Issue 33

G. Laboviciute et alii, Frattura ed Integrità Strutturale, 33 (2015) 167-173; DOI: 10.3221/IGF-ESIS.33.21

1 2

3 2

1 2

3 2









0   (2) This five parameter model, where the coefficients A and B are complex and the following assumptions are made 3 B i A r A i   , B B B r i i   , 0 D E   can be solved in terms of stresses or displacements [2]. The work reported in this paper was obtained using digital image correlation (DIC) and the displacement solution is more useful: 1 1 2 2 C   2     ( 3 ) A i B z ) iB z z Cz Dz B   ( ln( l ) z z  n( ) z y x  xy r i r i i E z  

( 

)      





u iu

) B iB z

2 ln( Ez

z

z

2

2(

)

 

x

y

r

i

4



  

  

1 2

1 2

C





( z B iB E z     2 )





E

z

ln( ) z

(3)

r

i

4

 

  

1 2

1 2

1 2

C

(    r

ln( ) 2 





3 ) A i B z

D

z z

Dz

z

i

2

2(1 ) E  

 

 

3 1

y u are the horizontal and vertical displacements respectively,

Where

x u and

;

(plane strain) or

3 4   











y u are shown explicitly below with the assumption

(plane stress).

x u and

0 D E   .

1 2

1 2

1 2







3

x u r 

2  









B E 



B E 



A

r

B

3 )sin B

r

2

(

(2

(

2 )cos

2 )cos

r

r

i

i

r

2

2

2

1 2

1 2











3

3

3

  

  

  

  

 

 

(4)





 

sin (1 2 )sin   

(1 2 )cos 



r

B

r

ln E r

sin

( ) cos 

 

i

2

2

2

2

2

C r



(1 )cos  



4

1 2

1 2

1 2







3

u r 

( 2 





2 B E r     2 )sin

B E 





B

3 )cos B

r

A

2

(

(

2 )sin

y

i

i

r

r

r

2

2

2

1 2

1 2











3

3

3

  

 

  

  

  

 

(5)

sin (1 2 )sin   



(1 2 )cos 







 

r

B

r

ln E r

cos

( )

co

s

i

2

2

2

2

2

 

C

(3 )si 



r  

n

4

C RACK GROWTH RATE TESTING

C

ompact tension (CT) specimens were machined from 2mm thick 2024-T6 aluminium CT specimen with non standard dimensions [2]. A jeweller’s saw with blade thickness of 0.15 mm was used to extend the notch tip into slits some 5 mm long at angles of 30°, 45° or 60° to the original horizontal notch plane; Fig. 1 shows typical CT specimens used in this work. A fatigue crack some 2 mm long was then grown in Mode I collinear with this slit. This was achieved by starting with a larger dimension CT specimen with additional loading holes in a similar fashion to the disk shaped compact specimen described by Ding et al [4]. The specimen was then machined to final dimensions and the inclined fatigue crack extended under vertical uniaxial loading, giving a combination of mixed Mode I and Mode II crack tip stresses. The applied load ratio was R = 0.1 and the peak load was 1.2 kN. A Dantec digital image correlation (DIC) system operating in 2D mode was used to measure the crack tip displacement field and to compare the predictions of the CJP model with the measured displacement field data. A facet size of 17 pixels with a centre-line pitch of 17 pixels was used with a magnification of 107 pixels per millimetre. Digital image correlation requires a fine speckle pattern to be sprayed onto the side of the specimen on which displacement is being measured. Increments in crack length during a period of fatigue cycling were monitored using acetate surface replicas taken on the opposite side of the specimen, which was polished to improve the visibility of the crack. The acetate replicas could then be inspected at magnifications up to 1,000x using an optical microscope and the

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