PanPrecipitation for Precipitation Modeling of Multi ...Precipitation Modeling: strategy Precipitation process is very complicated and we don’t have an universal model valid for

Weisheng Cao, Fan Zhang, Shuanglin Chen

Chuan Zhang, Jun Zhu, Duchao Lv

PanPrecipitation for Precipitation Modeling of Multi-Component Alloys

by

April 08, 2020

CompuTherm, LLC8401 Greenway Blvd, Middleton, WI, USA

http://www.computherm.com

CompuTherm LLC – www.computherm.com 1

Outline of Presentation

I. Introduction Materials Design by CALPHAD & ICME

Precipitation modeling and software design

Kinetic and strengthening models

II. Applications to multi-component Ni and Al alloys Precipitation behavior of Ni-based superalloys

Age hardening behavior of Al alloys

III. Discussion and software tutorial


Materials Design by CALPHAD & Integrated Computational Materials Engineering (ICME)

Material Properties and Performance

Microstructure

Chemistry

ProcessingConditions

Thermodynamic Calculation

Kinetic Simulation

0 30 60 90 120 1500

30

60

90

120

150

180 1080oC 1050oC 1020oC 990oC 960oC

Ave

rage

Siz

e (n

m)

Time (minute)

Microstructural Evolution Model Mechanical Property Model

Model Simulation+Key ExperimentsModern Materials Design


Vol

ume

Fra

ctio

n

log(Time)

Precipitation hardening

α’→ α +βα’: matrix phase (supersaturated )β: precipitate phaseα : stable solid solution

α’

L

α β

α +βTem

pera

ture

CB →A B

Concurrent nucleation, growth & coarsening advanced kinetic model Reliable thermodynamic data and mobility data smooth integration

Coa

rsen

ing

Nucleation

+Growth

Incu

batio

n


Precipitation modeling

Integrated Modeling Tools(PanPrecipitation)

Calphad Modeling(PanEngine)

Thermodynamic & mobility database

Problem To Be Solved

Alloy Chemistry &Processing Condition

Microstructure

Precipitationdatabase

Microstructure Modeling

driving forcephase equilibriummobility data

Modeling ofAge Hardening

volume fractionaverage sizePSD


Precipitation Modeling: strategy Precipitation Modeling: strategy

Precipitation process is very complicated and wedon’t have an universal model valid for everycases;

The model or model parameters may need to beadjusted case by case;

Extendibility and flexibility is the key (this is howPanPrecipitation is different);


User-Defined

System

Matrix Phase

KWN Fast Acting

Built-in Phase Models

Virtual Precipitate Phase

Top-Level IntegrationPanPrecipitation: Generic Data Structure


Built-in Phase Models

Growth

Nucleation Coarsening

Built-in Nucleation, Growth and Coarsening Equations

Can be replaced by user-defined equations

Low-Level IntegrationPanPrecipitation: Generic Data Structure

CompuTherm LLC – www.computherm.com

All calculation engines automatically inherit these features from Pandat Software Architecture

8

Low-Level IntegrationPanPrecipitation: Strategic Software Design

ModularDesign

Well suited to current PANDAT architecture Allows for integration with other applications

(i.e., integration with ESI ProCast)

GenericData Structure

Flexible to expand and easy to maintain User-friendly interface and KDB structure Simplifies integration with user-defined models

3-LayerArchitecture

Parallel development of software and database More efficient with better quality Minimizes the maintenance workload Easy to migrate and commercialize


Inputs/Outputs of PanPrecipitation


Precipitation models: the KWN model

Concurrent nucleation, growth and coarsening

Evolution of average quantities: volume fraction, number density, particle size

Evolution of PSD: Particle Size Distribution

Many size classes

The KWN (Kampmann-Wagner Numerical) Model:

R

N

Risize classes

* R. Kampmann and R. Wagner, Decomposition of Alloys: the early stages, pp. 91-103 (1984)


Precipitation models: nucleation

Classical nucleation theory:

Nv : Number of nucleation sites per unit volumeZ : Zeldovich factor accounting for decay of supercritical particlesβ* : Rate of solute atoms joining the critical nucleusτ : Incubation time∆G*: Activation energy for nucleation

*

*G

kT tvJ N Z e e

τ

β∆ −−

=

[1] Svoboda, J., et al., Materials Science and Engineering A, 2004. 385(1-2): p. 166-174.


