PSI - Issue 39

Dmitry O. Reznikov / Procedia Structural Integrity 39 (2022) 236–246 Author name / Structural Integrity Procedia 00 (2019) 000–000

241

6

m

1     i K    R i

N 

(8)

( )

N a a

i C



 

 

0

1

i



where min max / i R S S R const    ; here Y ( i ) is a correction function for the geometry of the crack and the loading pattern. In this example, the value of the correction function Y ( i ) for the surface crack in the expression for the stress intensity factor is taken equal to Y ( i )= 1.12 (Matvienko, 2006). Assuming that for all regular CA loading cycles (with the exception of the overload) Δ S i =Δ S = const., we can write down: ( ) K Y i S a      , i i i

m



 

a

N

.



i

1.12

( ) C S i   

N a a

 

 

1      R

0

1

i



The criterion of brittle fracture of a cracked component is applied:

I IC K K 

(9)

max 1.12 I K S a   . Expression (9)

where K Ic is the fracture toughness, K I is the mode I stress intensity factor

allows estimating the value of critical crack depth:

2

2

  



(1 ) 1.12     K R S     Ic

K

(10)

a



  

Ic

C

1.12

S





max

Then the failure condition can be written as follows: N C a a  .

(11)

According to Wheeler's model, crack growth retardation occurs due to its growth through the plastic deformation zone formed by the overload cycle. The retardation rate is proportional to the overload level and, as a consequence, to the ratio of the current regular r p and the overload R p,OL plastic zones. Thus, the key point in the framework of this model is to estimate the size of the plastic zones that arise at the crack tip due to the overloading and during crack propagation under constant amplitude loading cycles. The size of a plastic zone formed at the crack tip in the tension half-cycle when stresses rise up to the value S max is :

2

1 S    K

   

,

(12)

r

 

max

p



y

where β is a factor characterizing the degree of deformation constraint: β=2 for the plane-stress state, β=6 for plane strain state. In the compression half-cycle, the stresses decrease to the values S min = S max -ΔS, and the yield stress takes on the value of 2 S y , since the stresses in the compressed plastic zone r pc change from + S y to – S y . Wheeler's crack retardation model is based on comparing the sizes of the plastic zones due to constant amplitude (nominal) cycles of load and due to overload. The size of the plastic zone induced by the overload is equal to 2 , 1 / ( ) ( / ) p OL OL y R K S    . It is assumed that the effect of crack retardation persists until the plastic zone of the regular i * -th loading cycle, arising from the action of the nominal stress intensity factor K max , reaches the boundary of the plastic zone induced by the overload R p , OL (Fig. 2c). According to Wheeler's model, crack growth retardation