PSI - Issue 2_A

Dong-Jun Kim et al. / Procedia Structural Integrity 2 (2016) 825–831 Dong-Jun Kim et al. / Structural Integrity Procedia 00 (2016) 000–000

828

4

 

  



(2)

exp 0.5 1.5 m  

MDF



c

e 

where MDF means the multi-axial ductility factor and m  and e  are the equivalent and mean normal stress, respectively. When the accumulated damage calculated from Eqn. (1) becomes unity, localized failure occurs and progressive cracking is simulated by simply reducing Young’s modulus to almost zero. More detailed information on the damage model and failure simulation technique can be found in Oh CS et al. (2011) and Kim N.H. et al. (2013). 3.2. Plastic damage model Applied load in a typical short-term creep crack growth tests causes the effect of initial plasticity to be considerable. Hence, affecting the creep crack initiation and can also affect subsequent creep crack growth. Recently, Kim N. H. et al. (2011) proposed a simulation technique of ductile fracture which is similar to the method described in the previous sub-section. In the plastic damage, incremental plastic damage is defined by the ratio of incremental plastic strain p   and multi-axial tensile ductility   * f p  :     * p p f p       (3) For the multi-axial ductility of plasticity, the model by Rice and Tracey is also used and the following form is assumed: exp 1.5 m p e MPF              (4) where α and β are material constants. In the present work, these two constants are determined by comparing experimental results of tensile and J - R test with FE results. 3.3. Combination of plastic damage model and creep damage model To combine plastic and creep damage, it is assumed that plastic and creep damage can be linearly added and total incremental damage is given by:         * * p c c p f f c p                 (5) When the accumulated damage calculated from Eqn. (4) becomes unity, localized failure occurs and progressive cracking is simulated. 4. Finite element simulations 4.1. Creep constitutive model for FE damage analysis Simulating creep fracture requires accurate description of creep constitutive model for FE damage analysis. In this paper, creep curves were fitted using the following three-term equation: 3 3 1 1 2 2 1 2 3 n m n m n m c c c c A A A            (6) where stress is in MPa; time is in hour; and creep strain rate is in 1/h. Fitted constants are summarized in Table 1. Eqn. (6) is implemented into the user-defined CREEP subroutine within ABAQUS. Estimated creep strain and their rates as a function of time are compared with experimental data in Fig. 1(b), showing rather good agreement for all stress levels.