THE TEARING modulus approach to ductile fracture instability, as developed by Paris et al.
[ l] is based on the following main assumptions: (a) that the J-integral can be determined in terms of the system loading and crack length, while ignoring the detailed fracture mechanisms operative within a process zone near a crack tip, and (b) that crack growth is described by matching the resulting J,+r.p vs crack growth AC relation for the system against the material's Ju,,r vs AC curve, which is assumed to be independent of geometrical parameters, but which obviously does depend on the operative. fracture processes. Paris et al. define the material's tearing modulus as the normalised gradient TMar=(i?/Ys) dlMJdc of the material's JR curve, where c is the crack length, E is Young's modulus and Y is the yield stress. It is then argued that ductile fracture instability occurs when TNp = (El Ys)dJ App Id c exceeds TMaT; otherwise ductile crack growth remains stable d TM, is less than TMAT.
Adoption of this procedure allows advantage to be taken of stable crack growth when framing operational criteria for engineering components, since there can be a large safety margin in working to the critical J value (i.e. Jrc) associated with the onset of ductile crack extension from a preexisting defect. However, the approach presumes that the cleavage mode of fracture does not intervene during stable ductile crack growth. This note's purpose is to indicate that material inhomogeneity may cause ductile fracture instability which then allows the cleavage mode to operate, thereby leading to premature structural failure.
Consider initially the idealized situation where J App (I c with the slope increasing with applied stress level; this state of affairs is appropriate when stable crack growth proceeds under a gradually increasing applied stress. Suppose there are two cases (Fig. I): (a) where a crack propagates into a region with a higher tearing modulus and then back into the lower modulus material, and (b) where a crack propagates into a region of lower tearing modulus. In both cases ductile fracture instability ensues, and then as a result of strain rate effects at the unstable ductile crack tip, it is possible for this instability to lead to an unstable cleavage fracture. These idealised examples suggest that material inhomogeneity can cause ductile fracture instability followed by an unstable cleavage fracture and component failure, whereas the tearing modulus approach would predict stability, if the inhomogeneities are ignored.
The exnerimental results obtained bv Loss et al.121 for both unirradiated and irradiated A 533B nuclear reactor pressure vessel steels can be cited as a possible exampieof the effects described in this note. Schematically the measured IMAr vs AC is shown in Fii. 2, where there is a sharp discontinuity in the curve leading to cleavage fracture instability. The present author suggests that the tearing modulus increases because there is a material inhomogeneity, and this causes an unstable ductile fracture, which quickly develops into an unstable cleavage fracture.
As emphasized by Loss et a/. [2], there are clear practical implications of the effects described in this note, when a component is operating at a temperature where cleavage fracture is possible. With nuclear reactor pressure vessel steels, cracks can propagate by a cleavage mechanism at temperatures (i.e. in the upper shelf region) where static loading conditions only lead to stable ductile fracture. If there is concern that material inhomogeneity might lead to the effects described in this note, it would obviously be prudent to use the safety margin arising from stable ductile growth, only above that temperature where cleavage crack propagation cannot occur; otherwise it would be wise to use a fracture initiation criterion based on Jrc values. The problem is, of course, more relevant with thick steel sections where there is a greater likelihood of having material property variations, due to different regions not having the same cooling rates. Furthermore, welding of such sections also leads to material property variations.