McClintock1, 2 was one of the first to model continuous-cycling fatigue crack growth by assuming a succession of miniature low-cycle-fatigue (LCF) specimens at the crack tip. Elements ahead of the crack amass damage until the arrival of the tip itself. Such models had been summarized by Majumdar and Morrow,3 but the author was unaware of these papers at the time. The ideas were pursued further by Chakrabortty4 whose paper, again unknown to the author, was published in the same issue (1979, Vol. 2) of FEMS. In the original paper5 crack propagation is represented by successive regeneration at the crack tip, the process becoming progressively easier as the crack grows owing to an increase in strain concentration. These ‘initiation’ cycles were related to the ‘Coffin’ expression for crack initiation, thereby introducing two empirical constants k and α. The paper is of the class ‘ρ/N’ where ρ is the assumed size of a crack-tip process zone and N is the cycles required to traverse that zone. Expressions had been previously derived linking LCF with linear-elastic fracture-mechanics (LEFM) crack growth, using the parameter ΔJ.6 (It was later shown that this was identical to using an equivalent stress intensity parameter.7) It has been shown that the approach does not apply for crack depths < 180 μm.6 At elevated temperature the ΔJ approach was successful for describing crack growth in the range 0.2–1.2 mm for the cobalt-based alloy MAR-M509 at 600 °C.8 Other studies have in fact shown9 that crack growth rates are approximately constant below a depth of 200 μm. Even to this day short crack growth relations in LCF and their practical use are not as familiar as those in LEFM. It may justifiably be argued that for every paper published on LCF short crack growth, several hundred have appeared dealing with LEFM crack growth in terms of the ‘Paris’ law. One of the original referees' comments was that the paper5 should have been presented in terms of LEFM. The author nevertheless defended his approach because for small cracks it was thought useful to retain the crack depth explicitly. It will be shown that LCF crack growth data have a definite part to play in the assessment of components and structures. The paper assumes that the elastic stress concentration at the tip of a crack of depth a is of the form 2(a/r)1/2 where r is an effective crack tip radius. Because it was known that the crack opening displacement increases with increasing crack depth, so too does the effective radius. This was achieved via a power law, which introduced two empirical constants G and n. Exponential crack growth in 316 steel at 600 °C, see Eq. (7). Adapted from tabulated data in Ref. 13. Values of parameter B (circles) adapted from Fig. 1 compared with upper bound relation given by Eq. (6). It is appropriate to record that the original paper5 and this last reviewed paper13 were both published by permission of the former Central Electricity Generating Board.
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Jan 1, 2011
Masanori Kikuchi + 3
Open Access
