Modelling of Microstructural Evolutions in Structural ... · PDF fileof Microstructural...
Transcript of Modelling of Microstructural Evolutions in Structural ... · PDF fileof Microstructural...
Modelling of
Microstructural Evolutions in
Structural Materials
Yoshiyuki SaitoDepartment of Electronic and Photonic Systems
Waseda University
Contents1.Introduction Present State Target 2.Computational Models based on Thermodynamics and Phase Transformation Theory3.Computer Simulation(Topics) grain growth, spinodal decomposition 4. Future plan 3-D multiscale, Nanostructural materials
ProblemsModelling of microstructural evolutionds
in structural steels ・Synergetic effects grain growth, recrystallization, second
phase precipitation, spinodal decomposition, γtoα phase transformation, ・Multiscale several nm to several handeredsµm ・Multicomponent system
Phase separation
0
300
600
900
1200
0 0.25 0.50 0.75 1.00
Temp., K
Cr, at.frac
binodalspinodal
Grain growth
Modelling of microstructural evolution in structural steel
• 1st stage(1985-1995) Integrated model based on thermodynamics and phase transformation theory• 2nd stage(1995-2005) MC, PF for Grain growth, Spinodal decomposition
etc.• 3rd stage(2005- ) Multiscale 3-D simulation for microstructural evolution in structural steel.
Computational Models based on
Thermodynamicsand
Phase Transformation Theory
1.Theories of Microstructural Evolution Nucleation, Growth and Interface Migration2. Integrated Models for Predicting Microstructural
Evolution in HSLA steels Grain growth, Precipitation, Phase
Transformation
Modelling of microstructural evolution in structural steel
• 1st stage(1985-1995) Integrated model based on thermodynamics and phase transformation theory• 2nd stage(1995-2005) MC, PF for Grain growth, Spinodal decomposition
etc.• 3rd stage(2005- ) Multiscale 3-D simulation for microstructural evolution in structural steel.
Computer Simulation
• Discrete model Monte Carlo method• Continuum model Phase field model
Grain Growth
Classification of simulation models
Model
Soap frothPolycrystal
Direct Simulation Statistical
Deterministic Probabilistic
Equation of motion for velocity of boundary
・Vertex model
・tracking of boundaries
Monte Carlo Non Monte Carlo
・Cellular Automata(*)
Phase-field
Simulation of Grain Growth by
:the local free energy density:the gradient energy coefficients
: total number of orientation field variable
:Onsager’s phenomenological parameters(mobility of a interface)
Since the orientation field variables are non-conserved order parameter, the temporal evolutions of these parameters are written as follows
We can write the total free energy of an inhomogeneous system in terms of all the orientation field variables and their gradients as:
The Phase field model
Simulation of grain growth
0
0.025
0.050
0.075
0.100
0 1.25 2.50 3.75 5.00
Frequency
Normalized Grain Size,R/Rav
100200300400
0
0.0375
0.0750
0.1125
0.1500
0 1.25 2.50 3.75 5.00
Frequency
Normalized Grain Size,R/Rav
100180200220300400
-Isotropic Grain Growth
Variation in the scaled grain size distribution function
・3D-simulation
・2D cross section of 3D simulation
System size:3203
0
0.025
0.050
0.075
0.100
0 1.25 2.50 3.75 5.00
Frequency
Normalized Grain Size,R/Rav
100200300400
0
0.0375
0.0750
0.1125
0.1500
0 1.25 2.50 3.75 5.00
Frequency
Normalized Grain Size,R/Rav
100180200220300400
-Isotropic Grain Growth
Variation in the scaled grain size distribution function
・3D-simulation
・2D cross section of 3D simulation
System size:3203
0
200
400
600
800
1000
0 100 200 300 400 500
<Rv>^2
Simulation time
0
0.05
0.10
0.15
0.20
0 0.625 1.250 1.875 2.500
Frequency
Normalized Grain Size, R/Rav
t=50t=100t=200t=300t=400
0
3
6
9
12
0 5 10 15 20 25 30 35 40
Frequency, %
Number of faces per grain, Nf
t=50t=100t=200t=300t=400
0
3.1
6.2
9.3
12.4
15.5
0 100 200 300 400 500
average number of faces
simulation time
10.0
12.5
15.0
17.5
20.0
0 0.0625 0.1250 0.1875 0.2500
m(Nf)
1/Nf
Simulation of Grain Growth by
The Metropolis Algorithm
Importance Sampling--- Markov process
A configuration {s'} is generated from the knowledge of a configuration {s}.
