<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({750}\,^{\circ }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>750</mn> <mmultiscripts> <mspace width="0.166667em" /> <mrow /> <mo>∘</mo> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>C to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({850}\,^{\circ }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>850</mn> <mmultiscripts> <mspace width="0.166667em" /> <mrow /> <mo>∘</mo> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>C with varying <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( {p_{{\text{H}}_2{\text{O}}}}/{p_{{\text{H}}_2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mrow> <msub> <mtext>H</mtext> <mn>2</mn> </msub> <mtext>O</mtext> </mrow> </msub> <mo stretchy="false">/</mo> <msub> <mi>p</mi> <msub> <mtext>H</mtext> <mn>2</mn> </msub> </msub> </mrow> </math></EquationSource> </InlineEquation> ratios (0.0077 to 0.1268). Leave-one-out cross-validation yielded a symmetric mean absolute percentage error of 14.6&#xa0;&#xa0;pct [95&#xa0;&#xa0;pct CI: 10.0 to 19.3&#xa0;pct], while in-sample fitting achieved 10.6&#xa0;&#xa0;pct. Statistical analysis revealed that decarburization depth was primarily influenced by the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( {p_{{\text{H}}_2{\text{O}}}}/{p_{{\text{H}}_2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mrow> <msub> <mtext>H</mtext> <mn>2</mn> </msub> <mtext>O</mtext> </mrow> </msub> <mo stretchy="false">/</mo> <msub> <mi>p</mi> <msub> <mtext>H</mtext> <mn>2</mn> </msub> </msub> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

  • Georg Reiss,
  • Claudia Mugrauer,
  • Werner Eßl,
  • Peter Raninger,
  • Erich Wimmer,
  • Gerhard Angeli

摘要

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 \({750}\,^{\circ }\) 750 C to \({850}\,^{\circ }\) 850 C with varying \( {p_{{\text{H}}_2{\text{O}}}}/{p_{{\text{H}}_2}}\) p H 2 O / p H 2 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 \( {p_{{\text{H}}_2{\text{O}}}}/{p_{{\text{H}}_2}}\) p H 2 O / p H 2 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.