Thermal shock fracture associated with a unified fractional heat conduction

Recently, a unified fractional heat conduction model is newly proposed, which is a further improvement of the fractional thermoelasticity theory. It would be interesting to know how the newly developed fractional derivative definitions affects the thermal fracture behavior when some defects such as cracks exist in the medium. This work is aimed at analyzing the thermal fracture problem of an elastic half-space and strip with an insulated Griffith crack based on the unified fractional heat conduction model. Fourier and Laplace transforms are employed to solve the mixed boundary problem associated with a time-fractional partial differential equation. Temperature and stress intensity factors are evaluated by solving a system of singular integral equations. Effects of different fractional derivatives and different parameters on the thermoelastic fields are analyzed. A comparison of the temperature and stress intensity factors between the present model and the Fourier model is made. Numerical results show that different fractional definitions have different memory effects on the transient responses, and the effects of fractional definitions on the responses will vary accordingly with the parameter values.