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.

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.

Effect of Columbic Force on Piezoelectric Fracture

2004 ◽  
Vol 261-263 ◽  
pp. 81-86 ◽  
Author(s):  
Cun Fa Gao ◽  
Pin Tong ◽  
Tong Yi Zhang
Keyword(s):  
Fracture Behaviour ◽  
Piezoelectric Materials ◽  
Normal Component ◽  
Electric Displacement ◽  
Permeable Crack ◽  
Electric Loading ◽  
Non Linear Equation ◽  
Piezoelectric Solid ◽  
Electric Loads ◽  
Crack Faces

This paper studies the effect of the Columbic force on piezoelectric fracture. Bound charges emerge on the upper and lower surfaces of a permeable crack when a piezoelectric solid with the crack is subjected to far-field mechanical/electric loading. Taking into account the Columbic force between the bound charges, we obtain a non-linear equation governing the normal component of electric displacement D2(x1)on the crack faces. The results show that D2(x1)is, in general, not a constant along the crack faces and depends on the mechanical/electric loading conditions, the crack profile and the material properties outside and inside the crack. Furthermore, we examine the Columbic force under low mechanical/electric loads and then discuss the effect of the Columbic force on the fracture behaviour of piezoelectric materials.

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.

Solving Mid-Frequency Acoustic Problem by the Meshless Method

2013 ◽  
Vol 444-445 ◽  
pp. 1471-1476
Author(s):  
Shuang Wang ◽  
Qi Bai Huang ◽  
Shan De Li
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Radial Basis Function ◽  
Efficient Method ◽  
Basis Function ◽  
Meshless Method ◽  
Medium Frequency ◽  
Pollution Effect ◽  
Acoustic Problem ◽  
Engineering Problems

It is well known that traditional finite element (FEM) is an efficient method in solving engineering problems. However, when solving the acoustic problems in medium frequency, FEM suffers from the so-called pollution effect, which is directly related to the dispersion. In this paper, meshless method based on radial basis function (RBF) is introduced to solve the acoustic problem, which shows that the dispersion can be greatly reduced, thus it is very suitable for the solution of mid-frequency acoustic problem. In addition, an algorithm is presented to treat the boundary condition, which improves the performance of the meshless method.

On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic

2003 ◽  
Vol 70 (2) ◽  
pp. 246-252 ◽  
Author(s):  
S. Li
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Piezoelectric Ceramic ◽  
Piezoelectric Materials ◽  
Dielectric Medium ◽  
Crack Model ◽  
Permeable Crack ◽  
Global Energy

A permeable crack model is proposed to analyze crack growth in a piezoelectric ceramic. In this model, a permeable crack is modeled as a vanishing thin, finite dimension, rectangular slit with dielectric medium inside. A first-order approximation solution is derived in terms of the slit height, h0. The main contribution of this paper is that the newly proposed permeable crack model reveals that there exists a realistic leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a correct estimation of electrical and mechanical fields in front of a crack tip in a piezoelectric ceramic is obtained. To demonstrate this new finding, a closed-form solution is obtained for a mode III permeable crack under both mechanical as well electrical loads. Both local and global energy release rates are calculated based on the permeable crack solution obtained. It is found that the global energy release rate derived for a permeable crack is in a broad agreement with some known experimental observations. It may be served as a fracture criterion for piezoelectric materials. This contribution reconciles the outstanding discrepancy between experimental observation and theoretical analysis on crack growth problem in piezoelectric materials.

Electrically permeable crack with contact zones between two piezoelectric materials

2008 ◽  
Vol 44 (3) ◽  
pp. 296-303 ◽  
Author(s):  
V. B. Govorukha ◽  
K. P. Herrmann ◽  
V. V. Loboda
Keyword(s):  
Piezoelectric Materials ◽  
Permeable Crack ◽  
Contact Zones

Performance Characteristics of Finite Width Journal Bearings Under the Separation Boundary Condition

1986 ◽  
Vol 108 (2) ◽  
pp. 178-183 ◽  
Author(s):  
M. Nakai ◽  
T. Kazamaki ◽  
T. Hatake
Keyword(s):  
Boundary Condition ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Experimental Results ◽  
Finite Width ◽  
Separation Boundary ◽  
Physical Consideration ◽  
Calculation Results

The separation boundary condition is considered to be comparatively exact in the physical consideration of the supposition. The calculated performance characteristics applied to infinite width journal bearings are related to experimental results to some extent. However, performance characteristics applied to finite width journal bearings, which might be able to explain the experimental results more precisely, have been unknown. The present paper describes the application of the separation boundary condition to finite width journal bearings, and calculation results of some performance characteristics. The results are related to well-known experimental results in several respects.

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