Modified Kitagawa Diagram and Transition from Crack Nucleation to Crack Propagation
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EXTENSIVE work has been done to characterize fatigue life based on either stress- or strain-life criterion, or crack growth life using the damage-tolerance criterion by utilizing fracture mechanics methodology.[1–3] In the stress- or strain-life, the nucleation of a crack is considered as a major event of fatigue life; and correspondingly the design methodology is centered on preventing such formation in critical components under service-loads. In the damage tolerance approach, crack is assumed to be present in a structure, but its propagation resulting in the failure of a component under service-loads is considered. While the two approaches the stress or strain-life and the damagetolerance diverge from the philosophical perspective, there is a need to combine these two approaches in terms of life prediction of a component in service, since in K. SADANANDA and S. SARKAR, Senior Engineers, are with the Technical Data Analysis, 3190 Fairview Park Drive, Suite 650, Falls Church, VA 22042. Contact e-mail: kuntimaddisada@ yahoo.com Manuscript submitted April 25, 2012. Article published online September 22, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A
many cases total life includes both crack nucleation and propagation. This can be done, in principle, by using the modified Kitagawa-Takahashi diagram.[4] Our efforts[5–8] during the past decade were centered on establishing that fatigue involves two-independent load parameters, the peak or the mean stress, and the stress-amplitude. The two parameters manifest for stress-life in terms of maximum stress, rmax, and stress amplitude, Dre. The roles of these two parameters on stress-life have been considered in the past, starting from Goodman,[9] as the mean-stress or strain effects.[10] For crack growth, the two-load-parameter requirement manifests in terms of peak stress intensity factor, Kmax, and the stress intensity range, DK. The role of Kmax on crack growth has been recognized in the past, but mostly at the high end of crack growth rates, when monotonic modes of failure get superimposed on fatigue crack growth.[11] For the major part of the crack-growth life, the stress intensity factor range, DK, is normally considered as the only contributing factor for the crack tip driving force.[12] To account for the deviations due to R-ratio effects or deviations in the growth of small cracks, a non-fracture parameter namely, crack closure, has been brought in, with the assertion that there is a VOLUME 44A, MARCH 2013—1175
break-down of fracture-mechanics similitude.[13] The similitude implies for the same crack tip driving force the crack growth rate should be the same. Crack closure is not a fracture mechanics parameter. Our analysis using the two-load parameter approach, on the other hand, has established that all the above deviations from the long-crack growth behavior can be analyzed systematically without the consideration of crack closure. In fact, we have shown[14] that the plasticity-induced crack closure cannot be justified on the basis of dislocation theory, while
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