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
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
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
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.
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.
