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

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3

another. Predan et al. [2] presented numerical and experimental study of crack in parent base metal growing normally towards over-matched or under-matched thick welds. Literature review indicates that no theoretical model is available for crack in bi-materials joined by thick weld interlayers. Bhat et al. have separately presented strain based theoretical models for examination of mode I crack in front of a, thin and single, strength mismatched weld interface for weak-strong [3] and strong-weak [4] crack transition. Sequential and combined effect of two interfaces, due to the presence of the weld, over the crack tip is taken up in the present work with the principles reported earlier. 3. Analytical model Cracks are known to nucleate and propagate under cyclic loads. The model however considers crack under monotonic load say peak value of the cycle to analyze the phenomenon of yielding of the bi-material that differs from that of an identical cracked homogenous body. Yield characteristics of the bi-material that change with crack length are responsible for energy transfer in it. The energy transfer is viewed in conjunction with cracked homogeneous body that is made of the constituent of the bi-material containing the crack tip and in which energy transfer does not occur that causes tip J to be equal to applied J . Dugdale’s crack tip yield zone sizes A p r and W p r in hypothetical homogenous bodies made of parent and back up steels, A , and intermediate weld steel, W , are

2   

2   

   K 

   K 

W applied Y

A applied Y

respectively under plane stress condition in SSY or K

known to be equal to

and

8

8

applied K , of an edge crack of length, c , under

dominant regime where remote or applied stress intensity parameter,

K applied

p c  

 1.12

 p , in infinite domain is given by

monotonic far field tensile stress,

whereas remote

2 . Load line strain, r  , on crack axis at distance , r, from the crack

E K applied r E K applied   2 2

energy release rate, applied J , is equal to

=



tip in SSY regime is expressed as

[3, p.1200]. Hence load line strains at interfaces 1 and 2 in the bi

r

K 2 2  

K 2 2  

applied

applied

1

2

int  =

=



and

respectively

material that is elastically homogenous are written as

int

1

2

a E int

a E int

where 2 int a are distances of interfaces 1 and 2 from the crack tip respectively. Refer Fig. 1. For incipient crack in weak parent steel, A , facing interface 1 of stronger weld, W (Weak-Strong transition), the crack tip does not experience the effect of approaching weld as long as A Y int    1 or 1 int A p r a  , Fig. 1a), that results in 1 int a and

A

A

1

1

tip J J =

p r

a 







. Stage I of interface 1 (Stage I

1 ) commences when

or

, Fig. 1b), due to

applied

int

Y

int

which r  in the vicinity of the interface in the weld exceeds A

W Y  that causes energy 1 ) takes over as soon as

Y  but remains less than

I T E , towards the weld (Fig. 2a, Case I). Stage II of interface 1 (Stage II

density transfer,

W

W

1

1

int a  , Fig. 1c), i.e. when the weld in the vicinity of the interface begins to yield due to r 

p r







or

int

Y

II T E , towards the weld (Fig. 2b, Case II). This is in addition to I T E

W Y  that leads to energy transfer,

exceeding

Y  > r  >

due to already existing elastically affected zone in the weld where W

A Y  . Total energy density transfer,

T E , in Stage II I T E ). As the crack tip penetrates interface 1 and enters into stronger weld thus facing interface 2 of weaker back up steel, A (Strong-Weak transition), the procedure discussed previously for 1 is equal to ( II T E +