Analysis of an arbitrarily shaped interface cracks in a three-dimensional isotropic thermoelastic bi-material. Part 1: Theoretical solution

Abstract

The displacement and temperature discontinuity boundary integral-differential equation method is developed for the analysis of interfacial cracks in a three-dimensional isotropic thermoelastic bimaterial. The fundamental solutions for a unit point temperature and elastic displacement discontinuities on the interface are derived, and the explicit expressions for the temperature and displacements and stresses are derived. The hyper-singular boundary integral-differential equations of displacement and temperature discontinuities are obtained for a planar interfacial crack of an arbitrary shape. By virtue of the obtained boundary integral-differential equations and the method proposed for interface cracks in purely elastic media, the singular indices and the singular behaviors of the near crack-tip fields are studied. Meanwhile, the stress and heat flux intensity factors as well as the energy release rate are derived in terms of displacement and temperature discontinuities.