An opening crack model for thermopiezoelectric solids

• An opening crack in a thermopiezoelectric solid is simulated by using the thermal-medium crack model.
• Closed-form solutions of thermoelectroelastic fields induced by a crack are obtained.
• The effects of applied electromechanical loadings on the thermal stress intensity factor are studied.

In previous studies of thermoelectroelastic analysis for a cracked thermopiezoelectric solid, the crack-face thermal boundary condition is always assumed to be fully insulated or conductive. The effects of applied electromechanical loadings on the thermal stress field near crack tip have not been widely considered. In the present paper, the thermal-medium crack model is applied to simulate an opening crack in a thermopiezoelastic solid, which is filled with a dielectric. The heat flux and electric displacement at the crack surfaces are assumed to be dependent on crack opening displacement. Applying the Fourier transform technique, the thermal stress field in full plane is determined explicitly in terms of the elementary functions. The effects of applied electromechanical loadings and the thermal conductivity inside a crack on the normalized thermal stress intensity factor and crack center opening displacement are investigated through numerical results and shown in graphics. The observations reveal that the thermal stress intensity factor depends not only on applied thermal loadings but also on applied electromechanical loadings, the thermal conductivity and dielectric permittivity of crack interior.