Modeling constrained dendrite growth in rapidly directional solidification

Incorporating the effect of nonlinear liquidus and solidus, a constrained dendrite growth model was established for rapidly directional solidification, where both the interface and the bulk liquid are under local non-equilibrium conditions. The effect of nonlinear liquidus and solidus was first introduced into the interface kinetics, based on which the marginal stability criterion was then derived. By this way, not only the temperature dependent equilibrium partition coefficient k e, equilibrium liquidus slope m l and equilibrium solidus slope m s but also the derivation of k e with temperature are considered. The model is more physically realistic than the works in which the effect of nonlinear liquidus and solidus is not incorporated into the interface kinetics and hence the temperature dependent m s is not embodied. Applying the model to rapidly directional solidification of Ag–15 wt% Cu alloy, the effects of nonlinear liquidus and solidus and local non-equilibrium on the constrained dendrite growth were studied.