process simulations and computer aided process … · process simulations and computer aided...

IOM3 Hume-Rothery Seminar, Derby, 2017-01-18

Process Simulations and Computer Aided Process Development i) Microscopic

Anders Engström

Outline

Introduction

CALPHAD Extensions

Computational tools

Examples

Thermo-Calc Software

Providing computational tools in the field of materials engineering that allow for faster, cheaper and more sustainable innovation, development and production of both materials and components.

We have been supporting material engineers for two decades.

Important and useful tools

In a review of the 2015 literature, Thermo-Calc software products were referenced, mentioned or used in over 1000 publications, distributed on 231 journals, and by organizations from 59 different countries.

The topics range from the macro- to micro-level, from meteorites to platinum jewellery and power plants to nanowire systems.

64 theses published in 16 countries.

In 2015, at a minimum, sixty-four students, 64% at the PhD level, cited Thermo-Calc products.

46 patent citations (with a date of publication in 2015).

Phase Diagrams

Calculated phase diagram of CoCrFeNi-Al by using TCHEA1

Provides stable state, i.e. amount of equilibrium phases. To some extent we can account for non-equilibrium states. e.g. by suspending stable phases, or making certain assumptions on the diffusion rate in liquid vs. solid phases (Scheil-Gulliver). No information about the rate of transformation, nor the microstructure morphology.

The influence of chemistry on microstructure and properties

Heat treating can best be defined as “the controlled application of time, temperature and atmosphere to produce a predictable change in the internal structure (i.e. the microstructure) of a material.” Dan Herring, 100th Column of the “Heat Treat Doctor” published in Industrial Heating magazine

Materials by Design - Cohen’s Reciprocity

Processing

Structure

Properties

Performance

Morris Cohen’s “reciprocity” between the cause/effect logic of science and goal/means logic of engineering.

Cause and effect

Goal/means

The National Academies Press, 2008

Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security

ICME

ICME: an approach to design products, the materials that comprise them, and their associated materials processing methods by linking materials models at multiple length scales. Key words are "Integrated", involving integrating models at multiple length scales, and "Engineering", signifying industrial utility.

Need to predict Microstructure evolution during processing and in service

Unfortunately phase transformations is a non-trivial topic.

J. W. Christian, The Theory of Transformations in Metals and Alloys (Pergamon, Oxford, 1981).

MGI - Reinforcing the importance of data

CALPHAD is at the nexus of:

Experiments (on the data assessments are based and validated).

Digital data (databases)

Computational tools (software)

Fundamental databases and tools enabling reduction of the 10-20 years materials creation and deployment cycle by 50% or more.

June 2011

CALPHAD Method

Mobility and Diffusivity

10

2

1

M

M

M

M

9991

191211

DD

DDD

D

Atomic mobility Database

Self-Diffusivity Impurity Diffusivity Intrinsic Diffusivity

Chemical Diffusivity

• (n-1)2 elements in the inter-diffusion matrix. All depending on composition and temperature.

• n mobilities depending on composition and temperature.

J.O. Andersson and J. Ågren, J. Appl. Phys., 72 (1992) 1350.

Atomic Mobility Databases (in a CALPHAD spirit)

Experiments

Diffusion without a chemical gradient:

- Tracer diffusion coefficients

Diffusion under a chemical gradient:

- Chemical interdiffusion coef. - Intrinsic diffusion coefficients

Models

Estimates

- Correlation

Theory

- Ab-initio

Parameter optimization

Storage in mobility database

Applications

Mobility, Diffusivities

),,(ln PTxfRTM B

Ass

ess

me

nt

and

op

tim

izat

ion

P

red

icti

on

Thermodynamic database

𝐷𝑘 = 𝑐𝑘𝑀𝐾

𝜕𝜇𝑘𝜕𝑐𝑘

Modelling of the Atomic Mobility

energyActivationQ

factorFrequencyM

BelementforMobilityM

B

B

B

0

From absolute reaction-rate theory arguments Andersson and Ågren1) suggested:

When treating the composition dependency of the mobility, Jönsson2) found it superior to expand the logarithm of the mobility rather than the value itself, i.e.

