具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子

本文研究了两个材半限弹性的接合面附近存在与接合面平行的双裂纹，并承受剪切冲击时的瞬态应力，运用付里叶（Ｆｏｕｒｉｅｒ）和拉普拉斯（Ｌａｐｌａｃｅ）变换，将问题归结为求解二元积分方程，求解时将裂纹所在面上，下的位移差展成级数，并让其自动满足裂纹面外的位移差为零的条件，利用裂纹面上的边界条件和施密特（Ｓｃｈｍｉｄｔ）方法求解级数中的待定系数，在拉普拉斯像空间中，求得动应力强度因子，并将其数值地逆变换至     

Study of stress intensity factors near cracks in plates made of linearly viscoelastic fiber composites

For the first time a method is proposed for determining the stress intensity factors (SIF) near cracks in linear viscoelastic fiber composites using the data from polarization-optical measurements. The character of the change in the SIF in time near cracks in plates made of optically sensitive viscoelastic fiber composites exposed to constant tensile stresses (creep) was investigated. In describing the mechanical and optical properties of the materials, the composite was considered a homogeneous linearly viscoelastic orthotropic body. Equations were derived which correlate the fringe ordersm(t) with SIFK _j (j=1,2) and the longrange field stress _Ox in the vicinity of the apex of a crack whose direction coincides with the main direction of the axis of orthotropy. The SIF near linear cracks whose direction forms angles =90° and =45° with the direction of the tensile stresses were determined. It was found that the character of the change in SIF in time near cracks in creep, is a function of the angle between the direction of the crack and the direction of the tensile stress.Scientific-Research Institute of Mechanics, M. V. Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 321–328, May–June, 1997.     

压电材料中两平行不相等界面裂纹的动态特性研究

利用Schmidt方法,研究了压电材料中两个平行不相等的可导通界面裂纹对简谐反平面剪切波的散射问题．利用Fourier变换,使问题的求解转换为对两对以裂纹面张开位移为未知变量的对偶积分方程的求解．数值计算结果表明,动态应力强度因子及电位移强度因子受裂纹的几何参数、入射波频率的影响．在特殊情况下,与已有结果进行了比较分析．同时,电位移强度因子远小于不可导通电边界条件下相应问题的结果．     

Moving Cracks in Composite Materials with Initial Stresses

The dynamic problems of fracture mechanics for composite materials with initial stresses are considered in the case of cracks moving at a constant rate along a straight line. In the continuum approximation, composite materials are modeled by orthotropic nonlinearly elastic bodies with an arbitrary form of the elastic potential. A three-dimensional linearized theory of elasticity is used. The complex potentials of plane and antiplane problems of the linearized theory are used for dynamic problems. Exact solutions for Modes I, II, and III in the case of moving cracks are obtained using the Keldysh-Sedov methods. Asymptotic formulas for stresses and displacements near the crack tip for Modes I, II, and III are presented. The basic mechanical effects are analyzed with respect to the problems considered.     

The two-dimensional stressed state of a multiconnected anisotropic body with cavities and cracks

We present a method of determining the two-dimensional generalized stress-strain state and the stress intensity factors for an anisotropic body with cylindrical cavities and plane cracks. The method is based on the use of generalized complex potentials, conformal mappings, the method of least squares, and numerical passage to the limit to determine the stress intensity factors. We apply the method to study the stress-strain state and the change in stress intensity factors as functions of the geometric and elastic characteristics of an orthotropic cylinder with one or two cracks, an infinite anisotropic body with elliptic cavities and cracks, and an infinite body with a curvilinear cavity. Five figures. Six tables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 45–56.     

Collinear periodic cracks and/or rigid line inclusions ofantiplane sliding mode in one-dimensional hexagonal quasicrystal

For a one-dimensional (1D) hexagonal quasicrystal (QC), there is the periodic (x₁,x₂)-plane of atomic structures with the quasiperiodic direction x₃-axis along which there exists a phason displacement. The macroscopically collinear periodic cracks and/or rigid line inclusions are placed on the periodic (x₁,x₂)-plane for finding out the influence of phason displacement on the related physical quantities. These two models are reduced to the Riemann–Hilbert problem of periodic analytic functions to obtain the closed-form solutions for the antiplane sliding mode. It is found that the phonon and phason stress intensity factors of cracks as well as the phonon and phason stress field intensity factors of rigid line inclusions are not related to the coupling of phonon and phason fields. These mean that there is not the influence of phason displacement on both the phonon stress intensity factor (usual stress intensity factor) of cracks and the phonon stress field intensity factor of rigid line inclusions. However, the energy release rates of periodic cracks and/or rigid line inclusions are obtained and affected not only by the periodicity of cracks and/or rigid line inclusions but also by the phason displacement.     

