移动接触下求解二维闭合裂纹的双重迭代边界元法

使用子域边界元法对受移动接触弹性体作用下的二维闭合裂纹问题进行了数值计算。由于两弹性体的接触界面和裂纹表面的接触范围的大小和接触状态事先是未知的 ,对此 ,在两个接触表面同时采用迭代的方法进行了求解。在裂纹的每个裂尖上都采用了四分之一的奇异单元以保证裂尖位移场和应力场奇异性的满足。用我们编制的二维裂纹问题程序对一些中心裂纹问题进行了计算 ,计算结果与经典断裂力学的理论值比较吻合。在无摩擦的条件下 ,对一些具有不同角度且受移动接触弹性体作用下的闭合裂纹问题进行了数值计算 ,得到了一些耦合作用下的应力强度因子的计算结果     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

The Stress State of a Transversely Isotropic Ferromagnetic with a Parabolic Crack in a Homogeneous Magnetic Field

The magnetoelastic problem for a transversely isotropic ferromagnetic body with a parabolic crack in the plane of isotropy is solved explicitly. The body is in an external magnetic field, which is perpendicular to the plane of isotropy. The field induces elastic strains and a magnetic field in the body. The characteristics of the stress–strain distribution and induced magnetic field are determined; and their singularities in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

Elliptic cavity in a three-dimensional anisotropic body with inclined strata deformed by line loads and dislocations

Summary Analytical solutions are proposed for the stress and displacement fields in a quasi three-dimensional elastic anisotropic body containing an elliptic cavity or rigid inclusion. The directions of the principal elastic axes are allowed to be inclined arbitrarily with respect to the axes of the elliptic cavity. As an application, expressions for the stress intensity factors are formulated when the cavity reduces to a colinear crack.     

On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

含微裂纹弹性体的应力应变关系

本义建立了考虑裂纹闭合和裂纹表面摩擦影响的含微裂纹弹性体的应力应变关系，给出了柔度张量增量的显式表达式。对于二维平面应力和平面应变状态，给出了等效工程弹性系数。数值计算结果表明，裂纹闭合和裂纹面摩擦对裂纹体的应力应变关系和等效工程弹性系数有重要影响。     

含微裂纹弹性体的应力应变关系

本义建立了考虑裂纹闭合和裂纹表面摩擦影响的含微裂纹弹性体的应力应变关系，给出了柔度张量增量的显式表达式。对于二维平面应力和平面应变状态，给出了等效工程弹性系数。数值计算结果表明，裂纹闭合和裂纹面摩擦对裂纹体的应力应变关系和等效工程弹性系数有重要影响。     

Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack

The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations of the crack __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008.     

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006.     

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.     

用压电材料进行损伤鉴别的理论与数值分析

对压电材料用于损伤监测的理论和数值分析做了一些研究。首先,设计了一种用压电材料进行损伤监测的模型。然后,对这个模型进行分析,找出简单有效的解答办法,将求解过程分解为断裂力学分析和压电分析两部分,并通过适当的假设,进行了详细的理论推导。通过正电有限元程序进行仿真计算,将数值计算结果与理论解进行比较以验证提出理论的正确性,并分析得到了裂纹参数与压电层表面电势变化之间的关系和普通弹性材料泊松比对波峰参数的影响。最后,用提出的方法验算了两个例题。从结果来看,理论结果和数值结果非常接近。     

THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

The dynamic stress intensity factor history for a half plane crack in anotherwise unbounded elastic body,with the crack faces subjected to a tractiondistribution consisting of two pairs of combined mode point loads that move in adirection perpendicular to the crack edge is considered.The analytic expression for thecombined mode stress intensity factors as a function of time for any point along thecrack edge is obtained.The method of solution is based on the application of integraltransform together with the Wiener-Hopf technique and the Cagniard-de Hoop method.Some features of the solution are discussed and graphical results for various point loadspeeds are presented.     

Concentrated impact loading on one face of a semi-infinite crack in an anisotropic elastic material

The response of an unbounded anisotropic elastic body containing a semi-infinite crack subjected to a concentrated impact force on one of the crack faces is studied. An exact solution of the dynamic stress intensity factors is obtained from a linear superposition of the solution of Lamb’s problem and a solution of a dislocation emitting from the crack tip. The stress intensity factors exhibit square-root singularity upon the arrival of the Rayleigh wave at the crack tip. As the Rayleigh wave passes through the crack tip, the stress intensity factors either instantaneously assume the static values or gradually approach to zero. Several numerical examples are given for isotropic, cubic and orthotropic materials.     