Because iRTMln is often found to have a fairly linear composition dependency

1. Andersson, Ågren, J Appl Phys 72(1992)1350 2. Jönsson, Scand J Metall 24(1995)21

Composition dependency

BBB QMRTrepresentswhere 0ln

In a CALPHAD spirit the composition dependency is represented with a linear combination of the values at each endpoint of the composition space, and a Redlich-Kister expansion, i.e.

NiAl

Al

Al

Al

Ni

Al

,

Engström , Ågren, Z Metallkd 87(1996)92

Ni-Al

Example: FCC Ni-Al

NiAl

Ni

Al

Ni

Ni

Ni

,

Ni Al

-15.0

-14.5

-14.0

-13.5

-13.0

-12.5

-12.0

-11.5

LO

GD

C(F

CC

,AL

,AL

,NI)

0 0.05 0.10 0.15 0.20

Mole-Fraction Al

1573 1523 1473 1423 1373 1323 1273

Ferromagnetic ordering

Jönsson , Z Metallkd 83(1992)349

Activation energy for the mobility in the paramagnetic state

Contribution to the activation energy from magnetic ordering

Fe self-diffusion

Magnetic enthalpy H

Factor of proportionality mag D

2

Chemical ordering

Inspired by Jönssons work on the effect from magnetic ordering, Helander and Ågren suggested:

Activation energy for the mobility in the disordered paramagnetic state

Contribution to the activation energy from magnetic ordering

Contribution to the activation energy from chemical ordering

Contribution to the activation energy from chemical ordering of i-j atoms

Helander, Ågren, Acta Mater 47(1999)1141

Effect from chemical ordering in the Ni-Al system

Helander, Ågren, Acta Mater 47(1999)1141

Ni-0.45Al - pure Ni diffusion couple

Extension to multicomponent systems

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Mass F

racti

on

-1200 -800 -400 0 400 800 1200

Distance (m)

DICTRA (2006-05-09:20.57.50) :

TIME = 3600000

Al Co Cr Fe Mo Nb Ti

2006-05-09 20:57:50.12 output by user anders from NEMO

IN100 IN738

Symbols are experimental

data taken from Campbell et

al, Materials Sci & Eng A

407(2005), pp. 135-146.

Volume and bulk modulus – Pressure dependence

lattice parameter

molar volume

density thermal

expansion coefficient

relative length change

lattice mismatch

The effect of Si content on the densities

of Al-Si alloys

liquid solid Casting shrinkage

0 25 50 75 100

Mass percent Si

250

500

750

1000

1250

1500

Tem

pera

ture

[C

els

ius]

SI in DIAMOND_A4

SI in FCC_A1

SI in LIQUID

SI in DIAMOND_A4

SI in FCC_A1

SI in LIQUID

Liquid

Liquid + SiLiquid + Fcc

Fcc + Si

1 atm

1 GPa

To facilitate linkage among Thermodynamics, Process modelling, and Microstructure evolution Elasticity Elastic constants Young’s modulus Bulk modulus Shear modulus Possion’s ratio Viscosity (and diffusivity) in liquid Thermal conductivity and diffusivity Electric conductivity and resistivity Thermal radiative properties: emissivity, absorptivity, reflectivity, transmissivity

Further CALPHAD Extensions

Properties of interfaces

f(r)

r

Interfacial energy Grain boundary energy Surface tension

Classic or non-classic

thermodynamics

Atomistic modeling -

molecular dynamics

and Monte Carlo

method

First principles

Estimation of interfacial energy

1999Noble, Mater Sci Engr, A266, 80-85

Distribution of Al-Li /d’ interfacial

energy value found in literature

Our first approximation

Ds sc sol

A l

N ZE

N Z

2D sol P ME X X

For a binary matrix and precipitate of the same structure that

can be described by a regular solution model*

Misciblity gap of non-regular solution phase

Matrix and precipitate of different structure

Multicomponent system

D solE

* Based on Becker R. Ann Phys 1938;424:128

Estimation of interfacial energy

System Phases Estimation (J/m2) Literature (J/m2)

