Numerical and applied results of the analysis of singular solutions for a closed wedge consisting of two dissimilar materials

Abstract

This paper considers solutions that can determine the nature of the stress singularity in the vicinity of a singular point for two-dimensional and three-dimensional closed composite wedges. A comparative analysis of stress singularity exponents is carried out for closed composite wedges with perfectly bonded interfaces and homogeneous wedges with stress-free edges. Using analysis results, it is possible to evaluate a change in the nature of the stress singularity near the crack tip when the crack cavity is filled with a certain material. Results were obtained for different ratios of the wedge component’s opening angles, different values of elastic moduli, and different Poisson ratios of the wedge’s constituent materials. The anomalous nature of changes in singular solutions for a composite closed wedge is established for Poisson’s ratios of the wedge part corresponding to a weakly compressible or incompressible material. In the context of the model and applied problems, it is shown that the use of eigensolutions for composite wedges makes it possible to find material characteristics that ensure maximum reduction in the stress concentration near the crack tip in the case of the crack cavity being filled with a certain material. The dependence of these solutions on the Poisson ratio demonstrates a significant reduction in stress concentration at sufficiently large crack opening angles and at low rigidity of the material.