Local buckling of the elastic and viscoelastic coating around the penny-shaped interface crack

In the framework of the piecewise-homogeneous body model with the use of the three-dimensional geometrically non-linear exact equations of the theory of elasticity and viscoelasticity the local buckling (delamination) problem of the elastic and viscoelastic coating around a penny-shaped interface microcrack is studied. The method of solution of the considered problem is developed with the use of boundary form perturbation method, FEM and Laplace transform. All investigations are made on the sandwich circular plate and it is assumed that interface crack edges have an insignificant initial rotationally symmetric imperfection and as a buckling criterion the case where this imperfection starts to increase and grows indefinitely is taken. Numerical results illustrating the influence of the mechanical and geometrical parameters to the critical force for elastic coating and to the critical time for the viscoelastic coating are presented.     

Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack

Fracture analysis of sandwich beams with a viscoelastic interface crack under quasi-static and dynamic loading has been studied. Firstly, a three-parameter standard solid material model was employed to describe the viscoelasticity of the adhesive layer. And a novel interfacial fracture analysis model called three material media model was established, in which an interface crack was inserted in the viscoelastic layer. Secondly, a finite element procedure based on Rice J-integral and Kishimoto J-integral theories was used to analyze quasi-static and dynamic interface fracture behavior of the sandwich beam, respectively. Finally, the influence of viscoelastic adhesive layer on the quasi-static J-integral was discussed. In addition, comparison of quasi-static Rice J-integral with Kishimoto J-integral under various loading rates was carried out. The numerical results show that the oscillating characteristic of dynamic J-integral is more evident with shorter loading rise time.     

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known −1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.     

Scattering of inhomogeneous wave by viscoelastic interface crack

Summary The reflection, refraction and scattering of inhomogeneous plane waves of SH type by an interface crack between two dissimilar viscoelastic bodies are investigated. The singular integral equation method is used to reduce the scattering problem into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Then, the singular integral equation is solved numerically by Kurtz's piecewise continous function method. The crack opening displacement and dynamic stress intensity factor characterizing the scattered near-field are estimated for various incident angles, frequencies and relaxation times. The differences on crack opening displacement and stress intensity factor between elastic and viscoelastic interface crack are contrasted. And the effects of incident angle, incident frequency and relaxation time of the viscoelastic material are analyzed and explained by the features of phase lag and energy dissipation of the viscoelastic wave.     

Time-dependent boundary element analysis for an interface crack in a two-dimensional unidirectional viscoelastic model composite

Interfacial stress singularities in a unidirectional two-dimensional laminate model consisting of an elastic fiber and a viscoelastic matrix have been investigated using the time-domain boundary element method. First, the interfacial singular stresses between the perfectly bonded fiber and the matrix of a unidirectional laminate subjected to a uniform transverse tensile strain have been investigated near the free surface, but without any edge crack. Such stress singularity might lead to fiber-matrix debonding or an edge crack. Then, the overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed. The numerical procedure does not permit calculation of the limiting case for which the edge crack length vanishes.     

Stress intensity factors for an interface crack between a functionally graded coating and a homogeneous substrate

In this paper we consider the problem of a functionally graded coating bonded to a homogeneous substrate with a partially insulated interface crack between the two materials subject to both thermal and mechanical loading. The problem is solved under the assumption of plane strain and generalized plane stress conditions. The heat conduction and the plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the temperature and the displacement fields in the medium as well as the crack tip stress intensity factors. A crack-closure algorithm recently developed by the authors is applied to handle the problem of having negative mode I stress intensity factors. The Finite Element Method was additionally used to model the crack problem and to compute the crack-tip stress intensity factors. The main objective of the paper is to study the effect of the material nonhomogeneity parameters, partial insulation of the crack surfaces and crack-closure on the crack tip stress intensity factors for the purpose of gaining better understanding of the thermo-mechanical behavior of graded coatings.     

Steady interface crack propagation between two viscoelastic standard solids

The problem of a crack propagating steadily in Mode III along the interface of two bonded viscoelastic materials modeled as standard linear solids is investigated. The mathematical method consists of the application of a Fourier transform and the solution of simultaneous Wiener-Hopf equations. The results show that the variation of the stress intensity factor with crack propagation velocity may exhibit different domains of behavior depending upon the relative magnitude of the short and long-time wave speeds of each constituent. The accuracy of the method is checked by a comparison of the general results with special limiting cases.     