Interaction of multiple cracks in a rectangular plate

This paper is concerned with interaction of multiple cracks in a finite plate by using the hybrid displacement discontinuity method (a boundary element method). Detail solutions of the stress intensity factors (SIFs) of the multiple-crack problems in a rectangular plate are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. The numerical results reported here illustrate that the boundary element method is simple, yet accurate for calculating the SIFs of multiple crack problems in a finite plate.     

Closed-form solutions for two collinear dielectric cracks in a magnetoelectroelastic solid

The problem of two collinear electromagnetically dielectric cracks in a magnetoelectroelastic material is investigated under in-plane electro-magneto-mechanical loadings. The semi-permeable crack-face boundary conditions are adopted to simulate the case of two collinear cracks full of a dielectric interior. Utilizing the Fourier transform technique, the boundary-value problem is reduced to solving singular integral equations with Cauchy kernel, which then are solved explicitly. The intensity factors of stress, electric displacement, magnetic induction, crack opening displacement (COD) and the energy release rates near the inner and outer crack tips are determined in closed forms for two cases of possible far-field electro-magneto-mechanical loadings respectively. Numerical results for a BaTiO₃–CoFe₂O₄ composite are carried out to show the effects of applied mechanical loadings on the crack-face electric displacement and magnetic induction, the stress intensity factor and the COD intensity factor, respectively. The obtained results reveal that when the applied mechanical loading is stress, applied electromagnetic loadings have no influences on the stress intensity factor. When the applied mechanical loadings is train, the applied positive electromagnetic loadings decrease the intensity factors of stress and COD, and the applied negative ones increase the intensity factors of stress and COD. The variations of energy release rates are also given to show the effects of the geometry of two collinear dielectric cracks.     

压电压磁复合材料中一对平行裂纹对弹性波的散射

利用Schmidt方法对压电压磁复合材料中一对平行对称裂纹对反平面简谐波的散射问题进行了分析,借助富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程．在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式,最终获得了应力强度因子、电位移强度因子、磁通量强度因子三者之间的关系．结果表明,压电压磁复合材料中平行裂纹动态反平面断裂问题的应力奇异性与一般弹性材料中的动态反平面断裂问题的应力奇异性相同,同时讨论了裂纹间的屏蔽效应．     

The perturbed stress state of a closed cylindrical shell with longitudinal cracks on its inner surface

Using the Rice-Levy line spring model we find an approximate solution of the problem of elastic balance of a closed infinite circular cylindrical shell weakened by a periodic system of longitudinal interior cracks of identical length. The stress intensity factors are found at the center of a crack for various numbers of cracks with various parameters. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Investigation of stress intensity factors near interacting cracks in linear viscoelastic plates

Stress intensity factors as a function of time near interacting cracks during creep in plates made of linear viscoelastic materials are investigated. The interaction of collinear as well as parallel cracks disposed on different levels perpendicular to the tensile stress was studied. It was found that during interaction of collinear cracks, the stress intensity factor K₁(t) grew in creep and varied mainly due to the change in the distance between the tips of interacting cracks. There was practically no increase in the length of the crack. During interaction of parallel cracks, the value of K₁(t) decreased slightly in time, which was also due to an increase in the distance between the tips of the cracks in creep.Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 643–650, September–October, 1998.     

On a method of studying the stress state of orthotropic shells and plates weakened by a hole with cracks extending to its edge

On the basis of the Timoshenko kinematic hypothesis for shells we give a formulation of the problem of studying the stress-strain state of orthotropic plates and shells weakened by a combined stress concentrator (a hole with two symmetric cracks extending to its edge). We propose a method of solving such problems on the basis of the finite-element method. To simulate the singularity of the stresses and displacements in a neighborhood of the tip of a crack we apply special finite elements with degenerate faces and nodes displaced by 1/4 the length of an edge. The stress intensity factors are found in terms of the displacements of the nodes of such elements. We give the results of computation of the concentration coefficients and the stress intensity factors for spherical and cylindrical shells loaded by internal pressure and for a cylindrical shell and a plate under the action of a distending load with various concentrators: a circular hole, an isolated crack, and a combined concentrator. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 48–54.     

