PSI - Issue 66

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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K GRV = − , , − , Normalization

da/dN curve derived from the a-N Weibull cdf Gumbel cdf Experimental results

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(a) (b) Fig. 7. (a) Definition of the normalization required for the representation of the / − field as a Gumbel function; (b) Comparison between the fit achieved using the phenomenological model developed by Castillo et al [9] for the proposed novel methodology, and that from the direct application to the experimental results. 4. Conclusions The main conclusions derived from the present work are the following: • A unitary phenomenological approach is presented for the analytical description of the / − curve. The proposed methodology starts by applying the REX model in the evaluation of the experimental recorded − results. • The model provides the / − curve as a cdf of Gumbel for maxima fitted, as a unitary solution, jointly applicable to the three phases of the / − curve. • A linear representation of the variables as a log ( − log ) − log / scale allows a linear regression fit of the cdf Gumbel, based on its typical statistical paper representation. • The analytical definition of the functions handled in the proposed procedure allows the trend of the variable relation to be defined beyond the scope of the experimental data recorded in the test program. In this way, a more reliable estimation of the , and of the regions I and III of the / − curve is achieved from the reduced data set. • The definition of the upper asymptotic zone requires further study though its practical impact seem to have little significance. References [1] FKM -Guideline. Fracture Mechanics Proof of Strength for Engineering Components, 2009. [2] NASGRO. Fatigue Crack Growth Computer Program NASGRO Version 3.0- Reference Manual, 2000. [3] S. Blasón, Phenomenological approach to probabilistic models of damage accumulation. Application to the analysis and prediction of fatigue crack growth, University of Oviedo, 2019. [4] S. Blasón, A. Fernández-Canteli, C. Rodríguez, E. Castillo, Retroextrapolation of crack growth curves using phenomenological models based on cumulative distribution functions of the generalized extreme value family, Int. J. Fatigue. 141 (2020) 105897. https://doi.org/10.1016/j.ijfatigue.2020.105897. [5] J.L. Bogdanoff, F. Kozin, Probabilistic models of damage accumulation, John Wiley & Sons, New York, NY., 1985. [6] S. Mikheevskiy, S. Bogdanov, G. Glinka, Statistical analysis of fatigue crack growth based on the unigrow model, ICAF 2011 Struct. Integr. (2011). https://doi.org/10.1007/978-94-007-1664-3. [7] A. Fernández-Canteli, E. Castillo, S. Blasón, A methodology for phenomenological analysis of cumulative damage processes. Application to fatigue and fracture phenomena, Int. J. Fatigue. 150 (2021).