Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.