In this paper, the three-dimensional (3D) singularity index at the interface corner ${\lambda }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{r}}$ is newly analyzed for the prismatic butt joint in comparison with the two-dimensional (2D) singularity index along the interface edge ${\lambda }_{2\mathrm{D}}$ previously studied. The finite element eigenanalysis reveals that the ratio of the singularity index is in the range of $0.85\le {\lambda }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{r}}/{\lambda }_{2\mathrm{D}}\le 1.15$ for the all range of material combination. Under 2D bad pair condition expressed by Dundurs’ parameters $\left(\alpha ,\beta \right)$ as $\alpha \left(\alpha -2\beta \right)>0$, the ratio is in the range $0.85\le {\lambda }_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{r}}/{\lambda }_{2\mathrm{D}}\le 1$. The 3D bad pair condition when the singular stress appears at the corner is clarified on the $\left(\alpha ,\beta \right)$ map in comparison with 2D well-known expression $\alpha \left(\alpha -2\beta \right)>0$. Simple and convenient discriminant formula at the 3D interface corner is also indicated for the appearance of the stress singularity.

在本文中，界面角处的三维（3D）奇异性指数 ${\lambda }_{\mathrm{C}\mathrm{○}\mathrm{r}\mathrm{n}\mathrm{电子}\mathrm{r}}$ 与沿界面边缘的二维 (2D) 奇异性指数相比，新分析了棱柱对接接头 ${\lambda }_{2\mathrm{D}}$以前学过。有限元特征分析表明奇异性指数的比值在$0.85\le {\lambda }_{\mathrm{C}\mathrm{○}\mathrm{r}\mathrm{n}\mathrm{电子}\mathrm{r}}/{\lambda }_{2\mathrm{D}}\le 1.15$适用于所有范围的材料组合。Dundurs 参数表示的二维坏对条件下$\left(\alpha ,\beta \right)$ 作为 $\alpha \left(\alpha ——2\beta \right)>0$，比率在范围内 $0.85\le {\lambda }_{\mathrm{C}\mathrm{○}\mathrm{r}\mathrm{n}\mathrm{电子}\mathrm{r}}/{\lambda }_{2\mathrm{D}}\le 1$. 在拐角处出现奇异应力时的 3D 坏对情况在$\left(\alpha ,\beta \right)$ 与 2D 众所周知的表达式比较的映射 $\alpha \left(\alpha ——2\beta \right)>0$. 应力奇点的出现也给出了在3D界面角处的简单方便的判别公式。