A unified constitutive model for solder materials

Abstract

Solder joint reliability has been the main concern in electronic packaging since the advent of surface mount technology. In this study, a unified constitutive model was developed for finite element analysis of solder joint reliability. The model is based on the Anand model and Runge-Kutta time integration scheme. The constitutive behavior of tin-lead eutectic solder was examined based on published experimental data to establish the material database for the analyses. Procedures to determine the nine model parameters were developed. These parameters were determined using monotonic constant strain rate tensile test data. Two sets of parameters were extracted from representative groups of experimental data. The predictive capability of the Anand model under monotonic loading was assessed by comparing the predictions of the model under tension, strain rate jump, creep and stress relaxation tests with the experimental data. The capability of the model to capture the cyclic behavior of the alloy was also evaluated. Ratcheting effects, low cycle fatigue and load-history dependence of the solder behavior were simulated and compared with the experiments. The model is capable of predicting the behavior of solder materials under both monotonic and cyclic loading conditions for identical batch of specimens. However, the model is not able to simulate fracture of the material, tertiary creep, Bauschinger effects and variations in reported experimental data. A few recommendations were suggested to further improve the model by considering kinematic internal variables, damage and grain size parameters to better represent the behavior of solder materials.