Cr-C alloys. (1) Background : Fe-Cr-C system. (2) Experimental data. (3) Phase equilibria (stable + metastable) : TCQ + TCFE3

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1 Eutectic growth during solidification of Fe-Cr Cr-C alloys (1) Background : Fe-Cr-C system (2) Experimental data (3) Phase equilibria (stable + metastable) : TCQ + TCFE3 (4) Diffusion controlled growth of eutectics : DICTRA + TCFE3 (5) Going further

2 Fe - Cr - C system : why? (1) A base for industrial alloys : bearing steel 100Cr6 (AISI 52100) : Fe - 1% C - 1.5% Cr Mn Si (2) A "model" system for studying solidification paths * 2 different solute behaviours in austenite (Fe) C : interstitial solute + high mobility Cr : substitutional solute + low mobility preliminary study : "Comparison between experimental and calculated solidification paths for Fe-Cr-C alloys" - A. Antoni, C. Tassin, J. Ågren, Conf. Calphad, Stockholm, may 2002

3 Fe - Cr - C system : liquidus projection (stable phases) - TCFE3 w-f (Cr) M23C6 eutectic valleys BCC U2 U2-U1 : Liq + M7C3 U1-U3 : Liq + M7C3 U1 : 7.6 Cr 4.4 C 1451 K Liq + M7C3 + U1 Fe w-f (C) U3

4 3 solidification paths for Fe Cr 1.75 C w-f (Cr) M23C6 BCC U2 M7C3 * "equilibrium " for C and Cr only austenite γ () * "Scheil model" for C and Cr primary + (-) eutectic U1 * "Diffusion " : DICTRA primary + (-M7C3) eutectic Fe w-f (C) U3

5 3 solidification paths for Fe Cr 1.75 C * "equilibrium" only austenite (γ) * "Diffusion - DICTRA" only 5% eutectic (-M7C3) * "Scheil model" 20% eutectic (-) A. Antoni, C. Tassin, J. Ågren (2002)

6 Eutectic growth during solidification of Fe-Cr Cr-C alloys (1) Context : Fe-Cr-C system (2) Experimental data (3) Phase equilibria (stable + metastable) : TCQ + TCFE3 (4) Diffusion controlled growth of eutectics : DICTRA + TCFE3 (5) Going further

7 3 Fe Cr 1.75 C : Results from QDS experiments (LTPCM) v = 11 cm/h - G # 70 K/cm two main results only a few % eutectic S/L + carbide analysis (EPMA) 14.1% Cr - 6.4% C (wt%) (0.14 Cr C) M7C3 (0.29 Cr C) calculated at U1 point

8 Fe Cr 1.75 C : experiments / simulation Experimental results : solidification path ends with // Computed solidification paths "equilibrium" only austenite (γ) eutectic (- ) only a few % eutectic? "Scheil" 20% eutectic - "Diffusion - DICTRA" only 5% eutectic ( - M7C3)

9 Experimental / calculated solidification paths Discussion W (Liq, Cr) (1)? effect of other elements M23C6 Si in the 100 Cr6 steel (2) assuming diffusion model (DICTRA) as the most realistic BCC M7C3? solidification path ends at (3) metastable - eutectic B metastable γ- instead of A 2 3 (2) stable - M7C3 eutectic 1 W (Liq, C) A B : compositions studied by Okane and Umeda (Solidification Processing Sheffield (1997)

10 Competition between stable / metastable eutectics in Fe-Cr Cr-C already described by Okane & Umeda - Solidification Processing, Sheffield (1997) Growth interface temperatures T gr for the 2 eutectics : - M7C3 and - growth undercoolings T 1 T 2 vs V 1/2 slopes k 1 k 2 k 2 k Cr 4.0 C + M7C3 19 Cr 3.2 C

11 Criterion for microstructure selection Criterion : the observed microstructure is that with the highest growth temperature T gr T T eq T eq -M7C3 : at low velocity k 1 k 2 - : at high velocity Liq Liq+M7C3 Liq+ V cr 1/2 V 1/2 Fe w-f (Cr) at high rate V (for V > V cr ) γ - may grow at a higher T (faster) than γ - M7C3

