computational materials design: principles and examples · computational materials design:...

Computational Materials Design:

Principles and Examples

Charles Kuehmann, Ph.D.

Abhijeet Misra, Ph.D.

Weiming Huang, Ph.D.

Herng-Jeng Jou, Ph.D.www.questek.com

Phase Stability, Diffusion Kinetics

and Their Applications

(PSDK-IV)

October 27th, 2009

Contract: FA8650-05-C-5800

Materials By Design®

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Computational Materials Design


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Design Integration

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Engineering Systems Approach (N. Suh)

Client’s

Needs

Functional

Requirements

Design

Parameters

Process

Variables

Client

domain

Functional

domain

Physical

domain

Process

domain


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PROCESSING STRUCTURE

FCC MATRIX

Solid Solution

STRENGTHENING

DISPERSIONS

L12 – Al3(Sc,Zr)

Mg(Al,Cu,Zn)2

GRAIN SIZE AND

MORPHOLOGY

INCLUSIONS AND

EUTECTICS

PROPERTIES

PE

RF

OR

MA

NC

E

HOMOGENIZATION

SOLUTIONIZING

AGING

STRENGTH

TOUGHNESS

SCC RESISTANCE

PROCESSING STRUCTURE

FCC MATRIX

INOCOCULANT

DISPERSIONS

L12 – Al3(Sc,Zr)

GRAIN SIZE AND

MORPHOLOGY

INCLUSIONS AND

EUTECTICS

PROPERTIES

REFINING

ALLOYING

DEGASSING

FINAL ADDITIONS

SOLIDIFICATION

POROSITY

FLUIDITY

THERMAL

DIFFUSIVITY

CASTABILITY DESIGN PERFORMANCE DESIGN

HOT TEARING

RESISTANCE

System Flow-Block Diagram For Castable Al 7XXX Alloys


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Process-Structure Modeling


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Modeling Flow Chart

Databases Modeling Tools

Grain Size

• Segregation

• Solidification

Products

Strength

Strength Model

GP Zone, ’, Secondary L12

Precipitation

Alloy Strength

Thermodynamics

Diffusion

Inoculation Model

Primary L12 Precipitation

FCC Grain Inoculation

Solidification Model• DICTRA simulations

• Scheil simulations

Calculated Property


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Databases


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Development of Thermodynamic Database

Multicomponent thermodynamic database for stable and metastable phases

successfully developed for Sc-modified 7xxxx Al alloys

• Al-Zn-Mg-Cu description from COST507 database evaluated and revised

• Sc added to revised Al-Zn-Mg-Cu database, including all relevant binary and ternary compounds

• L12 Al3(Sc,Zr) thermodynamics developed, incorporating solubilities of other elements

• Thermodynamic descriptions developed for metastable GP zones and ’

Calculated phase fractions

in SSA038 alloy using

developed database

Calculated isopleth in

SSA018 alloy with varying

Sc content


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Eta Prime Thermodynamics Description

• Recent atom-probe work has revealed that

composition of phase is significantly

different from stable phase.

• Substantial amount of Al is dissolved in the

phase.

• Li et al. [99Li] have suggested chemical

stoichiometry of Mg2Zn5-xAl2+x for the

phase based on direct lattice imaging and

electron diffraction work.

• C. Wolverton [01Wol] has shown that a

stoichiometry of Mg4Zn13Al2 has the lowest

energy based on first-principles calculations

• Wolverton’s suggested structure is used as

the model structure for the phase in our

thermodynamic assessments. Mg and Al are

allowed to dissolve in the Zn sublattice to

account for deviation from stoichiometry.

• Thermodynamic assessment was carried out

based on experimental data from literature.

• Due to the small size of the precipitates,

there was significant overlap of matrix Al in

the atom-probe measurements. The reported

atom-probe data was corrected to account

for the matrix overlap by using an overlap

factor as measured by [05Dum].


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GP Zone Thermodynamic Description

• Berg et al. [01Ber] have suggested a

modification of the AuCu(I)-type cell with

Al dissolved in the Zn and Mg planes for

the structure of the GP Zones. This leads

to a possible stoichiometry of Mg9-

xZn7Al2+x.

• Wolverton [01Wol] has found that a

stacking sequence of Al4Mg1Zn2Mg1

gives the lowest energies than any of the

other considered stacking sequences.

This essentially translates to a

stoichiometry of Al2MgZn.

• Corrected experimental atom-probe data

agrees reasonable well with Wolverton’s

model. Hence Wolverton’s suggested

structure was used as the model structure

for the GP zones in our thermodynamic

assessments.

• Thermodynamic assessment was carried

out using experimental data from

literature.


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Development of Mobility Database

Mobility database successfully developed for Sc-modified 7xxxx Al alloys

for the Liquid and FCC phases.

