Finite element viscoelastic analysis of temperature and moisture effects in electronic packaging

Several workers have demonstrated the presence of singular stress fields near the edge of a bimaterial interface subject to thermal gradients. Many of the analyses in the literature are limited to linear elastic materials and are useful as first estimates of stresses in such assemblies. However, a time-dependent stress analysis is necessary when viscoelastic materials such as polymer films are bonded to elastic substrates. This paper shows the relevance of viscoelastic modeling in demonstrating the effects of combined temperature and moisture loading on bimaterial interfaces and viscoelastic films sandwiched between elastic substrates. A 2-D finite element method for linear hygrothermoviscoelasticity based on an incremental creep strain rate form is developed. The correspondence principle of linear viscoelasticity is invoked and comparisons between FEA and analytical solutions are demonstrated. Moisture is modeled using Fick's law and the thermorheologically simple material (TSM) postulate is extended to incorporate a moisture shift function in analogy with temperature. The analysis of a polyimide film sandwiched between elastic substrates subject to a thermal cycle with diffusion from the free edge shows stress reversals for the peel stresses that may explain failure modes not anticipated by an elastic analysis.