W({s},{s'}): the conditional probability to select {s'} starting from {s}.The equilibrium distribution:
Peq({s})=exp[-E({s})/kBT]/Z.
E: internal energy function, kB : the Boltzmann constant, T: temperature , Z : canonical partition function.
The procedure of the simualtion
• (1). A grain number from 1 to the system size, N, is assigned to each lattice point. • (2). A number corresponds to an orientation is randomly assigned to each grain.• (3). The evolution of microstructure is tracked by the change of orientations on
each lattice• (a). One lattice site is selected at random .• (b). If the lattice site belongs to grain boundary, then a new orientation is
generated.• (c).If one of nearest neighbor lattices has the same orientation as the newly
selected grain orientation, a re-orientation trial is attempted.• (d). The change in energy, ΔE, associated with the change of grain orientation is
calculated. The re-orientation trial is accepted if ΔE is less than or equal to zero. If the value ΔE is greater than zero, the re-orientation is accepted with probability,
• W = exp(-ΔE/kBT).
The change of interfacial energy accompanying re-orientation
Condition of the simulation
• System size: 1283
• The number of orientation: 16 or 32• 3-dimensional• J/KBT=0.75
0
52.254
104.508
156.762
209.016
0 2,000 4,000 6,000 8,000 10,000
Area
Time,MCS
0
1.25
2.50
3.75
5.00
0 0.625 1.250 1.875 2.500
frequency
R/Rav
400 MCS500 MCS750 MCS1000 MCS
0
2.5
5.0
7.5
10.0
0 10 20 30 40
Frequency, %
Number of faces per grain
400 MCS500 MCS750 MCS1000 MCS
10.0
12.5
15.0
17.5
20.0
0 0.0625 0.1250 0.1875 0.2500
m(Nf)
1/Nf
Phase Field vs. Monte Carlo
0
1.25
2.50
3.75
5.00
0 0.625 1.250 1.875 2.500
f(Rv/<Rv>)
Rv/<Rv>
MCMPFM Hillert-3D
0
2.5
5.0
7.5
10.0
0 10 20 30 40
frequency, %
number of faces per grain
MCMPFM
0
5
10
15
20
0 0.0625 0.1250 0.1875 0.2500
m(Nf)
1/Nf
PFMMC
Phase Field vs. Monte Carlo
Problems related to interface migration
Effect of anisotropy on grain growth Abnormal grain growthEffect of second phaseTexture controlSolute drag effectRecrystallizationPhase transforamtion
Spinodal Decomposition
• Background• Duplex stainless steel
• ・high strength, ・good weldability, ・high resistance to stress corrosion cracking → Chemical reactor
•
• Problem: 475°C embrittlement
• Hardening due to thermomechanical instability of ferrite phase in duplex stainless steels
• Prediction of long time stability of
• chemical reactor
0
300
600
900
1200
0 0.25 0.50 0.75 1.00
Temp., K
Cr, at.frac
binodalspinodal
Fe-Cr binary alloy
Second order differential parameter1D
3D
2D
Second order differential parameter1D
3D
2D
0
300
600
900
1200
0 0.25 0.50 0.75 1.00
Temp., K
Cr, at.frac
binodalspinodal
Fe-Cr binary alloy
Chemical free energy
f0=Ωx(1-x) +RT[xln(x)+(1-x)ln(1-x)]}
Phase boundary
Spinodal
Proto type simulation(Fe-40wt.%Cr ally)850K
0
0.225
0.450
0.675
0.900
0 6.25 12.50 18.75 25.00
Cr, at.frac.
