12.09.08 Aachen Thermodynamics and Microstructure: Recent Examples for Coupling of Thermodynamic and Mobility Data to the Software MICRESS Dr. Bernd Böttger ACCESS e.v. Aachen
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
Microstructure Simulation using the Software MICRESS
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
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:
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
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
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 www.micress.de
Thermodynamic Coupling Temperature, C 700 (Mg) 600 500 L (Mg) + Al 8 Mn 5 L + Al 8 Mn 5 L + (Mg) + Al 8 Mn 5 (Mg) + βmn (Mg) + Al 11 Mn 4 400 0 2 4 6 8 10 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
Application: Grain Size Prediction in AZ31
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
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 500 400 300 200 100 (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 1.0 0 0.0 0.2 0.4 0.6 0.8 1.0 wt.% Ca Mg 94.6 Al 3.0 Zn 1.0 Variation of Al, Zn, Ca, Mn
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
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
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
Principal Effect of Solute on Grain Refinement 10 aluminium concentration around a growing grain Al-Concentration [wt%] 9 8 9% Al 7 6 5 4 3 2 1 0 6% Al 3% Al 0 20 40 60 80 100 120 140 higher concentration higher solute pile-up growth restriction higher maximal undercooling x [μm] x [μm] Undercooling T Liq (c 0 ) - T [ C] 0 1 2 3 4 undercooling T Liq (c 0 ) - T [ C] ΔT min ΔT max 3% Al 6% Al 9% Al first nucleation latent heat release 5 0 2 4 6 8 10 time [s]
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%]
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%]
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)
Application: Hot Cracking in Continuous Casting
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% 0.047 0.022 0.13 0.011 0.001 0.029 0.009 0.004 0.014 0.014
Temperature and Fraction Solid Curves T curves fs curves Mn/wt%
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
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 0,001 5 1,526 0 0,021 0,019 0,005 3 0,002 4 0,003 8 0,021
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
Disturbed Growth Alloy B
Segregation Band Alloy B C Si Mn P S Al Cr Cu Mo N Ti Ni increased hot cracking potential!
Thank you for your attention!