Crack paths and the problem of global directional stability

Abstract

Crack paths of original Griffith crack and edge crack under biaxial remote mode-I loading after different local disturbances are calculated by using integro-differential equations of first-order perturbation and numerical simulation with FEM respectively.Considering the asymptotic behaviour for large crack lengths the problem of global directional stability is reinvestigated extending the work by Melin. For the Griffith crack, correct power functions for the asymptotic path with one or both crack tips growing have been determined. The wellknown critical stress biaxiality ratio R c = 1 for the global directional stability has been obtained independently whether the crack is disturbed by local imperfections in geometry or in loading. For an edge crack the calculated critical stress biaxiality ratio for the global directional stability R c = 0.616, also irrespective of the local disturbances, corresponds to a positive T-stress and is considerably smaller than the value R > 0.95 estimated by Melin (2002). In general, cracks need not propagate asymptotically in the direction perpendicular to the largest principal stress (without crack). This is found to be due to the effect of the boundaries.Considering the initial crack growth exclusively, it is shown that the solution for crack path prediction in series expansion form as derived by Cotterell and Rice (1980) for traction-free crack faces (after correction of a misprint) is exact in the two first terms in all cases. Thus, for small crack growth the Cotterell and Rice solution is universal with respect to all loading and geometrical situations.

Mixed mode crack tip parameters for different wheel positions relative to a vertical crack at the rail foot

“…One of the first theories to interpret this parameter was crack path theory, 28,29 where the stability in the path of crack extension was correlated to the sign and magnitude of T-stress. One of the first theories to interpret this parameter was crack path theory, 28,29 where the stability in the path of crack extension was correlated to the sign and magnitude of T-stress.…”

“…There have been many studies suggesting different theories on how the magnitude and/or sign of the T-stress are associated with various phenomena in fracture mechanics. One of the first theories to interpret this parameter was crack path theory, 28,29 where the stability in the path of crack extension was correlated to the sign and magnitude of T-stress. 22 Another theory proposed by Larsson and Carlson 30 was the effect of T-stress on the size and shape of plastic zone developing around the crack tip.…”