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

33

3

Fig. 1. Plastic zone size identification for Wheeler model, Wheeler (1972).

da

  n

  

C K

(1)

R

dN

     

y

  

R





y

a R a  

;

y

p

 

a a

   

(2)

p

R

 





1

a R a  

;

y

p

1        y K

1 4 2

(3)



R

(plane strain)

y



In Eq. 1, C - n are Paris-Erdogan constants. θ R is the retardation parameter related to plastic zone size. The summation of current crack size ( ɑ ) and diameter of current plastic zone (R y ) are compared with crack size at overload ( ɑ p ). Eq. 2 determines whether retardation effect is active or not. When there is no retardation effect Wheeler retardation parameter is equal to 1. In other words, Wheeler equation is the same with Paris-Erdogan Eq. For retarded crack growth, θ R must be calculated as a function of stress intensity factor, as given by Eq. 3. Wheeler model needs an empirical parameter y . Steps to determine y parameter are given below.  The slopes of crack growth rate after overload is nearly zero. As the number of cycle increases, the effect of retardation decreases and the slope catches the characteristics of the crack growth prior to the overload. The number of cycles in this interval is determined by experimentally.  Using Eq. 3 diameter of plastic zone sizes for certain cycle intervals are calculated.  Estimate a y value and calculate the necessary number of cycles to reach a value of θ R =1 using Eqs.1-2.  Update the estimated y until greater agreement is achieved with experimental observation. Some models based on the Wheeler model are also available in the literature Sheu et al. (1995), Yuen and Taheri (2006), Huang X et al. (2008). Sheu et al. (1995) proposed some modification on crack growth after a single overload. Plastic zone size after a single overload is modified as effective plastic zone size and number of delay cycle is calculated, which is slightly above the Wheeler model. The main idea in this modification is that the crack needs to take some more cycles to move out of the plastic zone caused by the overload. The Wheeler model stops the retardation