Transient thermal stress intensity factors for a circumferential crack in a hollow cylinder based on generalized fractional heat conduction

A generalized fractional heat conduction theory is applied to investigate the transient thermal fracture problem of a hollow cylinder with an embedded or surface circumferential crack. Integral transform technique is used to solve an associated initial-boundary value problem. Explicit temperature field and thermal stresses are given in the Laplace transform domain for a circumferentially cracked hollow cylinder subjected to thermal shock at the inner surface and with an insulated outer surface. Numerical results in the time domain are obtained by using numerical inversion of the Laplace transform. Transient thermal stresses induced by a crack are determined and thermal stress intensity factors at the crack front are calculated. The effects of fractional order, phase lag of heat flux on the transient temperature field, thermal stresses and thermal stress intensity factors are illustrated graphically for internal and surface cracks. The obtained results based on non-Fourier law of fractional heat conduction are compared with those using the classical Fourier law and hyperbolic heat conduction models, respectively.