Constitutive modeling of solder alloys for drop-impact applications

The stress-strain data of four solder alloys - Sn37Pb, Sn1·0Ag0.1Cu, Sn3·5Ag, and Sn3·0Ag0.5Cu - at seven initial strain rates between 0.005 s− 1 to 300 s− 1 have been generated using a combination of mechanical and drop-weight compression tests. Assuming negligible inertia of the test specimen, the stress-strain-strain rate characteristics σ(ε,ε̇(ε)) of a solder alloy can be readily evaluated from the measured time history of the impact force in a drop-weight compression test. The stress-strain-strain rate characteristics are transformed to the condition of isostrain rate σ(ε,ε̇iso) while being curve-fitted to the Johnson-Cook and the Pernzya models. The former represents the dynamic-yield model and the latter the viscoplastic model. The quality of the extracted material constants for the Johnson-Cook model are validated by (i) reproducing the impact force-time characteristic of the Sn37Pb solder test specimen using finite element analysis and using the extracted material constants; and (ii) extracting the material constants for the Sn37Pb solder alloy using the inherent optimisation capability of commercial finite element code.