Memory effects on the thermal fracture behavior of cracked plates via fractional heat conduction models

Studies have shown that fractional derivatives have important memory effect on the thermal shock fracture of structures. In the present work, four generalized fractional models are applied to investigate the thermal fracture problem of cracked plates. Laplace transform and finite sine transform are employed to obtain transient temperature and thermal stresses. Stress intensity factors around the crack tips are evaluated through the weight function method for edge and center cracks. Numerical results show that memory effects on the thermoelastic fields are different with different fractional derivative definition and fractional orders, and the effects will vary accordingly with crack geometry parameters.