Comparison of diffusivity predictions using developed mobility database (solid lines)

with experimental data (a) Zn tracer diffusion in Al (b) Cu tracer diffusion in Al-Zn-Mg

alloy


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Inoculation Model


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Integration of Primary L12 and Inoculation Simulation

Overall Compositions

User Input

O2Content

Surface Energy L12/LIQ

Surface Energy FCC/LIQ

TL (FCC)

LIQ Compositions

w/o L12

L12 Particle Size

Distribution (PSD)

Corrected L12PSD

dT/dt or T(t)

Thermo-Calc PrecipiCalcPrimary L12

PrecipiCalcInoculation

PSD WidthCorrection Grain Size


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) timen(incubatio nucleation transient with :Continuity /SS

t JeR

dt

dRf

t

f

f(R,t) — particle size (R) distribution function

with t as time

Ci — Equilibrium Solute Concentration

Dij — Diffusivity Matrix

— Surface Energy

)(),...,( and )(),...,( where

,...,2,, with21

2222

2

12

nnT

inn

T

i

mj

ji

T

i

kjk

ji

T

i

CCCCCCCCCC

nkjiR

VC

CC

GC

CDCC

GCR

dt

dR

0

3

0

30

3

4 where)1()(

3

4 : BalanceMass dRfRCdRRCfRC iii

mean field

particle matrix

iC

iC

iC

Basic Equations of Multi-Component PrecipiCalcTM


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PrecipiCalc predictions of alloy Al-0.7Sc at different cooling rates


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Modeling of Primary L12 Precipitation

Cooling

Mode

dT/dt

(oC/

sec)

L12 Mean Radius ( m)

SSA038

(0.58Sc-

0.17Zr) As-

Cast

SSA038-no

Cu (0.54Sc-

0.098Zr) As-

Cast

Al-Sc

(0.89Sc) As-

Cast

Exp.

(2D)

Calc.

(2D)

Exp.

(2D)

Calc.

(2D)

Exp.

(2D)

Calc.

(2D)

Sand

Mould

~7.5 6.33 5.97 5.64 5.35 - -

Iron

Wedge

~22 4.09 3.6 3.2 2.72 - -

Copper

Wedge

~200 1.2 1.47 1.18 1.2 1.15 1.95

Continuous cooling samples

• L12/liquid interfacial energy and liquid diffusion parameters adjusted within

PrecipiCalc model to match measured L12 mean particle size


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Heterogeneous Nucleation Treatment for Primary L12

• PrecipiCalc simulations using a homogenous nucleation model predicted a much narrower distribution of

primary L12 particle sizes as opposed to measured data.

• Oxygen leads to formation of oxide particles which act as heterogeneous nucleation sites for L12

particles, and broadens PSD width.

• Experimental data was analyzed to correlate measured oxygen content with the width of measured PSD,

and a calibration factor was deduced from the correlation.

Sand

Mould

Iron

Wedge

Copper

Wedge

SSA038 SSA038-No Cu Al-Sc

Solid points: Measured data

Black curve: Fit to measured

data

Red curve: Calibrated

PrecipiCalc PSD

Particles to the right of dashed

red line are active inoculants

2D

PS

D (

1/m

3)

R, m


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Inoculation Model Mechanism

Primary L12 particles act as inoculants for the formation of fine equiaxed grains.

Mechanism of grain initiation and growth (Greer et al., Acta Mat., 2000):

• Onset of growth is controlled by growth constraint rather than by nucleation.

• Initial FCC nucleus grows readily across the face of nucleant particle to form thin coating.

• Further growth possible only by reducing the radius of curvature of its interface with the

melt (free growth). This radius cannot go below the critical r* for nucleation unless the

undercooling is increased, thus reducing r*. The Critical condition for free growth is

particle size d = 2r*

Greer’s Inoculation Model implemented in PrecipiCalc:

1. Primary L12 PSD from previous step.

2. Melt cools below FCC liquidus temp.

3. Free growth of FCC grains allowed to occur on the largest inoculant particles which satisfy criterion d=2r* (r*=critical radius for nucleation).

4. As undercooling increases, r* decreases, and smaller L12

particles are activated as nucleants.

5. Growing FCC grains release latent heat, slowing the rate of cooling

6. Eventually the temperature rises (recalescence) – no more initiation of free growth, controlling the refinement of grain size.

Inoculant


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Grain Size Prediction vs. Experimental Data - Al-0.7Sc


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Output of FCC Grain Inoculation Model

Predicted SSA038 Grain Size Contours with Varying Cooling Rate and Oxygen Content

500 m

300

150

200100

7050

30

20

15

10

Cooling Rate for Primary L12, C/sec

MAGMA Simulation for

Component castings

Cooling rates explored

in wedge casting trials.

Sand

Iron

Copper

Mould

G.S

( m)

(Meas.)

G.S

( m)

(Pred.)

Sand 73 65

Iron 54 59.5

Copper 17 22.2

Inoculation model

predictions.


