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

22 2

Nomenclature int a

distance of crack tip from interface

c

crack length

C 1 - C 8

material constants modulus of elasticity

E

E T

energy density transfer across interface

J applied remote energy release rate J interface energy transfer across interface J tip crack tip energy release rate K applied remote stress intensity parameter K tip crack tip stress intensity parameter m, n Ramberg-Osgood constants  p uniform monotonic tension r SSY small scale yielding at crack tip t Weld thickness Y yield strength r  r p

distance from crack tip along crack axis yield zone size at crack tip in homogeneous body

load line strain at distance r from crack tip

int 

load line strain at interface

Y 

yield strain



poisson’s ratio

Superscripts A

parent steel/back up steel

W

weld

1,2 I,II

interfaces

Stages/Cases of energy transfer across them exist in such bi-materials, one interface between parent steel and the weld and the other between weld and back up steel. Mode I crack in these bi-materials experiences the effect of the interfaces upon growing across the weld interlayer due to the phenomenon of energy transfer across the interfaces that manifests by way of deviation in energy release rate at the crack tip, tip J , from the value away from the crack tip, applied J . A strain based analytical model is used for estimation of the effect of interface, J interface , and tip J at various crack locations in the bi-material. The weld interlayer is assumed to be homogeneous which possesses higher strength than that of the constituent steels. The modulus of elasticity is same throughout the bi-material. Effect of weld induced heat affected zones and residual stresses formed in the vicinity of the interfaces are minimal due to identical coefficients of thermal expansion of steels and are therefore ignored. The interfaces are considered to be strong and perfect to ensure continuity of strain across them. An edge crack of different sizes is investigated in infinite domain under monotonic far field tension in plane stress condition for demonstration of the model behaviour. 2. Literature review Few results are available for mode I crack in bi-materials joined by thick weld interlayers. Kim et al. [1] used finite element analysis to deal with the problem of the crack approaching normally towards a compositionally graded interlayer or weld between parent and interface bodies of different strengths. Effects of strength mismatch on shielding or amplification of crack tip driving force were determined. They noticed that the interlayer with homogeneous yield behaviour (i.e., when the yield strength of interlayer is the average of constituent metals) provided higher shielding effect than a graded interlayer in which the yield strength varies linearly from one end to