Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric MaterialSource: Journal of Applied Mechanics:;2007:;volume( 074 ):;issue: 005::page 833DOI: 10.1115/1.2711232Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: 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 (, 1958, Philos. Mag.3, pp. 625–646;, 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.
keyword(s): Piezoelectric materials , Fracture (Materials) , Electrical properties AND Displacement ,
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contributor author | Q. Li | |
contributor author | Y. H. Chen | |
date accessioned | 2017-05-09T00:22:23Z | |
date available | 2017-05-09T00:22:23Z | |
date copyright | September, 2007 | |
date issued | 2007 | |
identifier issn | 0021-8936 | |
identifier other | JAMCAV-26656#833_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/135050 | |
description abstract | 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 (, 1958, Philos. Mag.3, pp. 625–646;, 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. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material | |
type | Journal Paper | |
journal volume | 74 | |
journal issue | 5 | |
journal title | Journal of Applied Mechanics | |
identifier doi | 10.1115/1.2711232 | |
journal fristpage | 833 | |
journal lastpage | 844 | |
identifier eissn | 1528-9036 | |
keywords | Piezoelectric materials | |
keywords | Fracture (Materials) | |
keywords | Electrical properties AND Displacement | |
tree | Journal of Applied Mechanics:;2007:;volume( 074 ):;issue: 005 | |
contenttype | Fulltext |