PSI - Issue 3

Davide S. Paolino et al. / Procedia Structural Integrity 3 (2017) 411–423 Author name / Structural Integrity Procedia 00 (2017) 000–000

419

9

In particular, according to Eq. (1), the least squares estimates of

, th g c and

,  th g are given by:

        th g th g c   , ,

3



1.979 10 0.2916

,

(13)

where   denotes the parameter estimate. It is worth noting that the estimates  , th g c and  ,  th g are in agreement with the values proposed in the literature for , th g c (Li et al., 2010; Liu et al., 2008) and for ,  th g (Murakami, 2002; Liu et al., 2008; Li et al., 2010; Matsunaga et al., 2015). In order to estimate I c , I m , , th r c and ,  th r , the experimental number of cycles consumed in stage I must be computed from Eqs. (11) and (12). The two Paris’ constants in Eq. (12) (i.e., s c =4.6 ∙ 10 -12 and 3.21  s m ) are taken from the available literature (Schuchtar and Plumtree, 1988) for a very similar steel type. Fig. 6 shows the variation of the ratios of , / I min f N N and , / I max f N N with f N .

Fig. 6. Variation of the ratios and with the number of cycles to failure.

As shown in Fig. 6, the difference between

, I min N and

, I max N is negligible. Therefore, the average value

between

, I min N and

, I max N can be considered as a good approximation of the actual

I N . In agreement with the / I f N N increases rapidly with

literature (Tanaka and Akiniwa, 2002; Hong et al., 2014; Su et al., in press), the ratio f N and, for the experimental dataset, is larger than 99.5%. From the experimental

I N values and from the

measured

,0 d a and

, FGA max a values, it is also possible to compute the average crack growth rate within stage I:

a

a



, FGA max

,0

d

,

(14)

v



, a I

N

I

/ da dN in stage I. Fig. 7 shows the variation of

where

, a I v denotes the average

, a I v with

f N .