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.

电气产生的焦耳热在电子设备（尤其是具有双材料界面的电子设备）的破裂和故障中起着主导作用，但对于双材料界面裂纹的焦耳热对温度升高和热应力的影响仍未完全了解。为此，我们使用扩展的有限元方法为双材料界面裂纹建立了一个电-热-机械耦合模型。在电势和温度的有限元逼近中，引入了一种新颖的近尖端渐近函数作为富集场，很好地再现了双材料界面裂纹附近的电流和热通量的奇异性。使用交互积分的域形式，评估了双材料界面裂纹的复杂应力强度因子和能量释放率。几个基准测试的结果证明了所提出模型的准确性和鲁棒性。研究了焦耳热和材料性能的失配对界面裂纹尖端应力强度因子和能量释放速率的影响。结果不仅揭示了焦耳热效应对双材料界面裂纹的温度升高，热应力和能量释放速率的显着贡献，而且为多层电子器件的优化设计提供了实用建议，以降低热应力和热应力。防止裂纹扩展。研究了焦耳热和材料性能的失配对界面裂纹尖端应力强度因子和能量释放速率的影响。结果不仅揭示了焦耳热效应对双材料界面裂纹的温度升高，热应力和能量释放速率的显着贡献，而且为多层电子器件的优化设计提供了实用建议，以降低热应力和热应力。防止裂纹扩展。研究了焦耳热和材料性能的失配对界面裂纹尖端应力强度因子和能量释放速率的影响。结果不仅揭示了焦耳热效应对双材料界面裂纹的温度升高，热应力和能量释放速率的显着贡献，而且为多层电子器件的优化设计提供了实用建议，以降低热应力和热应力。防止裂纹扩展。