A Finite-Element Approach for the Partitioning of Carbon in Q&P Steel
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QUENCHING and partitioning (Q&P) supply a good combination of toughness and strength. This treatment has been extensively used for the manufacture of structural automotive parts for the last few years because the steels treated by this process achieve a final microstructure consisting of a martensitic matrix with carbon-enriched retained austenite.[1,2] Carbon partitioning from martensite into the austenite phase is paramount for the stabilization of the untransformed austenite at room temperature. The role of this retained austenite is to provide the transformation-induced plasticity (TRIP) effect, which enhances the elongation.[3] In this sense, Q&P steels are receiving increased attention for their promising potential to improve crashworthiness and reduce fuel consumption.[4] Today, the main focus of this field research is how to determine the most suitable parameters, like quenching temperature (QT), partitioning temperature (PT), and partitioning time (Pt), to yield cost-effective Q&P steels. Computational simulation depicts a profitable approach to tackle this issue. Early studies concerning the diffusion of carbon from supersaturated plates of ferrite in Fe-C alloys were conducted by Mujahid and Bhadeshia.[5] The authors reported a one-dimensional diffusion process and solved the governing equation by the finite-difference method. A similar method was
recently adopted by Seo et al.,[6] to study the kinetics of the partitioning of carbon and substitutional elements, and they subsequently compared their computational results with experimental data from three-dimensional atom probe tomography. In other respects, plenty of literature has reported the carbon profiles in the austenite and martensite phases by means of ThermoCalc (DICTRA).[7–10] However, this commercial software considers that martensite and ferrite have the same thermodynamic properties, dismissing the typical defect structure of martensite and giving rise to misleading results.[11] The present paper develops a numerical simulation of a nonlinear diffusion in a heterogeneous media based on the finite-element method in space coupled with the Crank–Nicholson modified algorithm in time, with the aim of further understanding the kinetics of carbon migration during the Q&P process of C-Si modified 22MnB5 at different PT and Pt conditions. The computational algorithm was implemented in the software program MATLAB. The thermodynamic information (i.e., the chemical potential and diffusion coefficient) that is required to evaluate the matrices are taken from the literature. Finally, the simulation results are compared with experimental measurements of the volume fraction and carbon content of the retained austenite of the aforementioned steel.
II. JULIO C. GONZALEZ L., WEI LI, YU GONG, and XUEJUN JIN are with the School of Materials Science and Engineering, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China. Contact e-mails: [email protected]; yugong@ sjtu.edu.cn Manuscript submitted October 25, 2018.
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