Modelling of Phase Transformations

The course includes the theoretical basis for understanding phase transformations in metals as well as models and methods for a mathematical and numerical description of some technological important phase transformations in metals (with emphasis on aluminium) that are determining for the evolution of microstructure and properties during casting/solidification and thermal processing (heat treatments/welding). The course starts with a short description of the thermodynamical basis for phase transformations, based on the consideration of simple binary phase diagrams. It is followed by an atomistic and mathematical description of diffusion together with structural aspects of phase boundaries. After that a more detailed presentation of phase transformations by nucleation and growth is given, including homogeneous and heterogeneous solidification, precipitation, growth and dissolution of second phase particles, recrystallization and grain growth, including the concepts of Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetics, additivity and iso-kinetic reactions. The topics will be presented and analysed by means of relevant mathematical/numerical models which the students themselves should implement and use/explore through 3 relevant mini projects.

After successfully completing the course, students will be able to:

• Develop and use thermodynamic models for alloys, including deriving and comparing solid-solution models, estimating temperature-dependent solubility and vacancy concentrations, and computing/analysing simple binary phase diagrams. They shall also understand the main ideas behind CALPHAD for multicomponent systems.
• Model diffusion in materials across scales, explaining atomistic vs. continuum descriptions, deriving key relations such as Darken’s equations, and solving representative diffusion problems analytically and numerically (including 1D explicit and implicit schemes with a critical comparison of their accuracy and stability).
• Model phase-transformation kinetics and microstructure evolution, including nucleation and growth (homogeneous vs. heterogeneous), particle growth/dissolution, JMAK kinetics, and iso-kinetic solutions, for both isothermal and non-isothermal heat treatments.
• Build coupled process-microstructure simulations, such as combining heat-transfer and microstructure models for solidification and using these to analyse how composition and thermal processing affect transformation behaviour.
• Critically evaluate models and scientific sources, assessing assumptions, validity, and limitations of theoretical/numerical approaches in relation to real materials and industrial processing, and judging the reliability of information from the literature.
• Work in teams and communicate results clearly, by collaborating on project work, producing well-structured analyses, giving professional oral presentations.

Each module involves working on a modelling project, including preparing a presentation, and ends with plenary presentations followed by individual questioning. The evaluation of the modelling projects serves as the basis for the final grade. Total work load is estimated to be about 200 hours (incl. independent home work).