Collinear Griffith Cracks Research Articles

Non-Fourier thermoelastic interaction of two collinear cracks in a functionally graded layer

Designed with a predetermined composition profile, functionally graded materials receive much attention in serving as the thermal barrier coating to resist severe thermal loading. By means of the dual-phase-lag theory, the non-Fourier effect is considered in establishing the theoretical thermoelastic model of the cracked layer under sudden thermal shocks. The novelty of the present work lies in revealing the interaction effects of two collinear Griffith cracks embedded in a functionally graded layer on the transient temperature and thermal stress fields under harsh conditions. Via employing the Fourier sine and cosine transforms, coupled with the Laplace transform, the dynamic mixed mode crack problem is transformed into a group of Cauchy-type singular integral equations. Numerical calculations are implemented to evaluate the transient temperature and stress intensity factors. The influences of the crack spacing, the nonhomogeneous parameters, and the thermal lags on the thermal and stress concentrations are explored. The results indicate that both mode I and II thermal stress intensity factors of the outer crack tips are noticeably higher than those of the inner crack tips, even up to 71% and 128%, respectively. A larger fracture risk may occur with the closer two adjacent cracks.

Study of collinear cracks in a composite medium subjected to time‐harmonic wave disturbance

AbstractThe article deals with the collinear Griffith cracks under the time‐harmonic waves, situated in an orthotropic strip sandwiched between two identical half‐planes. The outer cracks are considered to be situated on either sides of the central crack. The mathematical model is solved by applying the Fourier transform and then the unknown functions have been determined using Schmidt method. The approximate analytical expressions of the stress intensity factors (SIFs) have been obtained at the tips of the cracks. The values of the SIFs for the considered composite with Graphite epoxy material as the strip and E‐glass epoxy as the half‐plane are computed numerically for different crack lengths and wave numbers, and the obtained results are displayed graphically. The salient feature of the article is the pictorial presentations of the possibilities of arrest of the central crack due to the presence of outer cracks through finding the stress magnification factor for different particular cases.

Transient response of collinear Griffith cracks in a functionally graded strip bonded between dissimilar elastic strips under shear impact loading

This article analyses the interaction between a central and two symmetrically placed collinear Griffith cracks subjected to transient response under anti-plane shear impact loading. The cracks are situated in a strip constituted by functionally graded material (FGM) bonded between two dissimilar elastic strips of equal thickness. The material properties of FGM are assumed to vary exponentially as a function of thickness. Applying integral transforms, the boundary value problem reduces to a system of singular integral equations in the Laplace transformed domain. These equations are solved numerically using the Lobatto-Chebyshev collocation quadrature approach. The inverse Laplace transform is used to find the approximate expressions of dynamic stress intensity factors (DSIFs). The striking feature of the article is the study of phenomenal changes of shielding and amplification through dynamic stress magnification factors (DSMFs) at the tips of the cracks under the sudden impact loading applied at the upper material surface. The effects of impact load applied at different surfaces, positions of cracks’ axis and the thickness of the strips of the composite material on the possibilities of cracks’ arrest are depicted graphically for different particular cases.

P-wave diffraction by three collinear griffith cracks under normal impact

The boundary value problem of P-wave diffraction by three collinear Griffith cracks under normal impact has been considered. Laplace and Fourier transforms have been applied to convert the problem to a Fredholm integral equation of second kind in the Laplace transform plane. Stress Intensity Factor has been computed numerically by Laplace inversion using Zakian's Algorithm and plotted graphically against time for orthotropic material.

Investigation of interactions among collinear Griffith cracks situated in a functionally graded medium under thermo-mechanical loading

This study deals with the interactions between a central crack and two symmetrically situated collinear Griffith cracks in an infinite functionally graded medium under thermo-mechanical loading. These Griffith cracks are partially insulated. The considered medium is a non-homogeneous isotropic elastic one. The Fourier sine and cosine transforms are used to solve the elasticity and heat conduction equations which are reduced to a system of singular integral equations of the first kind. These equations are solved numerically by using Chebyshev polynomials of the first kind. The approximate expressions of the normalized mode I stress intensity factors and stress magnification factors are found analytically. The main objective of this article is to study the influence of the relative sizes of collinear cracks on mode I stress intensity factors and to find the possibility of crack shielding and amplification. The salient feature of this article is the pictorial presentations of temperature field, thermal crack surface stresses, stress intensity factors, and stress magnification factors under thermal, mechanical, and thermo-mechanical loadings for different particular cases.

