PSI - Issue 45

James Martin Hughes et al. / Procedia Structural Integrity 45 (2023) 44–51 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Crack closure is a well-known phenomenon in cyclic fatigue whereby a fatigue crack remains closed for a portion of the load cycle, even for tensile-tensile cycles. This phenomenon was first reported by Elber (1970) and has since been the subject of thousands of scientific studies. The overall effect of crack closure is a reduction in the stress intensity factor (SIF) range, which is the driving mechanism for crack growth in the Paris-Erdogan law (Paris and Erdogan, 1963). Elber (1971) subsequently proposed a modified crack growth equation which takes the crack closure effect into account:

da dN



 eff K

m

C  

(1)

where da/dN is the crack extension per load cycle, Δ K eff is the effective SIF range, and C and m are material parameters. If the crack opening/closure loads are known (or measured), the overall SIF range can be related to the effective SIF through Eq. (2):

max P P P P   max

op/cl

(2)

eff K  

K U K

  

min

where P max , P min , and P op/cl are the maximum load, minimum load, and opening/closure load, respectively, and U is often called the opening load ratio. There is typically some small difference between the opening and closure load, but in practice this difference is disregarded (see Fig. 3 and 4 of Ashbaugh et al., 1997). Although there remains some skepticism (Lout et al., 1993; Vasudeven et al., 1994; Vasudeven et al., 2001), it is well agreed that the theory of crack closure provides clear explanations for the short crack effect (Vormwald and Seeger, 1991; Breat et al., 1983; Pippan and Hohenwarter, 2017) and the stress ratio effect (Pippan and Hohenwarter, 2017; Moreno et al., 2019; Okayasu et al., 2006). Closure measurements can therefore be applied to collapse fatigue crack growth rate curves from constant, variable, or random amplitude load sequences into a single master curve. Although a number of studies have used finite element simulations and experimental techniques to investigate the effect of crack closure for simple constant amplitude load sequences (Fleck et al., 1983; de Matos and Nowell, 2009; Ashbaugh et al., 1997; Sehitoglu, 1985) or after overloads (Borrego et al., 2012; Nowell and de Matos, 2010), the on line measurement of crack closure in variable amplitude loading sequences has been met with considerable difficulty. A limited number of studies have extracted closure measurements for a small number of variable amplitude cycles with some success (Moreno et al., 2019), however, the on-line monitoring of large variable amplitude load sequences is yet to be achieved due to sensor limitations and large data. Such an advancement would enable the abovementioned collapsing of the fatigue crack growth rate curve, and provide essential knowledge and data to develop more sophisticated spectrum compression and truncation algorithms. Crack opening/closure loads can be identified using electrical, acoustic, or compliance-based techniques, although compliance techniques are preferred due to their accuracy (Fleck et al., 1983). Compliance-based techniques use the nonlinear load-displacement relationship to identify the closure/opening load. At sufficiently high loads, the crack is fully open, and the compliance of the specimen remains constant. Below the crack opening load, the compliance of the specimen is nonlinear and changes as the crack is incrementally opened. A variety of instruments can be used to measure specimen compliance, such as a back-face strain gauge, surface strain gauge, extensometer, push-rod system, or piezoelectric strain sensor. The compliance technique, originally proposed by Elber (1970), has since been refined to the current load-differential displacement curve method first proposed by Kikukawa (1976). More information regarding the measurement of crack opening using compliance-based methods can be found in the ASTM standards (2009) and other articles (such as Song and Chung, 2010). In this study a piezoelectric strain sensor (see Wallbrink et al., 2023) is used to track the crack closure/opening loads over the full life of a compact tension specimen. A variable amplitude spectrum containing blocks of constant amplitude loading is applied to the fatigue specimen. Fractographic imaging is used to determine the crack growth rate at various crack lengths for the different stress ratios. Additionally, the crack opening loads are measured using the