On the Accuracy of J-integral Value Evaluated by Finite Element Method for Mixed Mode

G. R. Irwin proposed that the stresses at the vicinity of a crack tip were approximately expressed by using the stress intensity factor K, and the critical K_c-value was denoted the fracture toughness characterized as one of the material properties for the cracked plate. Several cases of K-value were formulated by M. Isida, A. S. Kobayashi, O. L. Bowie, B. Gross and et al. However, for the K-value of a finite plate with the complex geometry, it is very difficult to obtain analytically. Thesefore the numerical methods were proposed, which were the boundary collocation method and the Finite Element Method (FEM) and so on. Recently, G. P. Anderson, I. R. Dixson, W. K. Wilson, Y. Yamamoto and et al. suggested the method to evaluate the K-value by using FEM. On the other hand, J. R. Rice proposed the J-integral method and indicated that the J-value was pathindependent. The J-value was expressed that J=G=K^2_I/E for the plane stress condition on Mode I. It is advantage of the method that small mesh divisions in the vicinity of crack tip are not required in order to evaluate the accurate J-integral value by suing FEM. Almost these investigation were for K_I (Mode I) and few analysis for mixture mode using by FEM. T. K. Hellen has defined that J=J_1-iJ_2 and theoretically proved that J_1=(K^2_I+K^2_<II>)/E, J_2=-2K_IK_<II>/E (plane stress) on mixed mode. Applying this new J-integral method to the numerical solutions of FEM were called ”direct method”, however, J_2-values contained many errors along the path of crack edges. The aim of this paper is to make less these errors by extending the ”superposition method” which is already proposed by authors for the Mode I. In order to investigate the accuracy of this method, the results are compared with the numerical results obtained by W. K. Wilson's method.