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

H. Okada, S. N. Atluri

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Some Characteristic behavior of the T*ε is identified in this paper through an extensive numerical study. T*ε is a near tip contour integral and has been known to measure the magnitude of singular deformation field at crack tip for arbitrary material models. In this paper, T*ε 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*ε 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 Δa→0 for low hardening materials. Thus, T*ε evaluated on a moving contour tends to zero as ε→0 and Δa→0, for low hardening materials. If the integral contour elongates as crack extends (elongating contour), then T*ε measures total energy inside the volume enclosed by Γε [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*ε, when the applied load is slightly perturbed, is identified. The CTOA is found to be quite insensitive to applied load change. T*ε is found to be roughly proportional to the square of the applied load. The functional shape of T*ε in terms of the size ε of integral contour (for the elongating contour case), is identified, using the crack tip asymptotic formula of Rice (1982). Also, the behaviors of CTOA and T*ε are discussed from the view point of Rice's asymptotic solution. It is recommended that as a crack tip parameter for ductile materials, T*ε 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.

Original languageEnglish
Pages (from-to)339-352
Number of pages14
JournalComputational Mechanics
Issue number4
StatePublished - May 1999


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