Process Simulations and Computer Aided Process Development i) Microscopic

Transcription

1 Process Simulations and Computer Aided Process Development i) Microscopic Anders Engström IOM3 Hume-Rothery Seminar, Derby,

2 Outline Introduction CALPHAD Extensions Computational tools Examples

3 Thermo-Calc Software We have been supporting material engineers for two decades. Providing computational tools in the field of materials engineering that allow for faster, cheaper and more sustainable innovation, development and production of both materials and components.

4 Important and useful tools In a review of the 2015 literature, Thermo-Calc software products were referenced, mentioned or used in over 1000 publications, distributed on 231 journals, and by organizations from 59 different countries. The topics range from the macro- to micro-level, from meteorites to platinum jewellery and power plants to nanowire systems. 64 theses published in 16 countries. In 2015, at a minimum, sixty-four students, 64% at the PhD level, cited Thermo-Calc products. 46 patent citations (with a date of publication in 2015).

5 Phase Diagrams Provides stable state, i.e. amount of equilibrium phases. To some extent we can account for non-equilibrium states. e.g. by suspending stable phases, or making certain assumptions on the diffusion rate in liquid vs. solid phases (Scheil-Gulliver). No information about the rate of transformation, nor the microstructure morphology. Calculated phase diagram of CoCrFeNi-Al by using TCHEA1

6 The influence of chemistry on microstructure and properties Heat treating can best be defined as the controlled application of time, temperature and atmosphere to produce a predictable change in the internal structure (i.e. the microstructure) of a material. Dan Herring, 100th Column of the Heat Treat Doctor published in Industrial Heating magazine

7 Materials by Design - Cohen s Reciprocity Goal/means Performance Properties Structure Processing Cause and effect Morris Cohen s reciprocity between the cause/effect logic of science and goal/means logic of engineering.

8 ICME The National Academies Press, 2008 Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security ICME: an approach to design products, the materials that comprise them, and their associated materials processing methods by linking materials models at multiple length scales. Key words are "Integrated", involving integrating models at multiple length scales, and "Engineering", signifying industrial utility.

9 Need to predict Microstructure evolution during processing and in service Unfortunately phase transformations is a non-trivial topic. J. W. Christian, The Theory of Transformations in Metals and Alloys (Pergamon, Oxford, 1981).

10 MGI - Reinforcing the importance of data June 2011 Fundamental databases and tools enabling reduction of the years materials creation and deployment cycle by 50% or more. CALPHAD is at the nexus of: Experiments (on the data assessments are based and validated). Digital data (databases) Computational tools (software)

11 CALPHAD Method

12 Mobility and Diffusivity (n-1) 2 elements in the inter-diffusion matrix. All depending on composition and temperature. n mobilities depending on composition and temperature. Atomic mobility Database M M M M Chemical Diffusivity D D D D 12 D D Self-Diffusivity Impurity Diffusivity Intrinsic Diffusivity J.O. Andersson and J. Ågren, J. Appl. Phys., 72 (1992) 1350.

13 Prediction Assessment and optimization Atomic Mobility Databases (in a CALPHAD spirit) Theory - Ab-initio ln Estimates - Correlation Models f ( x, T, P) RTM B Experiments Diffusion without a chemical gradient: - Tracer diffusion coefficients Diffusion under a chemical gradient: - Chemical interdiffusion coef. - Intrinsic diffusion coefficients Storage in mobility database Parameter optimization Mobility, Diffusivities D k = c k M K μ k c k Thermodynamic database Applications

14 Modelling of the Atomic Mobility From absolute reaction-rate theory arguments Andersson and Ågren 1) suggested: M M Q B B 0 B Mobility for element Frequency factor Activation energy B When treating the composition dependency of the mobility, Jönsson 2) found it superior to expand the logarithm of the mobility rather than the value itself, i.e. Because lnrtm i is often found to have a fairly linear composition dependency 1. Andersson, Ågren, J Appl Phys 72(1992) Jönsson, Scand J Metall 24(1995)21

