Prediction of Cooling Curves for Controlled Unidirectional Solidification Under the Influence of Shrinkage: A Semi-analytical Approach

Abstract

Quality of casting products can be significantly improved by controlling the crystal growth rate. Both dendritic and equiaxed grain structures depend strongly on crystal growth rate along the crystallographic direction. Uncontrolled solidification processes may lead to the formation of porous and columnar material with an extremely non-homogeneous composition distribution. These undesirable micro-structures can be avoided by adopting an optimal cooling rate (K/s) during the crystal growth. The present work focuses on determining suitable cooling curves to obtain desired unidirectional crystal growth rates, by implementing a semi-analytical model. Here, we defined cooling curve as the time history of temperature evolution at the cold boundary. The proposed semi-analytical heat transfer model is diffusion driven and accounts for shrinkage effect during solidification. The proposed model is found capable of predicting cooling curves for prescribed interface velocities. The model is self-sufficient in validating itself by means of solving inverse and forward problems. The cooling curve prediction by the model is validated by using it as the transient boundary condition for an existing enthalpy updating scheme-based numerical model. The proposed model is also applied to empirical data reported in literature, to validate the model against experimental results. All the validations showcased excellent fit. The proposed model will facilitate controlled unidirectional crystal growth rate by providing cooling rate (K/s) as an input for the experiments involving directional solidification.