A plastic flow induced fracture theory for K iscc
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I.
INTRODUCTION
THE stress corrosion cracking threshold intensity, Kxscc, is generally taken to be the stress intensity level below which, as indicated in Figure 1, crack growth rates are vanishingly small. Alternatively, this threshold is that stress intensity level below which incubation times for crack initiation, as measured experimentally, are very long. Accordingly, Kiscc is that fracture mechanics parameter quantifying the lowest applied stress situation for which certain environment related failure criteria are met in the vicinity of an existing or precrack, resulting in subsequent secondary crack initiation and joining with the precrack. It is known that at K~ values above threshold, repeated and time-dependent crack initiation and link-up events result in a finite crack growth rate. 1.2 The kinetics of this crack growth is the topic of a subsequent paper. 3 In what follows, we present a new mechanism and theory for K,scc, especially as it relates to hydrogen controlled stress corrosion cracking. In the existing threshold models, 4-8 the hydrostatic stress elevation in the near crack-tip region is presumed to cause the local hydrogen accumulation in this region, and fracture is said to result when the local maximum tensile stress from the applied loading exceeds the local fracture stress (a material property). The hydrogen accumulation, in a sense, allows the latter, fracture criterion, to be satisfied since the assumption in these models is that, in the presence of the excess hydrogen, the local fracture stress can drop to below the local crack-tip tensile stress. Recently Nair et al. 9 argued that tensile stress elevation in the near crack-tip region is not a sufficient condition for fracture initiation to occur since the local fracture stresses are much too high, and they proposed that a necessary condition for failure is that the local f l o w stress in the crack-tip plastic zone must exceed a critical magnitude before secondary cracks can initiate. This represented a marked departure from conclusions of these earlier analyses. In this paper, the new failure criteria 9 for threshold are developed in detail and are quantitatively applied toward the S.V. NAIR, formerly Associate Research Scientist, Henry Krumb School of Mines, Columbia University, is now Assistant Professor at the Department of Mechanical Engineering, University of Massachusetts at Amherst, Amherst, MA 01003. J.K. TIEN is Henry Marion Howe Professor of Metallurgy, Henry Krumb School of Mines, Columbia University, New York, NY 10027. Manuscript submitted June 28, 1984. METALLURGICAL TRANSACTIONS A
prediction of Ktscc in engineering materials. But first, earlier Kiscc models 4-s are critically reviewed with particular focus on the fracture criteria employed in these models. The physical contents of the prior models were invaluable in guiding our derivation.
II.
REVIEW OF MODELS FOR Kmcc
Fracture models for K~scc were developed by Oriani and Josephic, 4'5 Gerberich et al.,6'7 and Doig and Jones 8 based on the failure criterion introdu
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