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A computational model and experimental validation of shielding and amplifying effects at a crack tip near perpendicular strength-mismatched interfaces

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Abstract

The stress field around the crack tip near an elastically matched but strength-mismatched interface body in a bimetallic system is influenced when the crack tip yield or cohesive zone spreads to the interface body. The concept of crack tip stress intensity parameter, K tip, is therefore employed in fracture analysis of the bimetallic body. A computational model to determine K tip is reviewed in this paper. The model, based upon i) Westergaard’s complex potentials coupled with Kolosov–Muskhelishvili’s relations between a crack tip stress field and complex potentials and ii) Dugdale’s representation of the cohesive zone clearly indicates shielding or amplifying effects of strength mismatch across the interface, depending upon the direction of the strength gradient, over the crack tip. The model is successfully validated by conducting series of high cycle fatigue tests over Mode I cracks advancing towards various strength-mismatched interfaces in bimetallic compact tension specimens prepared by electron beam welding of elastically identical weak ASTM 4340 alloy and strong MDN 250 maraging steels.

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Abbreviations

a :

Distance of crack tip from interface

a* :

Radial coordinate of point near crack tip

A :

Parent body/parent steel containing crack

B :

Interface body/back up steel

b :

Length of cohesive zone across interface

c :

Crack length

c c :

Crack length ahead of load axis

c min :

Crack length required for linear elastic regime

C :

Paris constant

e, eav:

Percent difference between theoretical and experimental result, average of percent differences

E :

Modulus of elasticity

f(θ):

A function of angle w.r.t. crack axis

F :

Applied load

i:

Imaginary quantity, \({\sqrt{-1}}\)

K applied :

Applied stress intensity parameter

K C :

Plane stress fracture toughness of homogenous body

KC(bimetallic):

Plane stress fracture toughness of bimetallic body

K IC :

Plane strain fracture toughness of homogeneous body

K L :

Stress intensity parameter over cohesive zone in interface material

K tip :

Stress intensity parameter at crack tip

l :

Extension of cohesive zone into interface body

L :

Distance between load axis and left end of specimen

m :

Paris constant

n :

No. of data points

N :

Number of fatigue cycles

p ∞ :

Far field applied stress

r :

Cohesive zone length in homogeneous parent body

t :

Specimen thickness

T :

T stress

u :

Displacement in x direction in cohesive zone

v :

Displacement in y direction from crack axis in cohesive zone

W :

Weld

Y :

Yield strength

z :

Complex variable

Z f :

Distance from specimen right end to front weld interface

Z r :

Distance from specimen right end to rear weld interface

Δ:

Parameter under cyclic or fatigue load

κ :

A material constant

μ :

Shear modulus

ν :

Poisson’s ratio

ξ :

A variable

σ :

Cohesive stress

σ eff :

Effective cohesive stress

σ ij :

Crack tip stress field

σ x :

Stress in x direction

σ y :

Stress in y direction

δ ij :

Kronecker delta

τ xy :

Shear stress in xy plane

\({\varphi, \phi, \phi_1,\phi_2, \psi, \Omega_1, \Omega_2}\) :

Complex potentials

A :

Parent body/parent steel

B :

Interface body/back up steel

max:

Maximum value

min:

Minimum value

W :

Weld

*:

Value at fracture

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  1. School of Mechanical and Building Sciences, Vellore Institute of Technology, Vellore, TN, 632014, India

    Sunil Bhat & S. Narayanan

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  1. Sunil Bhat
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  2. S. Narayanan
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Correspondence to Sunil Bhat.

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Bhat, S., Narayanan, S. A computational model and experimental validation of shielding and amplifying effects at a crack tip near perpendicular strength-mismatched interfaces. Acta Mech 216, 259–279 (2011). https://doi.org/10.1007/s00707-010-0365-y

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