PSI - Issue 2_A

Ido Simon et al. / Procedia Structural Integrity 2 (2016) 205–212

210

I. Simon et al. / Structural Integrity Procedia 00 (2016) 000–000

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Table 3: The power law fitting parameters in eq. (6) for the plo ts seen in Fig. 4.

G Imax

∆ G Ie f f

R d

D

m

D

m

specimen no.

2 . 1 × 10 − 22 1 . 8 × 10 − 26 1 . 4 × 10 − 36 10 . 6 × 10 − 68

5 . 8 × 10 − 23 3 . 8 × 10 − 25 7 . 7 × 10 − 32 6 . 0 × 10 − 46

FTG-4-02 FTG-4-03 FTG-4-04 FTG-4-05

0.10 0.33 0.50 0.75

6.9 8.5

7.4 9.2

12.0 22.7

12.9 24.6

In eq. (6), D and m are fitting parameters and f ( G ) is a function of G according to the desired representation. The fitting parameters D and m for the plots seen in Fig. 4 are presented in Table 3. As mentioned in Section 1, in Jones et al. (2014a) a new formulation for the power law relation between the delamination propagation rate da / dN and the energy release rate G was presented as

da dN =

D ∆ K I

m

(7)

,

where

√

√

G Imax − 1 −

G Ithr

(8)

∆ K I =

.

G Imax A

In eq. (8), G Ithr represents the threshold value of G Imax and A is the cyclic fracture toughness. It was suggested in Jones et al. (2014a) that both G Ithr and A in eq. (8) be treated as fitting parameters which are chosen su ch that eq. (7) best represents the experimental data. Anther approach is taken here. Using the relation ∆ G Ie f f = G Imax − G Imin 2 = G Imax (1 − R P ) 2 , (9) it is assumed that when using the da / dN versus ∆ G e f f representation in Fig. 4b, all curves originate from a single point, namely

∆ G Ie f f thr ≈ constant .

(10)

One may then rewrite the relation in eq. (9) as

∆ G Ie f f thr (1 − R P ) 2

(11)

G Ithr = G Imax thr =

.

Substituting eq. (11) into eq. (8) results in a modified formulation which now has only four fitting parameters, namely, D , m , A and ∆ G Ie f f thr regardless of the number of load ratios R P used.