Thermal stress intensity factor expressions for functionally graded cylinders with internal circumferential cracks using the weight function method

• Mathematical expressions are derived for the thermal SIF of cracked FG cylinders.
• The weight function approach is used for the thermal fracture analysis.
• A fitting function is introduced to calculate the reference SIFs.
• Effects of the internal cooling and the FGM index on the thermal SIFs are studied.
• Predicted SIFs by the weight function agree well with direct FE SIF results.

In this paper, the weight function method is used to derive mathematical expressions in terms of the Gauss hypergeometric function for the mode-I thermal stress intensity factor of functionally graded cylinders with internal circumferential cracks. To determine the weight function coefficients, a unique function is fitted to reference stress intensity factors obtained from finite element analysis. Effects of the internal convection cooling coefficient and the material power law index are investigated, as well. It is shown that the thermal stress intensity factors predicted by the developed mathematical expression are in good agreement with those directly obtained from finite element analysis. Results of this study may be used in material selection, design optimization, safety assessment against fracture, and fatigue life evaluation of functionally graded cylinders.