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Equation-Informed Neural Networks (EINNs) are developed as an efficient method for extracting the coefficients of constitutive equations. Subsequently, numerical Bayesian Inference (BI) iterations were applied to estimate the distribution of these coefficients, thereby further refining them. We could generate coefficients optimally aligned with the targeted application scenario by carefully adjusting pre-processing mapping parameters and identifying dataset preferences. Leveraging graphical representation techniques, the EINNs formulation is implemented in temperature- and strain-rate-dependent hyperbolic Garofalo, Anand, and Chaboche constitutive models to extract the corresponding coefficients for lead-free SAC305 solder material. The performance of the EINNs-based extracted coefficients, obtained from experimental results of SAC305 solder material, is comparable to existing studies. The methodology offers the dual advantage of providing the coefficients' value and distribution against the training dataset. [ABSTRACT FROM AUTHOR]

An accurate and efficient analytical geometric method is presented for predicting the geometric parameters of the controlled collapse chip connection type solder joint using direct chip attach technology after a reflow process. By this method, the meridian of the solder joint is first discretized as a series of sufficiently fine fragmental arcs. After calculating the internal pressure inside the molten eutectic solder from the forces balance, the meridional and circumferential radii of curvature of each arc are then obtained from the Laplace-Young equation. As a result, the coordinates of each node of the arc and the solder joint geometry can be determined in turn. The factors that affect the final shape of the molten eutectic solder joints, including the solder volumes, external loading, pad size, surface tension of molten eutectic solder, and interfacial surface tension between the molten eutectic solder and the solid high-lead bump are considered herein. The results computed by the analytical geometric method are also compared with those obtained using the Surface Evolver program, the extended Heinrich's model, and the experimental results. The results of the various approaches are mutually consistent. [DOI: 10.1115/1.2229216]

This study presents an efficient method to accurately predict solder joint geometry after a reflow process. The proposed method can be utilized for Solder Mask Defined (SMD), Non-Solder Mask Defined (NSMD), or C4 type solder joints. The reflow process involves several design factors capable of influencing the final shape of the molten solder joint, such as solder joint volume, restoring force, surface tension, contact angle, pad thickness, and pad size. These factors are all considered in the calculations. The computed results are compared with those using the Surface Evolver program and also with available numerical/experimental results. Their excellent agreement shows that the method developed herein can be practically applied to predict the reflow shape of SMD/NSMD solder joints. The difference between SMD and NSMD is also examined in detail. Results in this study provide designers with a fundamental guideline for accurately predicting the liquid formation of solder joints during the reflow process. [DOI: 10.1115/1.1401738]