Thermodynamics and Microstructure: Recent Examples for Coupling of Thermodynamic and Mobility Data to the Software MICRESS

Transcription

1 Aachen Thermodynamics and Microstructure: Recent Examples for Coupling of Thermodynamic and Mobility Data to the Software MICRESS Dr. Bernd Böttger ACCESS e.v. Aachen

2 Outline Microstructure Simulation using the Software MICRESS Coupling to Thermodynamic Databases Applications: - Magnesium Alloys: Grain Size Prediction in AZ31 - Steels: Hot-Cracking in Continuous Casting

3 Microstructure Simulation using the Software MICRESS

4 The Software MICRESS MICRESS: MICRostructure Evolution Simulation Software Can be applied to composition, temperature or curvature controlled transformations on the microscale: Solidification (dendritic, cellular, peritectic, eutectic) Solid state reactions (grain growth, recrystallisation, phase transformations) Direct coupling to thermodynamic databases (contains TQ-interface*) or linear phase diagram approximation multi-grain *from Thermo-Calc Software, Sweden 1D, 2D or 3D multiphase multicomponent

5 The MICRESS Story 1995: first microstructure simulations at ACCESS 1996: multi-phase-field model published 1999: simulations comprising thermodynamic databases 2003: MICRESS is commercially available 2004: MICRESS becomes registered trademark 2005: MICRESS website is online 2006: stress solver incorporated 2007: coupling to external temperature fields 2008:

6 The Phase-Field Method MICRESS uses the phase-field method Main characteristic: Diffuse Interface, expressed by the phase-field parameter φ φ = f (x,t) can be interpreted as a density function for the phase state

7 Multi Phase-Field Equation used in MICRESS η ij = interface thickness μ ij = interface mobility (anisotropic) σ ij = interface energy (anisotropic) ΔG ij = driving force by superposition of pair-wise interactions with neighboring phases rate of change of each phase-field ( ) Δ φ φ η π + φ φ η π + φ φ φ φ σ μ = φ ij j i ij j i 2 ij 2 i 2 j j 2 i * ij * ij n j i G 2 & diffusion equation ( ) φ = = k i k i i N 1 i k c D dt / t x, dc r

8 Basic Structure of MICRESS loop over time M I C R E S S Nucleation Models Multi-Phase-Field Solver Multicomponent Diffusion Solver Temperature Solver Evolution of Phase Distribution φ α Composition c Al Temperature c Zn

9 Thermodynamic Coupling Temperature, C 700 (Mg) L (Mg) + Al 8 Mn 5 L + Al 8 Mn 5 L + (Mg) + Al 8 Mn 5 (Mg) + βmn (Mg) + Al 11 Mn Mg 99.6 wt.% Al Mn 0.4 Calphad Database TQ-Interface ThermoCalc nucleation undercooling driving force solute partitioning diffusion matrix latent heat data α M I C R E S S loop over time Nucleation Model Δ T > Δ? und T crit Multi-Phase-Field Solver = μ σ K + & φ ( w ΔG ) β αβ Multicomponent Diffusion Solver v c&v v = φ D c α αβ α α Temperature Solver α αβ

10 Application: Grain Size Prediction in AZ31

11 Simulation of Microstructure of Mg-Cast Alloys Input: alloy composition, heat extraction rate, distribution of nucleant particles AZ31 CastMicrostructure Output: temperature-time curve, grain size, grain morphology, microsegregation, secondary phases

12 Thermodynamic Data of Magnesium Alloys Calphad database of the system Mg-Al-Zn-Ca-Mn M.Ohno, R.Schmid-Fetzer Mg-Al3-Zn1-Mn0.4-Ca 700 Liquid 600 Liquid + (Mg) + Al 8 Mn 5 Liquid + Al 8 Mn 5 Temperature, C (Mg) + Al 8 Mn 5 (Mg) + Al 8 Mn 5 + (CaMg 2 ) (Mg) + Al 8 Mn 5 + Al 2 Ca (Mg) + Al 2 Ca + Al 11 Mn 4 (Mg) + Al 2 Ca + Al 4 Mn Liquid + (Mg) + Al 8 Mn 5 + (CaMg 2 ) (Mg) + Al 8 Mn 5 + (CaMg 2 ) + Al 2 Ca Starting composition for present simulations: AZ31: Mg - 3% Al - 1% Zn Mg 95.6 Al 3.0 Zn wt.% Ca Mg 94.6 Al 3.0 Zn 1.0 Variation of Al, Zn, Ca, Mn

