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.

Graphic Abstract

中文翻译：

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纯金属凝固过程中涂层对生长不稳定性影响的耦合模型

摘要

模具涂层是控制金属凝固过程中传热速率和微观组织发展的因素之一。在这项研究中，理论上研究了涂层对纯金属凝固过程中生长不稳定性的影响。凝固过程分为两个阶段：在第一阶段中，熔融金属与凝固壳之间的热传导随相变而变化，凝固壳与涂层之间以及涂层与模具之间的传热问题需要被建立。在第二阶段，应该对机械问题进行建模，其中包括由于应力分布而导致的层变形。提出的模型通过在不考虑热和机械问题耦合的情况下检查凝固早期涂层的作用来扩展先前的研究。在此模型中，热问题会影响层中的热应力分布，但机械问题不会影响热问题。该假设仅对凝固的早期阶段有效，因为热和机械问题之间的耦合在该过程的其他阶段起着重要作用。假设固化的外壳，涂层和铸模的热容为零，以便具有主要的分析解决方案。这些假设显然对所得预测的准确性施加了严格的限制，但是可以根据进行的分析保留一定的普遍性来证明它们的合理性，因此可以推断出材料特性和操作条件的变化对系统稳定性的影响。使用线性摄动法可以解析地解决问题的传热部分。但是，问题的机械部分是使用适用于刚性问题的可变步长变量阶校正器和预测器算法从数字上解决的。详细研究了工艺参数（如导热率，涂层厚度和各层之间表面的热接触电阻）对凝固壳厚度增长的影响。

图形摘要