An interface crack in an inhomogeneous stress field

Simonov, I. V.

doi:10.1007/bf00017934

Cited by 17 publications

(18 citation statements)

References 7 publications

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“…But as shown in [7], they influence only a fairly small (less than 10 −4 ) zone around the crack tips. Besides, relatively minor shear stresses appear along the sections with full contact.…”

Section: Problem Formulation and General Solutionmentioning

confidence: 93%

Dislocation model of an asymmetric weak zone for problems of interaction between crack-like defects

Simonov¹,

Karihaloo

2005

Philosophical Magazine

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Crack-like defect models range from the well-known traction free Griffith-Irwin cracks, Barenblatt cuts containing small process zones at tips, to cuts subjected to cohesive forces over their entire length. This last type of defect may be regarded as a weak zone (WZ) in the solid which is normally closed but which can open progressively under sufficiently large remote external tensile forces. The fact that the WZ begins to open only when the remote force has reached a certain threshold level distinguishes the WZ from a real cohesive crack. The adhesive forces can be of very different physical origin -atomic, dislocational, localized porosity, etc. Healed cracks in glaciers and in the earth's crust are also WZs. The length of WZs can thus range from a few nanometers to hundreds of kilometers. It is interesting to investigate the fundamental behaviour of the WZs during their interaction with other defects. Note that the direct approach using some cohesive force-opening relationship leads to a complicated problem which is reduced to the solution of a system of nonlinear singular integral equations in [1]. Another approach was suggested in [2], whereby the cohesive forces were expressed in a series containing N terms with N free parameters. The free parameters were determined by imposing physically consistent conditions on the solution. This paper focuses on two topics. Firstly, guided by the results obtained in [2], a general approach to examining the behaviour of a WZ embedded in a very asymmetric external tensile stress field is developed by prescribing a priori the WZ asymmetric opening by a two-parameter basis function which meets all physical constraints. Secondly, this approach is exemplified on the problem of interaction between a long interface crack subjected to wedge opening forces and a short collinear WZ. The latter is separated from the main crack by a small strong microstructural feature of the material (i.e. by a small obstacle). The key questions that will be addressed are: (i) when does the WZ become the nucleus of a cohesive crack on its own without linking with the pre-existing long crack, and (ii) when does the WZ force the obstacle to rupture allowing the pre-existing crack to link with it. The critical applied load levels corresponding to these limiting situations will be determined. An asymmetric weak zone modelled as a special dislocationIn contrast to the direct method used in [2], we shall take an inverse approach when the WZ is located in an asymmetric tensile stress field and search for a basis function of asymmetric opening displacement of WZ in the formThe function G(X, η) depends on the parameter of asymmetry, η, i.e. the distance by which the maximum of w(X) is displaced from the centre of WZ, X = 0. It is assumed that η > 0, if the maximum is displaced to the left of centre.We shall seek the unknown function G(X, η) under the following mathematical constraints which result from obvious physical and geometrical considerations: (i) it is even with respect to a simultaneous change 1

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Section: Problem Formulation and General Solutionmentioning

confidence: 93%

Dislocation model of an asymmetric weak zone for problems of interaction between crack-like defects

Simonov¹,

Karihaloo

2005

Philosophical Magazine

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“…An edge-slip region having a length l along the normal to the crack outline at the point Q and next to its opening zone of length l, can be considered. Then the undesirable oscillatory type stress field singularity becomes a monotonous one [10][11][12]. The lengths l, l, depending on the loading and bimaterial constant are defined below.…”

Section: General Asymptotics Near the Front Of Opening Interface Crackmentioning

confidence: 99%

“…The case l, h ,~ r~, 1, >> r~ is studied first. Then the stress-strain state has been shown to be similar to a complete opening crack edge at the boundary of the core region [11,12]. Second, such loads are possible that l >> r~ or h ,~ r~ and l, ,~ ri and the stresses behave according to the edge-sliding crack mode at distances r~ from the point Q.…”

Section: General Asymptotics Near the Front Of Opening Interface Crackmentioning

confidence: 99%

“…Nontrivial additional analysis of the solution of the plane problem [11][12] gives the more accurate region of 7 corresponding to the estimations (2.4), which is a little more narrow then (2.7) and tends to (2.7) at • ~ 0. Therefore, it is natural to use the results (2.1)-(2.3) for predicting the crack extension in the region of 7, (2.7).…”

Section: General Asymptotics Near the Front Of Opening Interface Crackmentioning

confidence: 99%

“…Using the way of the localization we take into consideration the concept of a core region [6,7] and also a slip-zone near the crack outline [10][11][12], or the crack is considered as a narrow slot. First we examine the case when the length of the slip-zone is very small and the stress field distribution on the boundary of the core region is close to it for the perfectly opening 1.~ Simonov crack.…”

Section: Introductionmentioning

confidence: 99%

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Prediction of arbitrary crack growth from the interface between two dissimilar elastic materials

Simonov

1992

Int J Fract

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Based on the universal laws of stress distribution around a crack edge, the general analysis of crack start from the interface is given. The solution for the original crack is assumed to be known. In order to classify different possible cases of crack growth beginning, both a slip-region ahead of the opening zone and a core region near the crack edge are introduced. The former provides non-overlapping of the crack surfaces and removes an undesirable oscillating stress field singularity which is produced mathematically at the assumption of a completely opening crack. The latter means that we consider the damage of an elementary volume (geometrical measure of the microstructure) as a discrete fracture operaton. Two asymptotical cases are studied: the slip-region is much smaller or much larger than the cross-section of the core region. Then the stress-strain state on the core region periphery qualitatively is the same as for a completely opening or shear interface crack, respectively. A characteristic crack opening appears instead of a characteristic length of the slip-region for a blunted crack. The angles of crack departure are predicted according to different known criteria of fracture. In passing, parametric, analysis of stresses and energy density angle distributions are given. Plane and penny-shaped cracks are examined as the illustration.

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Dislocation approach to study interaction of adhesively bonded weak zones

Simonov

2010

Continuum Mech. Thermodyn.

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An interface crack in an inhomogeneous stress field

Cited by 17 publications

References 7 publications

Dislocation model of an asymmetric weak zone for problems of interaction between crack-like defects

Dislocation model of an asymmetric weak zone for problems of interaction between crack-like defects

Prediction of arbitrary crack growth from the interface between two dissimilar elastic materials

Dislocation approach to study interaction of adhesively bonded weak zones

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