Transient response of a functionally graded thermoelastic plate with a crack via fractional heat conduction

Abstract

Based on the fractional heat conduction model, a functionally graded thermoelastic plate with an embedded crack subjected to heat shock at its surfaces is analyzed. The analytical temperature field and thermal stresses induced by the internal crack are obtained in the Laplace domain under the assumption that deformation can be altered by temperature, but it does not influence the temperature field. The superposition method is applied to solve the crack problem, and an associated initial-boundary value problem is converted to a singular integral equation. Thermal stress intensity factors at two crack tips are obtained through numerically solving the resulting singular integral equation with Cauchy kernel of the first kind. The effects of fractional order, phase lag of heat flux, and material properties on the thermal stresses and thermal stress intensity factors are illustrated graphically.