Thermal shock fracture of a cracked thermoelastic plate based on time–fractional heat conduction

Abstract

A time-fractional heat conduction equation is applied to analyze the thermal shock fracture problem of a cracked plate. For a thermoelastic plate subjected to heat shock at its surfaces, analytical temperature field and thermal stresses are obtained by using Laplace transform and finite sine transform under the assumption that crack and deformation do not alter the temperature field. With this solution, thermal stress intensity factors at the crack tips are numerically calculated through the weight function method for both an edge and a center crack, respectively. The influences of fractional order describing super-diffusion, normal diffusion, and sub-diffusion on the thermal stress intensity factors are discussed. Thermoelastic fields and the thermal stress intensity factors exhibit pronounced wave–like propagation characteristics for super-diffusion or strong diffusion, and have a similar trend to normal diffusion for sub-diffusion or weak diffusion. The most dangerous crack length and position are discussed for cold and hot shock. The classical thermal stress intensity factors can be recovered from the present results only setting the fractional order to unity.