Exact solutions of two semi-infinite collinear cracks in piezoelectric strip |
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Authors: | Zi-xing Lu Ping Liu Jun-hong Guo |
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Institution: | Zi-xing LU,Ping LIU,Jun-hong GUO (Institute of Solid Mechanics,Beihang University,Beijing 100191,P.R.China) |
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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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Keywords: | piezoelectric strip semi-infinite collinear crack complex variable function method field intensity factor mechanical strain energy release rate |
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