Applicability of the crack faces thermoelectric boundary conditions for thermopiezoelectric materials

• The applicability of the crack faces thermoelectric boundary conditions for thermopiezoelectric materials is investigated theoretically.
• The effects of thermal and electric conductivity of air or vacuum inside the crack are considered.
• The stress and electric displacement intensity factors at the notch tips, and thermal flux and electric displacement inside the notch are derived in closed-form.
• Four ideal crack surfaces thermoelectric boundary condition assumptions are the limiting cases of the proposed finite thickness notch model.

The applicability and effect of the crack surfaces thermoelectric boundary conditions in thermopiezoelectric fracture mechanics problem are discussed by using the finite thickness notch approach. The stress and electric displacement intensity factors at the notch tips, and thermal flux and electric displacement inside the notch are derived in closed-form. The numerical results are compared with the ideal crack solutions. It is found that the electrically impermeable crack boundary condition assumption is reasonable if the flaw in the material is a notch with finite width, and the thermal conductivity of air or vacuum inside the crack must be considered.