PSI - Issue 66

300 5 2.4. Calculation of the maximum SIF, , according to the conventional expressions of = ( ) √ and ( ) for the particular specimen tested 2.5. Calculation of the / − field from the former equations for / and , respectively Fitting the normalized / − curve as a Gumbel cdf for maxima according to the model proposed by Castillo et al [9], whose analytical definition is shown below: log ( / ) − og ( , / ) 1 − og ( , / ) =exp �− exp � − � � �� (6) A scheme of the proposed unitary methodology is shown in Fig. 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

Analytical definition of the − curve Analytical derivation of the da/dN − relation Conventional definition of = Semi-analytical definition of the da/dN − curve / fitting based on REX

Experimental data

Fatigue Crack Growth Curves

FCGR curves

10 -2

10 -4

10 -6 da/dN

10 -8

10 1

10 2

10 0

K

max

Fig. 2. Scheme of the methodology applied in the assessment of the crack growth rate curve.

3. Example of application With the aim to clarify the utility of the approach proposed, the crack growth data registered from a crack growth test on a 275 steel is evaluated according to the steps described above until the analytical definition of the FCGR curve. The mechanical properties of the material are: Young’s modulus, =200 , yield strength, = 362 and fracture toughness; = 52.9 − 67.0 MPa √ . The tests were performed on CT specimens of width, =48 , thickness, =5 and initial pre-cracked length =12 . The following sequence was then applied: As described in the foregoing Section, the curve was fitted as the cdf of a three-parameter Weibull assuming the validity of the REX model (see Fig. 3), where 0 is accurately estimated with Expr. (2) and can be initially set as =1.10 , which could be accepted as a conservative estimation that will be revised and enhanced, as an iterative procedure, in a further version approach. The assumption of a Markov process justifies the reconstruction of the crack growth curve from the hypothetic very early process beginning at 0 (REX model). Note that different curves for a unique specimen could be virtually envisaged as a function of the maximum stress applied, though leading to a unique CGR curve. The choice of the reference crack growth variable, as ∗ replacing , proves to lead to remarkably different curves in the latter growth phase III. This, significantly, affects the value of the predictive total number of cycles , see Fig. 3(a) to (c), which plays an important role as the normalizing variable in the crack growth process. The adoption of ∗ = ( 0 )/( − ) allows us, first, to take advance of the asymptotic trend of ∗ , then, to recover the