Electro-mechanical singularities of piezoelectric bi-material notches and cracks

The paper aims to carefully investigate an asymptotic in-plane problem of bi-material sharp notches with various geometry and interface cracks in several generally monoclinic piezoelectric bi-materials using the expanded Lekhnitskii-Eshelby-Stroh formalism. A special attention is paid to the change of the asymptotic solution connected with the transition of a very closed notch into an interface crack. Also the influence of arbitrary oriented poling directions upon asymptotic solution is investigated. Four pair-combinations PZT-5H/BaTiO3, PZT-5H/PZT-6B, PZT-5H/PZT-7A and PZT-6B/PZT-7A as representatives of the so-called epsilon-class of bi-materials and six pair-combinations PZT-4/BaTiO3, PZT-4/PZT-5H, PZT-4/PZT-6B, PZT-4/PZT-7A, PZT-6B/BaTiO3, and PZT-7A/BaTiO(3 )as representatives of the kappa-class of bi-materials are analysed. It is shown that the bi-material classification into epsilon-class and kappa-class introduced by Ou and Wu (2003) for interface cracks cannot be applied to a bi-material notch with a geometry characterized by an arbitrary angle. Ou and Wu bi-material classification also fails for interface cracks if one of the poling angles differs from 90 degrees. The two-state integral derived from Beth's reciprocal principle for piezoelectric bi-materials is used to evaluate general stress intensity factors (GSIFs) for various piezoelectric bi-materials and notch configurations. The accuracy of GSIFs calculations is tested by comparing the asymptotic solutions with the results obtained by finite element method using a very fine mesh.