Improved Submodeling Finite Element Simulation Strategies for BGA Packages Subjected to Thermal Cycling

Abstract

The finite element method has been widely used to enable fatigue life predictions for electronic assemblies subjected to thermal cycling. The potential critical region of interest within a solder joint is relatively small relative to the entire package assembly. High-density meshes are typically used to build a package model when using traditional FE modeling approaches. Therefore, long computational times can be expected for an analysis involving several thermal cycles. In order to reduce the complexity of the model and the use of oversize elements, and improve the efficiency of calculation, the technique of global/local modeling (submodeling) has been developed. In this approach, interpolated displacements from coarse model (global model) are applied as boundary conditions to a refined model (local/submodel) of the critical area of interest. The accuracy and efficiency of submodeling finite element simulations for electronic packages have not been evaluated completely in the literature.In this work, submodeling approaches for BGA assemblies have been explored in detail. A typical BGA package assembly was modeled using several coarse meshes as global models; and the maximum aspect ratio within the global model was varied up to 25, which is near the warning limit of many commercial finite element codes. Once the critical solder joint was identified, then the local model was built using the technique of cut boundaries, and meshed with refined elements. The maximum aspect ratio was also reduced to 5. The simulation result shows the accuracy of solution was sensitive to the mesh quality of the local model, as well as the load step size for both global and local models. An improved simulation strategy using submodeling was developed to obtain the best compromise in the global and local models between the mesh quality and load step size.Although the submodeling is a powerful tool for a better solution in a local region of interest far away from the cut boundaries, it is still crucial to identify the critical region correctly from the global model or a misguided local solution might be performed. Initially, the global models were built using coarse meshes with nonlinear material properties as seen in literature, and then an improved geometric simplification of the solder joint incorporating energy based fatigue criteria was developed. In addition, minimization of the local model volume is still required for a detail analysis of a complex configuration in local region where a high-density mesh is needed. In the investigated approach, we determined the minimized height of the local boundary, and have shown the influence between the height and the solution of volume averaged inelastic strain energy dissipation in the local model. The proposed approach achieves a large reduction in computational time, better detailed modeling of local interest region, and improved simulation accuracy.