phase field modeling of microstructure - ju li
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CAMM3-D Digital Structure (OSU)-2626753
Experimental and Computational Tools for the DigitalRepresentation and Prediction of Microstructure and its Incorporation
in the Designer’s Knowledge Base
Phase Field Modeling of Microstructure
Yunzhi WangDepartment of Materials Science and Engineering
The Ohio State UniversityColumbus, OH
AknowledgementD3D team members
Prof. M.J. Mills; Prof. R. Duherty; Dr. D. DimidukDr. N. Ma, C. Shen; M. Grober
CAMM3-D Digital Structure (OSU)-2626753
Input/Output for Phase Field Modeling of Microstructure
Sample data
Mechanisticdeterminations
Phase Field Modeling ofmicrostructural evolution,as a f(Service Exposure)
Inclusion of deformationmechanisms in CrystalPlasticity/FEM Model
Predictive CP/FEM-basedmodel for
microstructure/propertyAtomistics & Phase FieldModeling of dislocation-
microstructure interactions
MicrostructureDigitization Tool
(MDT)Direct 3DCharacterization
(D3D) Microstructure/PropertiesNeural network tool (PNN)
MSD tool (MSD:P)
Microstructure as a functionof Service Exposure
Neural network tool (MNN)MSD tool (MSD:M)
Stereology:2D→3D Rendition
(2DS)
Phase Field Modeling ofmicrostructural evolution,as a f(Service Exposure)
CAMM3-D Digital Structure (OSU)-2626753
“Prior β” Grain Boundaries α
β
α
Colony Microstructures in α/β Titanium Alloys
Colony Boundaries
α/β Lath BoundariesM.J. Mills (OSU)
CAMM3-D Digital Structure (OSU)-2626753
Οrientation relationship and slip vector mismatch
a1 a2
a3
b1
b2
[~3~53]β || [2~750]
α
αβαβ ]0112[||]111[,)0001(||)101(
• a1 and b1 misoriented by 0.56°• a2 and b2 misoriented by 11.5°• a3 has no mating slip vector in
β-phase
• Effectively creates three uniqueslip directions in the α/β colony
CAMM3-D Digital Structure (OSU)-2626753
Stress = 480 MPa
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5000 1 104 1.5 104 2 104 2.5 104 3 104 3.5 104 4 104
time (sec)
a1-prism
a2-prism
Anisotropy of α/βColonies in Compression
Significant differencesin yield and hardening
Remarkable differencesin creep response
Stra
in (%
)
a1-prism
a2-prism
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10
stre
ss (M
Pa)
strain (%)
ε = 10-4 s-1.Ti-5Al-2.5Sn-0.5Fe
Ti-5Al-2.5Sn-0.5Fe
CAMM3-D Digital Structure (OSU)-2626753
a1
• Residual matrix dislocationsof a1 (at entrance interface) and a3 (at exit interface)
a2 Prism
a1
a3
• Present only near regionsundergoing slip transmission
Dislocation-precipitate interactions
EntranceSide
ExitSide
a2
a2 Basal
β
200 nm
g =[~1010]B = 0001ZA
a3
EntranceSide
ExitSide
a1
g
CAMM3-D Digital Structure (OSU)-2626753
Ti 550 - Slip Accumulation Studies
200 nm[1-10]
Total plastic strain 1 %
50 nm
[10-1]
Total plastic strain 5 %
200 nm
[10-11]
B. Viswanathan and H.L. Fraser
CAMM3-D Digital Structure (OSU)-2626753
0.2 µm
2.0 µm
0.5 µm
Courtesy of M. F. Henry, GE
Disk alloy: sample was soaked above gamma prime and slowly cooled at a linear rate to below 500°C
γ/γ′ Microstructure in Ni-Base Superalloys
CAMM3-D Digital Structure (OSU)-2626753
Looping, shearing, and micro-twinning
200 nm 200 nm
(a) (b)(111) (c)
(d)
200 nm
1 nm
Creep deformation microstructure in Rene 88 after 0.5% Strain under 121 ksi at 650oC (Courtesy of B. Viswanathan and M. J. Mills)
(a) Orowan looping around large precipitates (b) Localized faulting of large precipitates
(c) and (d) Continuous faulting (micro-twinning) of both the γ-
matrix and γ'-particles
CAMM3-D Digital Structure (OSU)-2626753
Dramatic Effect of Microstructure ScaleOn Creep Response
• Strong effect of tertiary volume fraction on creep strength• Coarsening/dissolution of tertiary population occurs at these temp.• Different mechanisms active for the two microstructures
50nm
50nm50nm
121.6 ksi1200°F
Coarse Structure (75F/min) Fine Structure (400F/min)
50nm
CAMM3-D Digital Structure (OSU)-2626753
• Clearly, without these detailed insights into the operative mechanisms, any modeling attempt to describe micro structural evolution and creep deformation in these alloys will remain phenomenological and of limited predictive power.
