Relationship between local and global characterizing parameters of stress triaxiality constraint in crack tip regions

Abstract

The amount of stress triaxiality constraint in crack tip regions is a strong factor in a material's cracking resistance. According to the HRR solution, the triaxiality on the ligament ahead of a crack tip is only a function of the material' s strain hardening (n-value) in the plane strain case and can be expressed as ((ym/(ye) The formula does, however, break down for various real specimen geometries. Recently, Sun et al. have proven [1,2] that the stress triaxiality constraints in crack tip regions of real specimens vary with the variations of specimen geometries, crack depths and load levels, and are lower than those defined by the HRR solution, which is the essential reason for losing the J-dominance and causing the specimen-geometry-dependence of J~o in the plane strain case. Due to the dependence of triaxiality on the types of specimens and the complexity of triaxiality distribution, FEM methods have to be employed, which are very expensive. Therefore, it is necessary to reasonably express and evaluate the triaxiality in crack tip regions of real specimens.In general, the stress triaxiality is defined by the ratio of hydrostatic stress to von Mises effective stress, i.e., o'm/oe, which is a local parameter and difficult to determine. On the other hand, for a fracture mechanics criterion taking into account the triaxiaility, it is better that a global parameter, directly relative to the triaxiality, be given. Recent research indicated that the degree of crack tip triaxiality is related to the relationship between the J-integral and the CTOD, namely (J/oo.CTOD) [3] or (dJ/dSt) [4], which are the global parameters and easy to obtain. But further quantitative results on the relationship between (om/(ye) and the global parameters have not been developed.In the present report, Anderson's simple correction [4] for crack tip stresses, taking account of the loss of triaxiality for large scale yielding from the quasi-deformation assumption, was applied to find a relationship between the local and global characterizing parameters of stress triaxiality constraint in crack tip regions of real specimens.Anderson's corrected stress and strain perpendicular to the crack tip plane are given by Int Journ of Fracture 45 (1990)