Modeling constrained dendrite growth in rapidly directional solidification

Abstract

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 nonequilibrium 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 nonequilibrium on the constrained dendrite growth were studied.

Effect of Slow Solidification of Ultra-thick Continuous Casting Slab on Solidification Structure and Macrosegregation

“…The solidification coefficient is obtained by using Eq. (11). Then, substitute the solidification coefficient from Eq.…”

“…The "Continuous nucleation model" [11] is improved by Rappaz and Gandin in 1989. The model believed that the nucleation will occur different position in slab.…”

A vertical continuous casting machine for large blooms

“…and crystal grain growth is calculated based on a simplified KGT model [7], with growth speed of the dendrite tip…”

“…Rappaz [6] proposed a Gaussian distribution to describe nucleation intensity d n/ Δ T , and hence local crystal density, where total melt undercooling of the dendrite tip is and crystal grain growth is calculated based on a simplified KGT model [7], with growth speed of the dendrite tip where Δ T max and Δ T σ are the average and standard deviation of nucleation undercooling (K); Δ T c , Δ T t , Δ T r , and Δ T k are constitutional, thermodynamic, interface curvature, and growth kinetics of undercooling; and a 2 and a 3 are coefficients.…”

Simulation analysis on the round billet macrostructure of special steel vertical caster

“…The crystal grain growth is calculated based on a simplified KGT model [8], and the growth speed of the dendrite tip can be calculated as follows:…”