We derive an analytic solution to the plane problem associated with an edge dislocation interacting with a completely coated semi-infinite crack in the presence of remote in-plane loading. The semi-infinite crack and the parabolic coating–matrix interface are confocal, and the coating and the matrix have the same shear modulus but distinct Poisson’s ratios. Through the introduction of a conformal mapping function and the application of analytic continuation, a closed-form representation of a particular auxiliary function can be obtained leading to analytic expressions of the two pairs of analytic functions in the image plane characterizing the elastic fields in the two-phase composite. The local mode I and mode II stress intensity factors at the crack tip and the image force acting on the edge dislocation are then derived.

我们导出了一个平面问题的解析解决方案，该问题与边错位与存在远程面内载荷的情况下与完全涂覆的半无限裂纹相互作用相互作用有关。半无限裂纹和抛物线涂层-基体界面是共焦的，涂层和基体具有相同的剪切模量，但泊松比却不同。通过引入共形映射函数并应用解析连续性，可以获得特定辅助函数的闭合形式表示，从而在图像平面中生成两对解析函数的解析表达式，以表征这两个函数的弹性场。相复合材料。然后，得出裂纹尖端处的局部模式I和模式II应力强度因子以及作用在边缘位错上的像力。