Joule heating effect on thermal stress for a bi-material interface crack

The electric-induced Joule heat plays a dominant role for the fracture and failure in electronic devices, particularly in those with bi-material interfaces, yet the effect of Joule heat on temperature elevation and thermal stress for a bi-material interface crack remains incompletely understood. To this end, we develop a coupled electro-thermo-mechanical model for the bi-material interface crack using the extended finite element method. A novel near-tip asymptotic function is introduced as the enrichment field in the finite element approximations of electrical potential and temperature, which well reproduces the singularities of electric current and heat flux near the bi-material interface crack. Using the domain form of the interaction integral, the complex stress intensity factors and energy release rate are evaluated for bi-material interface cracks. The results of several benchmarking tests demonstrate the accuracy and robustness of the proposed model. The effects of the Joule heat and the mismatch of material properties on the stress intensity factors and energy release rate at the interfacial crack tip are investigated. The results not only reveal the significant contribution of the Joule heating effect on temperature elevation, thermal stress, and energy release rate for a bi-material interface crack, but also provide practical suggestions on the optimal design of multilayered electronic devices to reduce thermal stress and prevent crack propagations.