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1.
A Periodic Array of Cracks in a Functionally Graded Nonhomogeneous Medium Loaded under in-Plane Normal and Shear 总被引:5,自引:0,他引:5
Hyung Jip Choi 《International Journal of Fracture》1997,88(2):107-128
In this paper, the problem of a periodic array of parallel cracks in a functionally graded medium is investigated based on
the theory of plane elasticity for a nonhomogeneous continuum. Both the in-plane normal (mode I) and shear (mode II) loading
conditions are considered. It is assumed that the material nonhomogeneity is represented as the spatial variation of the shear
modulus in the form of an exponential function along the direction of cracks, and the Poisson's ratio is constant. For each
of the individual loading modes, a hypersingular integral equation is derived, in a separate but parallel manner in which
the crack surface displacements are the unknown functions. As the basic parameters in applying the linear elastic fracture
mechanics criteria, the mode I and mode II stress intensity factors are defined from the stress fields with the square-root
singularity ahead of the crack tips. Numerical results are obtained to illustrate the variations of the stress intensity factors
as a function of the crack periodicity for different values of the material nonhomogeneity. The crack surface displacements
are also presented for the prescribed loading, material, and geometric combinations.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
The article presents the problem of an edge crack under normal point loading terminating perpendicular to the surface of an
orthotropic strip of finite thickness which is bonded to another orthotropic half plane. Expressing the displacements and
stresses in plane strain condition in terms of harmonic functions, the problem is reduced to a pair of simultaneous integral
equations with Cauchy type singularities, which are finally been solved by the Hilbert transform technique. The analytical
expression of stress intensity factor (SIF) at the crack tip for large thickness of the strip is calculated, which corresponds
to the weight function of a crack under normal loading. The influences of elastic constants of two different orthotropic materials,
distinct arbitrary locations of normal point loading on the crack surface and length of the crack on the dynamic SIF are depicted
through graphs. 相似文献
3.
N. I. Ioakimidis 《International Journal of Fracture》1983,21(2):115-122
A new singular integral equation (with a kernel with a logarithmic singularity) is proposed for the crack problem inside an elastic medium under plane or antiplane conditions. In this equation the integral is considered in the sense of a finite-part integral of Hadamard because the unknown function presents singularities of order ?3/2 at the crack tips. The Galerkin and the collocation methods are proposed for the numerical solution of this equation and the determination of the values of the stress intensity factors at the crack tips and numerical results are presented. Finally, the advantages of this equation are also considered. 相似文献
4.
S. Ueda 《International Journal of Fracture》2000,106(1):13-31
The plane strain dynamic singular stress problem for glassfiber reinforced plastics with a broken layer at low temperatures is considered. With the order of stress singularity around the tip of the crack which is normal to and ends at the interface between orthotropic elastic materials, Laplace and Fourier transforms are used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved by using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and the dynamic stress intensity factors at different temperatures are shown graphically. 相似文献
5.
6.
The problem of a homogeneous linear elastic body containing multiple non-collinear cracks under anti-plane dynamic loading is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by the Gaussian–Chebyshev integration quadrature. The dynamic stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Numerical results are given for one crack and two or three parallel cracks under normal incidence of a plane horizontally shear stress wave. 相似文献
7.
采用Green 函数的方法, 研究了介质中同时存在夹杂与裂纹时对SH 波的散射, 构造了在含有半圆形夹杂的弹性半空间, 水平面上任一点承受时间谐和出平面线源载荷作用时的位移函数作为Green 函数。并推导了SH 波对夹杂与裂纹散射的定解积分方程组, 进而求得裂纹尖端的动应力因子。重点讨论了夹杂的存在对裂纹尖端动应力因子的影响, 给出了随夹杂介质参数及夹杂与裂纹距离对裂纹尖端动应力因子的分布曲线, 为工程设计提供参考依据。 相似文献
8.