12 Eutectic selection map from Okane & Umeda (1997) Critical growth rates for Cr compositions between 8 and 28% (wt%)

13 Eutectic growth during solidification of Fe-Cr Cr-C alloys (1) Context : Fe-Cr-C system (2) Experimental data (3) More on phase equilibria (stable + metastable) TCQ + TCFE3 (4) Diffusion controlled growth of eutectics : DICTRA + TCFE3 (5) Going further

14 Driving force for carbide precipitation : M7C3 / W (Liq, Cr) M23C6 BCC M7C3 metastable γ- U1 Alloy composition near pseudo peritectic point U1 Fe 9.5 Cr 4 C (U1) : Fe 7.6 Cr 4.4 C 1 W (Liq, C)

15 Fe 9.5 Cr 4 C : driving force DGM (*) vs Temperature Liq + + M7C3 M23C6 Liq + M7C3 decreasing T Liq M23C6 "not far from stability " even at low Cr content! (9.5 wt%) not forget M23C6 when studying microstructure selection see liquidus projection with metastable carbides

16 Fe - Cr C : metastable liquidus projection M23C6 / BCC U'2 U'1 M23C6 without M7C3 (rejected) large extension of the M23C6 liquidus surface / cementite phase diagram from Bunghard

17 Stable + metastable equilibria M7C3 / M23C6 / Expected microstructure selection M23C6 2 regions BCC U2 U'2 "high Cr" : M7C3 // M23C6 "low Cr" : M7C3 // M7C3 U1 U'1 what about the temperature difference between the 2 neighbouring valleys : T = f(% Cr)? next figure to be compared with nucleation undercooling of the stable M7C3 carbide

18 Temperatures of the monovariant eutectic lines : T eut vs Cr content 1600 Fe-Cr-C System - Monovariant eutectic lines TCFE3 database - (% Carbon = variable) U' M7C3 M23C6 M7C3 // M23C6 Temerature (K) M7C3 // U1 U'1 8.4 Cr (Okane) Liq discrepancy between computed T eut = T eq = K?? T gr eut (Okane) : K > T eq Cr (Weight Fraction)

19 Monovariant eutectic equilibria in the Fe-Cr Cr-C system Main results Extension of the metastable M23C6 liquidus surface toward low Cr content when the stable M7C3 carbide is "rejected" Need to take into account M23C6 in studying the eutectic selection 2 regions * "high and medium Cr" : +M7C3 /+M23C6 * "low Cr" (# 9 wt%) : +M7C3 / + Comparison is essential between * computed phase equilibria / solidification experiments need for assessed (reliable) data // acquire experimental data (DTA)

20 Eutectic growth during solidification of Fe-Cr Cr-C alloys (1) Context : Fe-Cr-C system (2) Experimental data (3) More on phase equilibria (stable + metastable) : TCQ + TCFE3 (4) Diffusion controlled growth of eutectics (5) Going further DICTRA + TCFE3

21 Simulation of eutectic growth with DICTRA 2 models volume diffusion simulation conditions T = To (time * T') To = Teut T' = K/s L = 10-6 m ; 10-4 m boundary diffusion lamellar growth (pearlite model) simulation conditions T = To (time * T') T' = K/s γ + M7C3 γ + γ + M23C6 M7C3 M23C6 Liq V Liq µm 100 µm interface velocity = result

22 Fe 9.5 Cr 4.4 C Liq + Liq Cr profiles vs cooling rate 100 µm T = * time T = * time LIQ LIQ * no back diffusion of Cr in solid phases * low Cr gradient in liquid for 0.2K/s * no back diffusion of Cr in solid phases * increased Cr gradient in liquid for 10K/s

23 Liq + Concentration gradient in liquid Liq 100 µm T Liq T diff = undercooling T diff create concentration gradient in liquid drive diffusion increases with increasing cooling rate Fe x γ x x L L x x E (Cr)

