Dielectric response of spherically anisotropic graded piezoelectric composites

A graded piezoelectric composite consisting of a spherically anisotropic graded piezoelectric inclusion imbedded in an infinite nonpiezoelectric matrix, with the physical properties of the graded spherical inclusion having a power-law profile with respect to the radial variable r, is studied theoretically. Under an external uniform electric field, the electric displacement field and the elastic stress tensor field of this spherically anisotropic graded piezoelectric composite are derived exactly by means of displacement separation technique, based on the governing equations in the dilute limit. A piezoelectric response mechanism, in which the effective piezoelectric response vanishes along the z direction (or x,y directions), is revealed in this kind of graded piezoelectric composites. Furthermore, it is found that the effective dielectric constant decreases (or increases) with the volume fraction p of the inclusions if the exponent parameter k of the grading profile is larger (or smaller) than a critical value. (C) 2007 American Institute of Physics.

Effective elastic properties of piezoelectric composites with radially polarized cylinders

Effective elastic properties of piezoelectric composites containing an infinitely long, radially polarized cylinder embedded in an isotropic non-piezoelectric matrix are theoretically investigated under an external strain field. Analytical solutions of elastic displacement and electric potentials are exactly derived, and the effective elastic responses are formulated in the dilute limit. Meanwhile, a vanishing piezoelectric response mechanism is revealed in the piezoelectric composite containing radially polarized cylinders. Furthermore, it is shown that the effective elastic properties can be enhanced (or reduced) due to the increase of the piezoelectric (or dielectric) constants of the cylinders. (C) 2009 Elsevier B.V. All rights reserved.

Effective properties of spherically anisotropic piezoelectric composites

Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions (i.e., piezoceramic material) in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease (increase) as the inclusion elastic (piezoelectric) constants increase.

Noninterferometric measurement of lead zirconate titanate inverse piezoelectric extension

A noncontacting and noninterferometric depth discrimination technique, which is based on differential confocal microscopy, was used to measure the inverse piezoelectric extension of a piezoelectric ceramic lead zirconate titanate actuator. The response characteristics of the actuator with respect to the applied voltage, including displacement, linearity, and hysteresis, were obtained with nanometer measurement accuracy. Errors of the measurement have been analyzed. (C) 2001 Society of Photo-Optical Instrumentation Engineers.

Abnormal ferroelectric response and enhancement of piezoelectricity of PbTiO3 under uniaxial compression

The ferroelectricity of rhombohedral PbTiO3 under uniaxial compression is investigated from first-principles study. Upon compression, the ferroelectricity decreases until a critical stress of -29 GPa and then increases with a further increase of the magnitude of the uniaxial compressive stress. We also find that uniaxial compression could enhance piezoelectricity and that the maximum piezoelectric coefficient d(33) occurs at sigma(33)=-49 GPa, which supports the experimentally observed piezoelectric behavior in rhombohedral Pb(Mg1/3Nb2/3O3)-0.32PbTiO(3) [Q. Wan, C. Chen, and Y. P. Shen, J. Appl. Phys. 98, 024103 (2005)]. Our calculated results show that the Pb, Ti, and O atoms have different contributions to the total polarization with increasing the magnitude of uniaxial compressive stress, and that when -sigma(33)>55 GPa, the Ti atoms no longer have contributions to the polarization, which leads to the changes of ferroelectricity and piezoelectricity. (C) 2008 American Institute of Physics.

Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D-2, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D-2 is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D-2 is also constant along the crack faces and the electric field E-2 has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates.

An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites

A three-phase piezoelectric cylinder model is proposed and an exact solution is obtained for the model under a farfield antiplane mechanical load and a far-field inplane electrical load. The three-phase model can serve as a fiber/interphase layer/matrix model, in terms of which a lot of interesting mechanical and electrical coupling phenomena induced by the interphase layer are revealed. It is found that much more serious stress and electrical field concentrations occur in the model with the interphase layer than those without any interphase layer. The three-phase model can also serve as a fiber/matrix/composite model, in terms of which a generalized self-consistent approach is developed for predicting the effective electroelastic moduli of piezoelectric composites. Numerical examples are given and discussed in detail.

Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading

The material response and failure mechanism of unidirectional metal matrix composite under impulsive shear loading are investigated in this paper. Both experimental and analytical studies were performed. The shear strength of unidirectional C-f/A356.0 composite and A356.0 aluminum alloy at high strain rate were measured with a modified split Hopkinson torsional bar technique. The results indicated that the carbon fibers did not improve the shear strength of aluminum matrix if the fiber orientation aligned with the shear loading axis. The microscopic inspection of the fractured surface showed a multi-scale zigzag feature which implied a complicated shear failure mechanism in the composite. In addition to testing, the micromechanical stress field in the composite was analyzed by the generalized Eshelby equivalent method (GEEM). The influence of cracking in matrix on the micromechanical stress field was investigated as well. The results showed that the stress distribution in the composite is quite nonhomogeneous and very high shear stress concentrations are found in some regions in the matrix. The high shear stress concentration in the matrix induces tensile cracking at 45 degrees to the shear direction. This in turn aggravates the stress concentration at the fiber/matrix interface and finally leads to a catastrophic failure in the composite. From the correlation between the analysis and experimental results, the shear failure mechanism of unidirectional C-f/A356.0 composite can be elucidated qualitatively.

Increasing Critical Sensitivity of the Load/Unload Response Ratio before Large Earthquakes with Identified Stress Acclumulation Pattern

The Load/Unload Response Ratio (LURR) method is proposed for short-to-intermediate-term earthquake prediction [Yin, X.C., Chen, X.Z., Song, Z.P., Yin, C., 1995. A New Approach to Earthquake Prediction — The Load/Unload Response Ratio (LURR) Theory, Pure Appl. Geophys., 145, 701–715]. This method is based on measuring the ratio between Benioff strains released during the time periods of loading and unloading, corresponding to the Coulomb Failure Stress change induced by Earth tides on optimally oriented faults. According to the method, the LURR time series usually climb to an anomalously high peak prior to occurrence of a large earthquake. Previous studies have indicated that the size of critical seismogenic region selected for LURR measurements has great influence on the evaluation of LURR. In this study, we replace the circular region usually adopted in LURR practice with an area within which the tectonic stress change would mostly affect the Coulomb stress on a potential seismogenic fault of a future event. The Coulomb stress change before a hypothetical earthquake is calculated based on a simple back-slip dislocation model of the event. This new algorithm, by combining the LURR method with our choice of identified area with increased Coulomb stress, is devised to improve the sensitivity of LURR to measure criticality of stress accumulation before a large earthquake. Retrospective tests of this algorithm on four large earthquakes occurred in California over the last two decades show remarkable enhancement of the LURR precursory anomalies. For some strong events of lesser magnitudes occurred in the same neighborhoods and during the same time periods, significant anomalies are found if circular areas are used, and are not found if increased Coulomb stress areas are used for LURR data selection. The unique feature of this algorithm may provide stronger constraints on forecasts of the size and location of future large events.

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).

Comparison of the Dynamic Response of a Saturated Soil Between Two Models

By comparing the dynamic responses of saturated soil to Biot's and Yamamoto's models, the properties of the two models have be pointed out. First of all, an analysis has been made for energy loss of each model from the basic equations. Then the damping of elastic waves in coarse sand and fine sand with loading frequency and soil's parameters have been calculated and the representation of viscous friction and Coulomb friction in the two models has been concluded. Finally, the variations of loading wave damping and stress phase angles with water depth and soil's parameters have been obtained as loading waves range in ocean waves.

Saturated duration for dynamic structural plastic response and fundamental periods of elastic vibration

The relationship is determined between saturated duration of rectangular pressure pulses applied to rigid, perfectly plastic structures and their fundamental periods of elastic vibration. It is shown that the ratio between the saturated duration and the fundamental period of elastic vibration of a structure is dependent upon two factors: the first one is the slenderness or thinness ratio of the structure; and the second one is the square root of ratio between the Young's elastic modulus and the yield stress of the structural material. Dimensional analysis shows that the aforementioned ratio is one of the basic similarity parameters for elastic-plastic modeling under dynamic loading.

Generalization of Response Number for Dynamic Plastic Response of Shells Subjected to impulsive Loading

A dimensionless number, termed as response number in Zhao [Archive of Applied Mechanics 68 (1998) 524], has been suggested for the dynamic plastic response of beams and plates made up of rigidly perfect plastic materials subjected to dynamic loading. Many theoretical and experimental results can be reformulated into new concise forms with the response number. The concept of a new dimensionless number, response number, termed as Rn(n), is generalized in Zhao [Forschung im Ingenieurwesen 65 (1999) 107] to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. The response number Rn(n) is generalized to the dynamic behaviour of shells of various shapes in the present paper.

Experimental Validation of Improving Aircraft Rolling Power Using Piezoelectric Actuators

Piezoelectric actuators are mounted on both sides of a rectangular wing model. Possibility of the improvement of aircraft rolling power is investigated. All experiment projects, including designing the wind tunnel model, checking the material constants, measuring the natural frequencies and checking the effects of actuators, guarantee the correctness and precision of the finite element model. The wind tunnel experiment results show that the calculations coincide with the experiments. The feasibility of fictitious control surface is validated.