Problems of interface cracks starting from the common corner points of pairs of perfectly glued wedges of different isotropic elastic materials are addressed. It is demonstrated that for a few particular configurations and a restrictive condition imposed on values of elastic constants (corresponding to vanishing of the second Dundurs parameter), the problem of elastic equilibrium may be solved by Khrapkov’s method. These configurations are: (i) the wedges forming a half-plane; (ii) the wedges forming a plane; (iii) one of the wedges being a half-plane. In all cases, the external boundaries are supposed to be free of stresses. By applying Mellin’s transform for all three configurations the problem has been reduced to vector Riemann’s problem, and the matrix coefficient has been factorized for the case of the mentioned restrictive condition. The first configuration, i.e. the problem of an inclined edge crack located along the boundary separating two wedges of different elastic isotropic materials forming a half-plane is considered in more detail. The solution has been obtained for both uniform (corresponding to remote loading) and non-uniform (loading applied at the crack faces) problems. Numerical results are presented and compared with the available results obtained by other authors for particular cases. The obtained solutions appear especially valuable for analysing extreme cases of parameters.

中文翻译：

---

具有界面裂纹的复合楔的弹性平衡的某些情况

解决了从不同各向同性弹性材料的完美粘合楔对的公共角点开始的界面裂纹问题。证明了对于一些特定的配置和施加在弹性常数值上的限制条件（对应于第二个 Dundurs 参数的消失），弹性平衡问题可以通过 Khrapkov 方法解决。这些配置是： (i) 楔形体形成一个半平面；(ii) 形成平面的楔子；(iii) 楔形之一是半平面。在所有情况下，外部边界都应该没有应力。通过对所有三种配置应用梅林变换，问题已简化为向量黎曼问题，并且矩阵系数已针对上述限制条件的情况进行了分解。更详细地考虑了第一种配置，即沿着分隔形成半平面的不同弹性各向同性材料的两个楔形物的边界定位的倾斜边缘裂纹的问题。对于均匀（对应于远程加载）和非均匀（加载在裂纹面上）问题，已经获得了解决方案。给出了数值结果，并与其他作者针对特定案例获得的可用结果进行了比较。获得的解决方案对于分析参数的极端情况尤其有价值。对于均匀（对应于远程加载）和非均匀（加载在裂纹面上）问题，已经获得了解决方案。给出了数值结果，并与其他作者针对特定案例获得的可用结果进行了比较。获得的解决方案对于分析参数的极端情况尤其有价值。对于均匀（对应于远程加载）和非均匀（加载在裂纹面上）问题，已经获得了解决方案。给出了数值结果，并与其他作者针对特定案例获得的可用结果进行了比较。获得的解决方案对于分析参数的极端情况尤其有价值。