A micromechanical model for cleavage-crack reinitiation
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I.
BACKGROUND
A. Review of Crack lnitiation
THIS paper
reports the preliminary development of a model of the reinitiation of an arrested cleavage crack. The phenomenon is of interest since there is experimental evidence showing that cleavage reinitiation requires a lower stress intensity than cleavage initiation from the tip of a fatigue precrack.:'2 In addition, reinitiation of an arrested cleavage crack in a compact specimen provides KI,. values that are more representative of very-large-specimen data than those obtained using either a blunted fatigue precrack or a growing ductile crack. 2'3 The model derived below assumes that the mechanism of cleavage-crack extension is independent of crack-tip morphology; slip-induced crack initiation at second-phase particles is followed by unstable propagation. Both shear stresses and normal stresses play a role. It is generally believed that a precrack blunts by shear-stress-induced plastic flow creating a crack-tip zone in which particle cracking can lead to cleavage-crack initiation. Conversely, the propagation of the initiated microcrack is controlled by normal stresses built up by the constrained nature of deformation at a blunting crack tip. Since blunting is accompanied both by an increasing plastic zone and a decreasing crack-tip stress concentration, the instability condition depends on a complex interplay of forces. Thus, in order to understand cleavage-crack reinitiation, relations describing both blunting and plastic zone size are needed. Furthermore, to understand the differences between initiation and reinitiation, the differences in crack-tip morphology in the two cases must be taken into account. In the fatigue-precracked case, acoustic-emission data 4'5 support the suggestion 6 that loading of a precracked specimen is accompanied by formation of a plastic zone which generates a number of stress-induced microcracks. With continued loading, a microcrack of critical size is formed at a second-phase particle and triggers cleavage. Fractographic
evidence 3'7'8 suggests that the triggering particles are distributed randomly ahead of the fatigue precrack. Reference 6 further suggested that cleavage-crack extension occurs when a critical array of microcracks is formed, the observed variability in Kt~ for cleavage being associated with the stochastic nature of microcracking. B. Review of Crack Arrest Developing a microstructurally-based model to explain the experimental observations of crack reinitiation presents a major difficulty. Some insight is provided by studies of crack arrest in steel. Empirically, the stress intensity at crack arrest (K/a) for large specimens is close to (2/3)Ktc, for the same specimens over a wide temperature range (Figure 19't~ indicating strongly that the two quantities may very well be related. Note that the symbol Ktc, is used here for reinitiation of an arrested crack, in contrast to K/c, which is measured using a fatigue precrack and is roughly twice Kit,. 2 This distinction is significant since our model incorporates microstruct
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