MICROSTRUCTURE EVOLUTION MODELING WITH …©s/OtiMoM... · AFP model SimRex module . CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 44 SEMI-EMPIRICAL APPROACH MEAN-FIELD APPROACHES

1

MICROSTRUCTURE EVOLUTION MODELING WITH INDUSTRIAL HOT FORMING SIMULATION

SOFTWARE

AUTHORS: A. SETTEFRATI, P. LASNE, J.L. CHENOT MATERIALS DEPARTMENT

2 CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 2

Typical forming process steps

Initial microstructure Final microstructure

Work hardening

Recovery

Recrystallization

Grain growth

Second phases precipitation/dissolution

Thermomechanical history of a

material point (T, 𝜖, 𝜖 … )

Influence on the

rheological behaviour

Properties

Process

Microstructure

Process

Properties

Microstructure


Microstructural evolution prediction

A multiscale approach

Transvalor have participated and participates in several projects concerning microstructure prediction

at different scales during forming processes

JMAK approach (semi-empirical)

Macroscopic

Macroscale

Length Scale

m mm m

DigiMicro

Full field

Mesoscale

AFP model

SimRex module

Mean field


SEMI-EMPIRICAL APPROACH

MEAN-FIELD APPROACHES

• AFP MODEL

• SIMREX

FULL-FIELD APPROACH

Length

Scale

m

m

m

m

OVERVIEW




• AFP MODEL

• SIMREX

FULL-FIELD APPROACH

Length

Scale

m

m

m

m

OVERVIEW

CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 6

SEMI-EMPIRICAL APPROACH - JMAK

Global description of the recrystallized fraction

In constant conditions (strain rate and

temperature)

• Sigmoidal shaped curves

• Described by the analytical Johnson-Mehl-

Avrami-Kolmogorov (JMAK) equation:

𝑋 𝑡 = 1 − 𝑒−𝑏.𝑡𝑛

Coefficients obtained by fitting the

experimental curves

[Humphreys, 2004]



Dynamic recrystallization

s

n

s

sdrx siX

drx

5.0

2lnexp1

drxa

drx

m

drx XT

dAd

3

03 exp33

srxn

srxt

tX

5.0

2lnexp1

srx

srx

m

f

n

srx XT

dAd

5

05 exp555

Static/metadynamic recrystallization

For constant given conditions

Parameters Dynamic Metadynamic Static

Strain Weak Weak Strong

Strain rate Strong Strong Weak

Temperature Strong Strong Strong

Three types considered Dynamic: nucleation and growth during deformation

Metadynamic: nucleation during deformation and

growth after deformation

Static: nucleation and growth after deformation

Recrystallized fractions and diameters dependent

on the process parameters



Dynamic recrystallization

s

n

s

sdrx siX

drx

5.0

2lnexp1

drxa

drx

m

drx XT

dAd

3

03 exp33

srxn

srxt

tX

5.0

2lnexp1

srx

srx

m

f

n

srx XT

dAd

5

05 exp555

Static/metadynamic recrystallization

For constant given conditions

Three types considered Dynamic: nucleation and growth during deformation

Metadynamic: nucleation during deformation and

growth after deformation

Static: nucleation and growth after deformation

Recrystallized fractions and diameters dependent

on the process parameters

Grain growth phenomena

Grain growth

tT

Addcr

6

60 exp66



Example of recrystallization on a ring-rolling process

Generalization for non constant conditions and multiple recrystallization steps

Definition of an average strain rate

dt

)t(

)t()t()dtt( f

ff

s

dtS

n

drxssfict

XLog/1

5.02ln

1

sk

s

srxfict

Xtt

1

5.0

1log

Scheil method for incubation

Fictive strain/time method for growth



Examples of recrystallization on a ring-rolling process

Dynamic recrystallized grains

Metadynamic recrystallized grains

Non recrystallized grains



Recrystallization calculations with FORGE®

Low CPU time

⇨ computation at each integration point

⇨ developed in user routines

Literatur review to increase the material

parameters database

• Austenitic stainless steels

• Ni superalloys

• General steels

• Microalloyed steels

Comparison of ASTM grain size after an orbital forging process

on Inconel718 (courtesy Tecnalia, ES)




• AFP MODEL

• SIMREX

FULL-FIELD APPROACH

OVERVIEW

Length

Scale

m

m

m

m


Models taking into account elementary physical phenomena

Nucleation

Volume conservation

Hardening

Recovery

Boundary migration

ρi

di

Work hardening Recovery Grain boundary migration Nucleation of new grains Precipitation

Macroscopic description of the microstructure based on “averaged” parameters

Homogenized grain

<ρ> Mean per grain

Model grain

Spherical grain (3D) : • Equiv. Diam. di

• Disloc. density <ρi>

Real grain

low high

Dislocation density

Selection of representative material parameters

• = dislocation density

• d = grain diameter

Identification of the physical laws governing the evolution

of these parameters

MEAN-FIELD APPROACH


Models taking into account elementary physical phenomena

Work hardening Recovery Grain boundary migration Nucleation of new grains Precipitation

