The interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material |
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| Authors: | Zhen-Gong Zhou Zeng-Tao Chen |
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| Institution: | aCenter for Composite Materials and Structures, Harbin Institute of Technology, P. O. Box 3010, No.2, Yikuang Street, Harbin, 150080, PR China;bDepartment of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada, E3B 5A3 |
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| Abstract: | In this paper, the interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material was investigated by using the generalized Almansi's theorem. In the analysis, the electric permittivity of the air inside the crack was considered. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the electric permittivity of the air inside the crack and the gradient parameter of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials. |
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| Keywords: | Crack Functionally graded piezoelectric materials Mechanics of solids |
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