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This work investigates the thermal fracture resistance of a functionally graded coating with an array of periodic edge cracks. The integral equation method is used to analyze the thermal stress intensity factors (TSIFs) at the crack tips and the critical thermal shocks that cause crack initiation. The effects of crack density (crack spacing) and thermal property gradients on the critical thermal shocks and TSIFs are examined using an Al
2O
3/Si
3N
4 graded coating on a Si
3N
4 substrate. Numerical results show that for a given crack density, the graded Al
2O
3/Si
3N
4 coating exhibits higher critical thermal shocks than the homogeneous Al
2O
3 coating, and hence higher thermal fracture resistance. For a given material gradation profile, a higher crack density (smaller crack spacing) enhances the critical thermal shock significantly.