The effect of the melt thermal gradient on the size of the constitutionally supercooled zone

A Prasad,P D Lee,M Easton,D Stjohn,L Yuan

doi:10.1088/1757-899x/117/1/012001

Abstract

Recent verification of the analytical Interdependence model by a numerical solidification model (µMatIC) confirmed the critical role of constitutional supercooling (CS) in achieving sufficient undercooling to trigger successful nucleation events. The location of the maximum amount of CS (ΔTCSmax) is some distance from the interface of the previously growing grain and this distance contributes to the final as-cast grain size. The effect of the thermal gradient, G, on the size of the CS zone (CSZ) was neglected in that work. However, G is expected to affect the size of the CSZ (i.e. the length of the CSZ, x’CSZ, and the location of ΔTCSmax, x’CSmax). This investigation assesses the effect of G on x’csz and x'CSmax. A range of G values is introduced into both the analytical and the numerical models to obtain a correlation between the value of G and the dimensions of the CSZ. The result of a test case from the analytical model shows that x’CSmax initially decreases rapidly and then decreases gradually approaching zero at very high values of G. Independent of the analytical model, the results from the numerical model replicate the trend obtained from the analytical model.

Highlights

The Interdependence model, which can predict the grain size of a casting, states that a new grain is nucleated when the amount of constitutional supercooling ( TCS) of an already growing grain is large enough to activate an inoculant particle, which requires a certain minimum undercooling [1,2,3,4]
Equation 1 shows the key distances of the Interdependence model for a near-zero thermal gradient at large distances from the advancing solid-liquid (S-L) interface
In the original model [4] the expression for xcs contains a ‘z’ term which sets the additional CS required for subsequent nucleation events where z is a function of the thermal gradient present in the system

Summary

Introduction

The Interdependence model, which can predict the grain size of a casting, states that a new grain is nucleated when the amount of constitutional supercooling ( TCS) of an already growing grain is large enough to activate an inoculant particle, which requires a certain minimum undercooling [1,2,3,4]. The effect of the thermal gradient is usually studied in directional solidification experiments and numerical models. The changing shape of TE(x) near the interface suggests that between the S-L interface and x’CSZ there exists a distance, x’CSmax, where TCS is at its maximum value TCSmax. Both x’CSZ and x’CSmax are shown schematically for TA4 in figure 1. A numerical model, MatIC [5, 6], is used to simulate the solidification of a grain in the presence of a thermal gradient and x’CSZ is estimated. The results from the analytical and MatIC models are compared

Analytical solution

Numerical solution