• A principle theme of our approach is to develop microstructure- and micromechanims-based models that account for the coupling between precipitate microstructure and dislocation activities.
Development of microstructure- and micromechanim-based models
CAMM3-D Digital Structure (OSU)-2626753
• Conventional phase field method at mesoscopic scales for microstructural evolution of precipitate and dislocations
• Digital representation and reconstruction of microstructures using phase field method
• Microscopic phase field modeling of dislocation core structures and dislocation-precipitate interactions
Multi-scale phase field modeling
CAMM3-D Digital Structure (OSU)-2626753
Phase Field Modeling of Formation and Coarsening of γ/γ′ Bimodal Microstructures in Ni-Al
Continuous cooling + heterogeneous and homogeneous nucleation
0.5 µm
• Landau polynomial/sublattice model for free energy• Diffusivity, interfacial energy, elastic constants and lattice
parameter from Ardell’s
∆G*het
∆G*hom
= 0.75
CAMM3-D Digital Structure (OSU)-2626753
Update from Billie
CAMM3-D Digital Structure (OSU)-2626753
3D quantitative phase field model calibration
CAMM3-D Digital Structure (OSU)-2626753
• Input: an arbitrary heat treatment schedule• Output: digital microstructural evolution• Model and data are being evaluated by NN, MDT, and MSD
CAMM3-D Digital Structure (OSU)-2626753
Sensitivity study of various input parameters
CAMM3-D Digital Structure (OSU)-2626753
Phsse Field Modeling of Microstructure Evolution in Ti-6Al-4V
CAMM3-D Digital Structure (OSU)-2626753
40µm
Growth of Globular α – Effect of Spatial and Size Distribution
1-pointcorrelation
2-point correlation
CAMM3-D Digital Structure (OSU)-2626753
Incorporation of effect from size and spatial distribution
−−
−−= tcccc
RD
Af
f βα
β02
1exp1ξ
0 200 400 600 800 1000 12000 .00
0 .02
0 .04
0 .06
0 .08
0 .10
0 .12
ξ=1.782
CAMM3-D Digital Structure (OSU)-2626753
OIM of substructures are being conducted at Drexel
Phase field modeling capability has been developed at OSU
Mechanisms of recrystallization
CAMM3-D Digital Structure (OSU)-2626753
Phase field modeling using OIM as direct input
• A software package has been developed to convert automatically OIM data to phase field input
OIM data from Michael G. Glavicic from UES
CAMM3-D Digital Structure (OSU)-2626753
0
0.05
0.1
0.15
0.2
0.25-1 -0.8
-0.6
-0.4
-0.2 0 0.2 0.4 0.6 0.8 1
f
log(A/<A>)
0
0.05
0.1
0.15
0.2
0.25
-1 -0.8
-0.6
-0.4
-0.2 0 0.2 0.4 0.6 0.8 1
f
log(A/<A>)
Without TextureWith Texture
Sensitivity Study
1400
1900
2400
2900
3400
3900
4400
4900
0 20 40 60 80 100
iso
ani
experiment
t(min)
A(um2)
1mm
CAMM
10% difference
CAMM3-D Digital Structure (OSU)-2626753
Direct OIM image from Grobhor and Ghosh
Phase Field Smoothing
Microstructure reconstruction using phase field
Phase field reconstruction using microstructuraldescriptors (MDF, ODF, micro-texture, size distribution, number of sides, …)– work in progress
CAMM3-D Digital Structure (OSU)-2626753
