A new domain-independent interaction integral for three-dimensional non-homogeneous thermoelastic materials

Abstract This work establishes a new domain-independent interaction integral for the evaluation of mixed-mode stress intensity factors (SIFs) in three-dimensional non-homogeneous materials with complex thermo-mechanical interfaces subjected to thermo-mechanical loadings. A new auxiliary field called Zero-Mean stress field is developed to deal with the mismatch of thermoelastic properties across the material interfaces. An area integral along with the material interfaces, which is indispensable to keep domain-independence of the conventional interaction integral using Williams’ auxiliary fields, is eliminated by using this new auxiliary. A crack-face integral is added to maintain the domain-independence of this new method. The expression of this new domain-independent interaction integral contains no thermal property parameters. Because of this feature, the new interaction integral holds domain-independent for both discontinuous mechanical properties and discontinuous thermal properties. Since tracking crack-planes is much easier than tracking a material interface in numerical implementations, it brings convenience to the practical applications to analyze three-dimensional non-homogeneous materials with discontinuous thermoelastic material properties. The new interaction integral, combined with the finite element method, is applied to investigate several representative examples, which demonstrates that the new interaction integral has good accuracy and domain-independence for thermo-mechanical interfaces.