An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized and the relations...An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized and the relations between energy release rate components and the stress intensity factors are given. Combining with the results of chasical plate theory analysis. a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived Then. an analytical solution for energy release rate components is deduced. In order to get energy release rate components under general loading condition. a mode mix parameter, Ω, must be determined separately. A methodology for determining Ω is discussed. Finally. several different kinds of laminates are examined and the results obtained could be used in engineering applications.展开更多
An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from ...An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.展开更多
The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed by using Stroh formula in anisotropic elasticity. It is shown from the solution that the ...The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity and electric displacement inside electrically permeable cracks are all constants.展开更多
Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-pla...Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.展开更多
Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the ...Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.展开更多
By using the method of stress functions, the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved. First, the crack problem of two-dimensional quasi-crystals was decomposed into a plane strain state...By using the method of stress functions, the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved. First, the crack problem of two-dimensional quasi-crystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly, by introducing stress functions, the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher- order partial differential equations. The solution of this equation under mixed boundary conditions of mode-Ⅱ Griffith crack was obtained in terms of Fourier transform and dual integral equations methods. All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.展开更多
This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initial...This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.展开更多
Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity f...Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity factor. a closed-form solution for complex. Stress intensity in terms of external loading and a mode mix parameter for fairly. general composite laminates is given. Then a procedure for determining this mode mix. parameter is presented. followed by numerical results for some laminates. Small scale contact condition is expressed in terms of external loading In particular, a symmetric property of interfacial toughness curye is proven. Finally. the accuracy of failure load predicled by elininating oscllation index is discussed. and an example is presented to show the validity and limitation of β=0 approximation.展开更多
In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, whi...In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.展开更多
The electrically permeable slit crack within a piezoelectric body is treated as a bonded interface in electrostatics. The electric boundary conditions along the interface should be the continuity of the tangent compon...The electrically permeable slit crack within a piezoelectric body is treated as a bonded interface in electrostatics. The electric boundary conditions along the interface should be the continuity of the tangent component of the electric field strength and the normal component of the electric displacement. Using such boundary conditions, the problems of antiplane strain of collinear cracks between bonded dissimilar piezoelectric materials are exactly analyzed. Solutions of the complex potentials in a closed form are given for a single and two interface cracks. It is shown from the solutions that the stress, strain, electric field strength and electric displacement have (1/2) type of singularity at the crack tip, and the energy release rate for crack propagation depends only on both stress intensity factor and strain intensity factor.展开更多
In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept o...In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.展开更多
A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed bo...A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of Gauss-Chebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. NumericM results reveal the effects of electric loadings and crack configuration on crack propagation and growth. The results seem useful for design of the piezoelectric structures and devices of high performance.展开更多
文摘An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized and the relations between energy release rate components and the stress intensity factors are given. Combining with the results of chasical plate theory analysis. a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived Then. an analytical solution for energy release rate components is deduced. In order to get energy release rate components under general loading condition. a mode mix parameter, Ω, must be determined separately. A methodology for determining Ω is discussed. Finally. several different kinds of laminates are examined and the results obtained could be used in engineering applications.
文摘An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.
文摘The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity and electric displacement inside electrically permeable cracks are all constants.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Scientific Research Key Program of Beijing Municipal Commission of Education (No.KZ201010005003)the Ph.D.Innovation Foundation of Beijing University of Aeronautics and Astronautics(No.300351)
文摘Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.
基金Project supported by the National Natural Science Foundation of China(Nos.10932001 and 11072015)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20101102110016)
文摘Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.
文摘By using the method of stress functions, the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved. First, the crack problem of two-dimensional quasi-crystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly, by introducing stress functions, the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher- order partial differential equations. The solution of this equation under mixed boundary conditions of mode-Ⅱ Griffith crack was obtained in terms of Fourier transform and dual integral equations methods. All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.
文摘This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.
文摘Classical plate theory has been used to find out interfacial stress intensity factors in composite laminates. By using a well-known relation between the crack-tip energy release rate and the complex stress intensity factor. a closed-form solution for complex. Stress intensity in terms of external loading and a mode mix parameter for fairly. general composite laminates is given. Then a procedure for determining this mode mix. parameter is presented. followed by numerical results for some laminates. Small scale contact condition is expressed in terms of external loading In particular, a symmetric property of interfacial toughness curye is proven. Finally. the accuracy of failure load predicled by elininating oscllation index is discussed. and an example is presented to show the validity and limitation of β=0 approximation.
基金Project supported by the National Natural Science Foundation of China (No. 10432030 and No. 10125209).
文摘In this paper the plane elasticity problem for a functionally graded strip containing a crack is considered. It is assumed that the reciprocal of the shear modulus is a linear function of the thickness-coordinate, while the Possion＇s ratio keeps constant. By utilizing the Fourier transformation technique and the transfer matrix method, the mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. The influences of the geometric parameters and the graded parameter on the stress intensity factors and the strain energy release rate are investigated. The numerical results show that the graded parameters, the thickness of the strip and the crack size have significant effects on the stress intensity factors and the strain energy release rate.
文摘The electrically permeable slit crack within a piezoelectric body is treated as a bonded interface in electrostatics. The electric boundary conditions along the interface should be the continuity of the tangent component of the electric field strength and the normal component of the electric displacement. Using such boundary conditions, the problems of antiplane strain of collinear cracks between bonded dissimilar piezoelectric materials are exactly analyzed. Solutions of the complex potentials in a closed form are given for a single and two interface cracks. It is shown from the solutions that the stress, strain, electric field strength and electric displacement have (1/2) type of singularity at the crack tip, and the energy release rate for crack propagation depends only on both stress intensity factor and strain intensity factor.
基金supported by the National Natural Science Foundation of China (Grant No. 11011140335)
文摘In this work, a novel numerical method is developed for simulating arbitrary crack growth in pipes with the idea of enriched shape functions which can represent the discontinuity independent of the mesh. The concept of the enriched shape functions is introduced into the continuum-based (CB) shell element. Due to the advantage of CB shell element, the shell thickness varia- tion and surface connection can be concerned during the deformation. The stress intensity factors of the crack in the CB shell element are calculated by using the 'equivalent domain integral' method for 3D arbitrary non-planar crack. The maximum en- ergy release rate is used as a propagation criterion. This method is proved able to capture arbitrary crack growth path in pipes which is independent of the element mesh. Numerical examples of different fracture patterns in pipes are presented here.
基金Project supported by the National Natural Science Foundation of China(Nos.11072160 and 11272223)the Natural Science Foundation of Hebei Province,China(E2013402077)
文摘A flat annular crack in a piezoelectric layer subjected to electroelastic loadings is investigated under electrically impermeable boundary condition on the crack surface. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. With the aid of Gauss-Chebyshev integration technique, the integral equations are further reduced to a system of algebraic equations. The field intensity factor and energy release rate are determined. NumericM results reveal the effects of electric loadings and crack configuration on crack propagation and growth. The results seem useful for design of the piezoelectric structures and devices of high performance.
