Controlling Decarburization in Steel: A Coupled Reaction-Diffusion Model for Annealing Processes

Abstract Hot-dip galvanizing lines require precise control of surface decarburization to achieve target mechanical properties in automotive steel sheets. This study presents a coupled surface-reaction and one-dimensional carbon diffusion model for predicting decarburization during non-isothermal annealing. The model incorporates thermodynamic equilibrium phase fractions from the Fe–C system to describe ferrite–austenite distribution as a function of local temperature and composition, with an effective diffusion coefficient that transitions smoothly between phase-specific diffusivities using a phase-transition parameter. Model parameters were optimized using differential evolution against Glow Discharge Optical Emission Spectroscopy measurements from nine annealing experiments at $${750}\,^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>750</mml:mn> <mml:mmultiscripts> <mml:mspace/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> </mml:mrow> </mml:math> C to $${850}\,^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>850</mml:mn> <mml:mmultiscripts> <mml:mspace/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> </mml:mrow> </mml:math> C with varying $$ {p_{{\text{H}}_2{\text{O}}}}/{p_{{\text{H}}_2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:msub> </mml:mrow> </mml:math> ratios (0.0077 to 0.1268). Leave-one-out cross-validation yielded a symmetric mean absolute percentage error of 14.6 pct [95 pct CI: 10.0 to 19.3 pct], while in-sample fitting achieved 10.6 pct. Statistical analysis revealed that decarburization depth was primarily influenced by the $$ {p_{{\text{H}}_2{\text{O}}}}/{p_{{\text{H}}_2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>p</mml:mi> <mml:mrow> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:msub> </mml:mrow> </mml:math> ratio, with soaking temperature showing only a slight effect within the investigated range. The model successfully captures temporal evolution of carbon concentration profiles during heating and cooling cycles, providing insights into diffusion-limited regimes at elevated temperatures. Limitations include exclusion of oxidation effects and indirect treatment of phase transformation kinetics through empirical phase-transition parameters. This framework enables cost-effective prediction of decarburization under various process conditions while identifying key atmospheric parameters for process optimization in hot-dip galvanizing lines.