Elastic thermal stresses in a hollow circular overlay/substrate system

• Thermal stress distribution is derived in a hollow circular overlay/substrate system.
• A closed form approximate solution of the thermal elastic field is obtained.
• The solution is applicable to a solid circular system and a tiny hole in a large thin film.
• Comparison of this solution with FEM models demonstrates the accuracy of this solution.
• Energy release rate is calculated for a circular crack in a solid circular overlay.

This paper investigates the thermal elastic fields in the hollow circular overlay fully bonded to a rigid substrate, which is subjected to a temperature change. Following our previous work for a solid circular overlay/substrate system (Yuan and Yin, Mech. Res. Commun. 38, 283–287, 2011), this paper presents a closed form approximate solution to the axisymmetric boundary value problem using the plane assumption, whose accuracy is verified by the finite element models. When the inner radius is reduced to zero, the present solution recovers the previous solution. When the outer radius approaches infinite, the solution provides the elastic fields for a tiny hole in the overlay. The effects of thickness and width of the overlay are investigated and discussed. When a circular crack initiates in a solid circular overlay, the fracture energy release rate is investigated. This solution is useful for thermal stress analysis of hollow circular thin film/substrate systems and for fracture analysis of spiral cracking in the similar structures.

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