PSI - Issue 14

Manish Kumar et al. / Procedia Structural Integrity 14 (2019) 839–848

844

6

Manish Kumar et. al/ Structural Integrity Procedia 00 (2018) 000–000

2 x

j n

1 x



ds

Fig. 2 : Domain considered near crack tip for creep crack characterization parameter   C t -integral

1

0      c b eff  A        c eff

b

c

c

(15)

*

W

d



  







eff

eff eff

1

b



The creep crack growth rate (CCGR) is correlated with the ( ) C t as,

  ( ) da C t dt   

(16)

where,  and  are the experimentally obtained constants. The crack growth increment is calculated after converged creep analysis from CCGR and added linearly to the accumulated crack growth of the last step. This process continues until a significant amount of crack growth is achieved, afterwards crack length is increased in the continuum. The crack growth direction is computed based on the maximum principal stress criterion which requires the evaluation of mode-I and mode-II stress intensity factors. An interaction integral approach (Rao and Rahman, 2003) is used to evaluate individual mode-I and mode-II SIFs. 2.4. Data transfer and null step analysis To carry the history dependency of plasticity and creep, the data has to be transferred from the integration points to the nodes before the crack increment and brought back to the new integration points after the crack increment as shown in Fig. 3. The approximation of the field values from the integration points to the nodes (Durand and Farias, 2014) is done as,   1 T T   v N N N w    (17) where, v is a vector having the nodal values, w is the vector having the approximated values of the field at the integration points and N  is the matrix having values of shape functions evaluated at the integration points.