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Thermo-mechanical reliability studies of lead-free solder interconnectsSolder interconnections, also known as solder joints, are the weakest link in electronics packaging. Reliability of these miniature joints is of utmost interest - especially in safety-critical applications in the automotive, medical, aerospace, power grid and oil and drilling sectors. Studies have shown that these joints' critical thermal and mechanical loading culminate in accelerated creep, fatigue, and a combination of these joints' induced failures. The ball grid array (BGA) components being an integral part of many electronic modules functioning in mission-critical systems. This study investigates the response of solder joints in BGA to crucial reliability influencing parameters derived from creep, visco-plastic and fatigue damage of the joints. These are the plastic strain, shear strain, plastic shear strain, creep energy density, strain energy density, deformation, equivalent (Von-Mises) stress etc. The parameters' obtained magnitudes are inputted into established life prediction models – Coffin-Manson, Engelmaier, Solomon (Low cycle fatigue) and Syed (Accumulated creep energy density) – to determine several BGA assemblies' fatigue lives. The joints are subjected to thermal, mechanical and random vibration loadings. The finite element analysis (FEA) is employed in a commercial software package to model and simulate the responses of the solder joints of the representative assemblies' finite element models. As the magnitude and rate of degradation of solder joints in the BGA significantly depend on the composition of the solder alloys used to assembly the BGA on the printed circuit board, this research studies the response of various mainstream lead-free Sn-Ag-Cu (SAC) solders (SAC305, SAC387, SAC396 and SAC405) and benchmarked those with lead-based eutectic solder (Sn63Pb37). In the creep response study, the effects of thermal ageing and temperature cycling on these solder alloys' behaviours are explored. The results show superior creep properties for SAC405 and SAC396 lead-free solder alloys. The lead-free SAC405 solder joint is the most effective solder under thermal cycling condition, and the SAC396 solder joint is the most effective solder under isothermal ageing operation. The finding shows that SAC405 and SAC396 solders accumulated the minimum magnitudes of stress, strain rate, deformation rate and strain energy density than any other solder considered in this study. The hysteresis loops show that lead-free SAC405 has the lowest dissipated energy per cycle. Thus the highest fatigue life, followed by eutectic lead-based Sn63Pb37 solder. The solder with the highest dissipated energy per cycle was lead-free SAC305, SAC387 and SAC396 solder alloys. In the thermal fatigue life prediction research, four different lead-free (SAC305, SAC387, SAC396 and SAC405) and one eutectic lead-based (Sn63Pb37) solder alloys are defined against their thermal fatigue lives (TFLs) to predict their mean-time-to-failure for preventive maintenance advice. Five finite elements (FE) models of the assemblies of the BGAs with the different solder alloy compositions and properties are created with SolidWorks. The models are subjected to standard IEC 60749-25 temperature cycling in ANSYS 19.0 mechanical package environment. SAC405 joints have the highest predicted TFL of circa 13.2 years, while SAC387 joints have the least life of circa 1.4 years. The predicted lives are inversely proportional to the magnitude of the areas of stress-strain hysteresis loops of the solder joints. The prediction models are significantly consistent in predicted magnitudes across the solder joints irrespective of the damage parameters used. Several failure modes drive solder joints and damage mechanics from the research and understand an essential variation in the models' predicted values. This investigation presents a method of managing preventive maintenance time of BGA electronic components in mission-critical systems. It recommends developing a novel life prediction model based on a combination of the damage parameters for enhanced prediction. The FEA random vibration simulation test results showed that different solder alloys have a comparable performance during random vibration testing. The fatigue life result shows that SAC405 and SAC396 have the highest fatigue lives before being prone to failure. As a result of the FEA simulation outcomes with the application of Coffin-Manson's empirical formula, the author can predict the fatigue life of solder joint alloys to a higher degree of accuracy of average ~93% in an actual service environment such as the one experienced under-the-hood of an automobile and aerospace. Therefore, it is concluded that the combination of FEA simulation and empirical formulas employed in this study could be used in the computation and prediction of the fatigue life of solder joint alloys when subjected to random vibration. Based on the thermal and mechanical responses of lead-free SAC405 and SAC396 solder alloys, they are recommended as a suitable replacement of lead-based eutectic Sn63Pb37 solder alloy for improved device thermo-mechanical operations when subjected to random vibration (non-deterministic vibration). The FEA simulation studies' outcomes are validated using experimental and analytical-based reviews in published and peer-reviewed literature.