PSI - Issue 19

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

545

8

From these results, the following equation can be obtained for the oxide layer growth behavior taking with consideration the applied stress.

RT Q

   

  



 m

X B 

mech t C | | 

(2)

exp

0

Where, ε mech is the applied mechanical strain [m/m]. The constants in Eq. 2 obtained from the experimental results are listed in Table 2.

Table 2. Constants in Equation 2. B 0 [mm/s 0.2176 ]

Q/R [ J]

c

m

1.518 × 10 3

1.159 × 10 4

0.7001

0.2176

3.3. As mentioned in sect Crack propagation mechanism considering with oxidation

As mentioned in section 3.1, the oxidation became significant around the crack tip under the higher temperature condition. In addition, the micro-cracking in the oxide layer can be observed at the crack tip. From these pieces of evidence, the growth and micro-cracking behaviors of oxidation layer might lead to accelerating the fatigue crack propagation by the mechanism shown in Fig. 14, schematically. The oxide layer is grown under the compressive stress at the elevated temperature during the TMF cycle. The increasing of oxide layer thickness at the crack tip per cycle, X N , is controlled with temperature, exposure time and the applied stress according to Eq. 2. When the applied stress (strain) in the oxide layer becomes larger than the critical fracture strength of the oxide, the micro-cracking occurs in the oxide layer, and the fatigue cr ack propagates by ∆ a env . The fatigue crack also propagates by the mechanical loading and the increase of crack length, ∆ a mech is controlled with the stress singular field determined by the stress intensity factor. As a result, under the higher temperature condition, the crack growth per cycle, ∆ a , becomes the summation of the ∆ a env and the ∆ a mech . The increasing of oxide layer thickness at the crack tip per cycle, X N , was estimated by using the FE analysis results and Eq. 2, namely, X N , was estimated by the 1 cycle integration of TMF cycle as follows. Where, the temperature, T , and the mechanical stress, ε mech , are a function of the time, t , and t c is the period of 1 cycle of TMF cycles. In this study, the mechanical stress, ε mech , was represented by the normal strain in the loading direction at the node front of the crack tip in the FE model. The distance between the crack tip and the representative node were approximately 2 μ m. The estimated results of X N is shown in Fig. 15 as a function of the stress intensity factor range of the fatigue crack. The estimated X N is almost comparable to the thickness of the oxide layer at the crack tip shown in Fig. 9; the increasing of the oxide layer per cycle is micrometers order under the higher temperature condition, on the other hand, that is nanometers order, namely almost negligible, under the lower temperature condition. Based on the crack propagation mechanism as shown in Fig. 14, the following summation law of the crack propagation rates controlled with the mechanical and environmental factors to predict the short crack propagation rate under the out-of-phase type thermomechanical fatigue is proposed in this study.   t dt m C RT Q X B c t   0 0 N mech        | | exp  (3)

p

K

    

     

dN da

dN da

dN da

env    

  

  q N

eff

L

L X 2

(4)

   

   

1

E

mech