PSI - Issue 16

Yuri Lapusta et al. / Procedia Structural Integrity 16 (2019) 105–112 Yuri Lapusta, Oleksandr Andreikiv, Nataliya Yadzhak / Structural Integrity Procedia

108

4

2

2

 

K l

( K l

l

)









fc I

fc p

max 0 2 K l fc p

l l 

,

;

p



  



(4)

max

2

K

I

max 2

l l 

,

,



 

fc

p

K

fc

where 2   – interpolation parameter; 0  – maximal deformation value near the stress riser in the initial state (without cracks) (Panasyuk (1988)) that can be defined as following:

1



2

v v

   

 

   

0    r     r  

K

I

1  





  

.

(5)

fc

0

K

fc

Here

2 4 fc K

r



.

(6)

0

E   

t fc

It can be seen from the formulas (4) and (5), if the initial crack length equals to zero 0 0 l  , then the maximal deformations are nonzero max 0   . Inserting the formulas (4) – (6) into the equation (3) gives a mathematical model for determination of fatigue crack growth rate:

1 2 

     



v v 

    

     

   

   

r E

  





   

t fc

2

2

2 4 2 th fc p K l 

max K l K l   fc I I fc p 

1   l



2

K

4

fc

2

2 2 fc fc fc p dl dN K l    (1 ) R

 



(7)

1

      

      



v v 

   

   

   

r E

  





   

t fc

2 K l

2

2

max K l K l  I I p

1    l



fc p

2

K

4

fc

with initial and final conditions:

0 0, (0) N l l   ,

(8)

* * * , ( ) . N N l N l  

In order to determine the period of subcritical crack growth, we integrate the equation (7) taking into account initial and final conditions (8):