15 Composition dependency LOGDC(FCC,AL,AL,NI) In a CALPHAD spirit the composition dependency is represented with a linear combination of the values at each endpoint of the composition space, and a Redlich-Kister expansion, i.e. where B represents RT ln M 0 B Q B Ni-Al Example: FCC Ni-Al Ni Al Ni Ni Al Ni Al, Ni Ni Ni Al Al Al Al, Ni Al Mole-Fraction Al Engström, Ågren, Z Metallkd 87(1996)92

16 Ferromagnetic ordering Contribution to the activation energy from magnetic ordering Activation energy for the mobility in the paramagnetic state mag D 2 H Factor of proportionality Magnetic enthalpy Fe self-diffusion Jönsson, Z Metallkd 83(1992)349

17 Chemical ordering Inspired by Jönssons work on the effect from magnetic ordering, Helander and Ågren suggested: Contribution to the activation energy from magnetic ordering Activation energy for the mobility in the disordered paramagnetic state Contribution to the activation energy from chemical ordering Helander, Ågren, Acta Mater 47(1999)1141 Contribution to the activation energy from chemical ordering of i-j atoms

18 Effect from chemical ordering in the Ni-Al system Ni-0.45Al - pure Ni diffusion couple Helander, Ågren, Acta Mater 47(1999)1141

19 Mass Fraction Extension to multicomponent systems DICTRA ( : ) : TIME = Al Co Cr Fe Mo Nb Ti IN100 IN Symbols are experimental data taken from Campbell et al, Materials Sci & Eng A 407(2005), pp Distance (m)

20 Temperature [Celsius] Volume and bulk modulus Pressure dependence 1500 lattice parameter molar volume 1250 Liquid 1 atm 1 GPa density thermal expansion coefficient solid liquid Casting shrinkage Liquid + Fcc Liquid + Si relative length change lattice mismatch 500 Fcc + Si The effect of Si content on the densities of Al-Si alloys Mass percent Si SI in DIAMOND_A4 SI in FCC_A1 SI in LIQUID SI in DIAMOND_A4

21 Further CALPHAD Extensions To facilitate linkage among Thermodynamics, Process modelling, and Microstructure evolution Elasticity Elastic constants Young s modulus Bulk modulus Shear modulus Possion s ratio Viscosity (and diffusivity) in liquid Thermal conductivity and diffusivity Electric conductivity and resistivity Thermal radiative properties: emissivity, absorptivity, reflectivity, transmissivity

22 Properties of interfaces f(r) r Interfacial energy Grain boundary energy Surface tension

23 1999Noble, Mater Sci Engr, A266, Estimation of interfacial energy Classic or non-classic thermodynamics Distribution of Al-Li /d interfacial energy value found in literature Atomistic modeling - molecular dynamics and Monte Carlo method First principles

24 Our first approximation For a binary matrix and precipitate of the same structure that can be described by a regular solution model* c NZ s N Z A s l DE sol DE X X 2 sol P M Misciblity gap of non-regular solution phase Matrix and precipitate of different structure Multicomponent system DE sol * Based on Becker R. Ann Phys 1938;424:128

25 Estimation of interfacial energy System Phases Estimation (J/m 2 ) Literature (J/m 2 ) Al-Li /d to Cu-Ti Cu/Cu4Ti , Ni-Al-Cr g/g Co-W-C Co/WC to 1.09 Further investigations: Entropy effect Diffusiveness of interface Incoherency Size effect Grain boundary energy

26 CALPHAD Bridging Atoms and Microstructure Towards prediction of microstructure evolution and material properties Interfacial energy & Volume & Elastic constants H or S Thermodynamics: Gibbs energy CALPHAD Phase Field Method Langer-Schwartz f(r t First Principles Calculation r Diffusion: Mobility CALPHAD-type genomic databases with thermodynamic, thermophysical as well as kinetic properties have been and will be the only feasible source to provide input data for simulation of materials processing and microstructure evolution in multicomponent systems.

