PSI - Issue 17

Sunil Bhat et al. / Procedia Structural Integrity 17 (2019) 21–28 S Bhat et al./ Structural Integrity Procedia 00 (2019) 000 – 000

27

7

W r p

A r p

II E dr T

I

J

T E dr

=

+





interface

2

a int

r p W

( ) ( ) ( ) ( 6 2 8 8 W C C int W C p a r −  Y

)

( ) ( ) 7 int W C p a r −

( ) ( 5 W C Y 

)

  

  

  

  

C

C

C C

C C

Z

Z

6

5

 

 −  

 

 −  

2 7 C

W

W

2

2

5 3

6 4

r

a

r

a

−

−

−

=

p

int

p

int

C

C

8

7

( ) ( ) ( 5 5 A C W C −  

)

  

  

C C

 

 

(6)

(

)

W

W

2

2

5 3

C C + − −

r

int a − +

a

r

in which RHS of Eq. (5)

by replaced is

Y

Y

p

int

p

2

1

As stated earlier, interface J obtained in Sections 3.2.1 and 3.2.2 represents energy transfer in one direction and is multiplied by the factor of 2 for fulfillment of the requirement of equal bi-axial stress state on crack axis in affected interface material under SSY regime that necessitates additional and equal energy transfer. 4. Results and discussion The properties of steels and the weld that are considered for computational purpose are:- MPa, 900 10.4, 0.0037, MPa, 570 = = = = w A A A Y m n Y MPa, 2 10 10.1, 0.0047, 5 = =  = = A W W W E E m n 0.3 = = A W   . A Y  and W Y  are 0.00285 and 0.0045 respectively. The initial length, i c , of crack in parent steel, A , is assumed as 45 mm with the distance of its tip from interface 1, 1 , i int a , equal to 10 mm. Weld thickness, t , is considered as 10 mm.  p is taken as 150 MPa to simulate SSY regime. Refer Fig. 3 and Fig. 4. There is no effect of weld over crack tip during crack growth from length, c , of 45 mm to 49.67 mm since A Y int    1 or 1 int A p r a  during this period. Stage I 1 starts at c of 49.67 mm that is found from,

1

+ c a

i

i,int

A

A

A

i,int c r c a + − = 1 i

1

1

a

r

c

=

=



=



, on using the condition,

or

.

is satisfied

P

int

Y

int

p

   

   

 2 2 2 p

2

1.12

8 

1

+

Y

A

at c of 49.67 mm. Stage I 1 exists up to c of 52.73 mm when Stage II 1 starts that is found from,

1

+ c a

i

i,int

W

W

1

1

W

i,int c a + − = 1 i

a

r

c r

c

=

=



=



, on using the condition,

or

.

is satisfied

int

Y

int

p

P

   

   

 2 2 2 p

2

1.12

8 

1

+

Y

W

at c = 52.73 mm. Stage II 1 continues till the crack tip touches interface 1 i.e. up to c of 55 mm. As the crack enters into weld, there is no effect of back up steel over crack tip during crack growth from 55 mm to 58.70 mm length since A Y int    2 or 2 int A p r a  during this period. Stage I 2 starts at c of 58.70 mm that is found from,

1

c a

t

+ + i,int

i

A

A

A

i,int t c r c a + + − = 1 i

2

2

a

r

c

=



=



=

, on using the condition,

or

.

is

P

int

Y

int

p

   

   

 2 2 2 p

2

1.12

8 

1

+

Y

A

satisfied at c of 58.70 mm. Stage I 2 exists up to c of 62.32 mm when Stage II 2 starts that is found from,

1

c a

t

+ + i,int

i

W

W

W

i,int t c r c a + + − = 1 i

2

2

a

r

c

=

=



=



, on using the condition,

or

.

is

P

int

Y

int

p

   

   

 2 2 2 p

2

1.12

8 

1

+

Y

W

satisfied at c of 62.32 mm. Stage II 2 then continues till the crack tip touches interface 2 i.e. up to c of 65 mm. Refer Fig. 5. Variation of applied J , tip J and interface J with crack length, c , is shown. Variation of applied K and tip K