Asymptotic Behaviour of the Elastic Solution near the Tip of a Crack Situated at a Nonideal Interface

Mishuris, Gennady; Kühn, G.

doi:10.1002/1521-4001(200112)81:12<811::aid-zamm811>3.0.co;2-i

Cited by 32 publications

(26 citation statements)

References 19 publications

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“…Although tractions along a linear elastic interface are bounded, their derivatives are unbounded, having logarithmic singularities at crack tips (Erdogan 1997;Antipov et al 2001;Lenci 2001;Mishuris and Kuhn 2001), cf. Távara et al (2010).…”

Section: Err In Lebim Evaluated By the Crack Closure Techniquementioning

confidence: 99%

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

et al. 2015

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A new linear elastic and perfectly brittle interface model for mixed mode is presented and analysed. In this model, the interface is represented by a continuous distribution of springs which simulates the presence of a thin elastic layer. The constitutive law for the continuous distribution of normal and tangential initially-linear-elastic springs takes into account possible frictionless elastic contact between adherents once a portion of the interface is broken. A perfectly brittle failure criterion is employed for the springs, which enables the study of crack onset and propagation. This interface failure criterion takes into account the variation of the interface fracture toughness with the fracture mode mixity. A unified way to represent several phenomenological both energy and stress based failure criteria is introduced. A proof relating the energy release rate and tractions at an interface point (not necessarily a crack tip point) is introduced for this interface model by adapting Irwin's crack closure technique for the first time. The main advantages of the present interface model are its simplicity, robustness and computational efficiency, even in the presence of snap-back and snap-through instabilities, when the so-called sequentially linear (elastic) analysis is applied. This model is applied here in order to study crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads. Firstly, this model is used to obtain analytical predictions about interface crack onset, while investigating a single fibre embedded in a matrix which is subjected to uniform remote transverse loads. Then, numerical results provided by a 2D boundary element analysis show that a fibre-matrix interface failure is initiated by the onset of a finite debond in the neighbourhood of the interface point where the failure criterion is first reached (under increasing proportional load); this debond further propagates along the interface in mixed mode or even, in some configurations, with the crack tip under compression. The analytical predictions of the debond onset position and associated critical load are used for several parametric studies of the influence of load biaxiality, fracture-mode sensitivity and brittleness number, and for checking the computational procedure implemented.

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Section: Err In Lebim Evaluated By the Crack Closure Techniquementioning

confidence: 99%

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

et al. 2015

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“…Evaluation of coefficients in asymptotic representations of displacements and stress fields represents an important issue for addressing vector problems of crack propagation in elastic materials (Bercial-Velez et al, 2005;Mishuris & Kuhn, 2001). The explicit derivation of weight functions is fundamental for the evaluation of stress intensity factors corresponding to a general distribution of forces acting on the crack faces, as well as for the calculation of higher order coefficients in the asymptotic expressions of the fields.…”

Section: Introductionmentioning

confidence: 99%

Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks

Radi

Movchan²,

Movchan

2012

Mathematics and Mechanics of Solids

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The focus of the article is on analysis of skew-symmetric weight matrix functions for interfacial cracks in two dimensional anisotropic solids. It is shown that the Stroh formalism proves to be an efficient approach to this challenging task. Conventionally, the weight functions, both symmetric and skew-symmetric, can be identified as a non-trivial singular solutions of the homogeneous boundary value problem for a solid with a crack. For a semi-infinite crack, the problem can be reduced to solving a matrix Wiener-Hopf functional equation. Instead, the Stroh matrix representation of displacements and tractions, combined with a Riemann-Hilbert formulation, is used to obtain an algebraic eigenvalue problem, that is solved in a closed form. The proposed general method is applied to the case of a quasistatic semi-infinite crack propagation between two dissimilar orthotropic media: explicit expressions for the weight matrix functions are evaluated and then used in the computation of complex stress intensity factor corresponding to an asymmetric load acting on the crack faces.

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“…In particular, the existence of weak solutions is proved in [2,14], while existence of classical solutions is studied in [33,34,38]. The presence of surface stresses in a model changes the solution behavior at singular points such as crack ends, holes, notches, and points and lines at which boundary conditions change form [22,23,[29][30][31]37].…”

mentioning

confidence: 99%

Mathematical study of boundary-value problems within the framework of Steigmann–Ogden model of surface elasticity

Eremeyev

Lébedev

2015

Continuum Mech. Thermodyn.

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Mathematical questions pertaining to linear problems of equilibrium dynamics and vibrations of elastic bodies with surface stresses are studied. We extend our earlier results on existence of weak solutions within the Gurtin-Murdoch model to the Steigmann-Ogden model of surface elasticity using techniques from the theory of Sobolev's spaces and methods of functional analysis. The Steigmann-Ogden model accounts for the bending stiffness of the surface film; it is a generalization of the Gurtin-Murdoch model. Weak setups of the problems, based on variational principles formulated, are employed. Some uniqueness-existence theorems for weak solutions of static and dynamic problems are proved in energy spaces via functional analytic methods. On the boundary surface, solutions to the problems under consideration are smoother than those for the corresponding problems of classical linear elasticity and those described by the Gurtin-Murdoch model. The weak setups of eigenvalue problems for elastic bodies with surface stresses are based on the Rayleigh and Courant variational principles. For the problems based on the Steigmann-Ogden model, certain spectral properties are established. In particular, bounds are placed on the eigenfrequencies of an elastic body with surface stresses; these demonstrate the increase in the body rigidity and the eigenfrequencies compared with the situation where the surface stresses are neglected.

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Asymptotic Behaviour of the Elastic Solution near the Tip of a Crack Situated at a Nonideal Interface

Cited by 32 publications

References 19 publications

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks

Mathematical study of boundary-value problems within the framework of Steigmann–Ogden model of surface elasticity

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