27 Computational tools / Products Software o o o o Thermodynamics - Thermo-Calc Diffusion kinetics - DICTRA Precipitation kinetics - TC-PRISMA Software Development Kits SDKs Databases o o Thermodynamic Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based HEA s, Solders, Cemented Carbides, Oxides, slags and ionic solutions Molten salts Compounds Aqueous solutions Kinetic Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys

28 Diffusion Module (DICTRA) 1D finite difference code for simulation of DIffusion Controlled TRAnsformations in multicomponent alloys. A numerical finite difference scheme is used for solving a system of coupled parabolic partial differential equations Solve Diffusion where Boundary conditions, etc. (External or Internal) Diffusivities Mobilities Gibbs Energy Kinetic DATABASES Thermodynamics All simulations depend on assessed kinetic and thermodynamic data, which are stored in databases

29 Diffusion Module (DICTRA) Two proven models for dealing with situations that involves more than a single phase. Program may switch automatically between them. Moving boundary problems with sharp interface g v n-1 unknowns: n-2 chemical potentials. Velocity of phase boundary, C k γ J k α c k α J k n-1 Flux Balance Equations: γ c k Sharp interface with assumption of local equilibrium z F-B Equations solved as:

30 Example 1 Casting / Solidification

31 Temperature Casting / solidification Case study: Micro-segregation during solidification - VESPISM (Virtual Experiments to Solve Problems In Steel Metallurgy). - Development of phase-field code (MICRESS) linked to Thermo-Calc. - Solidification experiments were performed for alloys A D below as one assignment in this project. 1,550 1,500 Liquid A B C D 1,450 1,400 d g 1, % Carbon

32 Temperature Casting / solidification Observed micro-segregation in Steel C Steel C: Fe - 0.8% Mn 0.7%Si 0.03%P 0.4% C Line-scans across the dendrite arms (performed by Corus-UK) d Liquid Steel C W% Si W% P W% S W% Mn Si g Mn P Peak drifting! % Carbon Question: Why does the P peak drift away from the Mn and Si peaks? µm

33 Casting / solidification Analysis using DICTRA Bcc Fcc Bcc λ/2 =100 μm υ Liquid Liquid υ Bcc Fcc υ Liquid l/2 Fcc υ Liquid Secondary dendrite arm spacing assumed to be 200 µm.

34 Temperature Casting / solidification Cooling function Cooling rate assumed to be 0.2 ºC/s - More advanced cooling functions may of course also be imposed. - Also possible to instead define a condition on the rate of latent heat removal from the system. Time (seconds)

35 Temperature Casting / solidification Solidification range L + d Peritectic reaction L + g Lever rule Scheil DICTRA Fraction Solid

36 Fraction Solid Casting / solidification Fraction of solid phases g d Peritectic reaction Time (Seconds)

37 Casting / solidification Carbon profiles during solidification 300 s 90 s 135 s 3000 s

38 Casting / solidification Silicon and Manganese Si 300 s 3000 s Mn 300 s 3000 s 90 s 135 s 90 s 135 s

39 Casting / solidification Phosphorus 300 s 90 s 135 s 3000 s

40 Casting / solidification Segregation profiles after 610 s (when the last melt disappears) Mn Si P C

41 Casting / solidification Segregation profiles after 1000 and 3000 s Mn Si P C after 1000 s Mn Si P C after 3000 s

42 Phosphorus activity Casting / solidification The solution 610 s Mn and Si increase the phosphorus activity s 1000 s Phosphorus diffusion much faster compared to Mn and Si diffusion. Distance (microns) At the late stage further phosphorus redistribution is controlled by slow Mn and Si diffusion.

43 Diffusion Module (DICTRA) Two proven models for dealing with situations that involves more than a single phase. Program may switch automatically between them. Moving boundary problems with sharp interface g v Multiphase problems with/without finite interface C k γ J k α c k α J k Flux between slices n-1 and n 1 N k n1 N k n N k n1 N k p N k γ c k Sharp interface with assumption of local equilibrium z J k 1 V m eff M x M x k k n1 k k eff n Dk Dz Effective rules M k x k from combining H. Larsson: CALPHAD 47 (2014) 1-8

