Crack closure

It has been shown, in Sect. 11.3, how the R-ratio effect can be explained in terms of AKeff that represents that part of the entire stress intensity factor excursion AK active in producing the growth of the crack. This AK g is, in practice, the 

in practice, is worth a reduction of the RCCF, daldN. As such. Fiber proposed a modified Paris-Erdogan equation 

Working with an aluminum alloy type 2023-T3, Elber found that the parameter U was not constant, but could be linked to the / -ratio by a relationship of the type 

Other researchers have confirmed the results obtained by Elber [18-21]. An interesting example regarding the Elber AST is provided in Fig. 11.20 that reports the experimental data obtained by Zhang et al. [22] on aluminum alloy type 7475-T7351. It can be observed the same / -ratio effect already seen in Fig. 11.11 for the titanium alloy and Fig. 11.16 for the aluminum alloy type 2219-T851. Zhang et al. 

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Crack extension is often observed to vary significantly at the same nominal value of AK (= Y AOpos Tta) for different values of R-ratio. Elber [26] was the first to explain this observation for metals in terms of the crack closure phenomenon. He determined, by measuring specimen compliance, that fatigue cracks open and close at the crack tip at positive values of stress due to contact between crack surfaces behind the crack tip. For elastic fatigue conditions it is generally found that P p = P, and Kop = K, where P is the applied load. 

W. Elber, The Significance of Fatigue Crack Closure , Damage Tolerance in Aircraft Structures, ASTM STP 486, 1971, pp. 230 242. 

S. Suresh and R. O. Ritchie, A Geometric Model for Fatigue Crack Closure Induced by Fracture Surface Morphology , Metallurgical Transactions, 13A, 1982, pp. 1627 1631. 

N. Walker and C. J. Beevers, A Fatigue Crack Closure Mechanism in Titanium , Fatigue of Engineering Materials and Structures, Wo[. 1, 1979, pp. 135 148. 

C. J. Beevers, R. L. Carlson, K. Bell and E. A. Starke, A Model for Fatigue Crack Closure , Engineering Fracture Mechanics. 

K. Minakawa and A. J. McEvily, Our Crack Closure in Ncar-Thrcshold Region , Scripta Metallurgica, Vol. 15, 1981, pp. 633 636. 

Several criticisms of these parameters have recently been pointed out. First, they have no specific association with a material plane (i.e., they are scalar parameters), despite the fact that cracks are known to nucleate on specific material planes. With traditional parameters it is difficult to account for the effects of crack closure under compressive loading. Traditional parameters have not been successful at unifying experimental results for simple tension and equibiaxial tension fatigue tests. Finally, a nonproportional loading history can always be constmcted for a given scalar equivalence parameter that holds constant the value of the scalar parameter, but which results in cyclic loading of material planes. For such histories, scalar parameters incorrectly predict infinite fatigue life. 

In order to accurately model the fatigue behavior of rubber, fatigue analysis methods must account for various effects observed for rubber during constant amplitude testing. Effects associated with load level, 7 -ratio (ratio of minimum to maximum loading level), and crack closure are presented in this section. 

The load-displacement curves for the orthogonal interlock fabric composites show a non-linear unloading sequence and an appreciable permanent deformation after unloading, with the crack tip not completely closed (Guenon et al., 1987). These observations are attributed to the crack closure process of the three-dimensional fabric composites where through-the-thickness yarns break near the outer surface of the specimen. 

Thompson, R. B., Fiedler, C. J., and Buck, O. (1984). Inference of fatigue crack closure stresses from ultrasonic transmission measurements. In Nondestructive methods for materials property determination (ed. C. O. Ruud and R. B. Thompson), pp. 161-70. Plenum Press, New York. [278]... 

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