Stresses Near the End of an Internal Electrode in Multilayer Electrostrictive Ceramic Actuators
- PDF / 358,465 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 89 Downloads / 175 Views
INTRODUCTION Recently, multilayer electrostrictive ceramic actuators, 1 ,2,3 capable of generating both large displacement and force, have been proposed due to their wide applications. To achieve better performance, individual layers are made thinner, usually on the order of several tens of microns, so that a higher electric field may be obtained for a given voltage. Due to technical limitations in forming the very fine insulator lines, the capacitor-type multilayer actuator structure is adopted as shown in Figure 1. However, this structure has a defect. It contains a electrostrictively inactive area in front of the internal electrodes. This causes distortion and concentration of the electric field, 4 thereby inducing incompatible strains which in turn produce stresses. It is suspected that the induced stresses are high enough to cause cracks which grow to fail the actuator 5 . Therefore it is necessary to predict the stress levels generated in the device precisely.
The attempt at solving the stresses caused by electrostriction was first made by Knops 6 in 1963. At the time, it was believed that the electric displacement, D, caused by the electric field, E, in electrostrictive material was the same as that in dielectric materials, meaning, D and E were linearly related to each other, i.e., D=eE, with e the electric permittivity. Thus the electrostrictive strains would be quadratic in the electric field. Knops verified the validity of ignoring the dependence of the electric field on the dielectric deformations for small strains, and suggested that the electric field could be determined from conditions of the undeformed body. Furthermore, he derived the field equations for the uncoupled problems. Based on this framework, some further theoretical and computational stress analyses in electrostrictive materials have been done. 1,4,7,8 However, questions arise concerning the above Internal assumptions. First, near the end of an internal electrode, the Electrode electric field is distorted and usually locally much higher than the applied electric field so that the D-E relationship of this kind of material, (e.g., PMN-PT), is no longer linear.9 ,10. 11 Second, such a highly distorted electric field causes incompatible strains which induce high stresses, meaning the electrical and mechanical coupling effects may no longer be neglected. These difficulties make it impossible for us to analytically solve the stresses caused by the electrostriction. External Thus a finite element program has to be developed to Electrode understand the details of the stresses. The following sections r Figure 1.Structure of a c:i discuss our attempts in developing the finite element program, type multilayer
and the results obtained. 83
Mat. Res. Soc. Symp. Proc. Vol. 360 01995 Materials Research Society
GOVERNING EQUATIONS When a material is subjected to a field of displacement, u, and electric potential, ý, the strain, y, and the electric field, E, can be derived from the gradients: -= I
(1)
Ei = -Oi
i~j + +iiuj),
Our attention is limit
Data Loading...
