The anti-plane solution for the edge cracks originating from an arbitrary hole in a piezoelectric material |
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| Institution: | 1. College of Engineering, Nanjing Agricultural University, Nanjing 210031, China;2. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China;1. School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK;2. Spencer Institute of Theoretical and Computational Mechanics, University of Nottingham, Nottingham NG7 2RD, UK;1. Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, PR China;2. The School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, PR China |
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| Abstract: | In this paper, a general and simple way was found to solve the problem of an arbitrary hole with edge cracks in transversely isotropic piezoelectric materials based on the complex variable method and the method of numerical conformal mapping. Firstly, the approximate mapping function which maps the outside of the arbitrary hole and the cracks into the outside of a circular hole is derived after a series of conformal mapping process. Secondly, based on the assumption that the surface of the cracks and hole is electrically impermeable and traction-free, the approximate expressions for the complex potential, fields intensity factors and energy release rates are presented, respectively. Thirdly, under the in-plane electric loading together with the out-plane mechanical loading, the influences of the hole size, crack length and mechanical/electric loading on the fields intensity factors and energy release rates are analyzed. Finally, some particular holes with edge cracks are studied in numerical analysis. The result shows that, the mechanical loading always promotes crack growth, while the electric loading may retard crack growth. |
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| Keywords: | Piezoelectric materials Arbitrary hole Edge cracks Complex variable method |
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