Yasuhide Shindo

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.

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.

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.

Analysis and Testing of Indentation Fracture Behavior of Piezoelectric Ceramics Under an Electric Field

To estimate the electric fracture toughness, indentation fracture (IF) tests were made on piezoelectric materials under combined mechanical and electrical loads. Lead zirconate titanate (PZT) ceramics from a commercial source were used. A three-dimensional finite element analysis was also employed to calculate the energy release rate and stress intensity factor. Surface cracks produced by indentation with Vickers indented were modeled as two point-force loaded half-penny-shaped cracks.

Electroelastic analysis of a penny-shaped crack in a piezoelectric ceramic under mode I loading

Abstract Following the theory of linear piezoelectricity, we consider the electroelastic problem for a piezoelectric ceramic with a penny-shaped crack under mode I loading. The problem is formulated by means of Hankel transform and the solution is solved exactly. The stress intensity factor, energy release rate and energy density factor for the exact and impermeable crack models are expressed in closed form and compared for a P-7 piezoelectric ceramic. Based on current findings, we suggest that the energy release rate and energy density factor criteria for the exact crack model are superior to fracture criteria for the impermeable crack model.

Mode I crack growth rate for yield strip model of a narrow piezoelectric ceramic body

A crack growth rate equation is found for a finite crack in a narrow transversely isotropic piezoelectric ceramic body under tensile loading. Use is made of the yield strip model. The crack is situated in the mid-plane and is parallel to the edges of the body. Integral transforms are applied to reduce the problem to a Fredholm integral equation of the second kind. The accumulated plastic displacement criterion is applied to crack growth at low stress levels. This results in a small crack growth rate equation with fourth-power stress intensity factor dependence. Numerical examples are given for piezoelectric ceramics and the crack growth rates are plotted as a function of body height to crack length ratio for various values of the electrical loads.

Effect of interface layers on elastic wave propagation in a fiber-reinforced metal–matrix composite

This study considers the scattering of P and SV waves in SiC fiber-reinforced Al composite with interfacial layers. The fibers are assumed to be parallel to each other and randomly distributed with a statistically uniform distribution. We assume same-size fibers and same-thickness layers with nonhomogeneous elastic properties. The scattering of time harmonic P and SV waves by a cylindrical inclusion with a nonhomogeneous interface layer is analyzed and the results of the single scattering problem are applied to the composite medium. Numerical values of scattering cross-sections, phase velocities and attenuations of coherent plane waves, and effective in-plane elastic constants are obtained for a moderately wide range of frequencies. The numerical results show significant dependence on parameters containing fiber volume fraction and interface properties.

Singular stresses in a transversely isotropic circular cylinder with circumferential edge crack

Abstract This paper concerns the analysis of the singular stresses arising in a transversely isotropic infinite cylinder having a circumferential edge crack. The problem is reduced to that of solving a singular integral equation of the first kind which is solved numerically by the use of the way proposed by Erdogan, Gupta and Cook[1]. The singular stresses are expressed in closed form and the influence of transverse isotropy upon the stresses is clarified numerically for some practical materials.

Double torsion testing and finite element analysis for determining the electric fracture properties of piezoelectric ceramics

This paper presents the results of an experimental and numerical investigation in electric fracture behavior of composite [Pb(Zr,Ti)O3] double torsion (DT) specimens. DT tests were conducted on a commercial piezoelectric ceramic bonded between two metals. Fracture loads under different electric fields were obtained from the experiment. Nonlinear three-dimensional finite element analysis was also employed to calculate the energy release rate for DT specimens based on the exact (permeable) and approximate (impermeable) crack models. The effects of applied electric field and domain switching on the energy release rate are discussed, and the model predictions are compared with the results of the experiments.