Al-Li /d’ 0.011 0.004 to 0.115

Cu-Ti Cu/Cu4Ti 0.035 0.067, 0.031

Ni-Al-Cr g/g’ 0.022 0.023

Co-W-C Co/WC 0.68 0.44 to 1.09

Further investigations:

Entropy effect

Diffusiveness of interface

Incoherency

Size effect

Grain boundary energy

Thermodynamics: Gibbs energy

Diffusion: Mobility

Phase Field Method

Langer-Schwartz

First Principles Calculation

CALPHAD f(r

r

Interfacial energy & Volume & Elastic constants

t

H or S

Towards prediction of microstructure evolution and material properties

CALPHAD-type genomic databases with thermodynamic, thermophysical as well as kinetic properties have been and will be the only feasible source to provide input data for simulation of materials processing and microstructure evolution in multicomponent systems.

CALPHAD – Bridging Atoms and Microstructure

Computational tools / Products

Software

o Thermodynamics - Thermo-Calc

o Diffusion kinetics - DICTRA

o Precipitation kinetics - TC-PRISMA

o Software Development Kits – SDKs

Databases

o Thermodynamic

Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based

HEA’s, Solders, Cemented Carbides,…

Oxides, slags and ionic solutions

Molten salts

Compounds

Aqueous solutions

o Kinetic

Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys

Thermo-Calc.pptx

Thermo-Calc.pptx

Thermo-Calc.pptx

DICTRA.pptx

TC-PRISMA.pptx

TC-PRISMA.pptx

TC-PRISMA.pptx

SDKs.pptx

TCMG3-TCAL3.pptx

CALPHAD.pptx

All simulations depend on assessed kinetic and thermodynamic data, which are stored in databases

A numerical finite difference scheme is used for solving a system of coupled parabolic partial differential equations

DATABASES Kinetic Thermodynamics

Mobilities Gibbs Energy

Diffusivities

Solve Diffusion where

Boundary conditions, etc. (External or Internal)

Diffusion Module (DICTRA)

1D finite difference code for simulation of DIffusion Controlled TRAnsformations in multicomponent alloys.


v g

Moving boundary problems with sharp interface

Ck

z

γ

kJ α

kJα

kc

γ

kc

Sharp interface with

assumption of local

equilibrium

Two proven models for dealing with situations that involves more than a single phase. Program may switch automatically between them.

n-1 Flux Balance Equations:

n-1 unknowns:

n-2 chemical potentials.

Velocity of phase boundary,

F-B Equations solved as:

Example 1 – Casting / Solidification

Case1_Casting-Solidification.pptx

Case study: Micro-segregation during solidification Te

mpera

ture

% Carbon

0 0.2 0.4 0.6 0.8 11,350

1,400

1,450

1,500

1,550

Liquid

d

A B C D

g

- VESPISM (Virtual Experiments to Solve Problems In Steel Metallurgy).

- Development of phase-field code (MICRESS) linked to Thermo-Calc.

- Solidification experiments were performed for alloys A – D below as one assignment in this project.

Casting / solidification

% Carbon

Tem

per

atu

re

g

Liquid

d

Steel C

Steel C:

Fe - 0.8% Mn – 0.7%Si – 0.03%P – 0.4% C

0.30000.150010.001.500

W%Si

W%P

W%S

W%Mn

µm

0 672.0

P

Mn

Si

Observed micro-segregation in Steel C

Line-scans across the dendrite arms (performed by Corus-UK)

Peak drifting!

Question: Why does the P peak drift away from the Mn and Si peaks?


Analysis using DICTRA

l/2

Secondary dendrite arm spacing assumed to be 200 µm.

