PSI - Issue 23

Tomáš Vojtek et al. / Procedia Structural Integrity 23 (2019) 481–486 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

485

5

If such dependence is taken into account, the closure ratio R cl takes the following form, where the exponent is m + 1 due to one more division by K max :

max cons t     m K

1

  

R

P ICC   f

(14)

cl

Eq. (14) has the same form as our proposed function (11), where n = m + 1:

   m

1



  

RICC K K 

OICC

R

P ICC   f

(15)

cl

K

max

and where m is equal to the exponent of the Paris law function and f PICC , K RICC and K OICC are the fitting constants. Although the behaviour of RICC is not known, Eq. (15) fits well the experimental data also for the lowest air humidity and represents a useful tool for quantitative investigation of the closure phenomena. The experimental data fitted by Eq. (15) are presented in Fig. 2(a). It reveals that Eq. (15) fits the data more accurately than Eq. (5). The fitting constants are f PICC = 0.4, K RICC = 6 MPa· m 1/2 , K OICC is 0 for low and 2 MPa· m 1/2 for high humidity and the exponent n = m + 1 = 4. The parameter f PICC is larger than that predicted by the model of PICC by Newman (1981) for plane strain (approximately 0.25), indicating that such estimates are not relevant for real specimens. The d a /d N vs. Δ K curves were reconstructed in the same way as those in Fig. 1(b), by Eq. (10), considering crack closure values by Eq. (15). Note that the reconstructed curves were obtained only by the effective crack growth rate curve described by Eq. (6) and the crack closure function (15). The threshold value of each reconstructed curve is automatically obtained from the calculation. It is not required as an input value.

experiment reconstructed low H

experiment

fit low H

fit high H

reconstructed high H

0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80

1.E-04

1.E-05

R cl = K cl / K max

1.E-07 d a /d N [mm/cycle] 1.E-06

1.E-08

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

6

12

24

(a)

(b)

K max [MPa·m

1/2 ]

Δ K [MPa·m 1/2 ]

Fig. 2. (a) Crack closure ratio R cl obtained by experiments (red circles) using Eq. (9) and the fitting curve for high air humidity (dashed green line) and low air humidity (solid green line) according to Eq. (15). (b) d a /d N vs. Δ K curves for the applied stress ratio R = 0.1 obtained by experiments (red circles) and reconstructed using Eq. (10) for high air humidity (dashed green line) and low air humidity (solid green line).