Strain rate-dependent tensile deformation and failure behavior in single-crystal β-Sn

Given that electronic components often undergo intricate thermal and mechanical loads during operation, comprehensively understanding lead-free solder, particularly solder based on $\beta$-Sn, in various complex load conditions, plays a crucial role in ensuring the structural integrity and functional reliability of integrated circuits. Therefore, investigating the mechanical properties and fracture behavior of $\beta$-Sn as a solder material holds paramount importance. In this study, we performed molecular dynamics simulations using the modified embedded atom method to investigate the mechanical properties and crack propagation of single-crystal $\beta$-Sn under different strain rates. The research findings demonstrate that as the strain rate increases, the single-crystal $\beta$-Sn exhibits elevated yield strength, fracture strength, and strain, while the elastic modulus decreases. Under higher strain rates, the relationship between dislocation density and strain rate in single-crystal $\beta$-Sn is quantitatively elucidated. The substantial increase in internal dislocation density imparts conspicuous strain hardening to the material, rendering plastic deformation more challenging. This observation sheds light on the microscale mechanism of strain hardening at the atomic level. Our results shall facilitate a deeper investigation into the mechanical behavior of single-crystal $\beta$-Sn while also paving the path for optimizing the design and application of lead-free solder materials in the electronics industry.