PSI - Issue 13

Fuminori Yanagimoto et al. / Procedia Structural Integrity 13 (2018) 116–122 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

6

121

0 100 200 300 400 500 600 700

0 Static stress intensity factor [Pa m]

500

1,000

1,500

Crack length [m]

Fig. 8 Static SIF calculated by FE analyses of Wide2017

4. Model modification

Closure effects caused by the unbroken shear lips is regarded to be a key factor for the long brittle crack problem. The conventional model employed the unbroken shear lip thickness, sl , expressed as sl = sl 6 ( app YS ( , ̇) ) 2 ( ) (1) where sl is a constant set to 2, app is SIF due to applied stress, YS ( , ̇) is a yield stress at temperature and plastic strain rate ̇ , is crack velocity, and ( ) is a monotonic function of the crack velocity to represent the degree of plastic constraint for crack velocity (Shibanuma et al., 2016a). This formulation leads that the unbroken shear lip becomes thicker when the crack length becomes longer under constant crack velocity. However, according to the observation of fracture surfaces, such monotonic growth of the shear lip thickness could not be found in Wide2017. Thus, because Eq. (1) is based on the concept of plastic constrain relaxation due to the expansion of plastic region, it is reasonable to consider that such plastic constrain relaxation should be determined by the effective SIF. Therefore, sl in the model is modified as sl = sl 6 ( app − cl YS ( , ̇) ) 2 ( ) (2) where cl is closure effect. Figure 9 shows the results of the temperature gradient crack arrest tests, Wide2016, conventional and modified model calculation results. The modified model shows good agreement with the temperature gradient crack arrest tests including higher temperature conditions. Moreover, although the crack was arrested in the condition of Wide2017 in the calculation of the conventional model, the crack penetrated the specimen in Wide2017 condition in the modified model. Therefore, this result indicates that the degree of the plastic constraint is determined by the effective SIF.

500

Temp. Grad. Arrest Test

400

Conv. Model Mod. Model

0 Crack arrest toughness [MPa m] 100 200 300 3.4 3.5

Wide2016(Exp.) Wide2016 (Mod. Model) Wide2016 (Conv. Model)

3.7 1000/ [ −1 ]

3.6

3.8

3.9

4.0

Fig. 9 Comparison of the modified model and experimental results