复合材料桥纤维拔出的动态裂纹模型

在无限大正交各向异性体弹性平面上对复合材料桥纤维平行自由表面的内部中央裂纹提出了桥纤维拔出的动态裂纹模型。通过复变函数将其转化为Reimann-Hilbert混合边界值问题。求得了裂纹在坐标原点受载荷Px/t、Px2/t作用的解析解。利用这一解析解可通过迭加原理求得任意复杂问题的解。     

Application of complex path-independent integrals to the solution of the problem of a straight crack in a finite plane isotropic elastic medium

The classical problem of a straight crack in a finite, plane, isotropic, elastic medium of arbitrary shape is reconsidered by the well-known method of Muskhelishvili for such a crack (but in an infinite medium). Both the crack and the boundary of the medium are assumed loaded in an arbitrary way. It is shown that this problem can be completely solved if the numerical values of the first complex potential (z) of Muskhelishvili are known along a closed contour surrounding the crack, probably along the boundary of the medium. To this end, complex path-independent integrals associated with (z) and Chebyshev polynomials have been used. Numerical results for the stress intensity factors are displayed in an application. Generalizations of the method are also proposed and the second fundamental crack problem, the problem of a crack in an anisotropic medium and the problem of an interface crack between two isotropic media are considered in some detail.     

DYNAMIC CRACK MODELS ON PROBLEM OF BRIDGING FIBER PULL-OUT OF COMPOSITE MATERIALS

An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was performed. A dynamic model of bridging fiber pull-out of composite materials was presented. Resultingly the fiber failure is governed by maximum tensile stress, the fiber breaks and hence the crack extension should occur in self-similar fashion. By the methods of complex functions, the problem studied can be transformed into the dynamic model to the Reimann-Hilbert mixed boundary value problem, and a straightforward and easy analytical solution is presented. Analytical study on the crack propagation subjected to a ladder load and an instantaneous pulse loading is obtained respectively for orthotropic anisotropic body. By utilizing the solution, the concrete solutions of this model are attained by ways of superposition.     

Asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials

An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is studied, and asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-homogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is ascertained by maximum tensile stress, the fiber ruptures and hence the crack propagation should also appear in the modality of self-similarity. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of unidirectional composite materials under the conditions of two increasing loads given is obtained, respectively. In terms of correlative material properties, the variable rule of dynamic stress intensity factor was depicted very well. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be gained.     

Relative displacements of the two sides of a plane crack

We consider a two dimensional deformation of an infinite anisotropic elastic material which contains a plane crack. When tractions are specified over the crack faces, we give a formula for the corresponding relative displacements of the two sides of the crack. We also consider the inverse problem of determining the elastic constants by measuring the tractions and the corresponding relative displacements on the crack.     

A dynamic model of bridging fiber pull-out of composite materials

An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is carried out. In this paper a dynamic model of bridging fiber pull-out is presented for analyzing the distributions stress and displacement of composite materials with the internal central crack under the loading conditions of an applied non-uniform stress and the traction forces on crack faces yielded by the fiber pull-out model. Thus the fiber failure is determined by maximum tensile stress, the fiber breaks and hence the crack propagation should occur in self-similar fashion. By reducing the dynamic model to the Keldysh–Sedov mixed boundary value problem, a straightforward and easy analytical solution can be attained. When the crack extends, its fibers continue to break. Analytical study on the crack extension under the action of an inhomogeneous point force Px/t, Pt is obtained for orthotropic anisotropic body, respectively; and it can be utilized to attain the concrete solutions of the model by the ways of superposition.     

Numerical simulation of hydraulic fracture crack propagation

The plane problem of crack motion in an elastic medium under the pressure of a viscous fluid is considered. Under the condition of a constant fluid flow rate, the fluid is injected at the center of the crack. Contrary to other formulations of the problem, this paper attempts to take into account a possible fluid lag behind the crack tip. The resulting numerical solution is compared with a semianalytic one. It is found that the proposed numerical model can be used to predict the characteristics of a hydraulic fracture crack formed in a medium of a prescribed strength.     

Subsonic Griffith crack propagation in piezoelectric media

The plane problem of a Griffith crack steadily propagating in an anisotropic piezoelectric medium is investigated through an analytical approach which is new in this topic. Complete solutions are provided in the subsonic regime under permeable and impermeable boundary conditions and the combined effects of mechanical and electrical far-fields are pointed out.     

Identification of a plane crack in an elastic body by invariant integrals

We consider the problem of plane crack identification in an elastic body from the results of static tests. We show that the crack plane, its volume under homogeneous normal loading, and the coordinates of the central point are uniquely determined from the results of three static tests by uniaxial tension in three mutually perpendicular directions. We obtain explicit formulas for these crack characteristics in terms of the corresponding invariant integrals, which can be calculated if the stresses and displacements are measured on the external boundary of the body in the experiments mentioned above. These formulas are exact for the problem about a crack in an infinite medium. If the elastic body boundedness is taken into account and it is assumed that the crack characteristic dimensions are small compared with the distance from the crack to the body boundary, then the obtained formulas can be considered as approximate ones.     

Elastic waves in crystals and anisotropic media

The results of investigation of propagation of elastic waves in anisotropic media are discussed taking into account the two-dimensional problem of a source in an infinite medium and the Lamb problem for a half-plane. The media considered in the investigation are those for which the equations of motion under plane deformation conditions are characterized by four constants.     

