Electrically permeable and thermally insulated collinear cracks in thermoelectric materials

We present a rigorous treatment to the plane problem of a thermoelectric medium with collinear cracks subjected to remote uniform thermal-electric loads based on the complex variable method. First, the general solutions for potential functions of thermoelectric fields and stress fields are derived by using the electrically permeable and thermally insulated crack model. Then, for special cases of one crack and two symmetric cracks, more explicit solutions are given for potential functions and intensity factor of stresses. Finally, numerical results are presented to discuss the effects of applied electric loading on the fracture behavior of thermoelectric media. It is found that the fields of electric flux possess no singularity in the vicinity of the cracks, whereas the thermal flux and stresses exhibit the traditional square-root singularity at the crack tips. In addition, the remote electric current only produces a mode I stress intensity factor.