PSI - Issue 13

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

1301

5

After tensile simulation, C(T) simulation was performed for unaged CF8A under monotonic loading. 2D model with first order plane strain element (CPE4) was applied. In the crack propagation area, 0.15mm mesh size was applied. Fig. 5a is the modelling of C(T) specimen. To calculate the incremental damage, Eq. 3 was applied with assumed multi-axial fracture strain energy. By trial and error, the multi-axial fracture strain energy, W f can be obtained as

  

  



(6)

p

W

3400exp 2.379 −

280

=

+

m

f

e 

with ω c =0.65. The C(T) simulation result calculated from the determined damage parameters is shown in Fig. 5b.

Fig. 5. (a) Modelling of 0.5T C(T) specimen (b) FE simulation results for monotonic C(T) of unaged CF8A

4. Numerical prediction of ageing effect on fracture toughness To predict the ageing effect of CF8A, thermal ageing constant “ C ” is introduced [Jeon et al]. The co ncept of “ C ” is that multi-axial fracture strain energy of aged CF8A, W f,aged p , is reduced as thermal ageing occurs and the amount of decrease is same as “ C ” times multi-axial fracture strain energy of unaged CF8A, W f,unaged p . (7) To find the thermal ageing constant “ C ”, monotonic tensile test simulation is performed for aged CF8A. Then average stress triaxiality is calculated at multi-axial fracture strain energy of locus point. After the calculation, thermal ageing constant “ C ” can be calculated as shown in Fig. 6a and the value of “ C ” is 0.15. To predict ageing effect on fracture toughness, damage model is used. As explained in the last chapter, two damage parameters should be determined to predict ageing effect. One is multi-axial fracture strain energy and the other one is critical damage value ω c . Multi-axial fracture strain energy is calculated by Eq. 6 and C =0.15. Critical damage value ω c varies depending on mesh size but same mesh size 0.15mm is used for the prediction. Therefore, identical critical damage value ω c is adopted. Fig. 6b shows the numerical prediction result of fracture toughness of aged CF8A under monotonic loading. 5. Numerical prediction of cyclic effect on fracture toughness 5.1. Cyclic constitutive equation To predict cyclic behavior, combined hardening model is applied with third order non-linear kinematic hardening model known as Chaboche model [Chaboche et al]. Combined hardening model is a combination of isotropic hardening and kinematic hardening model. Isotropic hardening is a theory that yield surface shows isotropic expansion with fixed yield surface center. Isotropic hardening function is given below. ( ) 0 1 eq b y y Q e    − = + − (8) , f aged W C W =  ,un p p f aged