PSI - Issue 76

Daniele Rigon et al. / Procedia Structural Integrity 76 (2026) 35–42

37

1 a e ff a 0

∆ σ g , th ∆ σ 0

(1)

=

+ 1

where ∆ σ 0 is the defect-free fatigue limit of the material, a 0 is the El Haddad-Smith-Topper material length pa rameter, and a e ff represents an e ff ective crack length derived from the equivalence between the Mode I stress intensity factor of the cracked component with characteristic size a , and a through-thickness crack in an infinite plate of length, a e ff . Consider that α is the shape factor that accounts for the notch geometry and the remote loading condition, used to estimate the Mode I stress intensity factor as K I = ασ g √ π a , the e ff ective crack length can be expressed as a e ff = α 2 a . In Rigon et al. (2024), an equivalence was proposed between the fatigue limit of specimen with as-built surface and that of a smooth specimen weakened by a single semicircular crack with a depth equal to the maximum micro-notch depth of the as-built surface. Since the maximum micro-notch depth is correlated with the areal parameter S v , which can be evaluated by optical profilometry over a control area A 0 , the deepest depression of the surface in a reference area A ref can be estimated by adopting a block maxima sampling of S v and using EVS. Let S v , j denote the j -th S v measured value, each made on A 0 . These values are well described by a Gumbel distribution: F ( x ) = exp − exp − x − λ δ (2) where λ is the location parameter and δ > 0 is the scale parameter that must be calibrated on the sample. The maximum value S v , max , i , which is expected to be found on the entire surface of the gauge part of the i -th specimen, A ref , has a return period:

A ref A 0

(3)

T =

and it can be estimated by means of the following equation:

S est v , max , i = λ − δ · ln − ln 1 − 1 T

(4)

In Rigon et al. (2024), the estimate S est v , max , i was assumed to be accurate to evaluate the maximum surface depth in the gauge section of cylindrical specimens, but this assumption could not be verified due to the unavailability of full-surface measurements. Thus, in this paper, a preliminary investigation was performed to see how this estimate is influenced by the number of sampling data by comparing it with the actual S v , max , i measured in the cylindrical A ref ( S mea v , max , i ). Lastly, for the i-th specimen, the initial a e ff will be calculated as:

2 a

2 S est

a e ff = α

= 0 . 728

(5)

v , max , i