PSI - Issue 52

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D. Kujawski et al. / Procedia Structural Integrity 52 (2024) 293–308 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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This postulate expressed by Eq. (2) assumes that a globally measured K op is equal to the local crack tip K op,tip . So, Eq. (2) can be generalized as: ( ) =1− (3) where m = K op,tip /K op ranges from 0 to 1 and represents the effectiveness of a globally measured K op with respect to the local K op,tip . In Elber’s model m = 1. On the other hand, due to the inadequacy of PICC to explain the results at the near-threshold regime, other types of crack closure mechanisms, such as oxide-induced (OICC) and roughness-induced (RICC) crack closure, have been proposed, Suresh (1991). 2. General Experimental and Theoretical Observations The first experimental attempt aims to assess Elber’s postulate given by Eq. (2) was conducted by Vicchio et al. (1986). They investigated the effect of crack closure on FCG behavior in a 2024 Al alloy by inserting an artificial asperity (e.g., a needle tip) in the wake of the crack and measured closure using load-displacement data and found little influence on the crack growth rate. They concluded that such artificial single asperity closure had little effect in the reduction of FCG rate observed. In addition to artificially induced closure, Vicchio et al. (1986) also conducted FCG tests at R=0.5 on Astroloy (planar slip nickel-based superalloy) using the same specimen geometry and identical load reduction procedures. Although the corresponding (da/dN) vs.  K appl for these two tests showed perfect agreement while the closure measurements for these tests were significantly different and didn’t correlate with their data. A similar conclusion was also drawn by Bowman et al. (1988) that most measurements of closure tend to grossly overestimate its effect on FCG. They observed inconsistency in P OP measured for a single specimen for which testing specifications were satisfied. In addition, they disputed the notion “ that all of the load is transmitted through the plastic wedge is not physically reasonable ”. Very recently two other articles pertaining to K OP and  K eff were published by Tong et al. (2019) and Gonzales et al. (2020). Tong et al. (2019) demonstrated that the variations in K OP do not notably affect the cyclic crack-tip deformation, even when the crack was visually closed at P min . They used both digital image correlation (DIC) and compliance curves to determine the “crack opening” levels. They concluded that crack closure, although observed in the compliance curves and DIC technique, does not appear to impact the global crack driving force, such as J integral, or measured strains field ahead of the fatigue crack tip, thus it could be a misconception. Gonzáles et al. (2020), on the other hand, conducted well controlled tests under constant ΔK and K max loading conditions using 3 different methods to quantify the opening loads K OP along the whole crack path at each test. Their records show that the FCG rates remained constant along the whole crack path in all tests, whereas the measured opening loads K OP gradually decreased as the crack grew. They concluded that the  K eff given by Eq. (1) is not a suitable driving force for FCG analysis. We will now examine the implications of some theoretical approaches related to crack flanks contacts/closure that include a single or multiple rigid asperities, a rigid wedge, and energy release rate. Without losing generality, these approaches will be illustrated for R=0 where applied values of K max,appl =  K appl . and assuming that K op or K cl is equal to about 0.5K max . In general, it is observed that K op /K max at R=0 varies between 0 and 0.5 depending on specimen’s geometry, loading conditions (plane stress or plane strain), measurement techniques used or numerical simulations. The first analytical assessment on the effect of crack flanks contact, using dislocation analysis, was given by Vasudevan et al. (1992) They have shown that premature crack flanks contact due to the presence of oxides/asperities exists, but the magnitude of the closure contributions to the crack tip shielding are about 0.25K cl determined from the experimental load-displacement measurements. Five years later, a similar dislocation analysis was conducted by Riemelmoser and Pippan (1997) for a linear elastic crack with a rigid single asperity and multi asperities. Their