Effect of precipitate: Coherent vs Incoherent Interfaces
incoherent interfaces
from incoherent to coherent from coherent to incoherent
Orange: Primary gamma primeBlue: High energy (incoherent) interfaces
CAMM3-D Digital Structure (OSU)-2626753
Effect of precipitates
Incoherent Mixed
CAMM3-D Digital Structure (OSU)-2626753
log(A/<A>)-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
f
0.000.020.040.060.080.100.120.140.160.18
Coherent vs incoherent interfacesincoherentmixed
Phase field model uniquely capable of capturing important features of microstructure:• Grain and phase boundary character and coherency• Size and spatial distribution of precipitates• Time evolution of precipitates (dissolution and coarsening)
CAMM3-D Digital Structure (OSU)-2626753
t*=10 50
Formation of dislocation networkDislocation-precipitate interaction
Benefit of the field description:
1. Arbitrary poly-domain microstructure
and dislocation configuration
2. Computational cost insensitive to the
complexity of the microstructure
Shen & Wang, Acta Mater 51(2003)2595; ibid 52(2004) 683; Jin, Artemev and Khachaturyan, Acta Mater. 49 (2001) 2309
Phase Field Model of Dislocations at Mesoscale
CAMM3-D Digital Structure (OSU)-2626753
γ’ cutting and Shockley partial nucleation for isolated faulting in Ni-base disk alloy
APB CSF SESF
γ’1/2<110>
B. Viswanathan and M. J. Mills
Micromechanisms of creep deformation of Ni-base superalloys
isolated faulting
Limitations of Conventional Phase Field Method
200 nmmicrotwinning
CAMM3-D Digital Structure (OSU)-2626753
y
z
x 32768∆
3276
8∆
GSF:S. Kohlhammer, PhD thesisData comparied to calculations bySchoeck
Dissociated dislocation core structure
CAMM3-D Digital Structure (OSU)-2626753
Model proposed by Decamps et. al. (1987, 1991, 1994) and Mukherji et. al. (1991):
• Precipitate sheared initially by 1/2<110> forming an APB
• APB transforms into SISF/SESF via nucleation on APB of 1/6<112> partial
B. Viswanathan and M. J. Mills
Mechanisms of isolated faulting
CAMM3-D Digital Structure (OSU)-2626753
Nucleation of SISF on APB
APBSISF
0 20 40 60 80 100 120-4
-3
-2
-1
0
1
2
0 degree45 degree
∆E=16.6 eV
∆E=11.0 eV(×
10.4
6 eV
)
Unrelaxed cores
R/d (d=2.07Å)
45 degree0 degree
Nucleation at “C”19nm
M
CSlipped γ-matrix Unslipped γ-matrix
Unslipped γ'
APB
SISF
(111)
τ app 0˚45˚
CAMM3-D Digital Structure (OSU)-2626753
Nucleation of SESF on CSF
(×10
.46
eV)
R/d (d=2.07Å)
1024d ~ 205 nm
CSF(111)
SESF
γ’
∆E=37.1 eV
CSF
CSF
APBSISFSESF
Unrelaxed cores
CAMM3-D Digital Structure (OSU)-2626753
Multiplane Generalized Stacking Fault Energy
n=1 n=2 n=∞…
0
( )( ) ,nn
E xxnS
γ ≡ 1,2,3,...,n = ∞
Ju Li (OSU)
CAMM3-D Digital Structure (OSU)-2626753
Ni3Al pseudo-twinning mGSF
VASP108 atoms
No z-relaxation(Ju Li, OSU)
CAMM3-D Digital Structure (OSU)-2626753
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Modified GSF Accounting for Re-ordering
Chemical re-ordering lowers the effective GSF surface
CSFSESF
Pseudo twin
η
mJ/
m2
VASP/MGSF for Ni3Al
0
50
100
150
