PSI - Issue 66

302 7 Finally, the quasi-analytical relationship between / and is identified as the field / − , represented in Fig. 6. Alfonso Fernández-Canteli et al. / Procedia Structural Integrity 66 (2024) 296–304 A. Fernández-Canteli et al / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 6. Representation of the quasi-analytical crack growth rate vs the SIF for the case under study, along with the original experimental data. As the final objective of the present proposal, the analytical definition of the / − curve is achieved. This is performed assuming its identification with a Gumbel cdf for maxima, according to the phenomenological approach proposed by Castillo et al [9]. Fig. 7 shows a comparison between both solutions, that, estimated using the semi analytical approach proposed in this work, and that from the direct application of the Gumbel solution to the experimental results. On the one hand, Fig. 7(a), shows, schematically, the normalization process as required for the identification of the / − field as a Gumbel cdf for maxima, while, on the other hand, Fig. 7(b) presents a more detailed comparison of the two approaches. A more detailed analysis of the latter figure reveals a fair correspondence between both proposals. While the definition of the upper zone (region III) of the FCGR curve is practically determined by the initial choice of the value in both cases, some disagreement is still perceived between the fits resulting from both procedures in the lower zone (region I) of the curve, particularly, in the , values. This proves the higher reliability implied in the estimation of the analytical / − curve using the proposed methodology based on the modified REX model. Furthermore, the application of the direct procedure in the estimation of the region I of the / − curve, comprising the , value, proves to be less reliable when the registered experimental data points in the region I is scarce or even, absent, as it occurs, notably, in the present case study. In any case, further study is required to ensure a reliable assessment of the region III with the suitable selection of the initial , value.