Liquid

Liquid Bcc

υ

Liquid Bcc

υ Fcc

υ

Liquid Fcc υ

Bcc

Fcc

λ/2 =100 μm


Cooling function

Time (seconds)

Tem

per

atu

re

- More advanced cooling functions may of course also be imposed. - Also possible to instead define a condition on the rate of latent heat removal from the system.

Cooling rate assumed to be 0.2 ºC/s


Solidification range

Tem

per

atu

re

Fraction Solid

Lever rule

DICTRA

Scheil

L + g

L + d Peritectic reaction


Fraction of solid phases

Frac

tio

n S

olid

Time (Seconds)

g

d

Peritectic reaction


Carbon profiles during solidification

90 s 135 s

300 s

3000 s


90 s

135 s

300 s

3000 s

90 s

135 s

300 s

3000 s

Silicon and Manganese


Si Mn

Phosphorus

90 s 135 s

300 s

3000 s


Segregation profiles after 610 s (when the last melt disappears)

Mn Si P C


Segregation profiles after 1000 and 3000 s

after 1000 s after 3000 s

Mn Si P C

Mn Si P C


610 s

1000 s

3000 s

The solution

Mn and Si increase the phosphorus activity.

Phosphorus diffusion much faster compared to Mn and Si diffusion.

At the late stage further phosphorus redistribution is controlled by slow Mn and Si diffusion.

Distance (microns)

Ph

osp

ho

rus

acti

vity



v g

Moving boundary problems with sharp interface

Multiphase problems with/without finite interface

Ck

z

γ

kJ α

kJα

kc

γ

kc

Sharp interface with

assumption of local

equilibrium

Flux between slices “n-1” and “n”

z

xMxMV

J keff

nkkeff

nkkm

kD

D

1

1

“Effective” from combining rules

kk xM

pkN

1nkN n

kN 1nkN1

kN

H. Larsson: CALPHAD 47 (2014) 1-8

Two proven models for dealing with situations that involves more than a single phase. Program may switch automatically between them.

Microsegregation during solidification

Homogenisation treatment

Precipitate growth and dissolution

Precipitate coarsening

Interdiffusion in coating/substrate systems

TLP bonding of alloys and much more…

Micro-segregation during solidification in alloy AA5182

Dissolution of Mg2Si precipitate in alloy A6401


0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Mass F

racti

on

-1200 -800 -400 0 400 800 1200

Distance (m)

DICTRA (2006-05-09:20.57.50) :

TIME = 3600000

Al Co Cr Fe Mo Nb Ti

2006-05-09 20:57:50.12 output by user anders from NEMO

IN100 IN738

40

45

50

55

Mo

le-P

erc

en

t N

i

-500 0 500 Position (microns)

Ni

NiAl-coating IN939

Interdiffusion between NiAl

coating and Ni-base superalloy

Multicomponent diffusion

couple

Example of applications:

Example 2 – Material selection / Life-time prediction

Case2_Lifetime-prediction.pptx

Materials selections / Lifetime prediction

Yu et al., Mater Sci. Eng. A394 (2005) 43.

Complex problem involving solving multicomponent diffusion problem in multiphase region. Need for multicomponent kinetic data in -NiAl, g and g’

Selected problem: Coating degradation due to interdiffusion

E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.

NiAl-coating / Ni-base superalloy system

NiAl-coating / GTD111

0.97

-

Mo

0.89

-

Ta

0.48

-

C

Bal

Bal

Ni

GTD111

NiAl-Coating

0.97 6.24 16.6 9.5 6.9

- - - - 50.5

W Ti Cr Co Al Temp. 1050°C Time 96h

0

10

20

30

40

50

60

Mo

le-P

erc

en

t A

l

-500 0 500

Position (microns)

30

35

40

45

50

55

60

65

70

Mo

le-P

erc

en

t N

i

-500 0 500

Position (microns)

Al

Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.

