A further study on the near tip integral parameter T_ε* in stable crack propagation in thin ductile plate

In this paper, some basic properties of the near tip integral parameter 7£ (Atluri, Nishioka and Nakagaki (1984)) are presented, for the case of stable crack propagation in thin ductile metal. The authors had carried out an investigation on the physical significances of the T_ε* integral for two kinds of integral contour geometries. Brust et al. (1986) used an integral contour geometry, which extends its frontal portion as the crack extends its length. In this paper, such an integral contour is called as "Elongating Contour". Also, it should be noted that a small contour which surrounds the propagating crack tip and moves along with the tip as the crack propagates, was originally thought (Atluri, Nishioka and Nakagaki (1984)). This one is called as "Moving Contour" in this paper. Discussions are presented based on simple energy balance statements. It has been found that, the T_ε* integral parameters, using the "Elongating" and "Moving" integral contours, measure different physical quantities. The first one measures the energy dissipation inside the small integral contour path Γ_ε, which is some finite value, and the energy release rate at the crack tip. However, the other one with the "Moving Contour" measures the energy release rate the crack tip. This one is nearly zero or very small. As conclusion to this research, the use of "Elongating Contour" is recommended in the case of stable crack propagation in thin ductile plate. Furthermore, the results presented in this paper are generic ones (do not depend on the type of materials). The results presented in this paper, can be applied to fracture problems with any other materials.