A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations. Issue 1 (24th March 2023)

• Record Type: Journal Article
• Authors: Westermann, Hendrik; Mahnken, Rolf
• Other Names: Böhm Ch. guestEditor.; Mang K. guestEditor.; Markert B. guestEditor.; Reese S. guestEditor.; Schmidtchen M. guestEditor.; Waimann J. guestEditor.; Kaliske M. editorInChief.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 22:Issue 1(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-03-24
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202200080
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Microstructure evolution during recrystallization annealing affects the macroscopic material properties for various steels. The phenomena include phase transformations and carbide precipitation. The requirements for most engineering components are both, high strength and sufficient residual ductility to withstand the mechanical burden and to offer preferable manufacturing conditions. In the present work a thermodynamic framework is proposed to combine two phase‐field approaches for the investigation of bimodal grain sizes. The developed prototype model studies phase transformations, diffusion of the carbon concentration and precipitation of carbides. Recystallization annealing enables the transformation of the purely martensitic microstructure into ferrite accompanied by carbide precipitation. The grain boundary movement is described by grain orientation and microstructure crystallinity. An adopted phase‐field approach describes the microstructure evolution driven by temperature and stored energy. The model is extended to capture carbide precipitation based on the diffusion kinetics of carbon atoms. Fractions of ferrite and carbide phases are depicted by the order parameters of a multiphase‐field model tied to the thermodynamic framework, thus yielding a novel constitutive framework capable of describing the complex material behavior of metals during thermo‐mechanical processing. Subsequently, a suitable algorithm for the presented phase‐field plasticity model in two dimensions is proposed. The evolution of phase fractions and carbide precipitation is illustrated in numerical examples by conclusive finite element simulations.