Integrating geometric effects on the thermomechanical behavior of solder joints using the Q parameter

Solder joints on printed circuit boards are constantly subjected to thermal loads. These joints come in various geometries, which can significantly affect their thermomechanical behavior. Previous studies focused on clarifying the thermomechanical behavior resulting from geometric changes by qualitatively analyzing the metallurgical microstructure, stress/strain distribution and strain energy within the solder joint. This research aims to quantify the relationship between joint geometry, and damage caused by thermal loading using a specific parameter. A history-dependent cohesive zone model was developed to calculate the dissipated energy ( DE th ) due to thermal cycling in solder joints with different geometries. The obtained DE th values increased from 75.3 to 147.6 J/m 2 for the Arcan-type specimen and from 90 to 191.2 J/m 2 for the DCB-type specimen as the thermal loading range increased from 25–105 °C to 25–165 °C. These results were subsequently correlated through the constraint parameter, Q . By plotting the DE th - Q diagrams for two specific geometries, a unique geometric locus is observed. Additionally, the variation in the calculated Q values with radial distance remained below 10% for all cases, confirming the numerical robustness of the Q evaluation procedure. The findings suggest that the Q parameter effectively quantifies the geometric effects on the thermomechanical behavior of solder joints. The developed DE th - Q methodology provides a unified and geometry-sensitive approach for thermal damage characterization, reliability assessment, and design optimization of solder joints in electronic packaging applications.