Exact Solutions of Two Semi-Infinite Collinear Cracks in a Piezoelectric Strip

LU Zi-xing; LIU Ping; GUO Jun-hong

doi:10.3879/j.issn.1000-0887.2011.11.005

Volume 32 Issue 11

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LU Zi-xing, LIU Ping, GUO Jun-hong. Exact Solutions of Two Semi-Infinite Collinear Cracks in a Piezoelectric Strip[J]. Applied Mathematics and Mechanics, 2011, 32(11): 1306-1313. doi: 10.3879/j.issn.1000-0887.2011.11.005

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Exact Solutions of Two Semi-Infinite Collinear Cracks in a Piezoelectric Strip

doi: 10.3879/j.issn.1000-0887.2011.11.005

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

Received Date: 2011-04-25
Rev Recd Date: 2011-08-30
Publish Date: 2011-11-15

Abstract

Abstract

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

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References(17)

References

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