Abstract
This paper deals with the interaction between a circular piezoelectric inhomogeneity (a circular piezoelectric fiber sensor) and a symmetrically branched crack. The piezoelectric inhomogeneity is embedded in a nonpiezoelectric, elastic matrix with a symmetrically branched crack near the inhomogeneity. The matrix is under a far field in-plane uniform tensile stress and an anti-plane electric field. By using the solution of a single dislocation interacting with an inhomogeneity as Green's function, the main crack and its two symmetrical branches are simulated by continuously distributed edge dislocations. The formulation results in a group of singular integral equations (SIEs). Through solving the singular integral equations numerically, the unknown distributed dislocation density functions can be obtained, and both the Mode I and Mode II stress intensity factors at the branch tips are thus evaluated. The influence of materials constants, geometrical configurations, as well as the far field electric and mechanical loading on the interaction between the branched crack and the piezoelectric inhomogeneity is discussed in detail. As the derivation procedure is very tedious, the analytical results obtained are verified by finite element computation.
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