An interaction energy integral method for T-stress evaluation in nonhomogeneous materials under thermal loading

•Interaction energy integral method is developed for thermal T-stress evaluation.•A domain-independent T-stress expression is proposed for materials with interfaces.•T-stress can be solved effectively with high efficiency using the present method.•The thermomechanical mismatch of material properties affects the T-stress greatly.

An interaction energy integral method is developed for the finite element evaluation of the T-stress in nonhomogeneous materials under thermal loading. A domain-independent integral expression for extracting the T-stress is proposed for nonhomogeneous materials even when the integral domain intersects the interface. Then it is set in the extended finite element method (XFEM) so that the T-stress can be solved with high accuracy and efficiency. Several representative examples are solved to show the validity and the domain-independence of the method. A crack problem in a functionally graded thermal barrier coating (TBC) is also analyzed. Finally, the influences of material continuity on the T-stress are investigated. It can be found that the discontinuity of both thermal expansion coefficient and Young’s modulus affects the T-stress dramatically.