Anti-plane Shear Impact Load Research Articles

Transient behavior of an orthotropic layer with imperfect FGM coating containing multiple interfacial and embedded cracks under anti-plane shear impact load

This paper investigates the transient response of an orthotropic strip with functionally graded (FG) coating weakened by multiple embedded and interfacial cracks. The first part of this paper is concerned with the dynamic response of embedded cracks in the orthotropic substrate with imperfect FG coating. In the second part, the solution of interfacial crack is obtained analytically to extract the dynamic stress intensity factors (DSIFs). In the third part, the proposed method is developed to examine the dynamic fracture behavior of coating–substrate system with an orthotropic FGM coating bonded to an orthotropic substrate through a layer of a bond-coat. In all parts, Laplace and Fourier transforms are used to reduce the problems to a set of singular integral equations with Cauchy kernels which are solved numerically in the Laplace transform domain. The dynamic stress intensity factors are obtained by the numerical Laplace inversion technique. Several examples are solved to obtain DSIFs with various crack lengths and the spring constant of imperfect bonding and material properties of the layers.

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.

A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress intensity factors (DSIFs) for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractionalwave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation (ODE). The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional differential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.

An interface crack in a functionally graded piezoelectric bi-layer under anti-plane shear impact

The transient response of an interface crack between two dissimilar functionally graded piezoelectric material (FGPM) layers under anti-plane shear impact loading is analyzed using the integral transform method. The properties of the FGPM layers vary continuously along the thickness, and the two layers are connected weak-discontinuously. Laplace transform and Fourier transform are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate are presented for the FGPM to show the effects on the electric loading, variation and gradient of material properties, and thickness of layers. Following things are helpful to increase the resistance of transient fracture of interface crack in FGPMs: (a) increase of the material properties from the interface to the upper or lower free surface; (b) decrease of weak discontinuity at the interface; (c) increase of the gradient of material properties; (d) certain direction and magnitude of the electric loading; and (e) increase of the thickness of the FGPM layer.

Crack-Tip Stress Fields in FGMs under Anti-Plane Shear Impact Loading Using the Non-Local Theory

A crack in an infinite plate of functionally graded materials (FGMs) under anti-plane shear impact loading is analyzed by making use of non-local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form and the Poisson’s ratio is assumed to be constant. The mixed boundary value problem is reduced to a pair dual integral equations through the use of Laplace and Fourier integral transform method. In solving the dual integral equations, the crack surface displacement is expanded in a series using Jacobi’s polynomials and Schmidt’s method is used. The numerical results show that no stress singularity is present at the crack tip. The stress near the crack tip tends to increase with time at first and then decreases in amplitude and the peak values of stress decreases with increasing the graded parameters.

The Anti-plane Dynamic Fracture Analysis of Functionally Graded Materials with Arbitrary Spatial Variations of Material Properties

Anti-plane dynamic fracture analysis is presented for functionally graded materials (FGM) with arbitrary spatial variations of material properties. The FGM with the material properties varying continuously in an arbitrary manner is modeled as a multi-layered medium with the elastic modulus and mass density varying linearly in each sub-layer and continuous at the interfaces between two adjacent sub-layers. With this linearly inhomogeneous multi-layered model, the problem of a crack in a graded interfacial zone bonded to two homogeneous half-spaces or in a coating bonded to a homogeneous half-space subjected to the anti-plane shear impact load is investigated. Laplace and Fourier transforms and transfer matrix are applied to reduce the associated mixed boundary value problem to a Cauchy singular integral equation which is solved numerically in the Laplace transformed domain. The dynamic stress intensity factors (DSIF) are obtained by using the numerical technique of Laplace inversion.

Dynamic characteristics of an eccentric crack in a functionally graded piezoelectric ceramic strip

The dynamic response of an eccentric Griffith crack in functionally graded piezoelectric ceramic strip under anti-plane shear impact loading is analysed using integral transform method. Laplace transform and Fourier transform are used to reduce the problem to two pairs of dual integral equations, which are then expressed to Fredholm integral equations of the second kind. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. The impermeable crack boundary condition is adopted. Numerical values on the dynamic stress intensity factors are presented for the functionally graded piezoelectric material to show the dependence of the gradient of material properties and electric loadings.

Dynamic Response of a Crack in a Functionally Graded Material under an Anti-Plane Shear Impact Load

Dynamic Response of a Crack in a Functionally Graded Material under an Anti-Plane Shear Impact Load

A subsurface eccentric crack in a functionally graded coating layer on the layered half-space under an anti-plane shear impact load

This paper considers a subsurface crack in a functionally graded coating layer on the layered half-space subjected to an anti-plane impact load. The over-coated layer is assumed as a functionally graded material. The second kind Fredholm integral equation is obtained using Laplace transform and Fourier transform. The dynamic stress intensity factors can be obtained through the use of numerical inversion of Laplace transform technique. Numerical results are given for different values of the non-homogeneous parameter, geometric constants and material properties.

Dynamic response of subsurface interface crack in multi-layered orthotropic half-space under anti-plane shear impact loading

This article contains a theoretical formulation and numerical solutions for a subsurface interface crack subjected to an anti-plane impact load in multi-layered orthotropic half-space. The second kind Fredholm integral equation is obtained using Laplace transform and Fourier transform. The dynamic stress intensity factors can be obtained through the use of numerical inversion of Laplace transform technique. Numerical results are given for the geometric constants and material properties.

An eccentric crack in a piezoelectric strip under anti-plane shear impact loading

We consider the problem of determining the singular stress and electric fields in a piezoelectric ceramic strip containing a Griffith eccentric crack off the center line under anti-plane shear impact loading with the theory of linear piezoelectricity. Laplace transform and Fourier transforms are used to reduce the problem to a pair of dual integral equations, which are expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic stress intensity factor and the dynamic energy release rate are obtained.

Dynamic response of a crack in a functionally graded material between two dissimilar half planes under anti-plane shear impact load

This article provides a theoretical and numerical treatment of a finite crack subjected to an anti-plane shear impact load in a media with spatially varying elastic properties. This variation is in a direction perpendicular to the crack surfaces. The elastic properties of the interfacial layer are assumed to vary continuously between that of two dissimilar homogeneous bonding layers. Laplace and Fourier transforms are applied to reduce this mixed boundary value problem to a system of dual integral equations which in turn will be reduced to a standard Fredholm integral equation of the second kind. The Fredholm integral equation is solved in the Laplace transform plane numerically. The time inversion is accomplished by a numerical scheme. The dynamic stress intensity factor is found to either increase or decrease with the crack length to the layer thickness depending on the relative magnitudes of the material properties of the adjoining layer.

Elastodynamic response of an interface crack in a layered composite under anti-plane shear impact load

The elastodynamic response of a four-layered composite with an interface crack under anti-plane shear impact load is considered in this paper. Laplace and Fourier transforms are applied to reduce this mixed boundary value problem to a Cauchy-type singular integral equation of the first kind in Laplace transform plane, which is solved numerically. A Laplace inversion technique developed by Miller and Guy is then used to get the solution in the physical plane. Finally, the elastodynamic stress intensity factors are obtained as function of time, geometrical parameters and material properties.