Development and Evaluation of Global-Local Finite Element Models for Solder Joint Reliability under Combined Vibration and Thermal Loads

This paper presents the development and evaluation of global-local finite element (FE) models to assess the reliability of solder joints under isothermal vibration loads. The study focuses on two lead-free solder alloys SAC105 and SAC305 and employs Anand models to capture their nonlinear viscoplastic behaviour. A global-local modelling approach is adopted to reduce computational costs while maintaining accuracy. The global model utilises shell and beam elements to simplify the structure, while sub-models with varying sizes and structures are developed to analyse localised stress and strain in solder joints. Simulations are conducted under both room temperature (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$25^{\circ} \mathrm{C}$</tex>) and high temperature <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left(125^{\circ} \mathrm{C}\right)$</tex> conditions to evaluate the impact of temperature on sub-models' performances. Results indicate that temperature significantly affects the accuracy of nonlinear models with higher temperatures leading to increased deviation of accumulated equivalent plastic strain. The study also highlights the importance of proper cut boundary conditions and the inclusion of solder masks in sub-models to minimise deviations from reference models. The application of nonlinear beam elements representing solder joints in the global model has no effect on the results, but increases the computational time considerably. Differences in results for different mesh sizes in the global model were amplified during the introduction of sub-model boundary conditions by interpolation. The findings demonstrate that the global-local approach, combined with appropriate material models and boundary conditions, can effectively be applied to predict solder joint reliability under isothermal vibrations, offering a computationally efficient alternative to full 3D FE models.