PSI - Issue 23

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

484

4

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. 1. (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. (5). (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).

4. Discussion

The experimental points showed that, indeed, the values of R cl get close to an asymptote, presumably the f PICC value. However, the fitting function (5) does not describe this dependence well. The value of this asymptote should be close to f PICC = 0.4 and the two curves for different OICC should merge together when approaching the Paris regime. Moreover, the decrease of R cl near the threshold should be much steeper and the threshold value for low humidity is not reconstructed well, see Fig. 1(b). Therefore a new function of R cl was proposed:

n   

  

K K  RICC

OICC

R

f   P ICC

(11)

cl

K

max

containing the exponent n > 1. The values of n between 3 and 4 provided the best fit of the experimental data. Physical explanation of this can be formulated. During near-threshold loading, oxide debris is produced due to repetitive fracture surface contact very close to the crack tip. This is the mechanism of OICC. The layer thickness of the oxide debris depends on the crack growth rate, since the crack tip gradually moves away. Therefore, the level of OICC should be inversely proportional to the crack growth rate (Suresh (1981)), i.e. K OICC ~ 1/(d a /d N ). Considering the Paris law function, the crack growth rate d a /d N is proportional to (Δ K ) m , where the exponent m is usually close to 3 for metals.

K

 ~ 1 OICC

  m K

(12)

For a certain stress ratio R and Δ K , the ratio between Δ K and K max is constant and does not change the exponent.

K

 max OICC ~ 1

 m K

(13)