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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
3 CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 3
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
4 CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 4
SEMI-EMPIRICAL APPROACH
MEAN-FIELD APPROACHES
• AFP MODEL
• SIMREX
FULL-FIELD APPROACH
Length
Scale
m
m
m
m
OVERVIEW
5 CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 5
SEMI-EMPIRICAL APPROACH
MEAN-FIELD APPROACHES
• 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]
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 7
SEMI-EMPIRICAL APPROACH - JMAK
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 8
SEMI-EMPIRICAL APPROACH - JMAK
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 9
SEMI-EMPIRICAL APPROACH - JMAK
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 10
SEMI-EMPIRICAL APPROACH - JMAK
Examples of recrystallization on a ring-rolling process
Dynamic recrystallized grains
Metadynamic recrystallized grains
Non recrystallized grains
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 11
SEMI-EMPIRICAL APPROACH - JMAK
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)
12 CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 12
SEMI-EMPIRICAL APPROACH
MEAN-FIELD APPROACHES
• AFP MODEL
• SIMREX
FULL-FIELD APPROACH
OVERVIEW
Length
Scale
m
m
m
m
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 13
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 14
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 15
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 16
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)
MEAN-FIELD APPROACH – AFP MODEL
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 17
Example : Reducer-rolling simulation
FORGE simulation
MEAN-FIELD APPROACH – AFP MODEL
X dm
m
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 18
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
19 CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 19
SEMI-EMPIRICAL APPROACH
MEAN-FIELD APPROACHES
• AFP MODEL
• SIMREX
FULL-FIELD APPROACH
Length
Scale
m
m
m
m
OVERVIEW
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 20
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)
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 21
FULL-FIELD APPROACH – DIGI-µ
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 22
FULL-FIELD APPROACH – DIGI-µ
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 23
FULL-FIELD APPROACH – DIGI-µ
Example: Localized heating – associated microstructural evolution
Thermal history
Polycristal generation
(RVE: 0,5mm x 0,5mm)
Microstructural evolution Statistics on grain sizes
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 24
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
CONFERENCE OPTIMOM, OXFORD (SEPT. 14-16TH, 2014) 25
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/