200
250
300
350
400
-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10
’gsf.prf’
SISFAPB
Ju Li (OSU)
CAMM3-D Digital Structure (OSU)-2626753
-1.5
-1
-0.5
0
0.5
0 2 4 6 8 10 12 14 16 18R/b
500MPa550MPa570MPa595MPa600MPa
(a) immediate reordering; (b) relaxed dislocation configurations; (c) applied stress
Reduced barrier height due to(×
10.4
6 eV
)
~ 46kT (@1000Kelvin)
CAMM3-D Digital Structure (OSU)-2626753
NEB Calculations
CAMM3-D Digital Structure (OSU)-2626753
NEB Calculations of Activation Energy as Function of Applied Stress
CAMM3-D Digital Structure (OSU)-2626753
β
200 nm
g =[~1010]B = 0001ZA
a1
a3
g
a2 Basal Slip Compression
• Accumulation of residual matrix dislocations causesincreased strain hardening
α αβbr’ -br’-a1
a2 b2 a2
-a3
EntranceSide
ExitSide
CAMM3-D Digital Structure (OSU)-2626753
GSFs
HCP
BCC
1/ 3[2110]
[0110]
1/ 2[111]
[112]
a1
a2
a3
b1
b2
(1-10)bcc
(0001)hcp
CAMM3-D Digital Structure (OSU)-2626753b1=1.0 b2=0.9 b1=1.0
animation
CAMM3-D Digital Structure (OSU)-2626753
Update from Chen
CAMM3-D Digital Structure (OSU)-2626753
CAMM3-D Digital Structure (OSU)-2626753
Summary• Phase field modeling capabilities at multiple length scales have been
developed for coupled microstructural evolution and dislocation process
• At mesoscopic level, 3D quantitative phase field model of microstructure evolution under non-isothermal conditions has been calibrated against experimental study
• At microscopic level, the phase field model has been shown to be a 3D generalization of the Peierls model. Using ab initio calculations as inputs, the model has been applied to study deformation mechanisms in Ni-base superalloys and α/β Ti alloys.
• 2D and 3D quantitative models and digital microstructures have been developed, and their usefulness is being evaluated by team member for NN, DMT, MSD tool development.
CAMM3-D Digital Structure (OSU)-2626753
1/2 <110>
0
20
40
60
80
100
120
140
160
180
200
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Temperature (°F)
Stre
ss (k
si)
Rene 88 (Coarse)Rene 88 (Fine)Rene 104
1/2 <110>
1/2 <110>
Dislocation LoopingDislocation Looping
1/2 <110>
1/6 <112>
Dislocation BypassDislocation Bypass1/2 <110>MicrotwinningMicrotwinning
Isolated FaultingIsolated Faulting
APB ShearingAPB Shearing
APB
Tertiary γ’ DissolutionTertiary γ’
DissolutionTertiary γ’Tertiary γ’
Mechanisms of Creep in Disk Alloys
CAMM
CAMM3-D Digital Structure (OSU)-2626753
Microstructures in Real Engineering Alloys
0.5 µm
α/β Ti alloy Ni-base superalloy(M. Henry)
CAMM3-D Digital Structure (OSU)-2626753
Advanced Microstructure Modeling using Phase Field Method
2 µm1 µm
Y. Jin et. al.
∂c r , t( )∂t
= ∇ D ∇δF
δ c r, t( )
+ ξ c r, t( )
∂η p r, t( )∂ t
= − L δFδη p r, t( )
+ ξ p r, t( )
M
The phase field method handles well arbitrary microstructures consisting of diffusionally and elastically interacting particles and defects of high volume fraction and accounts self-consistently for topological changes such as particle coalescence.
