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) 000–000

835

4

1

 

  

   



C t

1

n



  , n    ij

ij

(10)

 

1 I B r   n n ref



ref

2.4. Creep fracture mechanics parameter, C(t) C(t) -integral can be expressed by using the C * -value and take different equation whether type of loadings. In the primary loading condition, load control condition, C(t)/C * may be following by Joch, J. and Ainsworth, R. A. (1992) as:       1 * * 1 1 with 1 (0) 1 n n C t AC BJ C             (11) where  is the ratio of creep time for the redistribution time and J(0) means J -integral value when the creep time is zero. For secondary loading condition, displacement control condition, the reference stress method and elastic-follow up factor are used to describe C(t) -integral as the function of time by Lei, Y. (2005), which may be expressed as:

1

1

n

n





   

ref       o       ref  

 

ref

 

o

C t

Z

ref

(12)

with



 

*

1

Z

C



o      ref       



1

n





   

o



o

1 1        ref

ref



o

E



 





ref

In this case, the reference stress and reference strain involve the effect on the time. Superscript and subscript, o , means the value at the initial time. In order to indicate in a format that is similar to Eqn. (11), a portion of the denominator in Eqn. (12) is replaced  which is following as: 1 o ref o ref E      (13) 3. Modification of the existing formula for crack-tip stress fields 3.1. Load control condition The crack-tip stress fields with load control condition converge after the redistribution time and this convergence value is defined as:   1 * 1 1 , 0 n yy yy n ref n ref t C F n I B r                             (14) Combination of Eqn. (11) and (14), Eqn. (10) can be re-written as     1 1 1 1 1 yy n ref n F                (15) In order to satisfy the continuity of the time, Eqn. (20) may equal to the stress field under elastic-plastic region. In the present work, the stress field under elastic-plastic region is determined from the modified boundary layer analysis for T=0 (small-scale yielding, SSY) and is following as:   0 yy yy T     

(16)

D





  

  





ref

ref

0

t



0





Combining of Eqn. (15) and Eqn. (16) gives