44 Mass Fraction Mole-Percent Ni :57:50.12 output by user anders from NEMO Diffusion Module (DICTRA) Example of applications: Microsegregation during solidification Homogenisation treatment Precipitate growth and dissolution Precipitate coarsening Interdiffusion in coating/substrate systems TLP bonding of alloys and much more DICTRA ( : ) : TIME = Al Co Cr Fe Mo Nb Ti Micro-segregation during solidification in alloy AA NiAl-coating IN IN100 IN Ni Dissolution of Mg 2 Si precipitate in alloy A Distance (m) Multicomponent diffusion couple Position (microns) Interdiffusion between NiAl coating and Ni-base superalloy

45 Example 2 Material selection / Life-time prediction

46 Materials selections / Lifetime prediction Selected problem: Coating degradation due to interdiffusion Yu et al., Mater Sci. Eng. A394 (2005) 43. Complex problem involving solving multicomponent diffusion problem in multiphase region. Need for multicomponent kinetic data in -NiAl, g and g

47 NiAl-coating / Ni-base superalloy system E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp

48 NiAl-coating / GTD111 Mole-Percent Al Mole-Percent Ni Ni NiAl-Coating Bal GTD111 Bal Al C Co Cr Mo Ta Ti W Temp C Time 96h NiAl GTD Al Ni Position (microns) Position (microns) Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp eff i M x f M x i k k Rule of mixtures k k

49 NiAl-coating / GTD111 Mole-Fraction of Phase Mole-Fraction of Phase Mole-Fraction of Phase Mole-Fraction of Phase B g Position (microns) Position (microns) Micrograph from E. Perez et al. J. Phase Equilibria and Diffusion 27(2006), pp g Position (microns) Position (microns)

50 NiAl-coating / GTD111 Mole-Percent Co Mole-Percent Cr Co Cr Position (microns) Position (microns) Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp

51 NiAl-coating / GTD111 Mole-Percent Co Mole-Percent Cr Co g Cr g 20 5 g g Position (microns) Position (microns) Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp

52 NiAl-coating / GTD111 Mole-Percent Ti Mole-Percent W Ti W Position (microns) Position (microns) Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp

53 Computational tools / Products Software o o o o Thermodynamics - Thermo-Calc Diffusion kinetics - DICTRA Precipitation kinetics - TC-PRISMA Software Development Kits SDKs Databases o o Thermodynamic Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based HEA s, Solders, Cemented Carbides, Oxides, slags and ionic solutions Molten salts Compounds Aqueous solutions Kinetic Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys

54 Precipitation Module (TC-PRISMA) A general computational tool for simulating kinetics of diffusion controlled multi-particle precipitation processes in multicomponent and multi-phase alloy systems. 3D, 2006Jou TC-PRISMA is based on Langer-Schwartz theory, and it adopts Kampmann-Wagner numerical (KWN) method to compute the concurrent nucleation, growth, and coarsening of dispersed phase(s).

55 Time Integration LS (Langer-Schwartz) and KWN (Kampmann and Wagner Numerical) Approach 3D, Particle Size Distribution f, 1/m 4 N 0 f ( r, t) dr f r, t t Continuity equation ( r) f ( r, t) j( r, t) r 4 0 0, 3 C C C C f r t r dr Radius, nm Mass balance 1 N f ( r, t) dr r 0 N (, ) 0 3 f r t r dr f ( r, t) rdr

56 Models: Nucleation Rate D kt G N Z J s * * exp t J t J S exp * Z *2 * 4 4 r a 1 1 / 2 / / n i i i i i D X X X * 3 16 m m G V G D D Interfacial energy, Volume Classic Nucleation Theory (CNT) Grain size, dislocation density, etc. kt r N V Z A m * 2 2 D m m G V r 2 * 2004Svoboda

57 Q. Chen, J. Jeppsson, J. Ågren, Acta Mater. 56(2008) Models: Growth Rate Advanced Analytical Flux-balance Approximation / i c c c M / r i / i i 2 r i V m i Cross diffusion high supersaturation i i i Simplified Pseudo-steady state Approximation K DGm r 2Vm r K 2 / / i ( ) i ( ) i X r X r X () r M / i i i 1