Reinitiation of a crack reaching an interface

We consider here a bi-material made of two layers bonded together by an interface. The specimen is loaded in tension parallel to the interface and the existence of a mode I crack is assumed. The crack initiated in just one layer reaches the interface normally. We then study the second of the two possible cases: the crack crosses the interface and goes straight into the second layer, in mode I also; or the crack debonds the interface before reinitiating in the second layer at the debond tip.In the present study the conditions of the reinitiation of the crack in the second layer after debonding of the interface are presented. The maximum debond distance is calculated by means of a Shear Lag analysis associated with a damage constitutive equation.Qualitative rules for design are pointed out to make the interface a location of crack arrest or at least of crack growth delay. These rules are mainly: small thickness of the possibly cracked layer, strong interface and tough substrate.     

Steady state propagation of a mode III interface crack between dissimilar viscoelastic media

The steady state propagation of a semi-infinite crack between two dissimilar viscoelastic solids is considered. By means of the Wiener-Hopf technique, the stress intensity factor is found as a function of the crack tip velocity and the material parameters. Results for an interface crack between an elastic and a viscoelastic medium are obtained as a special case. Various limiting cases are examined as a check on the accuracy of the results. Finally, graphs are presented which examine the salient features of the stress intensity factor.     

Interaction between an interface crack and a parallel subinterface crack

In this paper, the pseudo-traction method addressed thoroughly in homogeneous cases is combined with the edge dislocation method to solve the interaction problem of an interface crack with a parallel subinterface crack. After deriving the fundamental solutions for a typical interface crack loaded by the normal and tangential concentrated tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is reduced to a system of singular integral equations which can be solved numerically with the aid of the Chebyshev polynomial technique. Numerical results for the stress intensity factors are shown in the figures in which six kinds of material combinations presented by Hutchinson et al. [1] are considered.     

Orthogonal crack approaching an interface

We consider the problem of a tensile crack approaching a sliding interface in the direction normal to it in an attempt to find the mechanisms that control the crack offset. The crack in a plane free of loading is driven by uniform load applied to its faces. The interface is assumed to have no resistance to opening. The common conception is that as the crack approaches the interface it creates a zone of opening. When the crack touches the interface this opening zone eventually arrests the crack such that the continuation of the crack growth through the interface is only possible from an offset position. Our computer simulations conducted for frictionless interface and supported by a simple analytical model show that the situation is more complex. As the crack tip gets close, the zone of opening shrinks and the opening displacement increases. After the crack tip touches the interface, the opening zone disappears. Frictionless interface produces concentration of this stress only at the ends of the interface which physically corresponds to the points where sliding is artificially arrested.     

Stress distribution near a crack crossing an interface

The stress distribution around a crack lying normally across the boundary between two media is calculated. It is assumed that the elastic properties vary continuously, but rapidly, across the interface, and that methods employed for homogeneous materials are applicable. It is shown that the stresses behave as r ^–1 in the vicinity of the junctions of the crack and the interface, and that an appropriate interfacial stress intensity factor can be defined.

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Résumé La distribution des tensions au voisinage d'une fissure se trouvant normalement à la zône de liaison entre deux milieux est calculée. On suppose que les propriétés élastiques varient de manière continue, encore que rapidement suivant l'interface, et que les méthodes utilisés pour les matériaux homogènes sont applicables. On montre que les contraintes varient en raison inverse du rayon au voisinage des jonctions de la fissure et de l'interface et qu'un facteur d'intensité des contraintes interfaciales approprié peut être défini.

     

Comparison of a viscoelastic frictional interface theory with a kinetic crack growth theory in unidirectional composites

In this paper we compare a frictional interface theory for fiber and matrix load sharing with a kinetic crack growth theory as applicable to the failure of unidirectional composites. First we formulate the creep lifetime prediction based on the viscoelastic frictional interface theory, and then we determine a parameter in the kinetic crack growth theory by fitting it to the frictional interface theory in terms of the creep lifetime prediction. Times-to-failure under a constant strain rate condition are then derived by these two models, and they are compared. The residual strengths after interrupted loading are also compared.     

