PSI - Issue 2_A

Dong-Jun Kim et al. / Procedia Structural Integrity 2 (2016) 832–839 Dong-Jun Kim et al. / Structural Integrity Procedia 00 (2016) 00–000

836

5





1

n





1

F





F D        

yy

with ' 1 

(17)



1



       1 1 '  n   

ref

1

n



The modified equation, Eqn. (17), is verified in Section 4. 3.2. Displacement control condition Like the load control condition, the stress field around crack-tip for the displacement control condition may be a combination of the existing expressions, Eqn. (10), (12), and (13) and can be re-written as:

   

   

ref      o ref

ref

F

o



ref

yy

(18)



1



    

    

 

 

ref

1

n



1

n



 

 

1             ref o ref





When time is initial, t=0, Eqn. (18) is same value of Eqn. (16). In order to satisfy this condition, modified factor,  , can be expressed as: 1 n F D          (19) The modified equation, Eqn. (19), is verified in Section 4. 4. Finite element analysis 4.1. Material properties In this paper, elastic-plastic creep condition was considered. The material properties were expressed by Eqn. (1) and (5). For elastic properties, the Young’s modulus, E and Poisson’s ratio were used to be E =200GPa and ν=0.3, respectively. For plastic properties, the yield strength, σ o was assumed to be σ o =300 MPa with two values of the strain hardening exponent, m =5 and 10. For creep properties, the following values were assumed: B =3.2x10 -15 for n =5 and B =3.2x10 -25 for n =10. 4.2. Geometry and Loading type 2D plane strain single-edge cracked bend (SEB) specimen was considered in this work, as described in Fig. 1. The width of specimen Wwas taken to be W=50mmwith the relative crack depth of a/W =0.5. Pure bending by load control was applied for primary loading condition. Three different values of loading magnitude, L r =0.5 and 1.0 were considered in this work. For secondary loading condition, displacement control was applied to the specimen. Displacement magnitude was determined to have same J -integral value in the load control case. 4.3. Finite element analysis Elastic-plastic creep finite element (FE) analyses were performed using ABAQUS v6.13. 2D plane strain elements with 8-node biquadratic and reduced integration (CPE8R) were used. In ABAQUS, an implicit method is selected for time-dependent creep calculation. According to eqn. (9), C(t) values should be calculated close to crack-tip. It was extracted from the second contour form the crack-tip by Kim, Y.J. et al. (2001) and the used mesh was verified from the relationship by Reidel, H. (1987). To verify the mesh, elastic creep analysis was performed. Fig. 2(a) depicts the FE mesh used in this paper. Fig. 2(b) shows that the FE mesh used can provide accurate C(t) values.