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Mathematics and Materials Science for Steel Production and Manufacturing

Periodic Reporting for period 2 - MIMESIS (Mathematics and Materials Science for Steel Production and Manufacturing)

Reporting period: 2017-10-01 to 2019-09-30

The last fifteen years have seen the development of ever more refined high-strength and multiphase steels with purpose designed chemical compositions allowing for significant weight reduction, e.g. in automotive industry. The production of these modern steel grades needs a precise process control, since there is only a narrow process window available in which the desired physical properties are defined. In combination with component walls getting thinner and thinner these new steels make also new demands on a more precise process control in metal manufacturing processes, such as welding and hardening.

Improved and optimized process control requires quantitative mathematical modelling, simulation and optimization of the complex thermal cycles and thermal gradients experienced by the processed material. Such models require an understanding of the behaviour of the materials from a materials science and phase transformations perspective. Unfortunately, it is almost impossible for companies to find graduates combining deep knowledge in materials science with expertise in mathematical modelling, simulation and optimization.

Filling this gap has been the central goal of this EID. The consortium consisted of two steel-producing companies, SSAB Europe and Outokumpu Stainless, a steel manufacturer, EFD Induction, and two scientific partners, for materials science the University of Oulu and for applied mathematics the Weierstrass Institute for Applied Analysis and Stochastics. The Berlin Mathematical School acted as a further non-beneficiary partner providing additional training opportunities for the MIMESIS ESRs.

A specific feature of the MIMESIS training concept has been to exploit its interdisciplinarity on the interface of applied mathematics and materials science. To this end, all students spent 3 months from May to July 2016 in Berlin for a course on “Finite Element simulation of multi-field problems”. For a second training block on “Physical metallurgy of metals and steels”, all students stayed at the University of Oulu from November 2016 to January 2017. Both courses were complemented with transferable skills trainings on time and self-management, presentation training and on “Scientific research and Ethics”. In the second half of the project there has been a stronger emphasis on hands-on industrial trainings.

The research focussed on three major topics - induction heating, phase transformations in steel alloys, and ladle stirring and has led two seven PhD theses and more than 30 research publications.
After a recruitment phase, seven MIMESIS students began their work in February 2016, one student started in May 2016. Four students had a background in materials science, the other four in applied mathematics and computational engineering.

Supported by an interdisciplinary training program between materials science and applied mathematics and secondments to at least two industrial partners, the students worked on ambitious PhD projects combining expertise in materials science and applied mathematics and covering a broad range of topics centred around three major topics - induction heating, phase transformations in steel alloys, and ladle stirring.

Two of the theses concern hardening: one was on the hardening of helical and bevel gears by an optimized single or multi-frequency approach. and the other is a novel idea about the hardening of the inner surface of pipes. Here, main achievements were the development of computational tools for a systematic approach towards induction coil design and experimental work using a thermomechanical simulator together with numerical simulations, which helped to find a feasible path to create a graded material structure with extremely good wear resistance on the inner surface leading also to a number of research papers involving two companies.

Two of the theses are related to induction heating applications, for the production of high-frequency welded pipes and for pre- and post-heating in the thermal cutting of steel plates. In high-frequency tube welding a break-through result could be achieved for the process simulation. An improved modeling of spatially dependent velocities in combination with a numerical stabilization procedure allowed for the first time for a complete three-dimensional process simulation with arbitrary feed velocities. Concerning the thermal cutting of steel plates, the consequential use of modern optimal control methods for partial differential equations allowed the computation of optimal preheating strategies and a feasibility study as a decision support tool for investing in this new technological approach.

Two further theses were concerned with phase transformations during steel production. The first one broadened the knowledge of quantitative prediction of intergranular corrosion while the second one achieved a better understanding of the microstructure of as-quenched low-carbon auto-tempered martensitic steels, which will help in making better, environmentally efficient, lightweight, and high-strength steels.
The final two theses were related to secondary metallurgy in the ladle. In the first one, computational fluid dynamics models of ladle treatments have been used to optimize the alloying practice and to reduce the consumption of nickel as an alloying element. The last one achieved an improvement of ladle stirring monitoring and control based on an optimal control approach utilizing vibration measurements.

The research work has led to seven PhD theses, one student took a parental leave in the last stage of his contract and decided not to come back and finish his thesis. The ESRs presented their achievements in international conferences and university seminars in Europe, America, and Asia. Moreover, they participated in activities like the “Long night of sciences” where they presented their work to the general public.

Practical aspects, simulation strategies and developed models have been taken up by the companies and will lead to further collaboration with the scientific partners.
The interdisciplinary research concept of MIMESIS on the interface of materials science and applied mathematics lead to significant progress beyond the state of the art. All projects have addressed challenging questions in materials sciences and engineering. A common mathematical feature is that one has to deal with multiple scales, which require an adequate mathematical treatment. In induction heating problems for instance, one has to deal with two time scales, one for the rapidly oscillating magnetic field and one for temperature diffusion. Due to the skin effect, one has to resolve a fine boundary layer where the eddy currents cause heating. In phase transition problems, the interface between different phases needs to be resolved adequately, and in the ladle problems a multiscale ansatz is needed to model turbulence.

All topics are relevant to the needs of the companies, leading to improved and more efficient processes with a more frugal use of energy and raw material, thereby contributing to the competitiveness of European industry and to a sustainable development.

Last but not least, the well-trained MIMESIS ESRs will take up positions in research and industry and contribute to the European economic development in the era of digitalization with their broad expertise in engineering and applied mathematics.
High Frequency welding of tubes, simulation of temperature distribution of different Vee-openings
Induction hardening for slurry transportation pipe: prior and final microstructure, final hardness
Optimal pre-heating strategy for flame cutting