58 Scope and data output Simulate concurrent nucleation, growth and coarsening of second phases in multicomponent systems. Input Alloy composition Temperature - Time Simulation time Thermodynamic data Kinetic data Property data (Interfacial energy, volume, etc.) Nucleation sites and related microstructure information TC-PRISMA Output Particle Size Distribution Number Density Average Particle Radius Volume Fraction Matrix composition Precipitate composition Nucleation rate Critical radius TTP

59 Some examples

60 Precipitation Module (TC-PRISMA) 2011 Version Version Thermo-Calc 2016a Link to Thermo-Calc and DICTRA Multi-component Nucleation and Growth Different Nucleation types Avdanced Model for Cross Diffusion and High Supersaturation Highly Intuitive GUI Non-Isothermal Conditions Multi-Modal PSD Analysis Interfacial Energy Model Multiple Nucleation Types Considering wetting angle Integration into Thermo-Calc...

61 Example 3 Heat Treatment / Aging

62 AA6xxx AA6005: Al wt% Mg wt% Si wt% Cu AA6061: Al wt% Mg wt% Si wt% Cu = J/m 2 TCAL3 and MOBAL3 Databases (Al) Myhr et al, Acta Mater. 49(2001) Bardel et al, Acta Mater. 62(2014) Al 3 Sc SSSS Clusters GP Zones β β, U1, U2, B β 530 C 30 min 185, 175 C 80, 8 hr

63 AA6xxx AA6005: Al wt% Mg wt% Si wt% Cu Precipitation of β from (Al) matrix

64 AA6xxx AA6061: Al wt% Mg wt% Si wt% Cu Precipitation of β from (Al) matrix

65 Example 4 Heat Treatment

66 R&D gg Microstructure in U720 Li Continuous cooling at K/s R. Radis et al., Acta Materialia, 57(2009)

67 R&D Influence from composition Ni-8Al-8Cr and Ni-10Al-10Cr

68 R&D Influence from composition Exp Continuous cooling from 1150 to 380 C with a cooling rate of 14 C/min.

69 R&D Influence from composition = J/m 2 Exp Ni-8Al-8Cr have larger misfit between g and g compared to Ni-10Al-10Cr. This will give an elastic energy contribution which has not been considered in the simulation.

70 R&D Influence from composition Vertical Section Ni-xAl-xCr Thermodynamic driving force

71 R&D Influence from composition Thermodynamic driving force Nucleation rate

72 Computational tools / Products Software o o o o Thermodynamics - Thermo-Calc Diffusion kinetics - DICTRA Precipitation kinetics - TC-PRISMA Software Development Kits SDKs Databases o o Thermodynamic Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based HEA s, Solders, Cemented Carbides, Oxides, slags and ionic solutions Molten salts Compounds Aqueous solutions Kinetic Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys

73 Interface Software Development Kits A prescribed set of subroutines, functions or classes by which a programmer writing an application program can make requests to Thermo-Calc. Thermo-Calc Application The trend is towards more and more advanced applications and in particular integration of thermodynamic calculation result for modelling of microstructure evolution and property prediction, aiming at designing products, the materials comprising them and their associated processing.

74 Example 5 R&D

75 Phase-field modelling Output: Detailed morphology Concentration fields Stress fields Plastic strain fields (dislocation density fields)... Need or can use input from Multicomponent thermodynamics Multicomponent diffusion analysis Interfacial energy and mobility Elastic coefficients and stresses Stress-free transformation strain tensor (eigen strains) Plastic relaxation Fluid flow (Navier Stokes)...

76 2D phase-field simulation of sigma-phase formation in duplex Stainless steel (SAF 2507) Fe-25Cr-7Ni-4Mo with continuous cooling from 1273K to 950K Malik et al. KTH (2015) Full CALPHAD Thermodynamics DICTRA Mobilities FCC FCC BCC FCC Sigma BCC FCC BCC

77 Spinodal decomposition Fe-45%Cr T=748K, time=1 Week Calculation cell is 20x20x20 nm Composition dependent gradient energy Full CALPHAD Thermodynamic & Mobility coupling Barkar et al. KTH (2016 )

78 Generating insights on materials and processing operations Thank You!