Dr. H. Yuan 《Acta Mechanica》1994,104(1-2):27-63
Summary In the present paper the asymptotic stress and deformation fields of dynamic crack extension in materials with linear plastic hardening under combined mode I (plane strain and plane stress) and anti-plane shear loading conditions (mode III) are investigated. The governing equations of the asymptotic crack-tip fields are formulated from two groups of angular functions, one for the in-plane mode and the other for the anti-plane shear mode. It was assumed that all stresses and deformations are of separable functional forms ofr and , which represent the polar coordinates centered at the actual crack tip. Perturbation solutions of the governing equations were obtained. The singularity behavior and the angular functions of the crack-tip in-plane and the anti-plane stresses obtained from the perturbation analysis show that, regardless of the mixity of the crack-tip field and the strain-hardening, the in-plane stresses under the combined mode I and mode III conditions have stronger singularity in the whole mixed mode steady-state crack growth than that of the anti-plane shear stresses. The anti-plane shear stresses perturbed from the plane strain mode I solutions lose their singularity for small strain hardening, whereas the angular stress functions perturbed from the plane stress mode I have a nearly analogous uniform distribution feature compared to pure mode III cases. An obvious deviation from the unperturbed solution is generally to be observed under combined plane strain mode I and anti-plane mode III conditions, especially for a large Mach number in a material with small strain-hardening; but not under plane stress and mode III conditions. The crack propagation velocity decreases the singularities of both pure mode and perturbed crack-tip fields. 相似文献
9.
Under the conditions of plane deformation, we study stresses in a piecewise-homogeneous isotropic body near the tip of a mode I crack appearing at the angular point on the boundary of two media. It is assumed that plastic strips (modeled by plastic slip lines) are formed on the boundary of the media. To determine the stresses, we use the Mellin integral transformation and the Wiener–Hopf method. The angular point is a stress concentrator with power singularity and, therefore, immediately after the appearance of lateral plastic strips (zones), a new plastic zone begins to develop from this point. We study the dependence of the power of singularity of stresses on the angle made by the boundary and the elastic characteristics of the media. 相似文献
10.
We study the initiation and propagation of a vertical crack in an elastic semi-infinite plate, reinforced on its boundary by an infinite discontinuous stringer within the limits of the theory of brittle failure. The plate is subjected to uniform distributed tensile forces at infinity, as well as to contact stresses due to application of forces to the stringer. We find the appropriate loading of the coherent stringer, and consequently we consider a problem where the stringer is cracked and a vertical crack has developed within the plate. We deduce the exact analytical solution for the principal singular integral equation for this case; hence the stringer is perfectly rigid and we calculate characteristic parameters of the problem. The results show that the crack tip has a logarithmic singularity, and the tangential contact stresses under the stringer at that end point are finite and generally differ from zero. 相似文献
11.
We study the dynamic interaction of plane cracks in an elastic half space with rigidly restrained surface. The problem is reduced to the solution of a system of two-dimensional boundary integral equations of Helmholtz-potential type for unknown functions of crack opening displacements. As an example, we consider the case of impact fracture loading of the crack surfaces whose time dependence is described by the Heaviside function. The time dependences of the stress intensity factors are established and analyzed. 相似文献
12.
13.
Gennady Mishuris 《International Journal of Fracture》2001,107(3):279-296
Asymptotic behaviour of displacements and stresses in a vicinity of the interface crack tip situated on a nonideal interface between two different elastic materials is investigated. The nonideal interface is described by special transmission conditions along the material bonding. The corresponding modelling boundary value problem is reduced to a singular integral equation with fixed point singularities. It is shown from the solution to the problem that asymptotic behaviour of displacement and stresses near the crack tip essentially depends on the model parameters. Some numerical examples are presented and discussed with respect to the stress singularity exponent and the generalized stress intensity factors. 相似文献
14.
15.
