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

    Source: Journal of Applied Mechanics:;2007:;volume( 074 ):;issue: 005::page 833
    Author:
    Q. Li
    ,
    Y. H. Chen
    DOI: 10.1115/1.2711232
    Publisher: 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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      Solution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material

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    http://yetl.yabesh.ir/yetl1/handle/yetl/135050
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    contributor authorQ. Li
    contributor authorY. H. Chen
    date accessioned2017-05-09T00:22:23Z
    date available2017-05-09T00:22:23Z
    date copyrightSeptember, 2007
    date issued2007
    identifier issn0021-8936
    identifier otherJAMCAV-26656#833_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/135050
    description abstractA 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.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleSolution for a Semi-Permeable Interface Crack Between Two Dissimilar Piezoelectric Material
    typeJournal Paper
    journal volume74
    journal issue5
    journal titleJournal of Applied Mechanics
    identifier doi10.1115/1.2711232
    journal fristpage833
    journal lastpage844
    identifier eissn1528-9036
    keywordsPiezoelectric materials
    keywordsFracture (Materials)
    keywordsElectrical properties AND Displacement
    treeJournal of Applied Mechanics:;2007:;volume( 074 ):;issue: 005
    contenttypeFulltext
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