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

26

6

1

1

  

  

  

  

A A

W W





W m

A m

A A

W W

Y

Y









relations,

and

respectively. The following expressions [3, p.1201]

n

n

1 T E and

I1 T E due to a point in the affected interface material:-

represent

1

(

)

A A

   

   

r 

m A A

2 1



A A A

I

2

E

E Y Y  − −

d





=

(1)



T

r

Y

n

A



Y

1

1

1

W

A A

A A

W W

   

   

   

   

   

   

r  

r  



m W A d Y W  −

m A A

m A A

2 1







2 1    +

 −  

Y

(2)

W

A

II

W

A

A

W

E Y =

d

Y

Y

Y

d









−



Y

Y

T

n

n

n

W

W

A







Y

Y

Y

interface J

3.2. Formulations for

E K applied   2 2

r Z where Z =

On substituting r  as

and employing various constants as functions of material

plasticity that are given as

1

1

2 1

2 1

1

1

1 1;

1 1;

  

  

A

W

m

m

A

W

  =  W

A

W

  =  A

; C Y C Y  = =

C Y

C Y

C

= + = + C

;

;

;



Y

Y

1

2

3

4

5

6

W

A

W

A

n

n

m

m

2 1

1

2 1

1

C

C

J

;

,

: - follows as nsfers energy tra elemental g integratin by obtained is

= −

= −

interface

7

8

A

W

m

m

2

2

3.2.1 Crack in parent steel, A, facing interface 1; Weak-strong transition (A-W) [3, p. 1202] Stage I 1 ( ) 2 ln 1 1 2 I 7 7 5 − − − − = =  C A C C A A p r interface a r Z C r a Z E E dr J A p 1 int p T

   

   

( ) ( ) ( ) ( 5 A C int p  Y

)

a r

   

   

C C

 

 −  

A

1

5 3

r

a

2 1

−

p

int

1

C

1

7

a

int

int

Stage II 1

(3)

W r p

A r p

II E dr

I

J

T E dr

=

+





interface

T

1

a int

r p W

( ) ( ) ( ) ( 6 1 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

 

 −  

 

 −  

1 7 C

W

W

1

1

5 3

6 4

r

a

r

a

−

−

−

=

p

int

p

int

C

C

8

7

( ) ( ) ( 5 5 A C W C −  

)

  

  

C C

 

 

(

)

W

W

1

1

5 3

C C + − −

r

int a − +

a

r

in which RHS of Eq. (3)

by replaced is

(4)

Y

Y

p

int

p

2

1

3.2.2 Crack in weld, W, facing interface 2; Strong-weak transition (W-A) [4, pp. 228-229] Stage I 2 ( ) 2 ln 2 2 2 I 7 7 5 − − − − = =  C A C C A A p r interface a r Z C r a r Z E E dr J A p 1 int p T

   

   

( ) ( ) ( ) ( 5 A C int p  Y

)

   

   

C C

(5)

 

 −  

A

2

5 3

r

a

2 1

−

p

int

2

C

a

2

7

a

int

int

Stage II 2