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Simpified Modelling of the PE / LENP transition

Simpified Modelling of the PE / LENP transition. Grenoble, May 9 2006. Growth of ferrite. Models Based on carbon diffusion in austenite Finite difference scheme 2 thermodynamic bounds possible LENP Para-equilibrium Mixed mode + dissipation in interface Spherical geometry Initial system

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Simpified Modelling of the PE / LENP transition

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  1. Simpified Modelling of the PE / LENP transition Grenoble, May 9 2006

  2. Growth of ferrite • Models • Based on carbon diffusion in austenite • Finite difference scheme • 2 thermodynamic bounds possible • LENP • Para-equilibrium • Mixed mode + dissipation in interface • Spherical geometry • Initial system • Austenite homogeneous carbon rich • Radius determine by the size of the system and the fractions • Radius = 0.5 * distance between centers of 2 ferrite grains~4µm

  3. Mixed PE LENP a gspike g a gspike g a gspike g %C %C %C mC mC mC %Mn %Mn %Mn mMn mMn mMn Growth of ferrite • Development of a mixed mode model : comparison PE, LENP, mixed mode

  4. G Dissipation Gg Ga C At. fraction CaLENP CaPE CgLENP CgPE Growth of ferrite • Condition at interface • LENP = PE + dissipation of energy in the spike • Idea: dissipation in the spike can vary between 0 and the LENP value

  5. Growth of ferrite • Flux through the interface • Driving force for jump of 1 mole through the interface • Hypothesis: • no accumulation in interface in function of time • Dissipation = Dissipation spike + dissipation interface • Extreme cases • PE: dissipation = 0 <->Lint~∞ • LENP: dissipation=dissipation LENP

  6. Growth of ferrite • LENP case • Lint~0 Assumed to be constant

  7. Growth of ferrite • Mixed case V>> -> PE V<< -> LENP Transition from PE to LENP function of Lint and v

  8. Estimation for Lint • Lint • Assumption: related to grain boundary diffusion

  9. Examples • 0.1%C, 1%Mn, R=10µm, 1°C/s, 3D

  10. Comparison with work of C. Hutchinson (2003) • Lambda~100

  11. Growth of ferrite • Estimation from intercritical annealing (RFCS project)

  12. Growth of ferrite • Comparison with experimental results (martensite fraction) Better description with the mixed mode than with LENP or PE hypothesis

  13. Conclusion • Simplified mixed mode model has been developed, with only computation of carbon diffusion • Fitting of the interface condition is based on grain boundary conditions • Possibility to reproduce with a good agreement the experimental results of C.Hutchinson between LENP and PE. • Perspective • Determination of the size of the cell remains the key parameter to master the phase transformation kinetics.

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