Further studies on the characteristics of the T e integral: Plane stress stable crack propagation in ductile materials

Some Characteristic behavior of the T e (Atluri, Nishioka and Nakagaki (1984)) is identi®ed in this paper through an extensive numerical study. T e is a near tip contour integral and has been known to measure the magnitude of singular deformation ®eld at crack tip for arbitrary material models. In this paper, T e is found to behave quite differently for different choices of near tip integral contours. If the integral contour moves with advancing crack tip (moving contour), then T e measures primarily the energy release rate at the crack tip. It is very small for metallic materials, and tends to zero in the limit as Da! 0 for low hardening materials. Thus, T e evaluated on a moving contour tends to zero as e! 0 and Da! 0, for low hardening materials. If the integral contour elongates as crack extends (elongating contour), then T e measures total energy inside the volume enclosed by Ce [i.e., the energy dissipated in the extending wake] plus the energy release at the crack tip. Furthermore, the difference in the behavior of CTOA and T e , when the applied load is slightly perturbed, is identi®ed. The CTOA is found to be quite insensitive to applied load change. T e is found to be roughly proportional to the square of the applied load. The functional shape of T e in terms of the size e of integral contour (for the elongating contour case), is identi®ed, using the crack tip asymptotic formula of Rice (1982). Also, the behaviors of CTOA and T e are discussed from the view point of Rice's asymptotic solution. It is recommended that as a crack tip parameter for ductile materials, T e with elongating path be used. CTOA is sometimes not very sensitive to the applied load change, therefore it may create some numerical problems in application phase crack propagation analysis.