2018 年 84 巻 864 号 p. 18-00013
In this paper, convenient analysis methods are proposed for analyzing the singular index and the intensity of singular stress field (ISSF) at the vertex on the interface in the three dimensional (3D) bonded body. The analysis methods focus on FEM stresses at and around the vertex. The singular index is determined from the FEM stress ratio at the vertex obtained by performing FEM analyses for the finely and coarsely meshed models. Then, the ISSF is determined from the average FEM stresses around the vertex obtained for the reference and unknown models by applying the similar mesh pattern. The validity of the present methods is examined by comparing the results of 3D bonded models with/without fixed free surfaces. It is found that the obtained singular index has the same accuracy as the FEM eigenvalue analysis. The asymptotic solutions with the singular index and ISSF obtained by the present method correspond to FEM stress distributions. Since the ISSF obtained by the body force method (BFM) is used as the reference solution, the present method for ISSF has the same accuracy as BFM. Moreover, the critical ISSF values are calculated from the experimental results of the butt joints under various adhesive thicknesses. The critical ISSF at the side of 3D butt joint is in good agreement with the critical ISSF of 2D butt joint model. It is shown that the critical ISSF at the vertex of 3D joint is constant as well as the critical 2D ISSF independent of the adhesive thickness.
