An integral equation approach to self-similar plane-elastodynamic crack problems

Georgiadis, H.G.

doi:10.1007/bf00041700

Cited by 14 publications

(4 citation statements)

References 24 publications

(27 reference statements)

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“…First of all, it can be seen that, similar to the case in Ref. [11, 12], shear stress vanish at circular wave front r = C 1 t . Therefore, in view of the third equation in Eq.…”

Section: The Modified Cohesive Zone Model For a Self‐similar Expandinsupporting

confidence: 67%

“…First of all, it can be seen that, similar to the case in Ref. [11,12], shear stress vanish at circular wave front r = C 1 t. Therefore, in view of the third equation in Eq. (10), the condition that the shear stress vanishes along the upper and lower faces of the crack, the cohesive zone and the wave front (along which…”

supporting

confidence: 64%

“…More specifically, the traction force in cohesive zone is assumed to be a symmetric function f ( t / x ) of variable t / x . For elastic mode‐I crack without a cohesive zone, a distributed pressure on the crack faces described by a polynomial of t / x has been studied in some previous works by an integral equation approach. However, to the best of the present authors' knowledge, no attempts have been made to an expanding crack with variable traction force in cohesive zone.…”

Section: Strain Hardening With Non‐uniform Traction Distribution In Tmentioning

confidence: 99%

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A modified cohesive zone model for a high‐speed expanding crack

2014

Fatigue Fract Eng Mat Struct

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A B S T R A C T The present work studies a self-similar high-speed expanding crack of mode-I in a ductile material with a modified cohesive zone model. Compared with existing Dugdale models for moving crack, the new features of the present model are that the normal stress parallel to crack faces is included in the yielding condition in the cohesive zone and traction force in the cohesive zone can be non-uniform. For a ductile material defined by von Mises criterion without hardening, the present model confirms that the normal stress parallel to crack face increases with increasing crack speed and can be even larger than the normal traction in the cohesive zone, which justifies the necessity of including the normal stress parallel to the crack faces in the yielding condition at high crack speed. In addition, strain hardening effect is examined based on a non-uniform traction distribution in the cohesive zone.C 1 , C 2 = longitudinal and transverse elastic wave speeds C R = Rayleigh wave speed f = traction distribution function F xx , ……G xt = eight analytic functions G = energy release rate G I = elastostatic energy release rate M, M 1 , M 2 = speed-dependent functions q 1 = a constant measuring traction distribution r = polar coordinate R = Rayleigh wave function S y = normal traction on cohesive zone t = time coordinates T = remote mode-I tensile loading u x , u y = components of displacement vector V a , V c = crack tip velocity and cohesive zone tip velocityx, y = rectangular coordinates Y = yielding stress of material α 1 , α 2 = the quantities (1 À V a 2 /C 1 2 ) 1/2 and (1 À V a 2 /C 2 2 ) 1/2 δ = crack tip opening displacement ζ , ζ d , ζ s = complex variables κ = dimensionless material parameter defined by Poisson's ratio μ = elastic shear modulus ν = Poisson's ratio ξ, η 1 , η 2 = rectangular coordinates in the transformed planes ρ = mass density σ xx , σ xy , σ yy = components of stress tensor φ, ψ = two wave functions Correspondence: C. Q. Ru.

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“…First of all, it can be seen that, similar to the case in Ref. [11, 12], shear stress vanish at circular wave front r = C 1 t . Therefore, in view of the third equation in Eq.…”

Section: The Modified Cohesive Zone Model For a Self‐similar Expandinsupporting

confidence: 67%

supporting

confidence: 64%

Section: Strain Hardening With Non‐uniform Traction Distribution In Tmentioning

confidence: 99%

See 1 more Smart Citation

A modified cohesive zone model for a high‐speed expanding crack

2014

Fatigue Fract Eng Mat Struct

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“…The problem of determining the dynamic stress field due to a plane dislocation moving in an infinite elastic medium was formulated by Ang and Williams [8] in terms of Fourier integral equation and solved in closed form. Recently, Georgiadis [9] has developed an integral equation approach to self-similar plane elastodynamic problems. He considered the elastodynamic problem of an expanding crack under homogeneous polynomial form loading and reduced it to the solution of a Cauchy integral equation.…”

Section: Introductionmentioning

confidence: 99%

Non-symmetric extension of a plane crack due to plane SH-waves in a prestressed infinite elastic medium

Das

Ghosh

1993

Int J Fract

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In an infinite isotropic elastic medium initially in a state of uniform anti-plane shear, the problem of non-symmetric extension of an infinitesimal flaw into a plane shear crack due to two identical linearly varying plane SH-waves with non-parallel wave fronts has been analyzed. Fracture is assumed to initiate at a point a finite time after the waves intersect there and the crack is assumed to extend non-symmetrically along the trace of the wave intersection. Following Cherepanov [i0], Cherepanov and Afanas'ev [11] the general solution of the problem has been derived in terms of analytic function of complex variable. Numerical results have been presented to illustrate the nature of variation of the stress intensity factors and the rate of energy flux into the crack edges with the speed of the crack tips and also with the time after fracture initiation.

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