Hilbert transform approach to solve a problem of collinear Griffith crack in the mid-plane of an infinite orthotropic strip

In this paper, an integral transformation of the displacement is employed to determine the solution of the elastodynamics problem of two collinear Griffith cracks with constant velocity situated in a mid-plane of an infinite orthotropic strip where the boundaries are assumed to be stress-free. By use of the integral transformation of the displacement, the problem is reduced to a solution of the triple integral equations and the finite Hilbert transformation technique is used to solve it. The expressions of stresses are obtained asymptotically for large values of strip depth. An analytical expression of the stress intensity factor at the crack tip is obtained and represented graphically for two different orthotropic materials.

Moving Three Collinear Griffith Cracks at Orthotropic Interface

This work deals with the interaction of P-waves between a moving central crack and a pair of outer cracks situated at the interface of an orthotropic layer and an elastic half-space. Initially, we considered a two-dimensional elastic wave equation in orthotropic medium. The Fourier transform has been applied to convert the basic problem to solve the set of four integral equations. These set of integral equations have been solved to to get the analytical expressions for the stress intensity factor (SIF) and crack opening displacements (COD) by using the finite Hilbert transform technique and Cooke’s result. The main objective of this work is to investigate the dynamic stress intensity factors and crack opening displacement at the tips of the cracks. The aims of the study of these physical quantities (SIF, COD) is the prediction of possible arrest of the cracks within a certain range of crack velocity by monitoring applied load. SIF and COD have been depicted graphically for various types of orthotropic materials. We presented a parametric study to explore the influence of crack growing and propagation. This result is very much applicable in bridges, roads, and buildings fractures.

Transient response of an infinite row of collinear Griffith cracks in a saturated porous medium

The transient stress distribution is obtained for a saturated porous medium containing an array of equally distributed collinear cracks when each crack is opened by suddenly applied internal pressure. The integral and Laplace transforms are employed to reduce the mixed boundary-value problem to solving the Fredholm integral equation. The influence of pore fluid and the size of the crack with respect to the distance between the neighbouring cracks on the dynamic stress intensity factor are investigated. Numerical results are presented and compared with the corresponding values of the dry medium.

Two interfacial collinear Griffith cracks in thermo-elastic composite media

The objective of the article is to find the stress intensity factors and crack energy for a pair of collinear Griffith cracks situated at the interface of the two orthotropic materials under steady-state temperature field. The problem is reduced to a pair of singular integral equations, which are solved using Jacobi?s polynomials. Numerical computations are carried out for two different pairs of orthotropic materials for different particular cases, which are depicted through figures. The effect of material constants and temperature coefficients on the behavior of physical quantities viz., stress intensity factors and crack energy of the interfacial cracks is the key feature of the present article.

Multiple collinear Griffith cracks in a one-dimensional hexagonal quasicrystalline layer

The fracture behavior of multiple collinear Griffith cracks in a one-dimensional quasicrystalline layer is investigated in this paper. Using the Fourier transform technique, the mixed boundary value problem is reduced to a system of Cauchy singular integral equations. The integral equations are further reduced to a system of algebraic equations. The stress intensity factors of the phonon and phason fields and the energy release rate are determined. Numerical results reveal the effects of geometric size, the distance of the cracks and loading parameter ratio of the phonon and phason fields on crack propagation and growth. The results seem useful for the design of quasicrystalline materials, structures and devices of high performance.

Interaction between Interfacial Collinear Griffith Cracks in Composite Media under Thermal Loading

AbstractThis article deals with the interactions between a central crack and a pair of outer cracks situated at the interface of orthotropic elastic half planes under thermo-mechanical loading. The mixed boundary value problem has been reduced to a pair of singular integral equations which has been solved numerically using Jacobi polynomial method. The interaction effects have been obtained in terms of stress magnification factors depending on the crack spacing and crack length. The phenomena of crack shielding and crack amplification have been depicted through graphs for different particular cases.