Precipitation models: Heterogeneous Nucleation

Heterogeneous nucleation can be considered by adjusting Nv and activation energy ∆G*.

Manually: the two variables can be assigned with a mathematical expression in KDB file

Theoretical estimation:


Precipitation models: growth

Growth model for multi-component alloys:

1 Morral, J.E. and Purdy, G.R., Scripta Metallurgica et Materialia, 1994. 30(7): p. 905-9082 Svoboda, J., et al., Materials Science and Engineering A, 2004. 385(1-2): p. 166-174.3 Svoboda, J., et al., Acta Materialia 56 (2008) 4896–4904.

The Simplified Model: based on the growth model proposed by Morral and Purdy 1

The SFFK2 Model for complex systems – the principle of maximum entropy production – modified for shape evolution3


Precipitation models: Shape Factors

Evolution of the aspect ratio of the precipitate stems from the anisotropic misfit strain of the precipitate and from the orientation dependence of the interface energy

σ = σ0 + σSS + σP

Depends on the mean solute concentration of each alloying element

= 3/2jjSS Ckσ

Does not change during ageing process

σI lattice resistance

σWH work hardening

σGB grain boundary hardening

Precipitation models: age hardening of Al alloys*

Yield Strength:Depends on the mean obstacle strength

M is the Taylor factorG is the shear modulus of the Al matrixβ Is a constant close to 0.5b is the magnitude of the burgers vectorR is mean particle size; Vf is volume fractionF is mean obstacle strength

2 1/2 3/ 23(2 )

2f

P

MFb

b

V

RGσ β

π−=

2

2

2 if ( )

2 if ( )

ii C

Ci

i C

RGb R R weak

RF

Gb R R strong

β

β

≤= ≥

ii

i

NF

N

F=

Hardness: HV = 0.33σ + 16.0

* Deschamps, A. et al., Acta Mater., 1998. 47(1): p. 293-305



I. Introduction Materials Design by ICME







Multi-Step Heat Treatment: IN100

PanNi thermodynamic and mobility was used

Primary γ′ Secondary γ′ Tertiary γ′Size (nm) 1700 208 23

Volume fraction 20% 29% 11%

Alloy Chemistry: Ni-4.85Al-18.23Co-12.13Cr-3.22Mo-4.24Ti (wt%).

1149C for 2 hours

time, hour

Tem

per

atu

re981C for 1 hour

732C for 8 hours

By K. Maciejewski, H. Ghonem, Materials Science & Engineering A, 560 (10) (2013), 439-449.

Experimental Data:


Multi-Step Heat Treatment: IN100

Exp data for T: 11%

Exp data for S: 29%

Exp data for P: 20%

Symbol for Exp Data

Effect of Cooling Rate on the Size Distribution of U720LI

The sample were soaked at 1180oC and then cooled continuously to 400oC at different speed

γ′ Solvus:

Calculated: 1157.5oCMeasured: 1160oC

Alloy Cr Co Ti Al Mo W Zr C B NiPM 16.26 14.73 5.05 2.50 3.01 1.27 0.036 0.023 0.018 Bal

C&W 16.06 14.52 5.04 2.54 3.08 1.20 0.047 0.013 0.018 Bal

78

3.25

0.0167


U720LI: Cooling Effect on PrecipitationFast Cooling (78K/sec)

1nm 14nm


U720LI: Cooling Effect on PrecipitationMedium Speed (3.25K/sec)

0.7nm 4nm 70nm


U720LI: Cooling Effect on PrecipitationSlow Cooling (0.0167K/sec)

Simulated: 0.4nm 7nm 126nm 1260nm

Measured:790nm19nm3nm










Age hardening of an AA6005 alloyComparison between measured and predicted responseof an AA6005 Aluminum Alloy to artificial ageing at 185°C

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.021.0

21.5

22.0

22.5

23.0

0.6 hra)

01Myh this study

log(

Num

ber

Den

sity

/ m

-3)

log( t / sec )

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.01.0

1.5

2.0

2.5

3.0

2.5 hr, 4.7nm

0.6 hr, 2.6 nm

b)

log(

R /

Α)

log( t / sec )

