Full Field Model Describing Phase Front Propagation, Transformation Strains, Chemical Partitioning, and Diffusion in Solid–Solid Phase Transformations. Issue 3 (26th January 2023)

• Record Type: Journal Article
• Authors: Pohjonen, Aarne
• Is Part Of: Advanced theory and simulations. Volume 6:Issue 3(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-01-26
• Subjects: diffusion -- eigenstrains -- full field model -- mechanics of deformable solids -- partial differential equations -- phase transformations; Science -- Simulation methods -- Periodicals; Science -- Methodology -- Periodicals; Engineering -- Simulation methods -- Periodicals; Engineering -- Methodology -- Periodicals; 507.21
• DOI: 10.1002/adts.202200771
• Languages: English
• ISSNs: 2513-0390

Abstract

Abstract: A novel mathematical formulation is presented for describing growth of phase in solid‐to‐solid phase transformations and it is applied for describing austenite to ferrite transformation. The formulation includes the effects of transformation eigenstrains, the local strains, as well as partitioning and diffusion. In the current approach the phase front is modeled as diffuse field, and its propagation is shown to be described by the advection equation, which reduces to the level‐set equation when the transformation proceeds only to the interface normal direction. The propagation is considered as thermally activated process in the same way as in chemical reaction kinetics. In addition, connection to the Allen–Cahn equation is made. Numerical tests are conducted to check the mathematical model validity and to compare the current approach to sharp interface partitioning and diffusion model. The model operation is tested in isotropic 2D plane strain condition for austenite to ferrite transformation, where the transformation produces isotropic expansion, and also for austenite to bainite transformation, where the transformation causes invariant plane strain condition. Growth into surrounding isotropic austenite, as well as growth of the phase which has nucleated on a grain boundary are tested for both ferrite and bainite formation. Abstract : Understanding austenite transformation to ferrite and bainite is important for modeling of microstructure evolution in steels during cooling. Mathematical formulation for the effect of strains caused by the transformation, as well as the partitioning and diffusion of carbon during transformation is described. Numerical examples show the concurrent operation of these phenomena, and their effects on the resulting phase morphology.