Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solv...Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.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
In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By...In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of displacements across the crack surfaces. In solving the triple integral equations, the unknown variable is expanded in a series of Jacobi polynomials. Numerical solutions are obtained. It is shown that the stress feld is independent of the electric feld and the magnetic fux.展开更多
In this paper, the interaction between two collinear cracks inpiezoelectric materials under anti-plane shear loading wasinvestigated for the impermeable crack face conditions. By using theFourier transform, the proble...In this paper, the interaction between two collinear cracks inpiezoelectric materials under anti-plane shear loading wasinvestigated for the impermeable crack face conditions. By using theFourier transform, the problem can be solved with two pairs of tripleintegral equations. These equations are solved using Schmidt'smethod. This process is quite different from that adopted previously.This makes it possible to understand the two collinear cracksinteraction in piezoelectric materials.展开更多
The singularities of collinear cracks both in anisotropic single medium and at the interface of anisotropic bimaterials are studied by combining Stroh formalism and the analytic function method. The formulae for calcu...The singularities of collinear cracks both in anisotropic single medium and at the interface of anisotropic bimaterials are studied by combining Stroh formalism and the analytic function method. The formulae for calculating the field potential and stress intensity factor (SIF) are obtained. It is found that the field potentials are explicitly related to material matrix L and the in-plane and anti-plane fields can be separately calculated when orthotropic bimaterials are considered.展开更多
In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane...In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.展开更多
Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cra...Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46（1）, 133-142 （1993）]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.展开更多
The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fou...The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. It can be obtained that the stress field is independent of the electric field and the magnetic flux.展开更多
The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping tec...The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. （1） When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. （2） The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 10761005)the Inner Mongolia Natural Science Foundation of China (Grant No 200607010104)
文摘Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.
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.
基金Project supported by the SRF for ROCS,SEM,the National Natural Science Foundation of Heilongjiang Province(No.A0301)and the Multidiscipline Scientifc Research Foundation of Harbin Institute of Technology(HIT.MD2001.39).
文摘In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of displacements across the crack surfaces. In solving the triple integral equations, the unknown variable is expanded in a series of Jacobi polynomials. Numerical solutions are obtained. It is shown that the stress feld is independent of the electric feld and the magnetic fux.
基金the Post-Doctoral Science Foundationthe Natural Science Foundation of Heilongjiang Province
文摘In this paper, the interaction between two collinear cracks inpiezoelectric materials under anti-plane shear loading wasinvestigated for the impermeable crack face conditions. By using theFourier transform, the problem can be solved with two pairs of tripleintegral equations. These equations are solved using Schmidt'smethod. This process is quite different from that adopted previously.This makes it possible to understand the two collinear cracksinteraction in piezoelectric materials.
文摘The singularities of collinear cracks both in anisotropic single medium and at the interface of anisotropic bimaterials are studied by combining Stroh formalism and the analytic function method. The formulae for calculating the field potential and stress intensity factor (SIF) are obtained. It is found that the field potentials are explicitly related to material matrix L and the in-plane and anti-plane fields can be separately calculated when orthotropic bimaterials are considered.
基金ministry of Human Resource Development for the financial support
文摘In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.
文摘Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46（1）, 133-142 （1993）]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.
文摘The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. It can be obtained that the stress field is independent of the electric field and the magnetic flux.
基金Project supported by the Postdoctoral Science Foundation of China (No.20070410944)
文摘The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. （1） When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. （2） The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.
