Analysis, Modellbildung und Simulation skalenübergreifender, mehrphasiger Erstarrung in Legierungssystemen

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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.