Impact response of a strip composite with a finite crack

The dynamic response of a central crack in a strip composite under normal impact is analyzed. The crack is oriented normally to the interfaces. Laplace and Fourier transform techniques are used to reduce the elastodynamic problem to a pair of dual integral equations. The integral equations are solved by using an integral transform technique and the result is expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time, the material properties and the geometrical parameters is discussed.     

Impact response of a finite crack in an orthotropic piezoelectric ceramic

Summary The transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.     

Torsional impact response of a penny-shaped crack lying on a bimaterial interface

The torsional impact response of a penny-shaped crack lying on a bimaterial interface is considered in this study. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution to the dual integral equations is expressed in terms of a Fredholm integral equation of the second kind with a finite integral kernel. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time and material constants is discussed.     

Transient analysis of a piezoelectric strip with a permeable crack under anti-plane impact loads

The problem of a through permeable crack situated in the mid-plane of a piezoelectric strip is considered under anti-plane impact loads for two cases. The first is that the strip boundaries are free of stresses and of electric displacements, and the second is that the strip boundaries are clamped rigid electrodes. The method adopted is to reduce the mixed initial-boundary value problem, by using integral transform techniques, to dual integral equations, which are further transformed into a Fredholm integral equation of the second kind by introducing an auxiliary function. The dynamic stress intensity factor and energy release rate in the Laplace transform domain are obtained in explicit form in terms of the auxiliary function. Some numerical results for the dynamic stress intensity factor are presented graphically in the physical space by using numerical techniques for solving the resulting Fredholm integral equation and inverting Laplace transform.     

Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear

Summary Following the theory of linear piezoelectricity, we consider the problem of determining the singular stress and electric fields in an orthotropic piezoelectric ceramic strip containing a Griffith crack under longitudinal shear. The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for piezoelectric ceramics are obtained, and the results are graphed to display the influence of the electric field.     

压电-压磁板条中反平面裂纹的电-磁-弹性分析

基于线性电磁弹性理论,获得了压电-压磁板条中反平面裂纹尖端附近的奇异应力、电场和磁场。假设裂纹位于和板条边界平行的中心位置,并且裂纹是电磁渗透型的。利用Fourier变换,将裂纹面的混合边值问题化为对偶积分方程,即而归结为第二类Fredholm积分方程。通过渐近分析,得到了裂纹尖端附近应力、应变、电位移、电场、磁场和磁感的封闭表达式。结果表明,对于电磁渗透裂纹,电场强度因子和磁场强度因子总为0;板条的宽度对应力强度因子有显著的影响;能量释放率总为正值。     

Effect of Couple-Stresses on the Transient Dynamic Stress Intensity Factors for a Crack in an Infinite Elastic Medium Under an Impact Stress Wave

This study applies linearized couple-stress theory to evaluate the dynamic stresses around a crack in an infinite elastic medium that is subjected to an incoming shock stress wave impinging normal to the crack. The boundary conditions with respect to the crack are reduced to dual integral equations using a Fourier transform in the Laplace domain. To solve these equations, the differences in the displacement and rotation at the crack are expanded by a series of functions that are zero-valued outside the crack in the Laplace domain.     

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.     

Dynamic stress intensity factors around a rectangular crack in an infinite plate under impact load

A three-dimensional solution is presented for the transient response of an infinite plate which contains a rectangular crack. The Laplace and Fourier transforms are used to reduce the problem to a pair of dual integral equations. These equations are solved with the series expansion method. The stress intensity factors are defined in the Laplace transform domain, and they are inverted numerically in the physical space.     

Torsional impact response of a penny-shaped interface crack in a layered composite

The torsional impact response of a penny-shaped interface crack in a layered composite is considered in this study. The geometry of the composite consists of two bonded dissimilar elastic layers which are sandwiched between two half-spaces made of a different material. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. These equations are solved by using an integral transform technique and the result is expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time, the material properties and the geometry parameters is discussed.     

Stresses in an orthotropic strip containing A Griffith Crack

The problem of determining the stress and displacement fields in an orthotropic elastic strip containing a Griffith crack situated symmetrically and oriented in a direction normal to the edges of the strip is considered. A general solution in terms of two potential functions is presented. The mixed boundary conditions lead to dual integral equations, which are reduced to Fredholm integral equation of second kind and are solved by the use of Gaussian quadrature formula. Numerical solutions for a fiber-reinforced composite material and some isotropic materials are carried out and the effect of orthotropy on various quantities of physical interest, in fracture mechanics, is discussed.     