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Strength Model


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Typical Thermal Profile for 7xxx Al Alloys

• Al3(Sc,Zr) precipitates homogeneously from an FCC Al matrix as fully coherent

particles at the homogenization temperature of 400-500oC.

• GP zones precipitate homogeneously at room temperature and above as fully

coherent particles, and act as the nucleating sites for subsequent ’ (eta-prime)

formation.

• nucleates heterogeneously on existing GP zones upon heating to T>70oC.

Homogenization

at ~450- 500oC

Time

Te

mp

era

ture

Secondary L12

particles precipitate

GP Zones

precipitate

Aging at

120-140oC

Eta-prime particles

precipitate

GP Zones

dissolve

Natural

aging


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Strength Model Flow ChartUser Input

PrecipiCalcSecondary L12

Strength Model

Strength

•Overall composition•Surface energy (L12/FCC)•Solution treatment (T(t))

Secondary L12

• Mean particle size

• Volume fraction

•Surface energy (GP Zone/FCC)

•Natural aging (T(t))

•Surface energy ( ’/FCC)•Artificial aging profile including heat-up (T(t))

•Grain size•Dislocation

density

PrecipiCalcGP Zone

PrecipiCalc

’GP Zone

GP Zone size distribution

Alloy composition for GP zone and ’

precipitation

• ’ mean particle size and volume fraction

• GP zone mean particle size and volume fraction

• Matrix composition


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Modeling Secondary L12, GP zone and ’ Precipitation

Secondary L12 GP zone

Eta-prime

• PrecipiCalc model was calibrated to existing

literature data for secondary L12, GP zone

and ’ precipitation.

• Solid lines: PrecipiCalc Simulations; Data

points: Experimental literature data.

• Predictions from calibrated precipitation

model were then tested against

experimentally measured data for SSA018

alloy.

(320oC/hr)

(30oC/hr)


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Characterization of Precipitates in SSA018 Alloy

Secondary L12

GP zone

Eta-prime

460oC/20hrs

(TEM)ST+ 30oC/ 2 days

(LEAP)

ST+ 30oC/ 2 days + 140oC/10hrs

(LEAP)


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Validation of PrecipiCalc model predictions

Secondary L12

GP zone

Eta-prime

• PrecipiCalc model predictions show

good agreement with experimentally

measured data for SSA018 alloy.

Atom Probe

PrecipiCalc


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1 103

1 104

1 105

1 106

1 107

0.6

0.8

1

1.2

Prediction/Data ratio

Aging time, s

Rat

io

1

13200

1 103

1 104

1 105

1 106

1 107

100

150

200

250

300

Model

Data

Model

Data

Data and model prediction

Aging time, s

CR

SS

, M

Pa

13200

Aging at 160oCHeat upAging at 160oCHeat up

Strength Modeling: Calibration• Mechanistic precipitation strength model for Al-alloys developed at QuesTek,

based on:

– Orowan by-pass and Friedel shear-cutting models.

– Solid solution strengthening: atomic size and elastic modulus mismatch.

– Dislocation strengthening: based on Nes’s dislocation recovery model.

– Hall-Petch grain size effect.

• Strength model was first calibrated to literature data.

• Developed model was used to predict the strength of aged SSA018 alloy, at different thermal treatment conditions.

Experimental data from A. Deschamps et al, Acta Mat., vol. 47, 1999, pg. 293-305


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Comparison of Measured Yield Strength Values with Predictions

Most predictions are within 5 ksi.

Explanation of T6 temper:

• For SSA0xx alloys:

460 C/48hrs+RT/2days+120 C/19hrs

• For 99Des alloys:

475 C/1hr+RT/3days+160 C/1-5hrs

• For wrought 7xxx alloys:

465 C/1hr+RT/1day(assumed) +

120 C/24hrs

Data Source

SSA0xx: O.N. Senkov et al., Met. & Mat. Trans. A, vol. 36A, Aug 2005, pp. 2115-2126.

99Des: A. Deschamps et al., Mat. Sc. & Tech., vol. 15, Sep. 1999, pp. 993-1000.

7xxx: ASM Metals Handbook, Desk Edition, 1995


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Solidification: Scheil and DICTRA simulations• Scheil solidification assumes that the liquid phase is uniform (infinite diffusion), and no

diffusion is allowed in the solid represents an extreme case of solute segregation.

• DICTRA moving-boundary back-diffusion model assumes realistic diffusion fields in both liquid and solid phases represents the most realistic case of solidification.

Scheil

DICTRA

Solute Segregation Solidification Curves

Results for

SSA038 Alloy


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Design Optimization


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Strength-Solidification Maps with Varying Zn, Mg, and Cu


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Simulation of Casting Process: Primary L12 <R> and FCC Grain Size

Assumed 80 ppm O

Primary L12 FCC Grain Size


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