Crack at an interface in a uniform stress field

Simonov, I. V.

doi:10.1007/bf00605924

Cited by 13 publications

(7 citation statements)

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“…This numerical result [2] was corroborated analytically in [3,4] and, by taking into account friction in the contact zones, in [5]. In most cases, the length of the contact zone is much smaller than the crack length (-10 -5) and, moreover, it is necessary to solve a nonlinear problem of the theory of elasticity.…”

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confidence: 58%

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Contact model of cracks in orthotropic materials

Лобода¹

1999

Mater Sci

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We consider a plane strain problem for an orthotropic half plane loaded at infinity and containing a crack along its fixed edge. To remove a singularity near the right crack tip, we introduce an artificial contact zone. The problem under consideration is reduced to the mixed Dirichlet-Riemann boundaryvalue problem. We present the exact solution of this problem and deduce formulas for stresses in the contact zone and on the continuation of the crack and for the stress intensity factors. By using both analytic and numerical methods, we prove that the energy-release rate is quasiinvariant in the process of crack propagation relative to the size of the contact zone. On the basis of these results, we propose an algorithm for the evaluation of the parameters of fracture of composites of finite dimensions with interface cracks. As a special case, we develop a model of interface cracks with actual contact zone and establish the dependences of the length of this zone on the external load and elasticity moduli of the material.Fracture of composites is most often explained by cracks appearing on the interfaces of the components of these materials. Therefore, the problem of interface cracks draws significant attention of researchers in the last decades. Actually, there are two basic well-developed and extensively used models of interface cracks, namely, the oscillation model proposed by Williams in [ 1 ] and the contact model first proposed by Comninou in [2].Note that basic assumptions of the oscillation model contradict mathematical results and, hence, the picture of mutual penetration of different phases given by this model is not realistic. In this case, it is impossible to determine the stress intensity factors (SIF) in the standard form and the complicated behavior of the components of strains in the vicinity of the crack tip significantly restricts the applicability of the oscillation model for numerical analysis.The contact model a priori allows crack lips to be in contact and the actual length of the contact zone is determined in the process of solution of the problem by using physical arguments. This numerical result [2] was corroborated analytically in [3,4] and, by taking into account friction in the contact zones, in [5]. In most cases, the length of the contact zone is much smaller than the crack length (-10 -5) and, moreover, it is necessary to solve a nonlinear problem of the theory of elasticity. Hence, the contact model (proposed in [2]) can hardly be used for the numerical analysis of cracked composites of finite dimensions.A model of interface cracks with artificial contact zone was proposed and analytically justified in [6]. At the same time, the analytic relations determining the fracture parameters of the models proposed in [1,2] in terms of the SIF of the model proposed in [6] were established in [7]. The indicated model is convenient for applications because, in this case, there are no oscillations and the problem remains linear.In the present work, we generalize the results obtained in [6] for the c...

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confidence: 58%

“…To satisfy conditions (23), we require that k 1 = 0 [3,6]. In view of relations (22), this condition yields the following equation for the parameter ~,:…”

Section: Xl(z ) = Iz-2e I~ Z+i~l +C+----~b +O(z -3) and X2(z) = Z-2e mentioning

confidence: 99%

Contact model of cracks in orthotropic materials

Лобода¹

1999

Mater Sci

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“…This is why studies of cracks growing to reach the interface of dissimilar media are of current importance. While problem solutions describing the growth of cracks located at interfaces of various media are addressed in the extensive literature [1,2,4,5,8,13,17,20,21], studies of cracks growing to reach such interfaces are much fewer.A crack reaching the interface between media with different mechanical properties may cause partial separation of the materials (fracture process zone) because of the high stress intensity at its tip, which was demonstrated in many studies. Such fracture process zones are usually modeled by discontinuity lines of the normal displacement in the case of brittle matrix (generalized Leonov-Panasyuk model [1,8,11]) or plastic slip lines in the case of plastic matrix (Cherepanov's modified model [3,5,17]).…”

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confidence: 99%

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Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media

