Cun-Fa Gao

A general solution for the plane problem in piezoelectric media with collinear cracks

Abstract The plane problem in a transversely isotropic piezoelectric medium with collinear cracks is studied, based on the exact electric boundary conditions on the crack faces. The complex potential method is used to reduce the problem to a Remmain–Hilbert problem. Explicit, closed-form solutions are obtained both in the piezoelectric medium and inside the cracks, when the medium is subjected to concentrated loads at an arbitrary point and uniform loads at infinity. It is shown in the case of uniform loads, that the stress intensity factors are the same as those in isotropic media, while the electric displacement intensity factor depends on material constants and the applied mechanical load, but not on the applied electric load. In other words, the uniform electric load has no influence on the field singularities.

Thermoelectroelastic Solution for Edge Cracks Originating from an Elliptical Hole in a Piezoelectric Solid

Thermoelectroelastic solution is derived for the generalized two-dimensional problem of edge cracks originating from an elliptical hole in a piezoelectric solid based on complex variable method. First, the heat complex function is solved, and then the expressions for the complex potentials and field intensity factors are presented under the electrically impermeable boundary condition. Numerical analysis is also made to discuss the influences of crack length and heat flux on the electroelastic fields and fields intensity factors. It is found that the heat flux has great effect on the stress intensity factors for the mode II cracks, but its influence on the stress intensity factors for the mode I cracks and the intensity factors of electric displacements is not significant.

Non-Axisymmetric Thermal Stress Around a Circular Hole in a Functionally Graded Infinite Plate

This paper presents the non-axisymmetric two-dimensional problem of thermal stresses in a functionally graded plate with a circular hole based on complex variable method. With using the method of piece-wise homogeneous layers, the general solution for the plate having radial arbitrary elastic properties is derived when it is subjected to uniform heat flux at infinity, and then numerical results are presented for several special examples. It is found that the stress around the circular hole in the functionally graded material plate can be effectively reduced by choosing the proper change ways of the radial elastic properties.

Evolutions of stress and microstructure in multilayer ferroelectric actuators under different temperature environments

ABSTRACT The multilayer ferroelectric actuator (MFA) with electrodes is an important smart structure and it has found wide application in engineering. Under the applied electric–elastic loads, the local stress concentration will be intensified near the tips of electrodes, and it finally may lead to the failure of the MFA. On the other hand, the temperature-dependent behavior of ferroelectrics results in the novel evolutions of local stresses and microstructure in the MFA under different temperature environments. In this work, the different temperature-induced nonlinear behavior and electroelastic field concentration around the electrode tip in the MFA is studied based on a phase-field approach containing the time-dependent Ginzburg–Landau equation. Using three-dimensional nonlinear finite element method, the temperature-induced domain switching behavior of the MFA and the evolution of the local stress near the electrode tips are simulated under different loadings and temperatures. It is found that the maximum tensile stress ahead of the electrode tip increases as the temperature increases from room temperature to a critical temperature. However, over the critical temperature, the stress decreases significantly due to the ferroelectric–paraelectric phase transition, which implies that by optimizing the environmental temperature, the local stress concentrations can be controlled.

Thermal Green's Functions for a Heat Source in a Piezoelectric Solid with a Parabolic Boundary

Using the Stroh formalism combined with the analytical continuation principle of Muskhelishvili, the Greens functions for a line heat source in a piezoelectric solid with a parabolic boundary are obtained in closed form. The obtained Greens functions not only satisfy all the given boundary conditions, but also ensure the displacement and electric potential to be single-valued. As special cases, the solutions for a piezoelectric half-plane are also presented, and they are shown to be consistent with previous works.

Analysis of Thermal Stress in a Functionally Graded Coating on a Parabolic Substrate

The thermal stress field in a functionally graded coating on a parabolic substrate, where the material properties vary along the thickness direction, is considered. The closed-form solutions of thermal stresses related to compositional gradient, coating thickness and substrate curvature were obtained based on force and moment balances, and then numerical results are presented for several special examples. It is found that the magnitude and distribution of thermal stress in the functionally graded coating system with general geometrical shape can be designed properly by controlling the compositional gradient, coating thickness and substrate curvature.

Collinear crack problems in a soft ferromagnetic solid

The 2D problems of a soft ferromagnetic solid with collinear cracks are studied based on the complex variable method. First, the general solutions for potential functions of magnetic fields and stress fields are derived by using magnetically permeable, impermeable and conducting crack models, respectively. Then, for special cases of one and two cracks, more explicit solutions are given for potential functions and intensity factors of total stresses. Finally, numerical results are presented to discuss the effects of applied magnetic loading on fracture behavior of the ferromagnetic solid. It is found that the total stresses always have the classical singularity of the r −1/2 type at the crack tips for the considered three crack models, and the applied magnetic loading may either enhance or retard crack growth depending on the adopted crack models.