Phase Field Modeling of Microstructure - Ju Li

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


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)


“Prior β” Grain Boundaries α

β

α

Colony Microstructures in α/β Titanium Alloys

Colony Boundaries

α/β Lath BoundariesM.J. Mills (OSU)


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


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


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


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


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


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


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


• 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


• 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


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


Update from Billie


3D quantitative phase field model calibration


• Input: an arbitrary heat treatment schedule• Output: digital microstructural evolution• Model and data are being evaluated by NN, MDT, and MSD


Sensitivity study of various input parameters


Phsse Field Modeling of Microstructure Evolution in Ti-6Al-4V


40µm

Growth of Globular α – Effect of Spatial and Size Distribution

1-pointcorrelation

2-point correlation


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


OIM of substructures are being conducted at Drexel

Phase field modeling capability has been developed at OSU

Mechanisms of recrystallization


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


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


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


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


Effect of precipitates

Incoherent Mixed


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)


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


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


y

z

x 32768∆

3276

8∆

GSF:S. Kohlhammer, PhD thesisData comparied to calculations bySchoeck

Dissociated dislocation core structure


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


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˚


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


Multiplane Generalized Stacking Fault Energy

n=1 n=2 n=∞…

0

( )( ) ,nn

E xxnS

γ ≡ 1,2,3,...,n = ∞

Ju Li (OSU)


Ni3Al pseudo-twinning mGSF

VASP108 atoms

No z-relaxation(Ju Li, OSU)


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)


-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)


NEB Calculations


NEB Calculations of Activation Energy as Function of Applied Stress


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


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


Update from Chen


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.


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


Microstructures in Real Engineering Alloys

0.5 µm

α/β Ti alloy Ni-base superalloy(M. Henry)


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


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


Model

Input/Output for Phase Field Modeling of Microstructure


Dislocation – Microstructure Interaction Modeling

Relevant mechanisms informed by experimental study

CP/FEMCP/FEM

Micro.-DislInteraction

Model


Model


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


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


Nucleation Movie I Nucleation Movie II

Phase Field Model of Nucleation

Formation of γ/γ′ Bimodal Microstructure


Homogeneous Nucleation under Continuous Cooling at 10oC/s


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%


Equilibrium VF(450C) :30.83%


Effect of Alloy Composition


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

Phase Field Modeling of Microstructure - Ju Li

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