Semi-analytical model of microsegregation during dendritic solidification

Based on mass conservation in a typical micro-solidification volume element combining with previous work, a semi-analytical model of microsegregation was established for binary alloys with dendritic solidification. The effects of back-diffusion and coarsening on microsegregation are both considered in the semi-analytical model, and the coarsening of arm spacing is directly calculated to make the semi-analytical model more precise. The semi-analytical model will be simplified to the BF model or the Mortensen model when back-diffusion or coarsening is considered only, respectively. The diffusion model and the coarsening model separately represented by the BF model and the Mortensen model are well unified by the semi-analytical model. Moreover, the semi-analytical model can be extended to multicomponent alloys. The Fe-C-X(Si, Mn, P, S) alloy was taken as an example to elaborate the solving process. The eutectic fractions of the Al-4.9%Cu alloy and the zero strength temperature (ZST) and zero ductility temperature (ZDT) of carbon steel Fe-C-X(Si, Mn, P, S) during solidification can be well predicted by the semi-analytical model.