PSI - Issue 16

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

111 7

l l  in order to determine the period of subcritical growth of a

The second step is to consider the case 0

p

subcr N . In the case of macrocrack growth, its length l exceeds the length of the plastic zone p l . Then

macrocrack

from the equation (7), the following formula implies:

2 2 4 fc I R K 

2 4 th fc K 

(1 ) fc 





dl dN

max





,

(13)

2 2 fc fc K

2

2

K K 



fc I

max

which with initial and final conditions

* * * , ( ) N N l N l  

, ( ) i i p N N l N l  

(14)

forms the model of fatigue macrocrack growth. The maximal stress intensity factor

max I K for the macrocrack growth in a plate with two side notches is given

by the formula:

2, 243 ( p l 

) b l A

  

p

0

K



.

(15)

I

max

l

b l

l

b l

 

 

p

p

2 2 0 A

1

4

(1, 25

4)









L

L

After integration of the equation (13), the period of subcritical crack growth of a macrocrack can be determined:

l

2 2 fc fc K

2

2

K K 



* 

fc I

max

N

dl





.

(16)

subcr

2

2 4 fc I K

2 4 th fc K 

(1 ) R 







fc

max

l

p

Since the total period of subcritical crack growth * subcr N equals to the sum of the initiation period and the period of subcritical growth of a macrocrack, we add the values i N and subcr N calculated by the formulas (12) and (16). Fig. 4 presents the plot of total subcritical growth period * subcr N as a function from the applied loading p . Thus contrary to the existing models, the proposed model describes correctly different cases of initial crack length, including the case of zero initial crack length.

Fig. 4. Dependence between the period of subcritical crack growth *

subcr N in a plate with two stress risers from the applied loading p .