Time integration procedures for a cyclic thermoviscoplasticity model for Pb-Sn solder applications

A semi-implicit time integration scheme has been developed for a cyclic thermoviscoplastic constitutive model with tensorial internal state variables for Pb-Sn solder, a common metallic constituent in electronic packaging applications. The procedure has been implemented numerically into the commercial finite element (FE) code ABAQUS (1995) by user-defined material subroutines. Several simulations are conducted to compare the numerical implementation to experiments including monotonic uniaxial tests at different temperatures, creep tests at four stress levels, and a test with two-step load-controlled cyclic loading for 62Sn36Pb2Ag solder. An explicit time integration scheme is used as well to compare with the semi-implicit scheme. The accuracy as well as the stability of the solutions are considered. Several suggestions are made for using the material constitutive model and the semi-implicit integration scheme for modeling solder connections. This work provides guidelines to implement user-defined material behavior into FE analyses to perform more sophisticated thermomechanical simulations for solder connections in electronic packaging applications