Contact Zone Approach for an Electrically Impermeable Crack in Piezoelectric Materials Under Thermal-Mechanical Loading

2012 ◽  
Vol 35 (9) ◽  
pp. 749-765 ◽  
Author(s):  
A. B. Zhang ◽  
B. L. Wang
Keyword(s):  
Contact Zone ◽  
Mechanical Loading ◽  
Piezoelectric Materials ◽  
Impermeable Crack

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

Impermeable Crack and Permeable Crack Assumptions, Which One is More Realistic?

2004 ◽  
Vol 71 (4) ◽  
pp. 575-578 ◽  
Author(s):  
Bao-Lin Wang ◽  
Yiu-Wing Mai
Keyword(s):  
Boundary Condition ◽  
Piezoelectric Materials ◽  
Finite Width ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Electrical Boundary Conditions ◽  
Engineering Problems ◽  
Electrical Boundary Condition ◽  
Crack Faces ◽  
Impermeable Boundary

This paper investigates the applicability and effect of the crack-free electrical boundary conditions in piezoelectric fracture. By treating flaws in a medium as notches with a finite width, the results from different electrical boundary condition assumptions on the crack faces are compared. It is found that the electrically impermeable boundary is a reasonable one for engineering problems. Unless the flaw interior is filled with conductive media, the permeable crack assumption may not be directly applied to the fracture of piezoelectric materials in engineering applications.

Influence of Geometric Features and Material Orientation in Piezoelectric Ceramic Materials

Aerospace ◽  
2005 ◽  
Author(s):  
Virginia G. DeGiorgi ◽  
Stephanie A. Wimmer
Keyword(s):  
Mechanical Loading ◽  
Material Property ◽  
Computational Study ◽  
Piezoelectric Materials ◽  
Tensile Specimen ◽  
Geometric Features ◽  
Electrical Loading ◽  
Loading Direction ◽  
Material Orientation ◽  
Multiple Loading

Orientation between loading and material property directions is a concern for both polycrystalline and single crystal piezoelectric materials. The design of devices fabricated from piezoelectric materials emphasizes alignment between principal actuation direction and a specific coupling coefficient direction. However, loading and actuation directions may not always be aligned. Complex component geometry, multiple loading types, multiple loading paths and fabrication tolerances may result in misalignment between mechanical loading direction, principal actuation direction, electrical loading direction and material property orientation. In this work a computational study is presented that examines the effects of off-axis loading as well as geometric features for piezoelectric ceramics. An ASTM dog-bone shaped tensile specimen is modified by the addition of cut-out features to provide geometry stress concentrations at various angles to the primary mechanical loading direction. Polycrystalline PZT-5A material properties are used. Mechanical loading is applied as in a standard tensile strength test. Electrical loading direction is aligned with the mechanical loading direction. The tensile specimen is also subjected to sequential mechanical and electrical loadings. In the initial condition the d33 axis is aligned with the mechanical loading direction of the tensile specimen. Additional runs are made after rotating the material axes away from the principal mechanical loading axes of the tensile specimen. Stress patterns and location of maximum stress levels, indicating initial failure sites, are discussed in terms of the complex relationship between geometric features, material orientation and loading condition.

Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material

2006 ◽  
Vol 74 (5) ◽  
pp. 833-844 ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Interface Crack ◽  
Hilbert Problem ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Variable Theory ◽  
Impermeable Crack ◽  
Silicon Oil

A semi-permeable interface crack in dissimilar piezoelectric materials is studied in detail. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and the crack tip energy release rate (ERR). The Stroh complex variable theory (Stroh, A. N., 1958, Philos. Mag. 3, pp. 625–646;Ting, T. C. T., Int. J. Solids Struct., 22, pp. 965–983) is used to obtain the solution, from which some useful numerical results for 21 kinds of dissimilar piezoelectric materials are calculated. They are combined from seven kinds of commercial piezoelectric ceramics. The distribution of the normal electric displacement component (NEDC) along the interface crack is assumed to be uniform and the corresponding problem is then deduced to a Hilbert problem with an unknown NEDC. Solving the Hilbert problem and determining the near-tip field for each of the 21 bimaterials, we determine the crack tip singularities and find that the crack-tip singularity for a certain combination of two dissimilar piezoelectric materials can be either oscillatory or nonoscillatory when the poling axes of both piezoelectric materials are perpendicular to the interface crack. Energy analyses for PZT‐4∕BaTiO3 as a typical nonoscillatory class bimaterial and those for PZT-5H∕BaTiO3 as a typical oscillatory class bimaterial are specially studied in detail under four different conditions: (i) the crack gap is filled with air or vacuum; (ii) the crack gap is filled with silicon oil to avoid discharge; (iii) the crack gap is conducting; and (iv) the electrically impermeable crack. Detailed comparisons are performed among the four cases. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR under the combined electromechanical loading. We also conclude that the previous investigations under the insulating crack model are incorrect or misleading since the model overestimates the effect of the electric field on the ERR very much and the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack. Whereas the previous investigations under the conducting crack model may be accepted in a tolerant, way, the results of the ERR show very small discrepancies from those for the semi-permeable crack model, especially when it filled with silicon oil.

