A unified energy-based framework is developed to predict fatigue life and interpret damage evolution in viscoplastic joints under combined thermal cycling and broadband random vibration. The methodology integrates the Anand constitutive model for nonlinear time-dependent deformation, Darveaux’s strain energy density method for low-cycle thermal fatigue, and a Basquin-type strain life relation for vibration-induced high-cycle fatigue. Using strain energy density as a physically grounded surrogate for the fracture driving force, we propose a coupling law with an explicit interaction term that links thermal and vibrational damage channels. We further derive an analytical lifetime bound showing that the coupled lifetime is upper-bounded by the harmonic mean of the single-mode lives. Dimensionless similarity groups are introduced to generalize the predictions across materials and geometries and to support rapid design screening. Finite-element case studies on micro-interconnects demonstrate nonlinear degradation under coupled loading. The predicted hot-spot locations qualitatively follow experimentally reported corner-joint and upper-interface initiation trends. The proposed framework provides quantitative life estimation, spatial localization of fracture-prone regions without explicit crack tracking, and mechanism-informed design guidance for layered structures containing viscoplastic interfaces in thermo-vibrational environments.
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