Twisting of an elastic plate containing a crack

The stress distribution caused by twisting an infinite plate containing a finite crack is analyzed in terms of Reissner's theory for the bending of thin plates. The singular character and the detailed structure of the stresses near the ends of the crack are determined in closed form. Numerical results are given for the magnitudes of the stress couples and stress resultants for a range of plate thicknesses.

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Zusammenfassung Due Spannungsvertcilung, hervorgerufen durch die Torsion einer unendlichen Platte mit einem Ri\ begrenzter Länge, wird mit Hilfe der Reissner-Theorie für die Biegebeanspruchung dünner Platten untersucht. Der singulare Charakter und die genauc Verteilung der Spannungen in Nähe der Ri\enden werden bestimmt. Zahlenmä\ige Ergebenisse für die Gro\e der Spannungsparre und ihrer Resultanten werden für eine Reihe von Plattenstärken angegeben.

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Résumé La distribution des contraintes dans une plague infinie comportant une fisure finic et soumise à torsion est analysée au moyen de la théorie de Reissner pour la flexion des tôles minces.Le caractère singulier, et la structure de détail des contraintes au voisinage des extrémités de la fisure sont explicités.Des résultats numériques sont fournis en ce qui regarde les grandeurs des couples de contraintes et de leurs résultantes, pour une certaine gamme d'éspaisseur de tôles.

     

The interaction of a crack with an interface crack as a theoretical model for debonding

A complex integral equation has been derived which describes the interaction of a crack with an interface crack as well as the limiting case of a kinked interface crack. With the help of this solution a model of the debonding process has been set up. Critical ratios of the energy release rates of the interface and the matrix material have been calculated for three different material combinations. These values can be used as estimates for interface design.     

Torsion of composite cylinder containing crack terminating at bimaterial interface

Considered in this paper is the Saint-Venant's torsion of a cylinder containing a dissimilar circular bar and a slanted crack. The authors gave a warping function that satisfies automatically the interface bonded condition, and reduced the torsional problem to a pair of mixed-type integral equations that could be evaluated numerically. The nature of stress singularity for a slanted crack terminating at the interface is studied, and it is shown that the power of singularity is not –0.5 at the interface tip of a crack. The expressions of singular stress around this tip are derived. For two typical composite cylinders, some numerical results giving mode III stress intensity factors, singular stresses, and torsional rigidities are presented.     

Dynamic crack growth across an interface

The growth of a crack first in an elastic solid, then across an interface and into an elastic-viscoplastic solid is analyzed numerically. The analyses are carried out within a framework where the continuum is characterized by two constitutive relations; one that relates stress and strain in the bulk material, the other relates the traction and separation across a specified set of cohesive surfaces. Crack initiation, crack growth and crack arrest emerge naturally as outcomes of the imposed loading, without any ad hoc assumptions concerning crack growth or crack path selection criteria. Full transient analyses are carried out using two characterizations of strain rate hardening for the viscoplastic solid; power law strain rate hardening and a combined power law-exponential relation that gives rise to enhanced strain rate hardening at high strain rates. Results are presented for two values of interface strength. For the higher strength interface the crack grows straight through the interface into the elastic–viscoplastic solid, while for the lower strength interface the crack deflects into the interface. This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-dimensional surface singularity of an interface crack

The three-dimensional singularity field near the terminal point of an interface crack at the free surface of an elastic bimaterial is investigated. The Finite Element Iterative Method (FEIM) is used for evaluating the asymptotic field. A spherical coordinate system r, , is used and the singular displacement field is assumed to be of a product form r g(, ), where and g(.) are in general complex. To validate the model, the method is first applied to the three dimensional surface crack in a homogeneous elastic material. The results for this case show excellent agreement with previously published analytical and numerical results. For an extreme effect of bimaterial property mismatch, on the surface crack singularity, an elastic material bonded to a rigid substrate is investigated (E1/E2=). The results show that the complex power singularity depends strongly on Poisson's ratio . The real part of the stress singularity is greater than 0.5 of the plane strain case and the imaginary part becomes almost zero at 0·25 instead of at =0.5. The second term in the expansion of the asymptotic field was shown to have a singularity of 0.5.