A constitutive model for creep of lead-free solders undergoing strain-enhanced microstructural coarsening: A first report

Lead-free solder joints in microelectronic applications frequently have microstructures comprising a dispersion of intermetallic particles in a Sn matrix. During thermomechanical cycling (TMC) of the solder joint, these particles undergo strain-enhanced coarsening, resulting in a continuously evolving, creep behavior. Because the extent of coarsening is dependent on the stress/strain state, which is dependent on the location within a joint, it is important that creep models used in joint-life prediction incorporate these effects. Here, an approach for incorporating the effect of in-situ second-phase particle coarsening in a dislocation-creep model applicable to lead-free solder alloys is proposed. The formulation, which can be expressed in a closed analytic form following some simplifications, incorporates the effects of both static- and strain-enhanced coarsening and accounts for the effects of inelastic-strain history and hydrostatic constraint. Predictions of coarsening based on the model agreed reasonably well with experimentally observed trends. Because of its simplicity, the microstructurally adaptive creep model proposed here can be easily incorporated in current finite-element codes for joint behavior simulation.