PSI - Issue 19

Yasuhiro Yamazaki et al. / Procedia Structural Integrity 19 (2019) 538–547 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

546

9

Where, L 1 , L 2 , p , q are the fitting constants as listed in Table 3. L 1 and p were obtained from the results under the lower temperature condition in Fig. 8. L 2 and q were obtained from the results of Fig. 8 and Fig. 15. δ in Eq. 4 is the delta function defined as follows.

for for

0 1

 

 

 

  





mech

c

(5)

    mech



mech

c

Where, ε c is the critical fracture strain of the oxide. In this estimation, the δ equals to 1 at any cycle because the fracture strain of alumina is much small (approximately 0.1%) compared with the applied mechanical strain. The damage summation equation expressed by Eq. 4 is formally identical with those proposed by Reuchet and Remy (1983) for environment-fatigue interactions. The predicted results according to Eq. 4 are shown in Fig. 16. It is found in Fig. 16 that the experimental results can be predicted with good accuracy by Eq. 4.

Fig. 14. Schematic illustration of the acceleration mechanism of the fatigue crack by the oxide layer growth under the higher temperature condition.

Fig. 15. Estimated result of the oxide layer growth according to Eq. 3.

Fig. 16. Predicted crack growth rates compared with the experimental results.

Table 3. Constants in Equation 4.

L 1

p

L 2

q

2.30 × 10 5

2.65

3.00 × 10 5

7.40