Interaction of moving interface collinear Griffith cracks under antiplane shear

The interaction between three moving collinear Griffith cracks under antiplane shear stress situated at the interface of an elastic layer overlying a different half plane has been studied. Fourier transform and finite Hilbert transform techniques have been employed to solve the problem. Approximate analytical expressions for stress intensity factors at the crack tips have been derived for large thickness of the elastic layer. Numerical results connected to the interaction effect have also been obtained. Depending on the spacing of the cracks, their common velocity of propagation and the depth of the layer, occurrence of shielding and amplification phenomena of the cracks have been noticed.

Diffraction of SH-waves by collinear Griffith cracks in an infinite transversely isotropic medium

Diffraction of SH-waves by collinear Griffith cracks in an infinite transversely isotropic medium

Stress intensity factors around two co-planar Griffith cracks in an orthotropic layer sandwiched between two identical orthotropic half planes

An integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of two collinear Griffith cracks located in an orthotropic elastic layer of finite thickness 2 h sandwiched between two identical orthotropic half planes. For large h analytical expressions for the stress intensity factors are determined up to the order h −4. Graphical plots of the numerical results are also presented.

Two collinear Griffith cracks subjected to uniform tension in infinitely long strip

The problem of determining the stress field in an elastic strip of finite width when the uniform tension is applied to the faces of two collinear symmetrical cracks situated within it is considered. By using the Fourier transform, the problem can be solved with a set of triple integral equations. These equations are solved using Schmidts method. This method is suitable for solving the strips problem of arbitrary width.

Two collinear griffith cracks subjected to anti-plane shear in infinitely long strip

Two collinear griffith cracks subjected to anti-plane shear in infinitely long strip

Surface instability in gradient elasticity with surface energy

Biot's theory of plane strain surface instability of an isotropic elastic body under initial stress in finite strain is extended to include higher order strain-gradients. Higher order straingradients are properly introduced in the definition of the strain energy density, leading to an anisotropic gradient elasticity theory with surface energy. Accordingly, the present theory includes two material lengths characterizing the volume strain energy and the surface energy of the elastic body. The consideration of these two material lengths leads to the occurrence of a boundary layer. This in turn, gives rise to interesting phenomena related to the stability of the half-space, i.e. extra surface instability modes, thin skin effects and significant weakening of the half-space. It is also shown that the appearance of surface instability is associated with the vanishing velocity of propagation of Rayleigh waves. Furthermore, results derived in the context of the present theory on the dependence of the critical buckling stress of the layer on the thickness, suggest that it can be used effectively for the homogenization of elastic bodies containing periodic arrays of collinear Griffith cracks.

Propagation of two collinear Griffith cracks in an orthotropic strip

An integral transform technique is employed to solve the elastodynamic problem of steady-state propagation of two collinear Griffith cracks located in a plane of elastic symmetry of a stressed orthotropic strip of finite thickness 2 h, The asymptotic expressions for the stresses are derived. For large h analytical expressions for the stress intensity factors are presented up to the order h −4. Graphical plots of the numerical results are also presented.

Elastodynamic crack problems in an orthotropic medium through complex variable approach

Complex variable technique is employed to solve the elastodynamic problems of (I) two equal collinear Griffith cracks, (II) an infinite row of parallel cracks and (III) a “grid” of cracks of equal arms, propagating with constant speed in a stressed orthotropic medium. Stress and displacement components are represented in terms of holomorphic functions defined in two appropriate complex domains. Stress intensity factors and some asymptotic results are represented and briefly discussed.

An array of no-slip tensile cracks at a bimaterial interface

The tensile strength of interdigitated bimaterial interfaces is strongly affected by the formation of multiple interfacial microcracks. Such is the case with cemented total-joint replacements where loosening and breakdown of the cancellous bone-PMMA cement interface occur by “damage” and formation of interfacial cracks. The problem of an array of interfacial cracks is addressed in this paper within the context of fracture mechanics. An analytical solution is presented for the plane-strain problem of a periodic array of no-slip interfacial cracks under uniaxial tension. A closed-form solution is readily available when the cracks are opened by constant pressure; the corresponding Mode I stress intensity factor is found to be identical to that obtained for an array of collinear Griffith cracks in a homogeneous medium. A more realistic situation involves cohesive stresses over the crack faces. Cohesive zone effects have been incorporated in the present model that allows for quantifying the reduction of the strength singularity at the crack tip, due to the pull-out resistance of cement pedicles to being forced out of mechanical interlocks at the interdigitated, bimaterial interface.