2008

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The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method Keywords: fracture process zone, interface, crack, Wiener-Hopf method Introduction. The high crack resistance of composites is due to crack growth inhibition at the interfaces between the components of these materials [15,16]. This is why studies of cracks growing to reach the interface of dissimilar media are of current importance. While problem solutions describing the growth of cracks located at interfaces of various media are addressed in the extensive literature [1,2,4,5,8,13,17,20,21], studies of cracks growing to reach such interfaces are much fewer.A crack reaching the interface between media with different mechanical properties may cause partial separation of the materials (fracture process zone) because of the high stress intensity at its tip, which was demonstrated in many studies. Such fracture process zones are usually modeled by discontinuity lines of the normal displacement in the case of brittle matrix (generalized Leonov-Panasyuk model [1,8,11]) or plastic slip lines in the case of plastic matrix (Cherepanov's modified model [3,5,17]). To gain insight into the failure mechanism of piecewise-homogeneous media, it is important to know the stress intensity at the crack tip, the type of its singularity, the size of the fracture process zones, and the way it affects the stress intensity. Knowing the singularities of stresses at the tip of a crack reaching an interface, we can more efficiently develop numerical methods for determining the stress state of compound piecewise-homogeneous bodies with cracks. Solving such problems is also needed for the development of the theory of failure of adhesive joints with allowance for the rheological properties of adhesives (plastic, brittle, viscoelastic, etc.) Symmetric plane solutions describing the fracture process zone at the tip of a crack reaching the nonsmooth interface of media that comprise a piecewise-homogeneous elastoplastic body were found in [3, 18] using plastic slip lines as models. We will solve a similar problem considering that the fracture process zone (partial separation zone) is modeled by discontinuity lines of the normal displacement at the interface (brittle matrix).1. Problem Formulation. Consider a piecewise-homogeneous isotropic elastic body under plane strain. It consists of different homogeneous parts with a thin binder interlayer between them. The interlayer is more brittle than the bonded parts. Let the tip of a rectilinear crack be at a corner point of the nonsmooth interface between two parts of the body. This domain is considered symmetric about the crack line.As the external load increases, a fracture process zone appears and grows at the crack tip. We will study only the initial stage of...

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“…The model of a crack proposed in [19] assumes that there are zones of smooth contact of crack faces at its tips. This model was further developed in [2,7,8,9], where analytic solutions were constructed and the friction in the contact zone was considered. Another way of modeling the tip zones of an interphase crack used in [3,4] is to carry out zones of weakened interpartiñal bonds to the continuation of the crack.…”

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Electrically permeable crack with contact zones between two piezoelectric materials

2008

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The paper addresses a plane problem for an infinite plane consisting of two different piezoceramic half-planes with an interfacial crack with smooth contact zones and subjected to the uniformly distributed electromechanical loading applied at infinity. Methods of complex-variable theory are used to reduce the problem to a Dirichlet-Riemann mixed homogeneous boundary-value problem. Its solution is found in closed form. A system with one crack that has one or two contact zones is calculated. Expressions for stresses, electric-flux density, and displacement discontinuities at the interface are written. Equations for the determination of the length of the contact zones and expressions for the stress intensity factors at the crack tips are derived Keywords: interfacial crack, piezoelectric material, contact zone, exact analytic solution Introduction. Study into the fracture of compounds of piezoelectric materials because of propagation of interfacial cracks is of practical importance since such compounds are used in many electromechanical products and devices. When a crack between two materials is treated using a standard mathematical model, an oscillating singularity takes place [10,21], which contradicts the physics of the problem because the materials penetrate each other. The model of a crack proposed in [19] assumes that there are zones of smooth contact of crack faces at its tips. This model was further developed in [2,7,8,9], where analytic solutions were constructed and the friction in the contact zone was considered. Another way of modeling the tip zones of an interphase crack used in [3,4] is to carry out zones of weakened interpartiñal bonds to the continuation of the crack. These models made it possible to eliminate the oscillation and to obtain a physically consistent stress-strain state. In most cases, however, the contact zones are extremely small, and the behavior of stresses at the tips remains very complicated, which considerably complicates the reliable determination of the stress intensity factors (SIFs) when using the model from [11]. The model of a crack between two materials proposed and analytically studied in [19] a priori assumes arbitrary length of the contact zone and determines its real length from physical considerations during solution. The key parameters of the oscillation [10] and contact [11] models are expressed in terms of the SIFs of this model. Determining the SIFs for finite bodies is much easier than for the above models. This model was used in [12,13], where analytic solutions for a crack with one contact zone between two different orthotropic and piezoelectric materials were obtained. Noteworthy are the publications [14,15,17,18] that address the SIFs in anisotropic elastic media, the electroelastic planar vibrations of a piezoceramic plate and half-disk, and the stress state of piezoelectric bodies with a crack or cavity.We will use a contact model to study a finite crack with contact zones at both tips between two piezoelectric materials under an electromechanical load appli...

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Crack at an interface in a uniform stress field

Cited by 13 publications

References 4 publications

Contact model of cracks in orthotropic materials

Contact model of cracks in orthotropic materials

Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media

Electrically permeable crack with contact zones between two piezoelectric materials

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