Screw dislocations in piezoelectric laminates with four or more phases

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Authors

  • X. Wang School of Mechanical and Power Engineering, East China University of Science and Technology, China
  • L. Chen School of Mechanical and Power Engineering, East China University of Science and Technology, China
  • P. Schiavone Department of Mechanical Engineering, University of Alberta, Canada

Abstract

We present an analytical solution to the problem of a screw dislocation in a four-phase piezoelectric laminate composed of two piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media. A new version of the complex variable formulation is proposed such that the 2 × 2 real symmetric matrix appearing in the formulation becomes dimensionless. Using analytic continuation, the original boundary value problem is reduced to the identification of a single 2D analytic vector function which is completely determined following rigorous solution of the resulting linear recurrence relations in matrix form. An explicit expression for the image force acting on the piezoelectric screw dislocation is obtained once the single 2 × 2 real matrix function is identified. We also discuss the solution for a screw dislocation in an N-phase piezoelectric laminate composed of N − 2 piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media.

Keywords:

four-phase piezoelectric laminate, screw dislocation, analytical solution, analytic continuation, recurrence relations of matrix form

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