doi:10.3850/978-981-08-5118-7_044

ABSTRACT

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. The uncertainties include inherent experimental error and insufficient number of experiments. In the case of costly computation, surrogate model is also employed to approximate the original response function using a finite number of analyses, which adds another uncertainty. In this study, all these 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 Moiré 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 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 and stresses 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.

Keywords: Anand model, Bayesian calibration, Kriging, Likelihood function, Markov chain monte carlo technique, Material identification, Solder joint, Viscoplasticity.

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