Analysis, Modellbildung und Simulation skalenübergreifender, mehrphasiger Erstarrung in Legierungssystemen

金属合金是工业应用中最广泛使用的材料，其凝固过程对铸件的材料性能和质量至关重要。该项目的目标是开发、分析和数值近似金属合金系统中多尺度多相凝固现象的新模型，并描述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，然后将相关的尖锐的接口模型的正式和严格的渐近。将应用均匀化方法，通过均匀化和平均化较小尺度上的演化规律，确定较大尺度上的生长规律。在这种情况下，我们的目标是分析获得概括的理论预测的杰克逊和亨特的情况下，共晶不一定稳定增长。我们工作的另一个重要部分将是多尺度凝固现象的数值模拟。最后，我们要使用新的建模和仿真技术来描述的整体凝固过程中的共晶晶粒/细胞，一次枝晶与中间共晶结构和螺旋共晶结构的生长的耦合生长。

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.