PSI - Issue 1

S. Blasón et al. / Procedia Structural Integrity 1 (2016) 110–117 Blason et al. / Structural Integrity Procedia 00 (2016) 000 – 000

112

3

Region I

Region II

10 -2

K c

10 -3

10 -4

da/dN [mm/cycle] 10 -6 10 -5

da/dN = C ( Δ K ) m

1

m

10 -7

Δ K th

Region III

10 -8

Log Δ K

Figure 1. Fatigue crack propagation regimes.

A recent model for fatigue crack propagation as proposed by Castillo-Canteli-Siegele (CCS) (Castillo et al. (2014), Blasón et al. (2015)) is a new solution for the fatigue crack propagation based on the assumption that the crack growth follows a cumulative distribution function – the Gumbel distribution. The inconvenience of dimensional parameters in existing crack propagation models, some of them previously described, is overcome in this new proposal by means of an appropriate dimensional analysis, carried out over the influent variables leading to adimensional normalized parameters. The identification of the crack growth rate curve, as a cumulative distribution function in which ΔK *+ is identified as the normalizing variable defined in the interval [0,1] leads to the consideration of log ( da/dN ) as the random variable. The proposed model represents an explicit fatigue cracks growth relation that was supported by mathematical and physical assumptions. This model is given by the following expressions: ∆ ∗+ = ∆ ∗ − ∆ ∗ ℎ ∆ ∗ − ∆ ∗ ℎ ∆ ∗+ = ( ∗ ∗ ) = [− ( − ∗ ∗ )] (5) This model depends on four parameters, α , γ , ∗ ℎ and ∗ which may be computed by the least-squares technique (Castillo et al. (2014), Blasón et al. (2015)). The normalized variables of the model suggested by the authors are given by the following relations: ∗ = ∗ = 0 ∆ ∗ = − (6)

∆ ∗ ℎ = ∆ ℎ ∆ ∗ = ∆