Prediction of Equilibrium and Stability of Molten Solder Geometries by Finite Element Analysis

Improving the reliability on solder joints is one of the major tasks to achieve downsizing of electronics products. Taking the molten solder profile as an object of study, a new procedure to model solder liquid with a structural FEM has been developed, which enables us to solve an issue of predefining the geometrical profile of solder liquid drops in a state of static equilibrium taking the surface tension into account, and also a problem concerning dynamic stability of the liquid drops. Molten solder liquid is treated as viscous fluid. Deformation of the material due to its viscosity can be represented by the structural analysis using rheological approach. Two types of the constitutive laws, creep model or viscoelasticity model, can be applied. Such a simple case as the Newtonian fluid, either constitutive law may be employed. Using these types of the constitutive laws in the analysis with time incremental steps, it becomes possible not only to obtain the stabilized shape of liquid drops, but also to analyze problems involved with transient (including dynamic effect) stability. As the size of a liquid drop is microscopic in a range of 100 to 1000 μm, the effect of the surface tension must become so predominant in the loading conditions. In most of the conventional theoretical researches, it is found that the surface tension is treated as the pressure difference varying according to the surface curvature. However, this method is not only so complicated, but also may lead to numerical instability particularly in the transient analysis subjected to large deformations. In this study, an effective method has been developed in which the surface tension can be represented with good accuracy through simplified input data with allocating the shell element generating a constant membrane force over the surface of a liquid drop.