A two-dimensional problem for an anisotropic body with a finite number of “tunnel” cracks

We give the results of studies of the stress state for an infinite anisotropic body with a number of planar cracks along a single plane. For the simplest types of load we prove that the stress intensity factors is independent of the type of anisotropy. We describe the results of numerical studies as functions of the geometric characteristics of the body. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 27–34     

Stress Intensity Factors near the Cracks on the Edges of Openings in Composite Plates

Based on the photoelasticity method, the behavior of stress intensity factors (SIFs) near cracks propagating from the edges of openings in plates made of elastic and linearly viscoelastic fibrous composite materials is studied. It is found that the relative value of the SIF, K ₁/K ₁ ⁰ (K ₁ ⁰=₀c), near the crack tips on the edges of openings in composite plates is a function of the ratio c/R, whose numerical values depend on the mechanical properties of materials of the plates. Using the quasi-elastic method for solving the viscoelastic problems, the effect of viscoelastic properties of the plate material on the value of K ₁/K ₁ ⁰ is estimated. It is shown that the values of the function K ₁(t)/>/K ₁ ⁰ near the cracks on the opening edges in plates made of linearly viscoelastic fibrous composites grow under creep.     

A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel element for modeling the singular stress state around the inclined interface crack which terminates at the interface is developed. This new singular element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed singular element is then applied in finite element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed singular element is independent of the element size and the SIFs of the crack can be solved directly without any post-processing.     

Deformation and strength of laminated quasiisotropic carbon-reinforced plastics

Conclusions The stress-strain state and strength of the quasiisotropic carbon-reinforced plastics depend strongly on the lay-up system of the adjacent plies because the magnitude of the interply stresses and their distribution greatly change when the reinforcement system is changed. The highest stress intensity is recorded at the free edge of the specimen. The magnitude of the residual thermal stresses is comparable with that of the mechanical stresses at the instant of formation of cracks in the weak plies of the composite. The first microcracks form inside the plies with the orientation 90 and ±45° in the direction of reinforcement. The IACs start to form at the free edges of the specimen and propagate into the material at strains from 12 to 39% of limiting strain _x ^l . Delamination of the laminated composite starts later than the formation of IACs (40–88% of _x ^l ) because the normal stress _x is higher than _z. The optimum lay-up system of the composite is [0/45/90/-45]_s because this system ensures higher stiffness of the material. The ±45 and 90° plies are not suitable for external surfaces of the composite since they start to crack very early. The quasiisotropic composites are less sensitive to the value of G_{2 3} than the composites with the ply lay-up [±]_s.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 449–454, May–June, 1985.     

Anti-plane analysis of an orthotropic strip weakened by several moving cracks

In this paper several finite cracks with constant length (Yoffe-type crack) propagating in an orthotropic strip were studied. The distributed dislocation technique is used to carry out stress analysis in an orthotropic strip containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in an orthotropic strip by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a strip weakened by moving cracks. Finally several examples are solved and the numerical results for the stress intensity factor are obtained. The influences of the geometric parameters, the thickness of the orthotropic strip, the crack size and speed have significant effects on the stress intensity factors of crack tips which are displayed graphically.     

Antiplane strain of a multiconnected anisotropic body with longitudinal cavities and plane cracks

Applying the theory of generalized complex potentials and the method of least squares, we solve the problem of the stressed state of a multiconnected anisotropic body under an antiplane strain. The problem is reduced to a system of linear algebraic equations in the unknown constants that occur in the required functions. By numerical studies we exhibit the influence of the elastic and geometric characteristics on the stress distribution and the variation of the stress intensity factors in a cylinder with one or two cracks and in an infinite body with circular cavities and cracks. One figure. Six tables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25. 1995, pp. 56–62.     

Model studies of stress-intensity factors near cracks interacting with fibers

The problem of determining the stress-intensity factors near cracks interacting with fibers is solved for the first time using data from optical-polarization measurements. Simplified models of composites are investigated — plates reinforced with single short fibers with cracks assigned on one of the ends of the fibers and tensioned in the direction of the fibers. The plates (dies) were fabricated from a photosensitive material, and the fibers were modeled by bars of steel, glass, and polymer. The stress-intensity factors were determined from Eq. (5) using data derived from optical-polarization measurements at several points by the nonlinear method of least squares. We investigated the influence exerted by several physical and geometric parameters on the stress-intensity factors. It was established that the stress-intensity factor K₁ near the end of a crack interacting with a fiber is higher than the factor K⁰ ₁ near a crack of corresponding length in the unreinforced plate. The ratio K₁/K⁰ ₁ depends on the mechanical properties of the fiber and die materials and the geometric dimensions of the crack and fiber. Despite the fact that these results were obtained using simplified models of composites, they are of interest for evaluation of the failure and serviceability of real composites.Scientific-Research Institute of Mechanics, M. V. Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 493–501.