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Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

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Abstract

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

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Authors and Affiliations

  1. Institute of Solid Mechanics, Beihang University, Beijing, 100191, P. R. China

    Zi-xing Lu  (卢子兴), Ping Liu  (刘 萍) & Jun-hong Guo  (郭俊宏)

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  1. Zi-xing Lu  (卢子兴)
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  2. Ping Liu  (刘 萍)
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  3. Jun-hong Guo  (郭俊宏)
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Corresponding author

Correspondence to Zi-xing Lu  (卢子兴).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10932001 and 11072015) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20101102110016)

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Lu, Zx., Liu, P. & Guo, Jh. Exact solutions of two semi-infinite collinear cracks in piezoelectric strip. Appl. Math. Mech.-Engl. Ed. 32, 1399–1406 (2011). https://doi.org/10.1007/s10483-011-1510-9

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  • DOI: https://doi.org/10.1007/s10483-011-1510-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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