PSI - Issue 13

Gyo Geun Youn et al. / Procedia Structural Integrity 13 (2018) 1305–1311 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1306

2

of aged CF8A under cyclic loading condition. Virtual four-point pipe bending test was performed using multi-axial fracture strain energy model to study the load ratio effect on the crack growth of CF8A. Also, virtual pipe system test was performed with different through-wall crack size to study the crack size effect on the crack growth of CF8A. Nomenclature A, B, ψ material constants in multi-axial fracture strain energy locus C thermal ageing constant J J -integral P max maximum load in cyclic loading P min minimum load in cyclic loading R load ratio W f p multi-axial fracture strain energy W p equivalent plastic strain energy σ m , σ e mean normal stress and equivalent stress ∆ ω , ω incremental damage and accumulated damage ω c critical damage

2. Determination of multi-axial fracture strain energy damage model parameters 2.1. Multi-axial fracture strain energy damage model

In this research, a damage model based on multi-axial fracture strain energy concept is adopted to simulate the crack growth behavior of pipe and piping system test. The multi-axial fracture strain energy is known to strongly depend on stress triaxiality as described in Eq. 1 [McClintock, Rice et al, Hancock et al and Johnson et al]. A , B and ψ are material constants and the definition of stress triaxiality is the ratio of mean normal stress σ m and equivalent stress σ e

  

m B     + 

(1)

p W A =

exp

−

f



e

when load is applied to material, the incremental damage, ∆ ω occurs due to plastic deformation and it is calculated (at each integration point in finite element) as below.

p

W



(2)

  =

p

W

f

when the sum of incremental damage becomes critical value, ω c as shown in Eq. 4, then the stress at the integration point is rapidly reduced to almost zero (30MPa) by ABAQUS user subroutine. This enables to simulate local failure. c    =  = (3) 2.2. Determination of the damage parameters CF8A cast stainless steel is applied for this paper. To study the thermal ageing effect of CF8A, unaged and aged CF8A are considered. To get aged CF8A, accelerated testing was performed. The test was performed in 400 o C for 4,189 hours to target 40 years ageing (equivalent to 32 effective full power years) using the Eq. 4 proposed by Chopra et al. ( ) 1000 1 1 log 19.143 273 673 age s Q P t T   = − −    +  (4) To decide the damage model parameters ( W f , ω c ), at least three experimental data with different stress triaxiality states are required. However, if the experimental data is insufficient, the Eq. 1 can be simplified into Eq. 5 [Nam et al] ( ) exp 1.5 1 p m f e W A n B     = − + +     (5)