Stress state in front of a crack perpendicular to bimaterial interface

Wang, T.C.; Ståhle, Per

doi:10.1016/s0013-7944(97)00150-1

Cited by 32 publications

(21 citation statements)

References 13 publications

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“…In this case: (1) the inverse square root asymptote also agrees well with the exact solution within about 0.15ε from the crack tip; (2) however, the asymptote increasingly overestimates stresses as the distance from the crack tip grows, reaching about 30% at R = 0.7ε; and (3) it grossly overestimates the values of stresses near the interface (R = 0). The observed stress distributions agree with the data reported by [Wang and Stahle 1998] who investigated the crack approaching the interface by means of the semi-analytical dislocation approach. The actual size of the K-dominance zone, which is proportional to ε, decreases for the crack approaching the interface.…”

Section: Stability Analysissupporting

confidence: 89%

“…Cook and Erdogan [1972] and Erdogan and Biricikoglu [1973] derived the integral equations and provided the numerical solutions for fully imbedded semi-infinite and finite cracks, and for cracks either terminating at or crossing the material interface. A similar dislocation approach was employed by [Wang and Stahle 1998] for the study of stress fields in the vicinity of a finite crack approaching the interface. Using the exact solution obtained for Mode III as a prototype, Atkinson [1975] introduced an asymptotic solution for the SIF with respect to a small distance ε between the crack tip and the interface.…”

Section: Introductionmentioning

confidence: 99%

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A closed-form solution for a crack approaching an interface

Nuller¹,

Ryvkin

Chudnovsky

2006

JOMMS

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A closed-form solution is presented for the stress distribution in two perfectly bonded isotropic elastic half-planes, one of which includes a fully imbedded semi-infinite crack perpendicular to the interface. The solution is obtained in quadratures by means of the Wiener-Hopf-Jones method. It is based on the residue expansion of the contour integrals using the roots of the Zak-Williams characteristic equation. The closed-form solution offers a way to derive the Green's function expressions for the stresses and the SIF (stress intensity factor) in a form convenient for computation. A quantitative characterization of the SIF for various combinations of elastic properties is presented in the form of function the c(α, β), where α and β represent the Dundurs parameters. Together with tabulated c(α, β) the Green's function provides a practical tool for the solution of crack-interface interaction problems with arbitrarily distributed Mode I loading. Furthermore, in order to characterize the stability of a crack approaching the interface, a new interface parameter χ , is introduced, which is a simple combination of the shear moduli µ s and Poisson's ratios ν s (s = 1, 2) of materials on both sides of the interface. It is shown that χ uniquely determines the asymptotic behavior of the SIF and, consequently, the crack stability. An estimation of the interface parameter prior to detailed computations is proposed for a qualitative evaluation of the crack-interface interaction. The propagation of a stable crack towards the interface with a vanishing SIF is considered separately. Because in this case the fracture toughness approach to the material failure is unsuitable an analysis of the complete stress distribution is required.

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Section: Stability Analysissupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

A closed-form solution for a crack approaching an interface

Nuller¹,

Ryvkin

Chudnovsky

2006

JOMMS

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“…Wang and Chen [5] used photoelasticity to determine the stress distribution and the stress intensity of a crack perpendicular to the interface. Wang and Stahle [6,7] used the dislocation simulation approach to investigate a crack perpendicular to and terminating at the bimaterial interface. Lin and Mar [8] presented a finite element analysis of the stress intensity factors for cracks perpendicular to the bimaterial interface.…”

Section: Introductionmentioning

confidence: 99%

Finite boundary effects in problem of a crack perpendicular to and terminating at a bimaterial interface

2005

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In this paper, the problem of a crack perpendicular to and terminating at an interface in bimaterial structure with finite boundaries is investigated. The dislocation simulation method and boundary collocation approach are used to derive and solve the basic equations. Two kinds of loading form are considered when the crack lies in a softer or a stiffer material, one is an ideal loading and the other one fits to the practical experiment loading. Complete solutions of the stress field including the T stress are obtained as well as the stress intensity factors. Influences of T stress on the stress field ahead of the crack tip are studied. Finite boundary effects on the stress intensity factors are emphasized. Comparisons with the problem presented by Chen et al. (Int. J. Solids and Structure, 2003, 40, 2731-2755 are discussed also.

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“…Digital photo-elastic experiments were carried out to confirm their theoretical analysis. Wang and Stahle [18] analyzed the effect of T stress on the normal stress ahead of the tip of a crack perpendicular to a bimaterial interface. Guo et al [19] examined the problem of a crack embedded in a functionally graded coating and perpendicular to an interface between the coating and a substrate.…”

Section: Introductionmentioning

confidence: 99%

Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

Xiao

Tan

2012

Acta Mech

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Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs' parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs' parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.

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Stress state in front of a crack perpendicular to bimaterial interface

Cited by 32 publications

References 13 publications

A closed-form solution for a crack approaching an interface

A closed-form solution for a crack approaching an interface

Finite boundary effects in problem of a crack perpendicular to and terminating at a bimaterial interface

Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

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