Mathematics as tough as steel

The Weierstrass Institute recently saw the launch of the European doctoral programme MIMESIS (Mathematics and Materials Science for Steel Production and Manufacturing). This programme enables young researchers -- in collaboration with trade and industry -- to develop new methods of steel manufacturing and processing. Professor Dietmar Hömberg, Project Manager at the Weierstrass Institute said: "In this project, we are combining the disciplines of mathematics and materials science, several different countries, and science and industry. The qualifications that our young researchers acquire in the context of this programme are in great demand on the employment market."

Professor Porter at the Centre for Advanced Steels Research in the University of Oulu adds: "This programme offers a unique opportunity for students with a mathematics background to learn about and apply their skills to engineering issues of practical importance to industry. Likewise, with the aid of the programme, students with a background in materials science or process metallurgy and an interest in mathematics and modelling can develop skills that will serve them well in both industry and academia."

The physical properties of steel can be precisely managed by using phase transformations. Particularly hard material is made by first heating it and then subjecting it to rapid cooling. This method might be used in the manufacture of a cogwheel, for instance, whereby the inner section of the product should remain softer than the outside in the interests of durability. The inductive heating of the material subjects it to various flow frequencies simultaneously: the high frequency only penetrates the tooth tip, the medium frequency the tooth root. A considerable number of parameters all play a role simultaneously. To be able to control this process technically, scientists have to be able to run computer simulations. To understand the process, the field of mathematics serves the purpose of optimisation whilst materials science provides an insight into factors at play inside the steel.

The modelling of phase transformations will also be an important part of three other topics to be tackled in the programme. One concerns being able to predict whether a harmful phase has formed in stainless steel during its production or during the fabrication of stainless steel parts. If it forms, the stainless steel is no longer stainless -- it becomes susceptible to corrosion. Another is concerned with being able to predict the detailed internal structure of the strongest steel microstructure -- martensite -- in order to be able to make it very tough as well as very strong. Yet another project will be concerned with modelling both phase transformations and induction heating to make steel pipes that, at the same time, are extremely wear resistant and tough.

Steel manufacturing is somewhat akin to cookery on a grand scale: the ingredients for making the steel -- the solid alloying elements -- are mixed into molten iron in a ladle by bubbling gas into the melt from underneath. Because this is a very complex process and it is not possible to sample the mixture in order to test whether the desired homogeneous chemical composition has been achieved, the project's researchers will use mathematical methods to simulate the flow processes taking place in the foundry ladle.

The way in which the mixture is stirred also influences the final result and therefore also needs to be optimally controlled. During the stirring process, an opening forms in the layer of slag that is present on the surface of the molten mixture. The size of this opening enables mathematicians to calculate the velocity of the flow. It is also possible to gather information about the flow by measuring vibrations on the outside of the foundry ladle. By using these methods, mathematicians are able to solve inverse problems.

The doctoral programme MIMESIS, with its research funding of € 2.1 million, encourages mobility on various levels: within the European Industrial Doctorate support programme in the Marie Skłodowska-Curie actions of the EU, the participating partner organisations recruit holders of scholarships who have lived for a maximum of one year in the last three in the country in which the partner is located. The junior researchers spend at least half the time they invest in their doctorates with an industry partner, thereby encouraging inter-sectoral mobility. Finally, the project has a clear interdisciplinary makeup: every fourth vacancy in the programme is for a doctoral position in mathematics or materials science. The Finnish University of Oulu is the WIAS's scientific partner, whilst companies in Norway, Sweden and Finland are the industry partners. "Such intensive industry contacts are of course beneficial for our whole institute," stressed Hömberg. He added: "In our choice of acronym for the project, we wanted to highlight the interconnectedness between mathematical models and their application to real problems: MIMESIS is a reference to the representative depiction of reality."