Analysis, Modellbildung und Simulation skalenübergreifender, mehrphasiger Erstarrung in Legierungssystemen

合金系统中跨尺度多相凝固的分析、建模和模拟

• 批准号: 5274752
• 负责人: Professor Dr. Harald Garcke
• 金额: --
• 依托单位: Lehrstuhl für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5274752?language=en
• 关键词: Analysis; Modellbildung; und; Simulation; skalen

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.

金属合金是工业上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有着重要的影响。本项目的目标是开发、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，并描述发生在不同长度尺度上的凝固效应的相互作用。我们计划开发相场模型，然后将通过正式和严格的渐近与尖锐界面模型相关联。均质化方法将通过在较小尺度上均质化和平均进化规律来确定较大尺度上的生长规律。在这种背景下，我们的目标是分析地获得杰克逊和亨特对共晶不一定稳定增长的情况的理论预测的概括。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，我们希望利用新的建模和仿真技术来描述共晶晶粒/晶胞的整体凝固过程、初生枝晶与中间共晶组织的耦合生长过程以及螺旋共晶组织的生长过程。