Ni

NiAl GTD111

i

kk

ieff

kk xMfxM

Rule of mixtures

0

0.2

0.4

0.6

0.8

1.0

1.2 M

ole

-Fra

cti

on

of

Ph

as

e

-500 0 500

Position (microns)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Mo

le-F

rac

tio

n o

f P

ha

se

-500 0 500

Position (microns)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mo

le-F

rac

tio

n o

f P

ha

se

-500 0 500

Position (microns)

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Mo

le-F

rac

tio

n o

f P

ha

se

-500 0 500

Position (microns)

B2 g

g´

Micrograph from E. Perez et al. J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.



Cr

0

5

10

15

20

25

30

35

40

Mo

le-P

erc

en

t C

r

-500 0 500

Position (microns)

Co

0

5

10

15

Mo

le-P

erc

en

t C

o

-500 0 500

Position (microns)


Co


Cr

0

5

10

15

20

25

30

35

40

Mo

le-P

erc

en

t C

r

-500 0 500

Position (microns)

0

5

10

15

Mo

le-P

erc

en

t C

o

-500 0 500

Position (microns)

g

g´

g

g´


0

1

2

3

4

5

6

7

8

9

10

Mo

le-P

erc

en

t T

i

-500 0 500

Position (microns)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Mo

le-P

erc

en

t W

-500 0 500

Position (microns)

Ti


W


IN939.pptx


Software





Databases

o Thermodynamic




Molten salts

Compounds

Aqueous solutions

o Kinetic


Thermo-Calc.pptx

Thermo-Calc.pptx

Thermo-Calc.pptx

DICTRA.pptx

TC-PRISMA.pptx

TC-PRISMA.pptx

TC-PRISMA.pptx

SDKs.pptx

TCMG3-TCAL3.pptx

CALPHAD.pptx

A general computational tool for simulating kinetics of diffusion controlled multi-particle precipitation processes in multi-component and multi-phase alloy systems.

Precipitation Module (TC-PRISMA)

TC-PRISMA is based on Langer-Schwartz theory, and it adopts Kampmann-Wagner numerical (KWN) method to compute the concurrent nucleation, growth, and coarsening of dispersed phase(s).

3D, 2006Jou

LS (Langer-Schwartz) and KWN (Kampmann and Wagner Numerical) Approach

,( ) ( , ) ( , )

f r tr f r t j r t

t r

3

00

4,

3C C C C f r t r dr

0

( , )N f r t dr

0

1( , )r f r t rdr

N

3

0

4( , )

3f r t r dr

Continuity equation

Mass balance

Time Integration

0

( , )N f r t dr

10 50 100 Radius, nm

3D, Particle Size Distribution

f, 1/m4

Models: Nucleation Rate

D

kT

GNZJ s

** exp

tJtJ S

exp

*22

1

Z

*2*

4

4 r

a

1

1/

2//

n

i ii

ii

DX

XX

2

23*

3

16

m

m

G

VG

DD

Interfacial energy, Volume

Classic Nucleation Theory (CNT)

Grain size, dislocation density, etc.

kTrN

VZ

A

m

2*2

D

m

m

G

Vr

2*

2004Svoboda

Models: Growth Rate

rMccc iiiiiii /

r

Vmii

2//

Q. C

hen

, J. J

epp

sso

n, J

. Ågr

en, A

cta

Mat

er. 5

6(2

00

8)1

89

0-1

89

6

Advanced – Analytical Flux-balance Approximation

2 mm

VKG

r r

D

Simplified – Pseudo-steady state Approximation

Cross diffusion

high supersaturation

1

2/ /

/

( ) ( )

( )

i i i

i i i

X r X rK

X r M

Scope and data output

Simulate concurrent nucleation, growth and coarsening of second phases in multicomponent systems.

Output

• Particle Size Distribution

• Number Density

• Average Particle Radius

• Volume Fraction

• Matrix composition

• Precipitate composition

• Nucleation rate

• Critical radius

• TTP

Input

• Alloy composition

• Temperature - Time

• Simulation time

• Thermodynamic data

• Kinetic data

• Property data (Interfacial energy, volume, etc.)