Stress Analysis of Wiresaw Slicing Piezoelectric Materials

2000 ◽  
Author(s):  
Fuqian Yang
Keyword(s):  
Electric Field ◽  
Contact Mechanics ◽  
Mechanical Loading ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Stress Singularity ◽  
Potential Fields ◽  
Mechanical Interaction ◽  
Electric Loading ◽  
Linear Piezoelectricity

Abstract Using linear piezoelectricity theory, the stress and electric potential fields in a half infinite piezoelectric material under anti-plane mechanical loading in wiresaw slicing process has been studied by using appropriate boundary conditions and contact mechanics. Both electric field and electric displacement field are singular at the edges of the contact zone between wire and workpiece. The singularity of electric displacement arises from the electric loading and electro-mechanical interaction. Similar to the conventional contact mechanics, stress singularity occurs due to the contribution of both mechanical and electric loading. At a given mechanical loading, electric loading can either increase or decrease the stress applied to the piezoelectric half space in the slicing process, which depends on the relative direction of the electric field to that of mechanical loading.

Towards a More Complete Understanding of PMN-PT 4 Point Bend Specimen Behavior

2010 ◽  
Author(s):  
Virginia G. DeGiorgi ◽  
Stephanie A. Wimmer
Keyword(s):  
Piezoelectric Material ◽  
Mechanical Loading ◽  
Electric Fields ◽  
Experimental Work ◽  
Computational Study ◽  
Piezoelectric Materials ◽  
Bend Specimen ◽  
Linear Behavior ◽  
Poling Direction ◽  
Point Bend

ASTM Standard C1161 is often used to determine fracture performance of piezoelectric materials. The basic geometry of C1161 is a four-point beam subjected to mechanical loading. When single crystal PMN-PT was recently subjected to this test unexpected results were observed. Fracture did not occur at the defects incorporated into the specimens nor did failure occur at locations of where maximum stress or strain was predicted by mechanical analyses. Computational tools were then applied to determine piezoelectric material response in this geometry with applied mechanical loading. Conventional finite element codes with piezoelectric material constitutive response using linear behavior models were used. Rather than duplicate the experimental work, the goal of this analysis was to provide insight into the electric fields that would be generated due to mechanical loading of the four-point bend specimen and the resulting variations in stress and deformations. Variation in poling directions is examined. Three different four-point bend configurations are considered. In each specimen the poling direction is aligned with one of the axes of the geometry. The computational study was done as a pre-screening analysis to determine if further understanding of the piezoelectric phenomenon could be expected in a series of experiments of similar design. Experimental work is currently under development based on the computational results of this study. The intent is to used computational analysis to advance understanding to enhance experimental design.

Analysis of Sputtered Zinc Oxide Films

1980 ◽  
Vol 38 ◽  
pp. 416-417
Author(s):  
T. A. Emma ◽  
M. P. Singh
Keyword(s):  
Electron Microscopy ◽  
Zinc Oxide ◽  
Piezoelectric Materials ◽  
Oxide Films ◽  
Optical Quality ◽  
Zno Films ◽  
Rf Power ◽  
X Ray Diffraction ◽  
Sputtered Films ◽  
Zinc Oxide Films

Optical quality zinc oxide films have been characterized using reflection electron diffraction (RED), replication electron microscopy (REM), scanning electron microscopy (SEM), and X-ray diffraction (XRD). Significant microstructural differences were observed between rf sputtered films and planar magnetron rf sputtered films. Piezoelectric materials have been attractive for applications to integrated optics since they provide an active medium for signal processing. Among the desirable physical characteristics of sputtered ZnO films used for this and related applications are a highly preferred crystallographic texture and relatively smooth surfaces. It has been found that these characteristics are very sensitive to the type and condition of the substrate and to the several sputtering parameters: target, rf power, gas composition and substrate temperature.

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