Material Parameter Identification of Viscoplastic Model for Solder Alloy in Electronics Package Using Bayesian Calibration

In this study, a method of computer model calibration is applied to quantify the uncertainties arising in the material characterization of the solder joint in the microelectronics package subject to a thermal cycle. In this study, all uncertainties are addressed by using a Bayesian calibration approach. A special specimen that characterizes the solder property due to the shear deformation is prepared, from which the Moire´ fringe is measured by running a thermal cycle. Viscoplastic finite element analysis procedure is constructed for the specimen based on the Anand model. Gaussian process model known as Kriging is employed to approximate the original finite element analysis (FEA) model. Posterior distribution for the unknown Anand parameters is formulated from the likelihood function for joint full-field displacements of computation and experiment. Markov Chain Monte Carlo (MCMC) method is employed to simulate posterior distribution. As a result, the displacements are predicted in the form of confidence interval. The results show that the proposed approach can be a useful tool in the estimation of the unknown material parameters in a probabilistic manner by effectively accounting for the uncertainties due to the experimental and computational models.