13 Distribution of Nucleant Particles = r r r N r n exp 2 ) ( particle density n radius r = r r 2r N r n exp ) ( N r Nucleant particles: grain refiner particles, impurities

14 Integrated Nucleation Model density nucleant distribution nucleant positioning r* radius critical undercooling Δ T crit Nucleation-Model Nucleation-Model v ( r) < ΔT ( c, T )? Multi-Phase-Field-Solver Multicomponent Diffusion-Solver new nucleus nucleants with different radii 2 r Δ ( r) T crit 2σ = Δ S r T & ( Q& / V dt + L f& sol ) / c p = Temperature-Solver M I C R E S S nuclei

15 Simulations with Variation of Aluminium Content Mg-3%Al-1%Zn Mg- 6%Al-1%Zn Mg- 9%Al-1%Zn AZ31 increased aluminium content decreased grain size AZ91

16 Principal Effect of Solute on Grain Refinement 10 aluminium concentration around a growing grain Al-Concentration [wt%] 9 8 9% Al % Al 3% Al higher concentration higher solute pile-up growth restriction higher maximal undercooling x [μm] x [μm] Undercooling T Liq (c 0 ) - T [ C] undercooling T Liq (c 0 ) - T [ C] ΔT min ΔT max 3% Al 6% Al 9% Al first nucleation latent heat release time [s]

17 Evaluation of Grain Size dependent on Aluminium Concentration mean grain radius [μm] Mg-3%Al-1%Zn + Simulation Parameters Software: MICRESS Method: Phase-field 1000 x 1000 cells Δx= 2 μm dq /dt= -5 Js -1 cm -3 Al-Variation Mg-x%Al-1%Zn aluminium concentration [wt%]

18 Evaluation of Grain Size dependant on Solute Concentration mean grain radius [μm] Mg-3%Al-1%Zn + Mn Simulation Parameters Software: MICRESS Method: Phase Field 1000 x 1000 cells Δx= 2 μm dq /dt= -5 Js -1 cm -3 Zn Ca Al concentration variation Δc [wt%]

19 Comparison with Growth Restriction Theory Grain size is described in linear approximation to the inverse of the Growth Restriction Factor r mean = a + b/ GRF Growth Restriction Factor: GRF = Σ m i c i (k i -1) c k Behaviour for Mn can only be understood as a multicomponent effect! liquidus slope partition coefficient m GRF concentration c (applied by D. StJohn, M. Easton to Mg-alloys)

20 Application: Hot Cracking in Continuous Casting

21 Example: Continuous steel casting initial stage Problem at initial stage of solidification (first few milimeters): highly non-stationary and non-linear temperature profile 1D temperature field (low resolution) normal 2D simulation domain (high resolution) is coupled to 1D temperature field simulation with realistic temperature profiles Q& (t) low-alloyed ferritic steel: C Si Mn P S Cr Cu N Ni Nb wt%

22 Temperature and Fraction Solid Curves T curves fs curves Mn/wt%

23 Determination of Zero Ductility Temperature (ZDT) using Critical Fraction Solid of 0.95 f S krit f S important for hot cracking! temperature / C ZDT

24 Microstructure Simulation of Peritectic Alloy B FCC Alloy B: T(95%) = 1438 C T(99%) = 1405 C T(FCC) = 1432 C T(TI4C2S2) = 1423 C T(MnS) = 1406 C T(TiN) = 1395 C TiN MnS Ti4C2S2 Fe C Si Mn P S Al Cr Cu Mo N Ti Ni Bal. 0,225 0,078 1,66 0,012 0, , ,021 0,019 0, , , ,021

25 Microstructure Simulation of Peritectic Alloy B: Rappaz-Kriterium & ε krit 2 G λ max = 2 GΔp v β A i ( 1+ β ) i Bi 180μ i i i A e punkt 0,0E+00 1,0E-03 2,0E-03 0 A 0 e cr 0,0E+00 2,0E-03 4,0E-03 6,0E-03 0,1 0,1 0,2 0,2 h [m] 0,3 h [m] 0,3 0,4 0,4 0,5 0,5 0,6 0,6

26 Disturbed Growth Alloy B

27 Segregation Band Alloy B C Si Mn P S Al Cr Cu Mo N Ti Ni increased hot cracking potential!

28 Thank you for your attention!