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.

中文翻译：

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由两种不同材料组成的封闭楔的奇异解分析的数值和应用结果

本文考虑了可以确定二维和三维闭合复合楔的奇异点附近应力奇异性性质的解决方案。对具有完美结合界面的闭合复合楔和具有无应力边缘的均匀楔进行应力奇异指数的比较分析。使用分析结果，可以评估当裂纹腔被某种材料填充时裂纹尖端附近应力奇异性的性质变化。结果是针对不同比例的楔形部件的张角、不同的弹性模量值和不同的楔形成分材料的泊松比获得的。对于对应于弱可压缩或不可压缩材料的楔形部分的泊松比，确定复合闭合楔形奇异解变化的异常性质。在模型和应用问题的背景下，表明使用复合楔的本征解可以找到材料特性，确保在裂纹腔被填充的情况下最大限度地减少裂纹尖端附近的应力集中某种材料。这些解对泊松比的依赖性表明，在足够大的裂纹张开角度和材料的低刚度下，应力集中显着降低。结果表明，对复合楔块使用本征解可以找到材料特性，以确保在裂纹腔被某种材料填充的情况下最大限度地减少裂纹尖端附近的应力集中。这些解对泊松比的依赖性表明，在足够大的裂纹张开角度和材料的低刚度下，应力集中显着降低。结果表明，对复合楔块使用本征解可以找到材料特性，以确保在裂纹腔被某种材料填充的情况下最大限度地减少裂纹尖端附近的应力集中。这些解对泊松比的依赖性表明，在足够大的裂纹张开角度和材料的低刚度下，应力集中显着降低。