Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

The problem of interaction of a plane time-harmonic SH-wave with an elastic fiber of quasi-square or quasi-triangular cross section, when an interface crack is present between an infinite elastic matrix and the fiber, is considered. The modified null-field method taking into account the asymptotic behavior of the solution at crack tips is exploited for obtaining numerical results. The effects of fiber shape, fiber/matrix material combination, debonding (crack size), and direction of wave incidence on the scattering amplitude in the far zone are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 245–254, March–April, 2008.     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

Interfacial fracture of layered magnetoelectroelastic materials

A problem for an interface crack located in a layered magnetoelectroelastic material strip of semi-infinite length is solved. A closed-form solution is obtained for anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for stresses and electric and magnetic fields, together with their intensity factors and the energy release rate, are obtained. The extreme cases of impermeable and permeable cracks are discussed. Using the basic solution for a single crack, solutions for two collinear interface cracks in an infinitely long layered magnetoelectroelastic medium, an interface crack in an infinitely long layered magnetoelectroelastic medium, and an edge crack at the interface of a semi-infinitely long layered magnetoelectroelastic medium are also obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 145–164, March–April, 2008.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Cryogenic mechanical response of multilayer satin weave CFRP composites with cracks

We deal with the thermomechanical response of multilayer satin weave carbon-fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties subjected to tensile loading at cryogenic temperatures. The composite material is assumed to be under the generalized plane strain. Cracks are located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. A finite-element model is employed to study the influence of residual thermal stresses on the mechanical behavior of multilayer CFRP woven laminates with cracks. Numerical calculations are carried out, and Young’s modulus and stress distributions near the crack tip are shown graphically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 479–492, July–August, 2008.     

Mode II Delamination of a Unidirectional Carbon Fiber/Epoxy Composite in Four-Point Bend End-Notched Flexure Tests

Results from an experimental study on the delamination of a unidirectional carbon fiber/epoxy composite by using the four-point bend end-notched flexure (4ENF) test are presented. It was found that the compliance data obtained in load-unload-reload and continuous loading tests were very similar. The R-curves for specimens of different thickness were also found experimentally. These curves showed an appreciable toughening with crack advance, which can be explained by the presence of fiber bridging. The finite-element method with cohesive elements allowing us to model the progressive delamination was used to analyze the 4ENF test. __________ Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 573–584, September–October, 2005.     

The effect of hydrostatic pressure on the crack resistance of particulate reinforced composite materials

The effect of hydrostatic pressure on the fracture toughness of disperse-reinforced composite materials is investigated. It is shown that increased hydrostatic pressure leads to an increase in the critical value of the stress intensity factor and, as a consequence, to an increase in the crack propagation rate. In this case, the pressure-time analogy method can be used to describe the effect of hydrostatic pressure on the characteristics of the crack resistance. This method enables us to represent the experimental data obtained in the form of a generalized dependence of the fracture toughness on the reduced loading rate. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 121–126, January–February, 2000.     

Guided ultrasonic waves in composite cylinders

The ultrasonic nondestructive evaluation of composite cylinders requires a thorough understanding of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied. The frequency equations obtained for free cylinders and the effect of increased fiber volume fraction (increased anisotropy) on the dispersion characteristics of the rod are explored. The numerical results reveal a number of previously unnoticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves propagating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 411–426, May–June, 2007.     

Fundamental two-dimensional solutions of electroelasticity for compound piezoceramic bodies

We construct fundamental solutions of the two-dimensional equations of electroelasticity for antiplanar strain of a piezoceramic space with an interphase defect. We study the orders of the powers of the singularities at the vertices of the defect for two cases: an interphase crack and a stiff fiber continuously joined to the upper half-space which has flaked off the lower half-space. The solution is constructed in closed form. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 62–67.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Effect of shearing forces on the stressed state of a half space with crack

Using the method of boundary integral equations, we study the stressed state in the neighborhood of a plane crack perpendicular to the boundary of a half space. The crack surfaces are subjected to the action of shearing forces. The problem is reduced to two-dimensional hypersingular integral equations, and their regular kernels, taking into account interaction between the crack and boundary of the half space, are written in explicit form. The dependences of stress intensity factors on the angular coordinate are presented for different loads of the crack. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 112–120, January–March, 2008.     

