PSI - Issue 16

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

110 6

2, 243 ( p l 

) b A

 

2 2, 243 1 4 (1, 25 4) p b b b L L     

p

0

K



K



,

,

(11)

I

I

max

l

b l

b





p

p

2 2 0 A 

1

4

(1, 25

4)









L

L

2

0 I A K 

where coefficient . Having inserted the expression (11) into the formula (9), we obtain a formula to determine the crack initiation period: p r 

1

      

      



v v 

   

   

   

r E

  





   

t fc

2 K l fc fc p

2

2

max K l K l   fc I I fc p 

1    l





2

K

4

fc

l

2 K l fc fc p

 

p

0 

N

dl





.

(12)

i

2

(1 ) R 

1 2 

      

fc



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

It may be shown that the proposed model allows effectively determining the number of cycles needed for crack initiation i N . The correctness of the proposed model is verified through comparison with experimental data (Yarema and Popovich (1985)). The experiment has been conducted on rectangular specimens of the width 44 mm L  with two symmetrical side notches of the depth 14 mm b  with bending radius in their tips 0.3 mm r  . Experimental specimens are manufactured from steel 1566 (65G). For the comparison the following values were used: 0.0136;   0.05; R  5 1.9 10 MPa; E   0.597; fc   0.002; th   0.17; c   8.5 MPa ; th K m  110 MPa ; fc K m  130 MPa ; c K m  560 MPa; t   5 11.37 10 m; fc     6 32.38 10 m c     . The graphical dependence on Fig. 3 shows a good correlation between the analytical results obtained by the formula (9) and the experimental data. Thus, the proposed model can be effectively used for the determination of the initiation period of a fatigue crack.

i N and the applied loading p . Solid line – analytical results, symbols – experimental

Fig. 3. Dependence between the crack initiation period

data (Yarema and Popovich (1985)).