• Nucleation sites and related microstructure information

TC-PRISMA

Some examples

Live demo of TC-PRISMA 2.0.pptx

2011

Version 1.0

• Link to Thermo-Calc

and DICTRA

• Multi-component

Nucleation and Growth

• Different Nucleation

types

• Avdanced Model for

Cross Diffusion and

High Supersaturation

• Highly Intuitive GUI

2013

Version 2.0

• Non-Isothermal

Conditions

• Multi-Modal PSD

Analysis

• Interfacial Energy

Model

2016

Thermo-Calc 2016a

• Multiple Nucleation

Types

• Considering wetting

angle

• Integration into

Thermo-Calc

• ....

Precipitation Module (TC-PRISMA)

Example 3 – Heat Treatment / Aging

Case3_Heat-treatment.pptx

AA6005: Al - 0.55wt% Mg - 0.82wt% Si - 0.016wt% Cu


= 0.115 J/m2

TCAL3 and MOBAL3 Databases

530˚C

30 min 185, 175˚C

80, 8 hr

AA6xxx

Myhr et al, Acta Mater. 49(2001)65-75. Bardel et al, Acta Mater. 62(2014)129-140

(Al)

Al3Sc

SSSS → Clusters → GP Zones → β’’ → β’, U1, U2, B’ → β

AA6xxx


Precipitation of β’’ from (Al) matrix

Example 4 – Heat Treatment

gg’ Microstructure in U720 Li

Continuous cooling at 0.0167 K/s

R. Radis et al., Acta Materialia, 57(2009)5739-5747

R&D

Ni-8Al-8Cr and Ni-10Al-10Cr

R&D – Influence from composition

Exp

Continuous cooling from 1150 to 380 °C with a cooling rate of 14 °C/min.


Exp

= 0.023 J/m2

Ni-8Al-8Cr have larger misfit between g and g compared to Ni-10Al-10Cr.

This will give an elastic energy contribution which has not been considered in the simulation.


Vertical Section Ni-xAl-xCr Thermodynamic driving force


Nucleation rate Thermodynamic driving force



Software





Databases

o Thermodynamic




Molten salts

Compounds

Aqueous solutions

o Kinetic


Thermo-Calc.pptx

Thermo-Calc.pptx

Thermo-Calc.pptx

DICTRA.pptx

TC-PRISMA.pptx

TC-PRISMA.pptx

TC-PRISMA.pptx

SDKs.pptx

TCMG3-TCAL3.pptx

CALPHAD.pptx

Software Development Kits

Thermo-Calc

Application

Inte

rfac

e

A prescribed set of subroutines, functions or classes by which a programmer writing an application program can make requests to Thermo-Calc.

The trend is towards more and more advanced applications and in particular integration of thermodynamic calculation result for modelling of microstructure evolution and property prediction, aiming at designing products, the materials comprising them and their associated processing.

Example 5 – R&D

Phase-field modelling

• Output:

– Detailed morphology

– Concentration fields

– Stress fields

– Plastic strain fields (dislocation density fields)

– ...

• Need or can use input from

– Multicomponent thermodynamics

– Multicomponent diffusion analysis

– Interfacial energy and mobility

– Elastic coefficients and stresses

– Stress-free transformation strain tensor (eigen strains)

– Plastic relaxation

– Fluid flow (Navier Stokes)

– ....

2D phase-field simulation of sigma-phase formation in duplex Stainless steel (SAF 2507)

Fe-25Cr-7Ni-4Mo with continuous cooling from 1273K to 950K

Malik et al. KTH (2015) Full CALPHAD Thermodynamics DICTRA Mobilities

BCC

BCC

FCC

FCC

FCC

FCC

BCC

Sigma

Spinodal decomposition – Fe-45%Cr

T=748K, time=1 Week

Calculation cell is 20x20x20 nm

Composition dependent gradient energy

Barkar et al. KTH (2016 )

Full CALPHAD Thermodynamic & Mobility coupling

Spinodal decomposition/748K1w.asf

Generating insights on materials and processing operations

Thank You!

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