Modeling and Simulation of Thermochemical Heat Treatment Processes: A Phase Field Calculation of Nitriding in Steel.

In order to provide greater improvements in material performance with respect to hardness, fatigue, wear resistance and corrosion resistance, among other mechanical properties, nitrogen is commonly introduced on steel surface at elevated temperature. Such enhancement, referred to as nitriding, results in the diffusion of nitrogen into the steel with development of continuous layers of iron-based nitrides and precipitation of alloying-element nitrides, depending on the nitriding kinetics. Up till now, the simulation of nitriding process is done only under restricted conditions by using classical models which describe the diffuse nitriding layers with sharp interfaces. However, the classical models lead to difficulties in the computation of the free boundary problem, since the position of the interface has to be calculated explicitly. This work provides a generalized approach for studying the evolution of the microstructure during nitriding process in steel. It presents the application of a phase field model to describe the nitriding of steel in order to numerically deal with the moving free boundary. The treated nitriding layers are described in terms of a phase field parameter which represents a property of the system that is non-zero in a distinct region of the steel surface and 0 otherwise. A partial differential equation is formulated to govern the time evolution of the phase field parameter and it is coupled to other equation that determines the relevant field of transport phenomenon. This allows the whole domain to be treated simultaneously. In particular, the interface is not tracked but is given implicitly by the value of the phase field parameter as a function of time and space. The set of coupled evolution equations the concentration field and the phase-field model equations, is solved by using a finite element software. The approach is applied to compute nitriding of a low-carbon steel and evolution of compound layer formation. The numerical calculations correlate with experimental measurements at different times. iv Acknowledgement My sincere gratitude goes to Prof. Dr. Michael Böhm and Prof. Dr.-Ing. Franz Hoffmann for their inspirational supervision and incredible openness throughout the duration of this doctoral thesis. They have provided an invaluable guidance, good recommendations and abundant zeal that catalyzed the completion of this work. I would like to thank Dr.-Ing. Martin Hunkel for his support and priceless magnanimity. The tremendous incentives provided by Prof. Dr. Peter Maaß, the courteous motivation of Prof. Dr. Angelika Bunse-Gerstner and the masterly advice of Prof. Dr. Alfred Schmidt cannot go without being acknowledged. I thank you all. My appreciation extends to the University of Bremen for providing the PhD scholarship that cushioned my financial liabilities throughout the dissertation. I am equally thankful to all academic, administrative and technical staff of the ’Zentrum für Technomathematik’ for their unrelenting support, in particular all members of ’AG Böhm’. My fellow colleagues at the graduate school Scientific Computing in Engineering (SCiE) have been fantastic: my ’Tandem’ S. Meier, for the successful cooperation, D. Kubalinska, J. Montalvo, L. Prünte, Z. Akbay, S. Vudathu, Y. Wang and Dr. D. Lorenz for their productive discussions and good working relationship. Furthermore, I am grateful to my wife Abibat, and children Abibat (Jnr) and Abdulsalam, for their numerous sacrifices and utmost perseverance throughout the duration of this programme. I will always love you all. I thank all the unmentioned people who supported me in one way or the other during my doctoral thesis. Finally, I thank God for making it possible. Yakub Adesoga Tijani Zentrum für Technomathematik