface cracks networks and the dependences of the behavior of stresses in the vicinity of tips of the considered spatial crack configurations are identified.