Analysis, Modellbildung und Simulation skalenübergreifender, mehrphasiger Erstarrung in Legierungssystemen

金属合金是工业应用中应用最广泛的一类材料，其凝固过程对铸件的材料性能和质量具有重要意义。本项目的目标是开发、分析和数值逼近金属合金系统多尺度多相凝固现象的新模型，并描述在不同长度尺度上发生的凝固效应的相互作用。我们计划开发相场模型，然后通过形式和严格的渐近性将其与锐化界面模型相关联。通过对较小尺度上的演化规律进行均化和平均化，将应用均匀化方法来确定较大尺度上的增长规律。在这一背景下，我们的目标是以分析的方式获得杰克逊和亨特的理论预测在共晶不一定稳步增长的情况下的推广。我们工作的另一个重要部分是多尺度凝固现象的数值模拟。最后，我们希望使用新的模拟和模拟技术来描述共晶颗粒/晶胞的整个凝固过程、初生枝晶与中间共晶组织的耦合生长以及螺旋共晶组织的生长。

The solidification process in metallic alloys, which are the most widely-used group of materials in industrial applications, is of great importance for the material properties and quality of the castings. The objective of this project is to develop, analyze and numerically approximate new models for multi-scale multi-phase solidification phenomena in metallic alloy systems and to describe the interaction of solidification effects occuring on different length scales. We plan to develop phasefield models which then will be related to sharp interface models by formal and rigorous asymptotics. Homogenization methods will be applied to determine growth laws on larger scales by homogenization and averaging of evolution laws at smaller scales. Within this context, we aim to analytically obtain generalizations of theoretical predictions by Jackson and Hunt to situations where eutectics are not necessarily steadily growing. Another important part of our work will be numerical simulations of multiscale solidification phenomena. Finally, we want to use the new modelling and simulation techniques to describe the overall solidification process of eutectic grains/cells, of the coupled growth of primary dendrites with an intermediate eutectic structure and of the growth of spiral eutectic structures.