24 Fe 9.5 Cr 4.4 C Liq + Liq C profiles vs cooling rate 100 µm T = * time LIQ T = * time LIQ * back diffusion of C in * low C gradient in liquid for 0.2 K/s * back diffusion of C in * increased Cr gradient in liquid for 10 K/s

25 Fe 9.5 Cr 4.4 C Liq + Cr profiles vs cell size T = * time Liq L L = 100 µm L = 1 µm LIQ LIQ * no back diffusion of Cr in solid phases on large distances * back diffusion of Cr in solid phases on small distances

26 Fe 8.75 Cr 4.2 C Liq + M7C3 M7C3 Liq Cr profile vs cooling rate 100 µm M7C3 T = * time M7C3 T = * time LIQ LIQ * low diffusion of Cr in solid phases * low Cr gradient in liquid * low diffusion of Cr in * increased Cr gradient in liquid for 10 K/s

27 Fe 8.75 Cr 4.2 C Liq + M7C3 M7C3 Liq C profile vs cooling rate 100 µm T = * time M7C3 T = * time LIQ M7C3 LIQ * back diffusion of C in * low C gradient in liquid * back diffusion of C in * increased C gradient in liquid

28 Liq + M7C3 Liq + Carbide interface velocities M7C3 Liq 100 µm T = * time M7C3 T = T * time

29 Simulation of eutectic growth with DICTRA Main results with volume diffusion model M7C3 M23C6 Liq µm Good description of solute diffusion in liquid and solid phases : back diffusion of C in solid phases : µm back diffusion of Cr only on small distances (# 1 µm) effect of cooling rate on solute gradient in the liquid phase effect of cell size Interface velocity

30 And now? Try to compute lamellar eutectic growth with DICTRA "pearlite model" no success until today! need for careful choice of parameters * lamellar spacings questions remain concerning * some "error messages"! Microstructure simulation : MICRESS γ + M7C3 γ + Liq V Comparison between simulation results / solidification experiments

31 (1) THANKS to Aiman Ezayani Annie Antoni LTPCM INPG CNRS Grenoble (2) PROCOPE Program 2005

32 T Fe 9.5 Cr 4.4 C Liq + Effect of cooling rate : 0.2 K/s 10 K/s Cr Liq 100 µm Liq x Liq T diff x L Cr, C x E x L V Fe x γ x x L L x x E (Cr) V distance T diff = undercooling create concentration gradient in liquid drive diffusion increased Cr gradient in liquid with higher cooling rate 2 velocities : V V derived from flux balance

33 M7C3 Cr = 8.0 wt% C = 4.37 wt% Teq = K T = T' *time Cr = 8.0 wt% C = 4.4 wt% Teq = T = T' *time U1 : M7C3 - Cr = 7.69 wt% C = 4.39 wt% Teq = K M7C3 Cr = 30.6 wt% C = 2.85 wt% Teq = K T = 1560 T' *time L = 10-6 m ; 10-4 m M23C6 Cr = 30.3 wt% C = 3.2 wt% Teq = K T = 1544 T' *time L = 10-6 m ; 10-4 m K

34 Fe - Cr - C system : experiments LTPCM (2002) * alloy preparation : induction melting in a cold crucible, casting into a copper cylindrical mould materials : (100 Cr6 + Cr) + C several meltings * QDS : quench interrupted directional solidification v = 11 cm/h G # 70 K/cm * DTA measurements T' = 5 K/mn Microstructure characterization : SEM + microprobe analysis "Comparison between experimental and calculated solidification paths for Fe-Cr-C alloys" - A. Antoni, C. Tassin, J. Ågren, Conf. Calphad, Stockholm, may 2002

35 Undercooling eutectic undercooling T = T n (nucleation) + T c (solute diffusion) + T r (curvature) + T t (thermal) Kurz T = 2 (K r K c ) 1/2. V 1/2 with T r = K r / λ and T c = K c λ V if 0 espacements primaires 500 µm C. Tassin - LTPCM - 24/01/ 2005

36 Fe - Cr C : metastable liquidus projection M23C6 / M7C3 suspended BCC U'2 M23C6 Fe Cr C U' U' U'1