The stress intensity factor history due to three-dimensional transient loading on the faces of a crack

Aprocedure is described for determining dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to tractions that result in variation of the stress intensity factor along the crack edge. The procedure is based on integral transform methods and the properties of analytic functions of a complex variable. The procedure is illustrated for the case of a pair of opposed line loads suddenly applied on the crack faces along a line perpendicular to the crack edge. An exact expression is obtained for the resulting mode I stress intensity factor as a function of time for any point along the crack edge. Some features of the solution, as well as possible extensions of the procedure, are discussed.     

Study for 2D moving contact elastic body with closed crack using BEM

Using a sub-regional boundary element method, an algorithm for the two-dimensional elastic bodies with a closed crack loaded by a moving contact elastic body is proposed. Since the extent and status of the contact surface of two elastic bodies and the crack within the body are all not known in advance, a double iterative contact algorithm is used. The BEM program for solving the closed crack problems is developed, some numerical examples are calculated, and the results of the center crack cases are shown to be in good agreement with the analytical solution in the classical fracture mechanics. In the condition of friction and non-friction, some coupling computational results of the SIF for the closed crack, with different angles and loaded by a moving contact elastic body, are also obtained by a numerical computation. The project supported by the National Natural Science Foundation of China (10172053) and NJTU Foundation of China (PD-157)     

The weight function for cracks in piezoelectrics

The weight function in fracture mechanics is the stress intensity factor at the tip of a crack in an elastic material due to a point load at an arbitrary location in the body containing the crack. For a piezoelectric material, this definition is extended to include the effect of point charges and the presence of an electric displacement intensity factor at the tip of the crack. Thus, the weight function permits the calculation of the crack tip intensity factors for an arbitrary distribution of applied loads and imposed electric charges. In this paper, the weight function for calculating the stress and electric displacement intensity factors for cracks in piezoelectric materials is formulated from Maxwell relationships among the energy release rate, the physical displacements and the electric potential as dependent variables and the applied loads and electric charges as independent variables. These Maxwell relationships arise as a result of an electric enthalpy for the body that can be formulated in terms of the applied loads and imposed electric charges. An electric enthalpy for a body containing an electrically impermeable crack can then be stated that accounts for the presence of loads and charges for a problem that has been solved previously plus the loads and charges associated with an unsolved problem for which the stress and electric displacement intensity factors are to be found. Differentiation of the electric enthalpy twice with respect to the applied loads (or imposed charges) and with respect to the crack length gives rise to Maxwell relationships for the derivative of the crack tip energy release rate with respect to the applied loads (or imposed charges) of the unsolved problem equal to the derivative of the physical displacements (or the electric potential) of the solved problem with respect to the crack length. The Irwin relationship for the crack tip energy release rate in terms of the crack tip intensity factors then allows the intensity factors for the unsolved problem to be formulated, thereby giving the desired weight function. The results are used to derive the weight function for an electrically impermeable Griffith crack in an infinite piezoelectric body, thereby giving the stress intensity factors and the electric displacement intensity factor due to a point load and a point charge anywhere in an infinite piezoelectric body. The use of the weight function to compute the electric displacement factor for an electrically permeable crack is then presented. Explicit results based on a previous analysis are given for a Griffith crack in an infinite body of PZT-5H poled orthogonally to the crack surfaces.     

Interaction between curved crack and elastic inclusion in an infinite plate

Summary In this paper, the curved-crack problem for an infinite plate containing an elastic inclusion is considered. A fundamental solution is proposed, which corresponds to the stress field caused by a point dislocation in an infinite plate containing an elastic inclusion. By placing the distributed dislocation along the prospective site of the crack, and by using the resultant force function as the right-hand term in the equation, a weaker singular integral equation is obtainable. The equation is solved numerically, and the stress intensity factors at the crack tips are evaluated. Interaction between the curved crack and the elastic inclusion is analyzed. Received 8 October 1996; accepted for publication 27 March 1997     

A half plane crack under three-dimensional combined mode impact loading

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is considered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented. The project supported by the National Natural Science Foundation of China