On the dugdaill model for a crack at the interface of different media

Kaminskii, A. A.; Kipnis, L. A.; Kolmakova, Vira

doi:10.1007/bf02682063

Cited by 25 publications

(26 citation statements)

References 2 publications

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“…A similar formulation was earlier used in [3,4] to analyze initial fracture process zones modeled by various displacement discontinuity lines located in the interface between media. An analysis of the associated solutions reveals that after a discontinuity line is introduced, the stresses cease to oscillate at the crack tip, and the singularity becomes a power-law one.…”

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confidence: 95%

“…In recent years, there has been intensive development of studues in the field of the fracture mechanics of various deformable bodies, including composite materials, welded and adhesive joints, fractured rocks, and concrete and polymers. That was owing to new models of fracture mesomechanics that account, more fully than in the classical models, for the features of fracture process zones at crack tips [2][3][4][10][11][12][13][14][15].Most theoretical studies in the field of the mechanics of interfacial cracks supposed that the fracture process zone is a surface on which the normal or tangential displacements discontinue. This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].…”

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confidence: 99%

“…This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].…”

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confidence: 99%

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confidence: 99%

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On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

2006

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The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated Keywords: piecewise homogeneous isotropic elastoplastic body, interfacial crack, process zone Introduction. In recent years, there has been intensive development of studues in the field of the fracture mechanics of various deformable bodies, including composite materials, welded and adhesive joints, fractured rocks, and concrete and polymers. That was owing to new models of fracture mesomechanics that account, more fully than in the classical models, for the features of fracture process zones at crack tips [2][3][4][10][11][12][13][14][15].Most theoretical studies in the field of the mechanics of interfacial cracks supposed that the fracture process zone is a surface on which the normal or tangential displacements discontinue. This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].The present paper addresses a piecewise-homogeneous body consisting of elastic and elastoplastic half-spaces. There is a rectilinear crack in the interface between the half-spaces. The body is under the conditions of plane strain. We examine the asymmetric case where a thin fracture process zone modeled by a line of discontinuity of tangential displacements develops in the body. The condition at infinity is formulated so as to account for the influence of the external field on the stress-strain state of the body. The integral Mellin transform is used to derive the functional Wiener-Hopf equation. Its exact solution is expressed in terms of Cauchy integrals and gamma functions. This solution is used to derive an equation for the determination of the length of the zone and to analyze the dependences of its length and angle on the external load and other parameters of the problem.1. Problem Statement. Consider the following plane-strain problem for a piecewise-homogeneous isotropic body: Determine the direction of development of a thin fracture process zone at the tip of a crack located in the interface between two dissimilar homogeneous half-planes with Young's moduli E 1 and E 2 and Poisson's ratios ν 1 and ν 2 . The material of the upper half plane is assumed elastoplastic; therefore, the preferential strains in the process zone, which is a thin layer, follow the shear mechanism. Because of this, we will simulate the thin process zone by a straight line that emanates from the crack tip at an angle α to the interface and on which the tangential displacement discontinues and the tangential stress is equal to a predefined material constant τ. The constant τ is the tangential stress averaged over the length...

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confidence: 95%

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confidence: 99%

“…This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

2006

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“…An analysis of the plastic zone for an interface crack was performed by Huang [1992], Wang and Shen [1993] and Pickthall et al [2002]. Plastic strips or prefracture zones in front of interface crack tips were analyzed by Kaminsky et al [1999] and Bakirov and Gol'dshtein [2004] for the case of isotropic bimaterials, while Loboda et al [2007] studied a permeable interface crack between two piezoelectric materials.…”

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Prefracture zone modeling for an electrically impermeable interface crack in a piezoelectric bimaterial compound

Govorukha

Kamlah

2008

JOMMS

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This work is concerned with the analytical characterization of the electromechanical nonlinear effects in the fields surrounding the tip of an interface crack located between two piezoelectric materials. It is assumed that a prefracture zone arises along a line segment in front of the crack tip. The prefracture zone is modeled by electrical displacement reaching a saturation limit and constant stress distribution. This reduces the problem to a linear interface crack analysis leading to a Hilbert problem, which is solved exactly. The prefracture zone length and the stress magnitude in this zone are found from algebraic and transcendental equations. The latter are derived from the requirement of stresses and electrical displacement to be finite at the end of prefracture zone towards the undamaged ligament. Numerical results for certain material combinations and remote loadings are presented and analyzed. In addition, energy release rate and crack opening displacements are introduced, which offers the possibility of formulating a fracture criterion based on the crack opening displacements.

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Literature Review on Cracks Located at the Interface of Dissimilar Materials (Interface Cracks)

Kozinov

Лобода

2020

Fracture Mechanics of Electrically Passive and Active Composites With Periodic Cracking Along the Interface

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On the dugdaill model for a crack at the interface of different media

Cited by 25 publications

References 2 publications

On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

Prefracture zone modeling for an electrically impermeable interface crack in a piezoelectric bimaterial compound

Literature Review on Cracks Located at the Interface of Dissimilar Materials (Interface Cracks)

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