The phase field method handles well arbitrary microstructures consisting of diffusionally and elastically interacting particles and defects of high volume fraction and accounts self-consistently for topological changes such as particle coalescence.
0.5 µm
CAMM3-D Digital Structure (OSU)-2626753
ExperimentalData
ExperimentalData
MobilityDatabase Mobility
Database
TDDatabase
TDDatabase
Chemical Diffusivity of Al
Interface Properties
Interface Properties
Elastic PropertiesElastic
Properties
Other properties
Input
Atomistic CalculationsAtomistic
Calculations
DICTRA DICTRA
Thermo_Calc
or PANDATThermo_Calc
or PANDAT
Phase FieldModel
GSF orγ-surfacesGSF or
γ-surfacesConstitutive equations for MNN and MSDM
training or direct design applications
Constitutive equations for MNN and MSDM
training or direct design applications
Output
Kinetic description
Optimizer
Digital Microstructureto MDT
Digital Microstructureto MDT
Thermodynamic description
Micro.-Disl. Interaction
Model
Micro.-Disl. Interaction
Model
Input/Output for Phase Field Modeling of Microstructure
CAMM3-D Digital Structure (OSU)-2626753
Dislocation – Microstructure Interaction Modeling
Relevant mechanisms informed by experimental study
CP/FEMCP/FEM
Micro.-DislInteraction
Model
Micro.-Disl. Interaction
Model
CAMM3-D Digital Structure (OSU)-2626753
Requirements and Challenges
• Quantitative prediction of detailed microstructural features including precipitate morphology, spatial arrangement and anisotropy– at the same level of complexity as experimental
observations– at the experimentally relevant length and time scales
• Multi-component, multi-phase, and polycrystalline• Very complex microstructural features:
– high volume fraction of precipitates– strong anisotropy and spatial correlation– elastic interactions among precipitates
• Coupling between precipitate microstructure evolution and plastic deformation (dislocation activities)
• Model robustness and computational efficiency
CAMM3-D Digital Structure (OSU)-2626753
Comparison between simulated and experimentally measured growth/coarsening
kinetics at 760C
0
2
4
6
8
10
12
14
16
18
20
0 100000 200000 300000 400000time (s)
mea
n pa
rtic
le ra
dius
(nm
)
simulation
experiment
Comparison between simulated and experimentally measured growth/coarsening
kinetics at 800C
0
5
10
15
20
25
0 20000 40000 60000 80000 100000
time (s)
mea
n pa
rtic
le ra
dius
(nm
)
simulation
experiment
3D quantitative simulation of Ni-23.27Cr-16.49Co-4.3Al-1.22Ti: Comparison with Exp.
Courtesy of Y. Wen and J. P. Simmons
CAMM3-D Digital Structure (OSU)-2626753
Nucleation Movie I Nucleation Movie II
Phase Field Model of Nucleation
Formation of γ/γ′ Bimodal Microstructure
CAMM3-D Digital Structure (OSU)-2626753
Homogeneous Nucleation under Continuous Cooling at 10oC/s
CAMM3-D Digital Structure (OSU)-2626753
Homogeneous Nucleation under Continuous Cooling at 20oC/s
CAMM3-D Digital Structure (OSU)-2626753
Homogeneous Nucleation under Continuous Cooling at 40oC/s
CAMM3-D Digital Structure (OSU)-2626753
Tinit= 950C Tfinal= 450C at 10oC/s
C = 0.163 C = 0.153 C = 0.143
Equilibrium VF (450C) : 44.11%
Final Simulation AF : 42.96%
Equilibrium VF (450C) : 37.47%
Final Simulation AF : 30.35%
Equilibrium VF(450C) :30.83%
Final Simulation AF : 10.91%
Effect of Alloy Composition
CAMM3-D Digital Structure (OSU)-2626753
2 Slip Systems:(111)[101];(111)[011], positive Misfit, [001] Compression (>931MPa)
x=32 y=32 z=32
Time evolution - (111) cross-section {100} cross-sections
γ′ rafting during creep