Interaction of contact cracks and narrow slits in plate bending

Abstract

The aim of the proceeding is to study the effect of interaction of rectilinear contact cracks and narrow slits for plate bending and on this basis to demonstrate qualitative differences in the concentration of stresses near defects of different nature. The crack is treated as a mathematical cut, the edges of which contact along the line on the plate outside. The slit is referred to as stress-free surfaces cut, the negative jump of normal displacement can occur on this cut. The problem of uniform bending of infinite plate weakened by through defects: cracks and slits, is considered in the two-dimensional formulation. The crack closure caused by bending deformation was studied based on the classical hypothesis of direct normal and the previously developed model of contact of edges along the line. A new boundary problem for a couple of biharmonic equations of plane stress and plate bending with interconnected boundary conditions on the cuts is formulated. The method of singular integral equations was applied to develop approximate analytical and numerical solutions of the problem. The results for the jumps of displacements and normal rotation angles, for the forces and moments intensity factors near the tips of defects, and for contact reaction on the closed edges of the cracks are obtained. Detailed analysis was carried out for parallel cracks and slits, depending on the parameter of their relative position. The comparison of findings with the known results for dyads: crack-crack and slit-slit is provided. As the results of the research show, the interacting contact crack and free slit are fundamentally different stress concentrators that produce qualitatively different patterns of local perturbations of stresses in the plate.