Thermal shock fracture of an elastic half-space with a subsurface penny-shaped crack via fractional thermoelasticity

This paper analyzes a thermal shock problem of an elastic half-space with a penny-shaped crack near the surface based on a fractional thermoelasticity theory. The embedded crack is assumed to be insulated. The Hankel transform and Laplace transform are employed to solve an initial-boundary value problem associated with a fractional partial differential equation. Explicit expressions of temperature and thermal stresses induced by the penny-shaped crack are obtained by solving a system of singular integral equations. Numerical results of the thermoelastic fields in the time domain are given by applying the numerical inverse Laplace transform. The temperature jump between the upper and lower crack surfaces and the thermal stress intensity factors at the crack front are illustrated graphically for various relaxation times and fractional orders, as well as the distance between the crack plane and the half-space surface. A comparison of the temperature, thermal stresses, and their intensity factors is made when adopting the fractional heat conduction model and the classical Fourier heat conduction model. Numerical results show that the temperature overshooting phenomenon may occur for the fractional heat conduction model, whereas it does not occur for the classical Fourier heat conduction model.