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

25

5





II

1

T E

   

W W

   

W W   ,



W m

W W

Y





n

W Y

1

I

T E

A A   ,

A A

   

   

A m



A A

Y





n

A Y

W

W

Y 

Y 

r 





A

r 

Y 

A

Y  (b) Case II Fig. 2. Magnitudes of Case I and Case II energy transfers (a) Case I

A

A

2

2

p r

a 

or

that

interface 1 remains the same. Crack tip does not feel the effect of back up steel till







int

int

Y

A

2 , Fig. 1d), due to which r  in back up W Y  that causes back up steel to yield thereby int

A

2

tip J J =

p r

a 

. Stage I

2 begins when

or

results in







applied

int

Y

A Y  but is less than that

steel in the vicinity of the interface exceeds

I T E , towards the weld. Stage II

W

W

2

2

p r

a 

2 starts when

or

, Fig. 1e),

causing energy density transfer,







int

int

Y

that leads to r  in back up steel in the vicinity of the interface exceeding W

Y  thereby resulting in energy density

I T E due to already existing yield zone in back up steel

II T E , towards the weld. This is in addition to

transfer,

where I T E ). Finally when the crack tip crosses interface 2 and enters the back up steel, the effect of interfaces left behind vanishes due to existence of compressive stresses at the interfaces and tip J is again equal to applied J . Energy transfer across each interface, interface J , in each of the stages is determined from   E dr T 2 where factor 2 accounts for energy transfer in both load line (perpendicular to crack axis) and in transverse direction (along crack axis). Integration is bound by the sizes of affected zones in the interface material. The limits of integration are ( ) 1 int A p r a − for case I energy transfer in Stage I 1 and ( ) W p A p r r − and ( ) 1 int W p r a − for case I and case II energy transfers respectively in Stage II 1 . Likewise the limits are ( ) 2 int A p r a − for case I energy transfer in Stage I 2 and ( ) W p A p r r − and ( ) 2 int W p r a − for case I and case II energy transfers respectively in Stage II 2 . Although yield zone is two dimensional, its transverse dimension in interface material is only considered for computation of interface J . Contribution in energy transfer due to load line dimension of yield zone is ignored as this dimension represented by opening displacement is very small in comparison with the length parameter. Conservation of energy release rate allows to write, interface applied tip J J J  = , that leads to the magnitude of tip J . interface applied tip J J J − = during weak-strong crack transition and interface applied tip J J J + = during strong-weak transition since energy transfer takes place towards stronger weld in both the transitions. Crack tip stress intensity parameter is determined from, tip tip EJ K = . 3.1. Formulations for T E Elastic-plastic, stress-strain ( )   − properties of steels, A , and weld, W , are governed by Ramberg-Osgood W Y  > r  > A Y  . Total energy density transfer, T E , in Stage II 2 is equal to ( II T E +