Sei Ueda

THERMALLY INDUCED FRACTURE OF A PIEZOELECTRIC LAMINATE WITH A CRACK NORMAL TO INTERFACES

The thermally induced fracture problem for a piezoelectric laminate having a crack under uniform electric and temperature fields is considered. The crack is oriented normal to the interfaces of the laminate. For the case of a crack that ends at the interface between the piezoelectric layer and the elastic layer, the order of the stress singularity around the tip of the crack is obtained. The Fourier transform technique is used to formulate the problem in terms of a singular integral equation. The singular integral equation is solved using the Gauss-Jacobi integration formula. Numerical calculations are carried out, and the main results presented are the variation of the the energy density factors as functions of the geometric parameters and the electrical boundary conditions of the layered composites.

The Crack Problem in Piezoelectric Strip Under Thermoelectric Loading

This paper investigates the thermoelectromechanical fracture behavior of a parallel crack in a piezoelectric strip under thermoelectric loading. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Numerical calculations are carried out, and the energy density factor as well as the stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the size and the location of the crack and the magnitude of the electric loading.

Transient Response of a Cracked Piezoelectric Strip Under Thermoelectric Loading

In this study, the theoretical analysis of a transient piezothermoelastic problem is developed for a piezoelectric strip with a parallel crack under static electric loading and thermal shock loading conditions. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Some numerical results for the temperature change, the stress and electric displacement distributions, and the energy density factor as well as the stress and electric displacement intensity factors in a transient state are shown in figures.

Numerical investigation on ferroelectric properties of piezoelectric materials using a crystallographic homogenization method

Polycrystalline piezoelectric materials are aggregations of crystal grains and domains with uneven forms and orientations. Therefore, the macroscopic ferroelectric property should be characterized by introducing a microscopic inhomogeneity in the crystal morphology. In this study, a multi-scale finite element modelling procedure based on a crystallographic homogenization method has been proposed for describing a macroscopic property of polycrystalline ferroelectrics with consideration of the crystal morphology at a microscopic scale. The proposed procedure has been applied to two kinds of piezoelectric materials, BaTiO3 and PbTiO3 polycrystals; the influence of microscopic crystal orientations on macroscopic ferroelectric properties was verified numerically. From the computational results, it has been shown that piezoelectric constants of polycrystalline ferroelectrics can be maximized by design of microscopic crystal morphology.

Thermal Intensity Factors for a Parallel Crack in a Functionally Graded Piezoelectric Strip

In this paper, the mixed-mode thermoelectromechanical fracture problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the thermoelectroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under the thermoelectric loadings. The crack faces are supposed to be insulated thermally and electrically. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.

Thermal Stress Intensity Factors for a Normal Crack in a Piezoelectric Material Strip

This paper investigates the electromechanical fracture behavior of a normal crack in a piezoelectric material strip subjected to a uniform heat flow far away from the crack region. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to singular integral equations, respectively, which are solved numerically. Both the cases of an internal crack and an edge crack are studied. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the crack location and length on the temperature distribution and the stress intensity factors.

Effects of Crack Surface Conductance on Intensity Factors for a Functionally Graded Piezoelectric Material Under Thermal Load

Effects of crack surface conductance on intensity factors for a functionally graded piezoelectric material under thermal load are investigated. The heat flux through the crack is assumed to be proportional to the local temperature difference. Moreover, two models for more realistic crack face electric boundary conditions are proposed. By using the Fourier transform, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations, respectively, which are solved numerically. Detailed results are presented to illustrate the influence of the thermal and electric conductance on the stress and electric displacement intensity factors.

Transient Thermoelectromechanical Response of a Piezoelectric Strip with Two Parallel Cracks of Different Lengths

This work is concerned with the thermoelectromechanical fracture behavior of two parallel cracks of different lengths in a piezoelectric material strip under thermal shock loading. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to two systems of singular integral equations, respectively, which are solved numerically. A numerical method is employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors versus time for various geometric parameters are calculated and presented in graphical forms. Temperature change, the stress and electric displacement distributions in a transient state are also included.

Transient dynamic response of a coated piezoelectric strip with a vertical crack

Abstract In this study, the dynamic response of a coated piezoelectric strip containing a crack vertical to the interfaces under normal impact load is considered. Based on the superposition principle and the integral transform techniques, the solution in the Laplace transformed plane is obtained in terms of a singular integral equation. The order of stress singularity around the tip of the terminated crack is also obtained. The singular integral equation is solved by using the Gauss–Jacobi integration formula, and the numerical Laplace inversion is then carried out to obtain the resulting dynamic stress and electric displacement intensities. The effects of the material properties and the geometric parameters on the dynamic stress intensity factor and the dynamic energy density factors are shown graphically.

Thermoelectromechanical Response of a Center Crack in a Symmetrical Functionally Graded Piezoelectric Strip

The thermoelectromechanical fracture problem for a symmetrical functionally graded piezoelectric strip containing a center crack parallel to the free boundaries is considered in this study. It is assumed that the thermoelectroelastic properties of the medium vary continuously in the thickness direction, and that the strip is under thermomechanical loadings. The crack faces are supposed to be insulated thermally and electrically. By using the Fourier transform, the thermal and electromechanical problems are reduced to singular integral equations, respectively, which are solved numerically. Numerical calculations are carried out, and detailed results are presented to illustrate the influence of the crack length and the material nonhomogeneity on the temperature-stress distributions and the stress intensity factor.