Burgers vector

Shear modulus

Grain boundary mobility

Diffusion coefficients

Interfacial energy

…

Input parameters

Dislocation density

Grain sizes

Nucleation rate

Recrystallization ratio

Flow stress

Output

Suitable methods for coupled calculations (low CPU times)

MEAN-FIELD APPROACH


Gra

in R

ad

ius

R

ecry

sta

lliz

ati

on

ra

tio

Temperature = 1100°C – Strain-Rate = 1 s-1

Recrystallization ratio and grain sizes

Developed at Aachen University for microalloyed steels

Precipitation model for V(C,N)

MEAN-FIELD APPROACH – AFP MODEL


Flo

w S

tre

ss

D

islo

ca

tio

n D

en

sit

y

Determination of the flow stress as a function of

the mean dislocation density

m

mb

mp

AArg

bc

TKMbM

5

2

9

sinh

XX xdm 1

d

ddddd A

ArgAAAAAdt

d

52/5

4

2/5

2210 sinh

Dislocation evolution model

Temperature = 1100°C – Strain-Rate = 1 s-1

Recrystallization ratio and grain sizes

Developed at Aachen University for microalloyed steels

Precipitation model for V(C,N)



Example : Reducer-rolling simulation

FORGE simulation


X dm

m


Developed in Cemef

Account for microstructure heterogeneity

MEAN-FIELD APPROACH - SIMREX

Set of representative grains (d,)

d = grain size = dislocation

density

Distribution of d and

Material representation

<ρi>

di

Evolution of • Grain sizes (distribution)

• Dislocation densities (distribution)

• Recrystallized fraction

• Flow stress

Incremental formulation • Anisotherm transformations

• Variable strain rate

• Multi-pass conditions

8

10

12

14

30

40

50

60

70

80

2

4

6

8

10

12

14

x 10-4

Densité de dislocations (x 1e14 m-2)

Taille de grains (µm)

Pro

babilité

Pro

ba

bili

ty / g

rain

s n

um

be

r




• AFP MODEL

• SIMREX

FULL-FIELD APPROACH

Length

Scale

m

m

m

m

OVERVIEW


FULL-FIELD APPROACH – DIGI-µ

Local computation at the mesoscopic scale

Introduction of physical laws at the grain scale

Microstructure components fully modeled

Prediction of almost all local phenomena

induced by thermomechanical processes

Topological aspects taken into account

Simulations performed on a Representative Volume Element (RVE)

Help for understanding of microstructural phenomena • Complex physical phenomena modeled (crystal plasticity, large deformations, recrystallization,

grain growth)

• More realistic description of materials in terms of microstructural features

Calibration and/or optimization of higher scale models (scale transitions)



Principle

Polycrystal generation in a FE context

• Definition and construction of a RVE

• Respect of grains topology

• Respect of grain size distribution

Use of the Level-Set approach to describe the interfaces

between the physical entities

Adaptive anisotropic mesh (refinement near grain boundaries)

Simulation of the evolution of these entities



Recrystallization and grain growth modeling

Global kinetic law

Grain boundary mobility

Driving force

Outside unitary

normal to the grain

boundary

Grain boundary mobility Dislocation line energy

Dislocation density

difference through the

grain boundary

GB curvature

Interfacial energy

Stored energy gradient

Driving force



Example: Localized heating – associated microstructural evolution

Thermal history

Polycristal generation

(RVE: 0,5mm x 0,5mm)

Microstructural evolution Statistics on grain sizes


CONCLUSION

Transvalor active on this topic

Modeling at different scales

Semi-empirical approach:

• very low CPU times

• input parameters obtained by fitting the experimental

curves

• literature review to increase the material parameters

database

Mean-field approaches:

• suitable methods for coupled computations

• elementary physical phenomena taken into account

• input parameters with a physical meaning

Full-field approach:

• more realistic description of microstructural evolution

prediction

• microstructure components fully modeled

Models

development

Macroscale

Mesoscale Length

Scale

m

m

m

m


PERSPECTIVES

Semi-empirical approach:

• Increase of the material parameters database

(steels, aluminum, titanium alloys…)

Mean-field model SimRex:

• Computation at each integration points (for all

grain categories)

Full-field model DigiMicro:

• Second phase particles / Precipitation

• Development of a first industrial 2D version for

recrystallization and grain growth modeling

Real multiscale modeling approach

Scale

transitions

Macroscale

Mesoscale

Le

ng

th S

cale

m

m

m

m

26

THANK YOU FOR YOUR ATTENTION

ADDRESS: 694, av du Dr. Maurice Donat Parc de Haute Technologie 06255 Mougins cedex France

CONTACT: +33 (0)4 9292 4200 +33 (0)4 9292 4201 [email protected] http://www.transvalor.com/

Documents

MICROSTRUCTURE EVOLUTION MODELING WITH …©s/OtiMoM... · AFP model SimRex module . CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 44 SEMI-EMPIRICAL APPROACH MEAN-FIELD APPROACHES