An analytic model is proposed for an opening mode of crack face displacement with crack-tip dual zones, i.e. an elastic core zone plus a plastic strip zone. A presence of such dual zones in the vicinity of the crack tip was experimentally observed in a recent study based on the generation of dislocations. A Papkovich-Neuber formulation of the resulting four-part mixed boundary value problem leads to a set of quadruple integral equations which are solved with an application of finite Hilbert transform technique. With conditions of boundedness on the stresses in the plastic strip zone, the results show an inverse square root of the distance type singularity at the base of the crack tip and a relaxation of stresses in the crack-tip elastic core zone is realized. The stress intensity factors and the crack-tip opening displacements are presented in exact forms involving elliptic integrals and Heuman's lambda function and are shown to depend upon the crack size, the applied loading and the crack-tip dual zone lengths. The analytic and graphical solutions are compared with the Dugdale model to which they reduce as a limiting case of vanishing elastic core zone.
Résumé On propose un modèle analytique pour décrire la déformation d'ouverture selon le mode I, en utilisant une approche de mécanique des milieux continus pour décrire la double zone-élastique et plastique-située à la pointe d'une fissure.相似文献
16.
《International Journal of Engineering Science》2006,44(11-12):807-818
The problem of two periodic edge cracks in an elastic infinite strip located symmetrically along the free boundaries under thermal shock is investigated. It is assumed that the infinite strip is initially at constant temperature. Suddenly the surfaces containing the edge cracks are quenched by a ramp function temperature change. Very high tensile transient thermal stresses arise near the cooled surface resulting in severe damage. The degree of the severity for a subcritical crack growth mode is measured by determining the stresses intensity factors. The thermoelastic problem is treated as uncoupled quasi-static. The superposition technique is used to solve the problem. The thermal stresses obtained from the uncracked strip with opposite sign are utilized as the only external loads to formulate the perturbation problem. By expressing the displacement components in terms of finite and infinite Fourier transforms, a hypersingular integral equation is derived with the crack surface displacement as the unknown function. Numerical results for stress intensity factors are carried out and presented as a function of time, cooling rate, crack length, and periodic crack spacing. 相似文献
17.
In this paper, the scattering of harmonic antiplane shear waves by a finite crack is studied using the non-local theory. The
Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual integral equations is solved
using the Schmidt method instead of the first or the second integral equation method. Contrary to the classical elasticity
solution, it is found that no stress singularity is presented at the crack tip. The non- local dynamic elastic solutions yield
a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis.
The finite hoop stress at the crack tip depends on the crack length.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
The boundary value problem of an elastic bi-material layer containing a finite length crack under compressive mechanical loadings has been studied. The crack is located on the bi-material interface and the contact between crack surfaces is frictionless. Based on Fourier integral transformation techniques the solution of the formulated problem is reduced to the solution of singular integral equation, then, with Chebyshev`s orthogonal polynomials, to infinite system of linear algebraic equations. The expressions for contact stresses in the elastic compound layer are presented. Based on the analytical solution it is found that in the case of frictionless contact the shear and normal stresses have inverse square root singularities at the crack tips. Numerical solutions have been obtained for a series of examples. The results of these examples are illustrated graphically, exposing some novel qualitative and quantitative knowledge about the stress field in the cracked layer and their dependence on geometric and applied loading parameters. It can be seen from this study that the crack tip stress field has a mixture of mode I and mode II type singularities. The numerical solutions show that an interfacial crack under compressive forces can become open in certain parts of the contacting crack surfaces, depending on the applied forces, material properties and geometry of the layers. 相似文献
19.
The paper considers splitting a plane elastic wedge-shaped solid through the application of a rigid punch. It is assumed that the coefficient of friction on the contact area is constant, the problem has a plane of symmetry with respect to loading and geometry, and the crack lies in the plane of symmetry. The problem is formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution is obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area. 相似文献
20.
《International Journal of Engineering Science》2005,43(13-14):1107-1120
In this paper, the interaction of two collinear cracks in anisotropic elasticity materials subjected to an anti-plane shear loading is investigated by means of the nonlocal theory. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surface. To solve the triple integral equations, the displacement on the crack surface is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tip. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress hypothesis as a fracture criterion. The magnitude of the finite stress field depends on the crack length, the distance between two cracks and the lattice parameter of materials. 相似文献