PSI - Issue 76

Daniel Perghem et al. / Procedia Structural Integrity 76 (2026) 107–114

112

Fig. 4. (a) Definition of long crack threshold based on the R-curve; (b) Experimental cyclic R-curve at the stress ratios R = -1 and0.1.

3.2.3. Chapetti model Chapetti (2003) proposed a simplified model to describe the Kitagawa diagram, based on a short crack approach incorporating the cyclic R-curve. The Chapetti model relies on a microstructural threshold defined by the following Eq.4:

√ π

ef f th

= F · ∆ σ w , 0 ·

· d

(4)

∆ K

where ∆ K ef f th represents the starting point of the R-curve and d is the minimum crack size capable of propagation. The parameter d can be expressed as:

1 π 

∆ K ∆ a = 0 th F · ∆ σ w , 0  2

d =

(5)

Importantly, in the Chapetti model, the material threshold for crack propagation as a function of crack length is directly described by the R-curve reported in Eq.3. In terms of threshold stress, the Chapetti model can be expressed as reported in Eq.6: ∆ σ w =  ∆ K ∆ a = 0 th +  ∆ K th,LC − ∆ K ∆ a = 0 th  ·  1 − v i · exp  − ∆ a l i  (6) √ area , of each fatigue series with the El-Haddad and Chapetti models, expressed as functions of crack length, it is necessary to convert √ area into an equivalent crack length a eq . The stress intensity factor (SIF) range is ∆ K = F · ∆ σ · √ π · a and it can be expressed using Murakami’s parameter to account for irregularly shaped anomalies as Eq.7: ∆ K = Y · ∆ σ ·  π · √ area (7)   n  i = 1 F · √ π · a if a ≥ d if a < d ∆ σ w , 0 To compare the experimental data points, ∆ σ −