A study of the coarsening in tin/lead solders

This paper presents a model, which is capable to simulate the coarsening process observed during thermo- mechanical treatment of binary tin±lead solders. Fourier transforms and spectral theory are used for the numerical treatment of the thermo-elastic as well as of the di€usion problem encountered during phase separation in these alloys. More speci®cally, the analysis is based exclusively on continuum theory and, ®rst, relies on the numerical computation of the local stresses and strains in a representative volume element. Second, this information is used in an extended di€usion equation to predict the local concentrations of the constituents of the solder. Besides the classical driving forces for phase separation, as introduced by Fick and Cahn±Hilliard, this equation contains an additional term which links the mechanical to the thermodynamical problem. It connects internal and external stresses, strains, temperature, as well as concentrations and allows for a comprehensive study of the coarsening and aging proces