Mathematical theory of polycrystalline materials

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Metal and alloys typically form as polycrystals, consisting of different single crystal grains, each grain corresponding to a different orientation of the underlying atomic lattice. Under thermal treatment or applied forces alloys develop microstructure within each grain due to phase transformations involving a change of shape of the lattice, and to dislocations (defects in the lattice structure), this microstructure having to fit together geometrically both within each grain and across grain boundaries. The geometry of the grains, the orientation of the crystal lattice in each grain, and the microstructure within each grain, are all crucial for determining the macroscopic behaviour of the material. The aim of the proposal is to analyze the behaviour of polycrystals using rigorous mathematical theory, covering all the aspects described above, and to apply the results to different metals and alloys, in particular to the development of new high-performance steels in collaboration with Tata Steel.