A Periodic Array of Parallel Edge Cracks in a Functionally Graded Plate Subjected to Finite Cooling Rates

Abstract This work investigates the effects of cooling rate on the thermal fracture behavior of a functionally graded plate (FGM plate) with a periodic array of parallel edge cracks of alternating lengths. The thermal properties of the FGM are assumed to be continuous and piecewise differentiable functions of the coordinate in the plate thickness direction. A linear ramp function describes the rate of boundary temperature variation at the surfaces of the FGM plate. The integral equation method is used to analyze the thermal stress intensity factors (TSIFs) at the crack tips. The asymptotic solutions of TSIF are obtained using a closed form, short time solution of temperature field in the FGM plate. The effects of cooling rate and crack length ratio on the TSIF are examined using an Al2O3/Si3N4 FGM. Numerical results show that for given material gradation profile and crack morphology parameters, a lower cooling rate leads to a lower peak TSIF. For a given cooling rate, an appropriate material gradation profile reduces peak TSIFs. Finally, the variations of the TISF for the long and short cracks with the cooling rate and crack length ratio exhibit a complex pattern due to the interactions between the long and short cracks. Keywords functionally graded material, heat conduction, cooling rate, thermal stress intensity factor