Cooperative Growth of Pearlite

Transcription

1 Cooperative Growth of Pearlite Ingo Steinbach Acknowledgement: Katsumi Nakajima, Markus Apel, JFE Steel Corporation for financial support

2 Cooperative Growth of Pearlite The microstructure of steels and cast iron by Durand-Charre Micrographs by Irsid-Arcelor

3 Introduction 1200 Eutectoid steel Fe-C system Temperature(K) γ ~50K Fe 3 C β β 950 λ(spacing) 900 C (mass%)

4 Introduction The "Zehner-Hillert-Tiller-Jackson-Hunt Model Pearlitic: ΔT= const. Eutectic: v= const. v (a.u.) large ΔT medium ΔT small ΔT ΔT = T eq. -T int. (a.u.) large V medium V small V spacing λ(a.u.) a 1 v = ΔT/λ -a 2 /λ spacing λ(a.u.) ΔT = a 1 vλ + a 2 /λ

5 Introduction Temperature (K) Model: Diffusion in γ phase nodule velocity (mm/s) Experiment Ridley 0.81C Frye 0.78C Grainboundary diffusion Diffusion in Ferrite Diffusion due to composition dependent strain Spinodal decomposition in supersaturated Ferrite Finite interface mobility Reduced transformation due to transformation strain Anisotropic interface mobility and energy

6 Outline Spacing selection in pearlite growth, diffusion in austenite only The effect of diffusion in ferrite and growth of cementite from ferrite The effect of composition dependent strain on diffusion and growth The effect of transformation strain on growth Conclusion

7 Selection of spacing, diffusion in Austenite only initial ΔT= 30K Diffusion only in γ phase [atom%] 0.2 µm λ= 0.15 µm λ= 0.25 µm λ= 0.4 µm

8 Selection of spacing, diffusion in Austenite only transition ΔT= 30K Diffusion only in γ phase [atom%] 0.2 µm λ= 0.15 µm λ= 0.25 µm λ= 0.4 µm Overgrow Max velocity

9 Selection of spacing, diffusion in Austenite only final ΔT= 30K Diffusion only in γ phase [atom%] 0.2 µm λ= 0.15 µm λ= 0.25 µm λ= 0.4 µm Overgrow Max velocity

10 Selection of spacing, diffusion in Austenite only Relationship between Spacing and Velocity Zener model Calculation (mobility : ) (mobility : finite) Diffusion only in γ phase Nodule Velocity v (μm/s) Overgrow Lamellar Spacing λ (μm) v = 2D v 1 / (f f cm ) (C e γ/ C e γ/cm ) / (C cm/γ C /γ ) 1/λ (1 λ 0 /λ) D v : diffusion coefficient in γ phase λ 0 : spacing where all energy is consumed for formation of interfaces f :S /(S +S cm ) f cm :S /(S +S cm ) ΔT=50 ΔT=30 ΔT=10

11 Diffusion in Ferrite and growth of Cementite from Ferrite Carbon diffusion coefficient C γ/cm γ C γ/ C /γ γ phase ~ 5.5*10-9 cm 2 /s phase ~ 8.6*10-7 cm 2 /s C /cm Equlibrium concentrations Cem Cem γ phase ~ 3.7 at % phase ~ 0.1 at % The diffusion path through ferrite was first proposed by Onsager 1948, but neglected later due to the lack of experimental evidence Flux potential D*c eq γ phase ~ cm 2 /s at % phase ~ cm 2 /s at %

12 Diffusion in Ferrite and growth of Cementite from Ferrite initial ΔT= 30K λ= 0.3 µm [atom%] Diffusion in γ and phase Diffusion in γ phase

13 Diffusion in Ferrite and growth of Cementite from Ferrite transition ΔT= 30K λ= 0.3 µm [atom%] Diffusion in γ and phase Diffusion in γ phase

14 Diffusion in Ferrite and growth of Cementite from Ferrite final ΔT= 30K λ= 0.3 µm [atom%] Diffusion in γ and phase Diffusion in γ phase

15 Diffusion in Ferrite and growth of Cementite from Ferrite Temperature (K) Diffusion in γ phase Diffusion in γ Diffusion in γ nodule velocity (mm/s) v = 2D v 1 / (f f cm ) (C e γ/ C e γ/cm ) / (C cm/γ C /γ ) 1/λ (1 λ 0 /λ) Experiment Ridley 0.81C Frye 0.78C Phase Field Calculation Diffusion in γ and phase Diffusion in γ phase Model Diffusion in γ phase kδd b = cm 3 /s (fitting value) k : partition coefficient δ : interface thickness D b : diffusion coefficient in boundary

16 Phase-field model coupled to elastic strain i ch f = f + f + f el f f f β 2 σ ηβ = φ φ β η 2, β π ch = φf i 4 ch el β + φ φ ( c ) + μ c φ c * 1 * 1 ( ε ε ε c ) C ( ε ε ε ) 1 = φ c 2 β φ& = 1 n β μ β δf δφ δf δφ β = 1 n β μ β chem ( I + ΔG + ΔG el ) β β β m 2 δf δ f 1 c& = M φ = φ + ε σ M c δ 2 c k= 1 δc * 1 ( ε ε ε ) 0 = σ = φ C c Steinbach, Apel: Physica D 54 (2006)

17 The effect of composition dependent strain on diffusion and growth lamellar spacing 0.3 μm, ε 1 austenite = c hydrostatic stress [J/cm 3 ] carbon concentration [at%]

18 The effect of composition dependent strain on diffusion and growth chemical + stress driven diffusion: v= 1.6 μm/s chemical diffusion only: v= 0.76 μm/s carbon concentration [at%] carbon concentration [at%]

19 The effect of composition dependent strain on diffusion and growth chemical diffusion only chemical + stress diffusion diffusion fluxes J chem = D austenite c = 8.4*10-5 [at% cm/s] J chem+stress = D austenite c + M *ε 1 σ = 4.2* *10-5 [at% cm/s] = 7.4*10-5 [at% cm/s]

20 The effect of composition dependent strain on diffusion and growth 1000 Temperature (K) Diffusion in γ + stress driven diffusion (extrapolated) Diffusion in γ+ Experiment Ridley 0.81C Frye 0.78C Phase Field Calculation Diffusion in γ and phase Diffusion in γ phase + Diffusion due to Stress (extrapolated) 880 Model Diffusion in γ phase nodule velocity (mm/s)

21 The effect of transformation strain on growth Lattice constants: austenite ferrite cementite a = Å/atom a = Å/atom a = 1.98 Å/atom; b = 2.23 Å/atom; c = Å/atom [J/cm³] [at%] Phase distribution Hydrostatic stress Carbon concentration

22 The effect of transformation strain on growth Phase distribution Hydrostatic stress [J/cm v = 6 μm/s!! 3 ] Carbon concentration [at%]

23 The effect of transformation strain on growth Temperature (K) Diffusion in γ Diffusion in γ nodule velocity (mm/s) Experiment Ridley 0.81C Frye 0.78C Phase Field Calculation Diffusion in γ and phase Diffusion in γ phase + Diffusion due to Stress (extrapolated) + transformation strain + faceted anisotropy of cementite Model Diffusion in γ phase

24 Conclusion Many features are nessesary to explain the kinetics of pearlite transformation spacing selection through growth restriction by curvature of the austenite/ferrite interface enhanced diffusion in ferrite stress driven diffusion in austenite faceted surfaceface structure allowes preferential growth of cementite into austenite Phase-field simulation offers the metodology to investigate these effects and their interrellation (allmost) quantitatively Steel metallurgy is not only the past of solidification, it is also part it s future