Uncoupled Modeling of the Effects of Coating Layer on the Growth Instability in Pure Metal Solidification

Abstract

The mold coating is one of the factors to control the heat transfer rate and development of microstructure in metal solidification. In this study, effects of the coating layer on growth instability in solidification of pure metals are theoretically examined. Solidification process is modeled in two phases: In the first phase, the heat conduction with phase change between the molten metal and the solidified shell, and the heat transfer problems between the solidified shell and the coating layer and the coating layer and the mold need to be established. In the second phase, mechanical problem which includes deformations in the layers due to stress distributions should be modeled. Presented model extends previous studies by examining the effects of coating layer in the early stages of solidification under the assumption that the thermal and mechanical problems are uncoupled. In this model, the thermal problem affects the thermal stress distribution in the layers, but the mechanical problem does not affect the thermal problem. This assumption is valid only for the early stages of solidification since the coupling between the thermal and mechanical problems plays an important role in further stages of the process. The thermal capacitance of the solidified shell, the coating layer and the mold is assumed to be zero in order to have a predominantly analytical solution. These assumptions clearly place severe restrictions on the accuracy of the resulting predictions, but they can be justified on the grounds that the resulting analysis retains some generality and hence permits deductions to be made about the effect of changes of material properties and operating conditions on the stability of the system. The heat transfer part of the problem is solved analytically using a linear perturbation method. However, the mechanical part of the problem is solved numerically using a variable step variable order corrector and predictor algorithm which is suitable for stiff problems. Effects of process parameters such as thermal conductivities, coating thickness and thermal contact resistances at the surface between each layer on the growth of solidified shell thickness are investigated in detail.