PSI - Issue 21

Mehmet F. Yaren et al. / Procedia Structural Integrity 21 (2019) 31–37 Yaren M. F. et al / Structural Integrity Procedia 00 (2019) 000 – 000

34 4

effect if the current plastic zone reaches the overload plastic zone. However, Sheu B.C. model proposes that the current crack length go out of the overload plastic zone and then the retardation effect is terminated. Huang, X. et al. (2008) propose calculation of plastic zone size using equivalent stress intensity factor. This approach makes it possible to calculate the crack growth life at different stress ratios. First, the da/dN curves at different stress ratios are shifted to R = 0 by the proposed equations, but this process requires some empirical coefficients. Another model is proposed by Yuen and Taheri (2006). They focused on application of interaction effects in more detail than Wheeler. For modeling crack growth rate after overload, a delay retardation term is defined. Delay retardation and interaction parameters are added to Wheeler model. Delay retardation term is used to calculate a sudden decrease on crack growth rate, which is seen after the overload. 2.2. Willenborg Model Willenborg model is another widely used crack retardation model. The application of this model is simpler than Wheeler model. Any empirical data obtained from tests is not necessary for Willenborg model. Plastic zone size is a function of stress intensity factor. An equation is given to calculate residual stress intensity factor which is used to decide for retardation. In addition, Willenborg model based on Forman crack growth equation which includes stress ratio in its formulation. This allows the Willenborg model to be used for different stress ratios.   1 ( ) m F eff eff C eff C K da dN R K K      (4)

K K

eff

min,



R

(5)

eff

eff

max,

min, K K K   min eff

max, K K K   max eff

;

(6)

r

r

0 5 .

1 Z           OL a





K K 



K

(7)

r

max

max

OL

2

    1 K



   

max OL

 

Z

(8)

OL

 

y

Crack growth rate is calculated by Eq. 4. C F and m are material constants which are used in Forman equation. Negative values of maximum or minimum effective stress intensity factors, K max,eff , K min,eff , are taken as zero. The residual stress intensity factor K r is calculated by using plastic zone size Z OL and its formulation is given in Eq. 8.



0 0

 

K

max, , eff i K and K

i

min, , eff i

  

, eff i K K

K

(9)

  

max, , eff i

min, , eff i

0

0



K

max, , eff i