A theoretical evaluation of crack closure
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I.
INTRODUCTION
S I N C E 1970, tl'21 premature crack closure during unloading has been considered important in the evaluation of the crack tip driving force necessary to quantify fatigue crack growth data. Crack closure* reduces the ap*From here on, crack closure implies premature crack closure before complete unloading.
plied stress-intensity amplitude, AK~pl, by a factor related to the stress intensity at which closure occurs, Ka. The magnitude of Kc~, which is generally measured by observing the change in the compliance at the point of closure, depends on material, microstructure, environment, and loading conditions. The effective stressintensity factor amplitude at the crack tip, 2~Keff,is given by AKeff = Kmax -
Kd < mKapl, if Kcj > Kmi n
= AKapl = Kmax - Kmin, if Kd --< gmin where Kmax and g m i n a r e the stress intensities at maximum and minimum loads, respectively. For tests involving high R ratios (gmin/Kmax) i.e., for R > 0.6 to 0.7, Kmi, > Kcl, there is no crack closure, pj and the effective driving force is equal to the applied driving force. While crack closure has become a major concern in fatigue crack growth which cannot be easily predicted or measured, its effect is considered significant, particularly for near-threshold crack growth at low R ratios. Crack closure is considered primarily responsible for several fatigue crack growth phenomena, such as the effects of the following: (a) R ratio on fatigue crack thresholds, z~Kth , and on fatigue crack growth rates, da/dN; (b) environment, viz, vacuum, air, humidity, hydrogen, and corrosive environments; (c) microstructure that contributes to crack path tortuosity; (d) retardation due to overloads, underloads, and thermal history; and (e) acceleration of short cracks, etc. (For details, see Suresh, t31 Benerjee, 14j and a recent ASTM symposium [51 on crack N. LOUAT, President, and M. DUESBERY, Vice President, are with Fairfax Materials Group, A r l i n g t o n , VA 22310. A . K . VASUDEVAN, Program Manager, is with the Office of Naval Research, Arlington, VA 22217. K. SADANANDA, Section Head of Deformation and Fracture, is with the Materials Science and Technology Division, Naval Research Laboratory, Washington, DC 29375. Manuscript submitted January 14, 1993. METALLURGICAL TRANSACTIONS A
closure.) Since 1970, there have been more than a thousand articles and several symposia dealing with crack closure and its implications in the observed fatigue crack growth behavior. In spite of such enormous effort, understanding of crack closure and estimation of its true contribution to crack growth are still elementary. These problems are compounded in the application of fatigue crack growth data for structural design. For example, it is not only difficult but also questionable to translate the laboratory fatigue crack growth data to predict the life of a structure, since closure levels and, hence, effective crack tip driving forces under service conditions are difficult or impossible to evaluate. In a recent article, [6J the authors presented a critical
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