PSI - Issue 13

Gyo Geun Youn et al. / Procedia Structural Integrity 13 (2018) 1297–1304 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1302

6

Fig. 6. (a)Determined multi-axial fracture strain energy versus stress triaxiality curve for aged CF8A via thermal ageing constant concept (b)fracture toughness prediction result of CF8A under monotonic loading

In the equation above, σ y is yield strength, σ y0 is initial yield strength, ε eq is equivalent plastic strain and Q and b are the material constants for isotropic hardening model. Kinematic hardening is a theory that the size of yield surface remains constant wherever the center of the surface moves. To describe the movement of surface center, back stress, α , is introduced as below. Note that Chaboche model has three back stress components. d ε eq and dε p stand for increment of equivalent plastic strain and plastic strain increment, respectively. C i and γ i are material constants for each back stress component in kinematic hardening model. 3 1 2 , 3 p i i i i i eq i d d d C d d        = = = −  (9) 5.2. Numerical simulation of ductile tearing under cyclic loading To predict fracture toughness under cyclic loading, two assumptions are applied. The first one is that energy required for fracture is the same regardless of the loading type. This assumption leads to the conclusion that it is possible to use the same multi-axial fracture strain energy value and critical damage value as described in Eq. 10. (10) The second one is that damage is only accumulated at crack opening state. To describe this state, ABAQUS user fortran is made out to calculate damage accumulation when the principal stress at the integration point is bigger than zero. 5.3. Prediction of cyclic effect on fracture toughness To predict the fracture toughness under cyclic loading, cyclic tensile test simulation should be performed preferentially. The tensile specimen is the same as monotonic loading test. Therefore, the same FE model is used which is shown in Fig. 5a. Combined hardening model with third order nonlinear kinematic hardening (Chaboche) model is applied for cyclic material property. The result for cyclic tensile test simulation is given in Fig. 7. The determined combined hardening parameters are given in Table 2. , f monotonic W W = ,cyclic & p p cyclic   monotonic monotonic f c   = = 

Table 2. Combined hardening material properties for unaged and aged CF8A Material σ 0 (MPa) Q (MPa) b C 1 γ 1

C 2

γ 2

C 3

γ 3

Un-aged CF8A Aged CF8A

180 190

100

7 5

50,000 51,200

860 320

20,000 22,000

200 200

2,500 2,800

10 10

80

After cyclic tensile test simulation, FE prediction for fracture toughness under cyclic loading is performed. By two assumptions mentioned in section 5.2, multi-axial fracture strain energy, W f and critical damage value, ω c under monotonic loading condition are applied. The multi-axial fracture strain energy, W f is provided in Eq. 5 for unaged