Numerical simulation of diffusion induced phase separation and coarsening in binary alloys

Solder materials are solid mixtures and show a variety of micro-structural changes, for example, separation of phases and phase coarsening (Ostwald ripening). The micro-structural changes influence strength and life expectation of these materials. They may be of significant effect, in particular, in very small components such as solder joints in microelectronic packages. er to analyze the micro-morphological evolution with a diffusion theory of heterogeneous solid mixtures we apply an extended Cahn–Hilliard phase field model. The underlying equations involve a bipotential operator and, accordingly, fourth-order spatial derivatives. Thus, the variational formulation of the Cahn–Hilliard problem requires approximation functions which are piecewise smooth and globally C 1 -continuous; standard finite element techniques cannot be applied here. In our contribution we fulfil the continuity requirement by means of rational B-spline finite element basis functions. To illustrate the versatility of this approach numerical simulations of phase decomposition and coarsening controlled by diffusion and by mechanical loading are discussed and compared with experimental results. Studies of error and convergence are provided.