PSI - Issue 66

2

Alfonso Fernández-Canteli et al. / Procedia Structural Integrity 66 (2024) 296–304 A. Fernández-Canteli et al / Structural Integrity Procedia 00 (2025) 000–000

297

1. Introduction and motivation Since the publication of the Paris FCGR solution that establishes a linear relationship between the crack growth rate and the stress intensity factor (SIF), a long list of related models has been proposed as empirical regression solutions. Once the sigmoidal shape related to the phases I, II and III of the FCGR curve was recognized, the models focused on fitting the experimental results beyond the linear Paris region, in an attempt to extend their applicability to the crack growth phases I and III. Some of them provide solutions that may include crack closure effect and the influence of the stress ratio with uncertain accurateness. In the last time, seems to be preferred to ∆K as the general reference variable (GRV) to describe, in a more convenient way, the SIF and stress ratio effects. Unfortunately, most of the proposed models present dimensionality inconsistencies, see FKM norm [1], apart from other limitations. In spite of its worldwide recognition, as the most celebrated proposal to define the FCGR curve, the NASGRO equation [2], defined as: = �� 1 − 1 − � ∆ � � 1 − ∆ ℎ ∆ � � 1 − � (1) evidences inconsistencies, unexpected in a widely and generally accepted advanced reference model, such as: • Dimensional inconsistency. • Independent assessment of the three characteristic regions of the / − field. • Consideration of the two Paris parameters, C and n , to define the linear region, which are correlated to each other. • Gratuitous definition of two model parameters: ∆ ℎ for 10 −7 cycles (ISO-12108), or 10 −8 cycles (ASTM E-647-15), to define the twofold asymptotic matching of the FCGR curve and ∆ as determined by . Furthermore, a unitary approach encompassing the analytical definition of the − curve and its subsequent transformation is so far missed. The phenomenological REX model proposed by Blasón et al to fit the − curve, see [3,4], implies the complete analytical definition of the monitored crack growth process from the prospective early stage, at which the crack starts, to the virtual asymptotic growth beyond the interruption of the stable crack growth as an instable fracture toughness failure when the is reached. This suggests the development of a compact and novel phenomenological methodology that contemplates the crack growth as a unitary process from the definition of the − curve till that of the fatigue crack growth rate (FCGR) curve. In this way, each of the different intervening functions relating crack size, number of cycles, crack size rate, stress and maximum stress intensity factor, can be analytically described over the whole conversion process. In this work, the crack growth process is contemplated as a damage phenomenon can be described as a Markovian process in the sense given by Bogdanoff- Kozin [5,6]. Both curves − and / − are assumed to be stochastic sample functions, which, once normalized, are identified as cumulative distribution functions (cdf) of the statistical extreme value family [7]. The high quality fitting observed confirms without contradictions the general methodology applied. The main objectives of the present work are: • To propose a unitary methodology that implies the application step by step of successive analytical definitions, from the − curve till, lastly, the definition of the / − curve to reduce, as much as possible, the uncertainty in the definition of the / − curve. • To provide insight into the interpretation of the experimental registration of results congruent with the physical reality of the crack growth process. This provides a possible phenomenological justification between damage processes and sample functions identified as cdfs of the extreme value family. • To contribute to avoiding the contradictions in establishing the different basic relations in the crack growth process aiming at achieving an enhanced reliability of its definition.