Distance, nm
00.25hr0.5hr1hr2hr5hr10hr20hr50hr100hr200hr
Fe-40%Cr binary alloy
Simulation of Phase Separation
Cahn-Hillirad equation for Fe-X-Y ternary alloys
Cahn-Hillirad equation for Fe-X-Y ternary alloys
Condition
Mobility, M:
Energy gradient coefficient
L:
Aging temperature T:
Composition:
K:
Condition
Mobility, M:
Energy gradient coefficient
L:
Aging temperature T: 800KComposition:
Fe-40at.%Cr-5at.%Mo Fe-40at.%Mo-5at.%Cr
K:
Diffusion coeeficient D:
Interaction parameter Ω:
Diffusion coeeficient D:
Interaction parameter Ω:
1D simulationFe40Cr5Mo(800K)
1D simulationFe40Cr5Mo(800K)
Cr Mo
100時間後
Cr Mo
16 nm
Fe40Cr5Mo 2D simulation
Cr Mo
100時間後
0.83 0.11
0.09 0.01
Cr Mo
16 nm
Fe40Cr5Mo 2D simulation
Cr Mo
1000時間後
Cr Mo
16 nm
Fe40Cr5Mo 2D
Cr Mo
1000時間後
0.82
0.01
0.12
0.09
Cr Mo
16 nm
Fe40Cr5Mo 2D
Cr Mo
1000時間後
0.82
0.01
0.12
0.09
Cr Mo
16 nm
Fe40Cr5Mo 2D
Isosurface of Cr Isosurface of Mo
1000時間後
0.82Cr Mo
0.11Fe40Cr5Mo3D simulation
Isosurface of Cr Isosurface of Mo
1000時間後
0.82Cr Mo
0.65
0.11
0.06
Fe40Cr5Mo3D simulation
Cr Mo
MoCr
3D1000時間後 Fe40Cr5Mo
0.82
0.09
0.11
0.01
Cr Mo
MoCr
16 nm
3D1000時間後 Fe40Cr5Mo
0.82
0.09
0.11
0.01
Cr Mo
MoCr
16 nm
3D1000時間後 Fe40Cr5Mo
Monte Carlo Simulation
Lenard –Jones Parameter
:equilibrium atomic spacing
Interatomic potential at equilibrium atomic spacing
Lenard-Jones potentila
Normalized Lenard-Jones parameter
Condition
Fe-40at.%Cr-5at.%Mo 750K800K850K
Fe-40at.%Mo-5at.%Cr
62.0 KJ/mol
0.9537 1.2296 0.9809 1.3001 1.6390
Monte Carlo Simulation
Separation of peaks of Mo
Behavior of element Y along the trajectory of peak top of element X
Behavior of element Y along the trajectory of peak top of element X
Regular solution model
Modelling of microstructural evolution in structural steel
• 1st stage(1985-1995) Integrated model based on thermodynamics and phase transformation theory• 2nd stage(1995-2005) MC, PF for Grain growth, Spinodal decomposition
etc.• 3rd stage(2005- ) Multiscale 3-D simulation for microstructural evolution in structural steel.
Microscopic model Thermodynamics model Kinetic model →Prediction of microstructure +FEM → Prediction of mechanical propertiedMesoscopic model Phase field model Monte Carlo methodNeural networkMathematical method
Dynamics and Microstructure Evolution in Metals during and after the process of Severe Plastic Deformation
Tetsuya Ohashi (Kitami Institute of Technology), Mitsutoshi Kuroda (Yamagata University), Yoshiyuki Saito (Waseda University), Tadanobu Inoue (National Institute of Material Science)
Objectives of this study group are to clarify underlying mechanisms for the development of fine-grained microstructures and to understand the mechanical response of metal polycrystals with high-density lattice defects by using numerical techniques of macro- and meso-mechanics. In the macroscopic analyses, strain histories in materials processed by ARB or ECAP are quantitatively evaluated. The crystal plasticity analyses are performed to understand the characteristics and particularities of dislocation accumulations under different deformation modes. Macroscopic mechanical responses of nano-structured metals are also predicted by crystal plasticity analyses. Thermodynamic stability of ultrafine grained structures is discussed with phase field simulations.
Crystal plasticity analyses of dislocation
accumulation
Phase field simulation of microstructural
evolutions
Macroscopic analyses of giant straining process
item 2000 20052010
2015 needs
Precipitation
Dynamic recrystallization
Dynamic phase
transformation
Fracture mechanics
Microstructure vs
properties
Modelling of microstructure during TMCP
Mechanical properties
Corrosive p@roperties
Modelling Equilibrium state Calphad Dynamics Microstructural evolution Properties
Modelling ofMechanical propertiesMagnetic properties、Corrosive properties
Microstructure vs. mechanical propertiesMD,MC、PFM、FEM、neural networkMechanical properties, magnetic properties
Ab-initio,・PFM・FEM
Database, Knowledge base Thermodynamic DB、Diffusion coefficient DBの拡充、Properties DB
Database
Ab-initioMD,MCPFMFEMEmpirical
ThermodynamicsDBDiffusion Coeffi. DBMicrostructure DBProperties DB
Computed phase diagram
Microstructural evolution
Computational mechanics deformation, fracture
Multiscale 3D-modelMicrostructure Phase field+MC and FEMProperties FEM Neural network