Estimation of laminate stiffness reduction due to cracking of a transverse ply by employing crack initiation-and propagation-based master curves

The applicability range of toughness-and strength-based criteria for progressive cracking of a transverse layer in a cross-ply composite laminate subjected to tensile loading is considered. Using a deterministic cracking model, approximate relations for the crack density as a function of stress are derived for initiation-and propagation-controlled types of cracking. The master-curve approach is applied to progressive cracking in glass/epoxy laminates. The accuracy of estimation of laminate stiffness reduction by using crack density master curves is evaluated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 633–646, September–October, 2008.     

Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

Strip saturation model solution for a piezoelectric plate by linearly varying electrical loads under mode-I conditions

A strip saturation model solution is obtained for a poled cracked piezoelectric ceramic plate. The plate is cut along a straight finite hair line crack whose rims are perpendicular to the poling axis of the plate. A mechanical load and an electric field applied open the rims of the crack and, as a result, saturation zones develop ahead of its tips. To arrest the crack from further opening, a linearly varying saturation limit normal electrical displacement is prescribed on rims of the saturation zones. The technique of complex variables is used to obtain the solution to the problem. A case study is presented for PZT-4, PZT-5, and PZT-7 ceramics. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 85–92, January–February, 2009.     

Dynamics of a bridged crack in a discrete lattice

The paper addresses a problem of partial fracture of a latticeby a propagating fault modelling a crack bridged by elasticfibres. It is assumed that the strength of bonds within thelattice alternates periodically, so that during the dynamiccrack propagation only weaker bonds break, whereas the strongerbonds remain intact. The mathematical problem is reduced tothe functional equation of the Wiener–Hopf type, whichis solved analytically. The load–crack speed dependenceis presented, which also has implications on the stability analysisfor the bridged crack propagating within the lattice. In particular,we address the evaluation of the dissipation rate, which isfound to be strongly dependent on the crack speed. In this latticemodel, our results also cover the case of the supercriticalcrack speed.     

Steady-state vibrations of a thin two-layer plate with delamination

We consider the problem of harmonic vibrations of a thin two-layer plate with horizontal crack. The problem is solved with the help of the null-field approach. The influence of the shape of the crack contour on the amplitude-frequency characteristics of plate vibrations is investigated. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 83–89, April–June, 1998.     

K-theory of Continuous Deformations of C＊-algebras

We study K-theory of continuous deformations of C＊-algebras to obtain that their K-theory is the same as that of the fiber at zero. We also consider continuous or discontinuous deformations of Cuntz and Toeplitz algebras.     

Initiation of Cracks in Griffith’s Theory: An Argument of Continuity in Favor of Global Minimization

The initiation of a crack in a sound body is a real issue in the setting of Griffith’s theory of brittle fracture. If one uses the concept of critical energy release rate (Griffith’s criterion), it is in general impossible to initiate a crack. On the other hand, if we replace it by a least energy principle (Francfort–Marigo’s criterion), it becomes possible to predict the onset of cracking in any circumstance. However this latter criterion can appear too strong. We propose here to reinforce its interest by an argument of continuity. Specifically, we consider the issue of the initiation of a crack at a notch whose angle ω is considered as a parameter. The result predicted by the Griffith criterion is not continuous with respect to ω, since no initiation occurs when ω>0 while a crack initiates when ω=0. In contrast, the Francfort–Marigo’s criterion delivers a response which is continuous with respect to ω, even though the onset of cracking is necessarily brutal when ω>0. The theoretical analysis is illustrated by numerical computations.     

Investigation of free vibrations of composite beams by using the finite-difference method

The free-vibration behavior of symmetrically laminated fiber-reinforced composite beams with different boundary conditions is examined. The effects of shear deformation and rotary inertia, separately and/or in combination, on the free-vibration properties of the beams are investigated. The finite-difference method is used to solve the partial differential equations describing the free-vibration motion in each case. The effect of shear deformation on the natural frequencies is considerable, especially for higher frequencies, whereas the influence of rotary inertia is less significant. The study includes comparisons with results available in the literature. In addition, the impact of such factors as the span/depth ratio, fiber orientation, stacking sequence, and material type on free vibrations of the composite beams is investigated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 331–346, May–June, 2006.