FEM-study for Solder Model Comparison on Solder Joints Stress-Strain Effects

This paper presents a numerical comparison of stress-strain conditions in solder joints by the application of a unified primary-secondary creep model and state of the art stationary creep model approach. Both extracted material models are fitted on the same set of solder material and measurement results, taken by the authors. So, individual setup influences stay constant. The first model is the commonly utilized Garofalo approach based on a hyperbolic-sine equation [1], the other is a unified viscoplastic constitutive model based on propositions by Chaboché et al. Both material models allow the calculation of mechanical stress and strain condition in dependency on temperature from $- 40^{\circ}\mathrm{C}$ to $150^{\circ}\mathrm{C}$ and strain rates from 1e-6/s to 1e-3/s. Differences in modelling occur in the degree of freedom to integrate materials effects, such as relaxation, stress recovery and hardening. The characterization measurement setup and extraction of material properties has been shown in previous publications [1], [3]. Previous work also already indicated the importance of primary creep, however the vastness of the effect towards component sizes and types is yet to be shown. Therefore a finite-element study has been conducted here to analyze the influence of the modelling approaches in thermo-mechanical application. Geometries of various 2-Pole-SMT components and BGA components have been used. The resulting stress and creep strain progressions in the solder joints are shown for every component. Generally higher strains and lower stresses have been registered with the unified model. The comparison of the resulting strain portions per cycle on a typical chip resistor shows that the accumulated strain increases by approx. 20 % for the unified approach. This difference also largely occurs in the meniscus region of the joints. The results for the BGA variations indicate a 50% increased accumulated strain for the unified approach. Interestingly the bottom portion of the joint towards the substrate pad exhibited heavy increases. For both components the deviations between both modelling approaches are not small or negligible. The work presented here has shown that only the unified model is able to fully describe the primary and the secondary creep state throughout the whole temperature range. The unified model almost identically follows the measured behavior. Hence the stress and strain situation around the solder joint can be modelled more accurately. This is especially important when the joints are surrounded by other rather stiff materials (e.g. IMS or ceramic substrates). Only an accurate solder-modelling can lead to correct damage behavior assumptions. Also only with the correct assumptions and accurate strain calculations a reliable lifetime-model can be established.