A variational-damage-based thermo-mechanical phase-field model for fracture analysis of electronic packaging structures

The transformed phase-field cohesive zone model (Tpfczm) exploits a bridge relation between the unified phase-field theory and the variational damage model, enabling the constitutive parameters to be derived without the approximation required in the PF-CZM, thereby enhancing convergence robustness while retaining length-scale insensitivity. However, the Tpfczm has so far been limited to purely mechanical fracture problems. In this work, the Tpfczm is extended to thermo–mechanically coupled fracture. The proposed framework incorporates thermal strains into the elastic constitutive relation, introduces a damage-dependent thermal conductivity to capture the thermal barrier effect of cracks, and adopts a tension–shear energy decomposition to account for shear-dominated failure modes. The resulting three-field coupled model — governing the displacement, temperature, and damage fields simultaneously — inherits the improved convergence robustness and length-scale insensitivity of the original Tpfczm. A benchmark comparison against the PF-CZM further confirms the efficiency advantage of the Tpfczm in terms of iteration count and computational time. The proposed framework is applied to a series of representative electronic packaging problems involving intermetallic compound (IMC) layer fracture and through-glass via (TGV) thermo-mechanical damage. The numerical examples illustrate coefficient of thermal expansion (CTE)-mismatch-driven crack-evolution patterns in representative electronic packaging structures, including interfacial cracking, void-induced changes in crack paths, and progressive interfacial fracture.