Thermoelastic stress intensity factors for a cracked layer between two different anisotropic solids

Steady-state anisotropic thermoelasticity equations are used to obtain the stress intensity factors for a cracked layer sandwiched between two different anisotropic elastic solids. The anisotropy is assumed to arise from discrete fibers whose orientation could alter with reference to the crack edges. A generalized plane deformation prevails in the dissimilar media domain with a line of discontinuity disturbing a uniform heat flow. The flexibility/stiffness matrix approach is used such that the crack problem reduces to solving two sets of singular integral equations. Numerical values of the crack tip stress-intensity factors are obtained for various crack size, crack location, crack surface insulation, fiber volume fraction and orientation angles. The results are displayed graphically.     

GREEN''''S FUNCTIONS FOR A 2D ANISOTROPIC MEDIUM WITH A HYPERBOLIC BOUNDARY

By using Stroh's formalism and the conformal mapping technique, this paper derives simple explicit Green's functions of a piezoelectric anisotropic body with a free or fixed hyperbolic boundary. The corresponding elastic fields in the medium are obtained, too. In particular, degenerated solutions of an external crack from those of a hyperbolic problem are analysed in detail. Then the singular stress fields and the fracture mechanics parameters are found. The solutions obtained are valid not only for plane and antiplane problems but also for the coupled ones between inplane and outplane deformations.     

Use of the energy criterion of fracture to determine the shape of a slightly curved crack

An asymptotic formula is obtained for the total-energy increment during quasistatic growth of a semiin finite crack in an anisotropic elastic plane under complex loading. It is assumed that the shear loads are much larger than the tearing loads. The shape of the slightly curved crack was determined using the Griffith criterion in two versions: global and local. It is shown, in particular, that the first version leads to an improbable result. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 119–130, September–October, 2006.     

弹性半平面中边界裂纹研究的新方法

讨论了载荷作用在裂纹面上的弹性半平面边界裂纹问题.研究以线弹性断裂力学为基础,采用复变函数方法以及Riemann-Hilbert(R-H)边值问题的一般理论,将问题分拆为含有限裂纹的全平面问题与无裂纹的半平面问题的叠加,计算得到裂纹尖端的应力强度因子.与文献结果比较,该方法具有精度高的优点.     

Note on the Radial Deformation and Stresses in Anisotropic Nonhomogeneous Elastic Media

Abstract

In this paper we study the elasticity problem of a cylindrically anisotropic, elastic medium bounded by two axisymmetric cylindrical surfaces subjected to normal piessures (plane strain). The material of the structure is orthotropic with cylindrical anisotropy and, in addition, is continuously inhomogeneous with mechanical properties varying along the radius. General solutions in terms of Whittaker functions are presented. The results obtained by St. Venant for a homogeneous cylindrically anisotropic medium can be deduced from the general solutions. The problem of a solid cylinder of the same medium under the external pressure is also solved as a particular case of the above problem. Problems of the type covered in this paper are encountered in nuclear reactor design.     

On diffraction of normally incident SH-waves by a line crack in micropolar elastic medium

The problem of diffraction of waves due to plane harmonic SH-waves incident normally on a line crack situated in an infinite micropolar elastic medium has been considered. The solution of the problem is obtained for both low and high frequencies for small coupling parameter. The stress-intensity factors in micropolar elastic medium have been derived. The stress-intensity factor for such problem in an elastic medium can be deduced from results obtained in this paper. It is also found that the effect of micropolarity in the propagation of waves is more significant in high frequencies than low frequencies.     

A note on diffraction of normally incident P-wave by a line crack in micro-polar elastic medium

The problem of diffraction of waves due to plane harmonic P-wave incident normally on a line crack situated in an infinite micro-polar elastic medium has been studied in this paper. The problem has been solved for both low and high frequencies for small coupling parameter. The stress intensity factors (SIF) have been obtained in micro-polar elastic medium from which the corresponding stress intensity factor for classical elastic medium can be deduced.     

On interface crack in laminated anisotropic medium

In this paper, the interface crack problems of a multilayered anisotropic medium under a state of generalized plane deformation are considered within the framework of anisotropic theory. A general solution procedure is introduced such that it can be uniformly applied to media with transversely isotropic, orthotropic, monoclinic, etc. layers. The problem is reduced to the solution of a system of singular integral equations by means of Fourier transform method and the stiffness matrix formulation. A Jacobi polynomial technique is then used to solve the integral equations numerically. The stress intensity factors are provided. The stress intensity factors have been calculated numerically and displayed graphically.     

New solution of the plane problem for an equilibrium crack

We consider the classical plane problem of elasticity about a crack in an isotropic elastic unbounded plane resulting in a singular solution for the stresses near the crack edge. Relations of generalized elasticity with a small parameter characterizing the medium microstructure are derived, and the higher order of these relations permits eliminating the singularity of the classical solution. An experimental method for determining the medium parameter is proposed, and the corresponding experimental results are given.     

Elastoplastic near field solution for mode II crack loaded by remote shear stress in an infinite plate

A suitable elastic stress field near the crack line which satisfied the far field boundary conditions and the boundary conditions of the crack surfaces has been obtained and successful analysis has been made of a near crack line field for an infinite elastic-perfectly plastic medium containing a quasi-statically propagating plane stress crack subjected to far field shear stress. It is shown that the solutions of the problem of mode II crack loaded by remote shear stress from the Westergaard method in some previous papers is used as the elastic stress field near the crack line, are inappropriate.