01Myh this study

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.040

50

60

70

80

90

100

2.5 hrc)

01Myh this study

Har

dnes

s (V

PN

)

log( t / sec )

Alloy Composition: Al-0.55Mg-0.82Si-0.16Cu-0.2Fe-0.5MnReference: Myhr, O.R., Grong, and Andersen, S.J., Acta Mater.,

2001. 49(1): p. 65-75

number density

average size

hardness


Comparison between measured and predicted responseof an AA6005 Aluminum Alloy to reheating at 350°C

14000 14500 15000 15500 16000 1650018

19

20

21

22

23

a)

01Myh This Study

Time / sec

log(

Num

ber

Den

sity

/ m

-3)

14000 14500 15000 15500 16000 165001.0

1.5

2.0

2.5

3.0

Time / sec

log(

R /

A)

01Myh This Study

14000 14500 15000 15500 16000 1650020

30

40

50

60

70

80

90

100

01Myh This Study

Har

dnes

s (V

PN

)

Time / sec

Reheating of an AA6005 alloy

Alloy Composition: Al-0.55Mg-0.82Si-0.16Cu-0.2Fe-0.5MnReference: Myhr, O.R., Grong, and Andersen, S.J., Acta Mater.,

2001. 49(1): p. 65-75

hardnessnumber density

average size

reheat at 350C

4 hours at 185C

time, hour

Tem

per

atu

re


Reheating of other alloys

0 1 2 3 4 50

10

20

30

40

50

60

70

80

90

100

a)

Har

dnes

s (V

PN

)

log(Time/sec)

250C 300C 350C

0 1 2 3 4 50

10

20

30

40

50

60

70

80

90

100

b)

Har

dnes

s (V

PN

)

log(Time/sec)

250C 300C 350C

0 1 2 3 4 50

10

20

30

40

50

60

70

80

90

100

c)

Har

dnes

s (V

PN

)

log(Time/sec)

250C 300C 350C

Experiment: Myhr, O.R., Grong, and Andersen, S.J., Acta Mater., 2001. 49(1): p. 65-75

a) AA6005:Al-0.54Mg-0.56Si-0.2Fe-0.0062Mn

b) AA6060 Alloy: Al-0.35Mg-0.56Si-0.21Fe-0.0064Mn

c) AA6063 Alloy: Al-0.74Mg-0.58Si-0.21Fe-0.0061Mn

reheat

3 hours at 195C

time, hour

Tem

per

atu

re


Comparison with experiments

Comparison between measured and predicted number density of different

aluminum alloys

16 17 18 19 20 21 22 23 2416

17

18

19

20

21

22

23

24

Pre

dict

ed

Measured

01Myh: 75Asb:

20 30 40 50 60 70 80 90 100 11020

30

40

50

60

70

80

90

100

110

Alloy II reheatingAlloy III reheatingAlloy IV reheating

Experimental Data: 01Myh

Pre

dict

ed

Measured

Experimental Data: 01MyhAlloy IV ageing at 185oCAlloy IV reheating

Comparison between measured and predicted hardness of different

aluminum alloys










PanPrecipitation Module

Databases Needed: Thermodynamic database, Mobility database, Kinetic database

What can be calculated? • Temporal evolution of average particle size and number density

• Temporal evolution of particle size distribution

• Temporal evolution of volume fraction and composition of precipitates

• Co-precipitation of more than one precipitates, such as γ′ and γ′′ in nickel 718

• Interfacial energy estimation based on the generalized broken bond method

• Models for heterogeneous nucleation at grain boundary/edge/corner or at dislocations

• Evolution of aspect ratio to describe the morphology evolution of precipitate

• Strengthen model to consider multiple particle size groups with weak/strong pair coupling or bowing mechanisms


Workspace and Projects

Create a new workspace, or Add a new project Select the PanPrecipitation module


Thank You for Your Attention!

http://www.computherm.com

This work was financially supported by the USAF through SBIR, STTR and MAI

projects

Documents

PanPrecipitation for Precipitation Modeling of Multi ...Precipitation Modeling: strategy Precipitation process is very complicated and we don’t have an universal model valid for