Bayesian calibration of ball grid array lifetime models for solder fatigue

Abstract

One of the primary failure modes for solder joints is caused by temperature cycling of the component. The induced stress causes creeping which leads to crack initiation and propagation until failure. Finite element analysis can be used to simulate occurring creep-strain for different temperatures and geometries. Subsequently, creep-strain is used as damage parameter together with a lifetime model to estimate the reliability of the component. Economic factors constrain data available for calibration of the lifetime model, leading to uncertainties in parameter estimates and reliability. Therefore, we propose a model calibration method for solder fatigue with the Coffin–Manson lifetime model based on Bayesian inference. The approach is able to incorporate respective uncertainties from data variability and sparsity, and takes prior knowledge into account. We show how to obtain reliability estimates from the calibrated model considering uncertainties from parameter estimation. Furthermore, we apply the Bayesian calibration method to experimental data obtained from ball-grid arrays with lead-free SAC305 solder joints. In our ablation study we show that our approach is more robust and accurate upon the prevalent calibration method used, especially if only limited data is available.