Fumio Narita

Singular stress and electric fields of a piezoelectric ceramic strip with a finite crack under longitudinal shear

SummaryFollowing the theory of linear piezoelectricity, we consider the problem of determining the singular stress and electric fields in an orthotropic piezoelectric ceramic strip containing a Griffith crack under longitudinal shear. The crack is situated symmetrically and oriented in a direction parallel to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for piezoelectric ceramics are obtained, and the results are graphed to display the influence of the electric field.

Electroelastic analysis of a piezoelectric ceramic strip with a central crack

The theory of linear piezoelectricity is applied to solve the plane strain electroelastic problem of an orthotropic piezoelectric ceramic strip with a central crack, which is situated symmetrically and oriented in a direction normal to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. They are then reduced to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for some piezoelectric ceramics are obtained, and the results are graphed to display the electroelastic interactions.

Electroelastic intensification near anti-plane shear crack in orthotropic piezoelectric ceramic strip

Abstract The theory of linear piezoelectricity is applied to solve the antiplane electroelastic problem of an orthotropic piezoelectric ceramic strip with a finite crack, which is situated symmetrically and oriented in a direction normal to the edges of the strip. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. They are then reduced to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate for some piezoelectric ceramics are obtained and the results are displayed numerically to exhibit the electroelastic interactions.

Scattering of antiplane shear waves by a finite crack in piezoelectric laminates

SummaryFollowing the dynamic theory of linear piezoelectricity, we consider the scattering of horizontally polarized shear waves by a finite crack in a composite laminate containing a piezoelectric layer. The piezoelectric layer is bonded between two half-spaces of a different elastic solid. The crack is normal to the interfaces and is placed at an equal distance away from them. Both cases of a partially broken layer and a completely broken layer are studied. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a singular integral equation. The propagation of symmetric first mode is studied numerically, and the dynamic stress intensity factor and the dynamic energy release rate are obtained for some piezoelectric laminates.

Electroelastic analysis of piezoelectric ceramics with surface electrodes

Following the theory of liner piezoelectricity, we consider the static behavior of the elastic and electric variables in the vicinity of a surface electrode attached to a piezoelectric ceramic. Fourier transforms are used to reduce the mixed boundary value problem to the solution of a pair of dual integral equations. The integral equations are solved exactly and the displacement and electric potential are expressed in closed form.

Dynamic anti-plane shear of a cracked piezoelectric ceramic

The dynamic theory of antiplane piezoelectricity is applied to solve the problem of a line crack subjected to horizontally polarized shear waves in an arbitrary direction. The problem is formulated by means of integral transforms and reduced to the solution of a Fredholm integral equation of the second kind. The path-independent integral G is extended here to include piezoelectric effects, and is evaluated at the crack tip to obtain the dynamic energy release rate. Numerical calculations are carried out for the dynamic stress intensity factor and energy release rate. The material is piezoelectric ceramic.

Electric fracture and polarization switching properties of piezoelectric ceramic PZT studied by the modified small punch test

The fracture behavior of a piezoelectric ceramic under applied electric fields has been discussed through experimental and theoretical characterizations. The modified small punch (MSP) tests were performed on a commercial piezoelectric ceramic. The fracture initiation loads under different electric fields were obtained from the experiment. Fracture surface was examined for the MSP specimens to identify the failure mechanisms under high electric fields. A nonlinear three-dimensional finite element analysis was also employed to calculate the fracture deflection and MSP energy. A procedure is presented for determining the fracture and polarization switching properties due to electrical effects by experimental and theoretical means.

Impact response of a finite crack in an orthotropic piezoelectric ceramic

SummaryThe transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.

Comparison of energy release rate and energy density criteria for a piezoelectric layered composite with a crack normal to interface

A critical comparison of the energy release rate and energy density criteria is made using the example of a piezoelectric layer bonded between two half-spaces of a different elastic solid containing a crack normal to the interfaces. Numerical values of stress intensity factor, energy release rate and energy density factor are presented to exhibit electroelastic interactions. Considered are the exact (permeable) and impermeable crack models. The energy release rate criterion led to negative values which are unphysical. This is consistent with previously published results that seem to contradict with experimental observation related to crack growth enhancement and retardation. The energy density factor always remains positive. This shows that a knowledge of the stress intensity factors alone is not sufficient to explain the behavior of fracture in piezoelectric materials.

The interface crack problem for bonded piezoelectric and orthotropic layers under antiplane shear loading

The primary objective of this paper is to study the influence of the electroelastic interactions on the stress intensity factor in bonded layers of piezoelectric and orthotropic materials containing a crack along the interface under antiplane shear. Attention is given to a two-layer hybrid laminate formed by adding a layer of piezoelectric ceramic to a unidirectional graphite/epoxy composite or an aluminum layer. Electric displacement or electric field is prescribed on the surfaces of the piezoelectric layer. The problem is formulated in terms of a singular integral equation which is solved by using a relatively simple and efficient technique. A number of examples are given for various material combinations. The results show that the effect of the electroelastic interactions on the stress intensity factor and the energy release rate can be highly significant.