Issue 47

S. Akbari et alii, Frattura ed Integrità Strutturale, 47 (2019) 39-53; DOI: 10.3221/IGF-ESIS.47.04





0 1 ( 6 12 ) 1.6 Y Y   

M

(15.c)

A

3

Q

2

In the same way, substituting Eqs. 7 and 13 into Eqn. 3 and using Eqn. 11, the constants M iB

for the deepest point of the

crack can be determined as





1 0 (30 18 ) 8 F F  

M

(16.a)

B

1

Q

2





0 1 (60 90 ) 15 F F  

M

(16.b)

B

2

Q

2

 

0 1 (42 60 ) 8 F F  

M

(16.c)

B

3

Q

2

Four equations are obtained by curve fitting on the FEM results under uniform and linear reference loadings in order to achieve Y 0 , Y 1 , F 0 and F 1 . These fitting equations are function of R o /R i , a /c and c/B. The concluded WF specifications which are the novel results of this work and given by:

3 3 3      1 1 1 j l i

1 ( ) ( ) ( ) i j l o R a c   1



1

Y

A

0,1 k 

(17)

k

kijl

R c

B

i

3 3 3      1 1 1 j l i

1 ( ) ( ) ( ) i j l o R a c   1



1

F

B

0,1 k 

(18)

k

kijl

R c

B

i

In addition, values of coefficient A kijl

and B kijl

are listed in Tab. 3 and Tab. 4, respectively.

k

i

j

l

1

2

3 0 0 0 0 0 0 0 0 0 0

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

0.921 0.161 0.004 0.027 0

- 0.227

1

1.884

0

0.067

0

2

- 1.572 - 0.161

0.897

0 0 0 0

0

3

0.358

- 0.339

- 0.017 - 0.055

0.372

0.250 0.063

1

1.080

0

0

0.016

0.023

1

2

- 0.001

- 0.893 - 0.221

0.5

0 0 0 0

0 0

0

3

0.223 0.003

- 0.221

0.338

Table 3 : Coefficient A kijl

in the boundary correction factor for the reference loads.

45