Impact response of a cracked orthotropic medium-revisited

Elastodynamics response of an infinite orthotropic medium containing a central crack under impact loading has been investigated. Laplace and Fourier transforms have been employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform domain which has finally been solved by the method of iteration in the low frequency case. Analytic expressions for the stress intensity factors and crack opening displacement are also obtained for low frequency.     

The linear thermoelastic problem of uniform heat flow disturbed by a two-dimensional crack in a strip

Under the assumption of plane strain, a solution for a thermoelastic problem concerning a strip is obtained by the method of dual integral equations. It is assumed that the crack is parallel to the edges of the strip. The variation with the strip width of stress-intensity factor is shown graphically.     

Axisymmetric elastodynamic response of a flat annular crack to normal impact waves

The axisymmetric response of a flat annular crack in an infinite medium subjected to normal impact load is investigated in this study. A step stress is applied to the crack surface. The singular solution is equivalent to solutions of the problem of diffraction of normally incident tension wave by a flat annular crack, and the problem of the sudden appearance of a flat annular crack in a uniform tensile stress field. Laplace and Hankel transforms are used to reduce the problem to the solution of a set of triple integral equations in the Laplace transform domain. These equations are solved by using a integral transform technique and the result is expressed in terms of a singular integral equation of the first kind with the kernel which is improved by means of a contour integration on the Riemann surface. A numerical Laplace inversion routine is used to recover the time dependence of the solution. Numerical results of the dynamic stress intensity factor are obtained to show the influence of inertia, the ratio of the inner radius to the outer one and Poisson's ratio on the load transmission to the crack tip.     

Transient thermoelectroelastic response of a functionally graded piezoelectric strip with a penny-shaped crack

Transient response of a penny-shaped crack in a plate of a functionally graded piezoelectric material (FGPM) is studied under thermal shock loading conditions. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the crack faces are completely insulated. By using both the Laplace and Hankel transforms, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations which are solved numerically. The intensity factors vs. time for various crack size, crack position and material nonhomogeneity are obtained.     

Weight Function for a Crack in a Two-dimensional Orthotropic Medium Under Impact Shear Loading

The paper examines the elastodynamic response of an infinite two-dimensional orthotr- opic medium containing a central crack under impact shear loading. Laplace and Fourier integral transforms are employed to reduce the problem to a pair of dual integral equations in the Laplace transformed plane. These equations are reduced to integral differential equations, which have been solved in the low frequency domain by iterations. To determine time dependence, these equations are inverted to yield the dynamic stress intensity factor (SIF) for shear point force loading that corresponds to the weight function for the crack under shear loading. It is used to derive SIF for polynomial loading.     

Sudden twisting of an external circular crack in an infinite medium with a cylindrical inclusion

In this paper the torsional impact response of an external circular crack in an infinite medium bonded to a cylindrical inclusion has been investigated. The infinite medium and cylindrical inclusion are assumed to be of different homogeneous isotropie elastic materials. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. These equations are solved by using an integral transform technique and the results are expressed in terms of a Fredhol integral equation of the second kind. By solving Fredholm integral equation of the second kind the numerical results for the dynamic stress-intensity factor are obtained which measure the load transmission on the crack.     

Impact response of a crack in a semi-infinite body with a surface layer under longitudinal shear

Summary The impact response of a crack in a semi-infinite body with a surface layer which is subjected to antiplane shear deformation is considered in this study. The semi-infinite body contains a crack near an interface. Using Laplace and Fourier transforms, the case of a crack perpendicular to the interface is reduced to a set of triple integral equations in the Laplace transform plane. The solution to the triple integral equations is then expressed in terms of a singular integral equation of the first kind. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factors at the crack tips are obtained for several values of time, material constants, and geometrical parameters.With 8 Figures     

Diffraction of transient horizontal shear waves by a finite crack at the interface of two bonded dissimilar elastic solids

Scattering of transient horizontal shear waves by a finite crack located at the interface of two bonded dissimilar elastic solids is investigated in this study. Laplace and Fourier transform technique is used to reduce the problem to a pair of dual integral equations. The solution of the dual integral equation is expressed in terms of the Fredholm integral equation of the second kind having the kernel of a finite integration. Dynamic stress intensity factor is obtained as a function of the material and geometric properties and time.     

Crack propagating in a functionally graded strip under the plane loading

In the present paper, a finite crack with constant length (Yoffe type crack) propagating in the functionally graded strip under the plane loading is investigated by means of the Schmidt method. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of the material properties, the thickness of the functionally graded strip, and speed of the crack propagating upon the dynamic fracture behavior.