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SFB 761 „Stahl ab initio“
Mechanism Maps and
Deformation Mechanisms
M. Sc. Alireza S. AkbariProf. Wolfgang Bleck
International Workshop on High-Mn SteelsPohang, November 3-5, 2009
Contents
• Introduction to mechanism maps
• Backgrounds of calculations
• Thermodynamics-based SFE model
• Variations of SFE maps
• Experimental validation and observations
• Future works
2
What is the mechanism map?
• A composition- and/or temperature-dependent2-D diagram
I l di th di t d i t t l h ft• Including the predicted microstructural phases afterdeformation
• Including the approximated Stacking Fault Energy(SFE) values using the thermodynamics-basedmodels
• Flexibility for additions of further alloyingelements, variations of temperature, and changesof grain size!
Why do we need these maps?
• A new way for steel design particularly inhigh-Mn steels
• Better adjustment of chemical composition,grain size, and deformation temperature
• Probably an alternative for the TTT diagrams whenworking with the single-phase austenitic steels!
• Developing new alloy concepts• Developing new alloy concepts
3
Microstructural Phases in High-Mn Steels
Schumann
Distribution of Phases in Fe-Mn-C System After Deformation5
Source: V. H. Schumann: Neue Hütte, 1972, vol. 17, pp. 605-609
How to Estimate the SFE?
• ab initio techniquese.g. the Density Functional Theory (DFT) to simulate theirregularities in the stacking of atomic layers
• Transmission Electron Microscopy (TEM)e.g. variations in the size of the dislocation nodes
• Inference from the experimental datae.g. observation of TRIP and TWIP mechanisms in practice
• Themodynamics-based modelse.g. subregular solution model
4
Thermodynamics-based Calculation of SFEεγεγ σργ /22 +Δ= →Gfcc
FeCCFeFeMnMnFeCCMnMnFeFe XXXXGXGXGXG +ΔΩ+ΔΩ+Δ+Δ+Δ=Δ →→→→→→ εγεγεγεγεγεγ
exmgMnCCMn
FeCCFeFeMnMnFeCCMnMnFeFe
GGXX Δ+Δ+ΔΩ →εγ
42500)/( =ΔΩ → molJFeCεγ
)(5322180)/( MnFeFeMn XXmolJ −+=ΔΩ →εγTmolJGFe 309.438.2243)/( +−=Δ →εγ
TmolJGMn 123.100.1000)/( +−=Δ →εγ
Subegular Solution Model7
-22166)/( =Δ → molJGCεγ
10)/( 2/ ≈mmJεγσ
69102)/( =ΔΩ → molJMnCεγ
SGTE Dataset
SFE increases as the grain size decreases below 5 µm
Higher disequilibrium concentration of carbon when quenching from the lower temperature or for a short period of soaking to get a smaller grain
Effect of Grain Size on SFE?
size, increases the SFE
Internal stresses which affect the dissociation of dislocations, are changing by the grain size
The final calculated SFE including the grain size can be called as the apparent SFE!
8Remarks from the Literature
Source: P. Y. Volosevich, V. N. Grindev, and Y. N. Petrov: Phys. Met. Metallogr., 1976, vol. 42, pp. 126-30.Source: Y. Lee et al.: Met. Mat. Trans. A 31 (2000) pp.355-360.
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Gibbs Excess Energy εγεγ σργ /2)(2 +Δ+Δ= →
exfcc GG
exfcc GG Δ++Δ= → ρσργ εγεγ 222 /)
55.18)(exp(06.170)/( mdmoleJGex
μ−=Δ
Excess TermSFE without G.S. effect
G.S. (μm)
2ρΔGex
(mJ/m2)5 7
10 52/00002530
Assumption for our Fe-Mn-C alloys:
Method9
20 330 250 1
150 0
2/.0000253.0 matomg≈ρ
Source: Y. Lee et al.: Met. Mat. Trans. A 31 (2000) pp.355-360.
Source: S. Takaki et al.: Mater. Trans. JIM; 34 (1993) pp. 489-96.
Source: H. Schumann: J. Kristall Technik; 10 (1974) pp. 1141-50.
Composition-Dependent SFE Map
296 K10
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Composition-Dependent SFE Map
296 K11
Temperature Dependency of SFE
22 wt.% Mn
12Iso-Mn vs. Temperature SFE Maps
2 µm 94 µm
7
Validation of the Predicted Mechanisms
Summary of SFE Measurements for Fe-22 wt.% Mn-0.6 wt.% C
___________________________
Assuming:1. No grain size contribution2. σ = 10 + 5 mJ/m2
3. Temperature: 296 K
13Experimental Plan
Resultant SFE is: 18 – 38 mJ/m2
Material: Fe-22Mn-0.6C
Annealing treatment: NA, 1173 K / 60 min., 1303 K / 60 min.
Tensile tests: Strain rate = 0 0004 s-1
Fe-22Mn-0.6C
Tensile tests: Strain rate = 0.0004 s 1
Temperature = 233 K, 296 K, 373 K
Avg. Grain size: 2 µm, 24 µm, 94 µm
LOM
Hardness Mapping
Average grain size: Jeffries planimetric procedure (ASTM E 112-96 (2004) standard)
14Experimental Proc.
Hardness Mapping
EBSD (voltage: 25 kV, probe current: 10 nA, 50-200 nm step size)
TEM
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SFE ValuesK
373 47 mJ/m2 40 mJ/m2 37 mJ/m2
296
3
37 mJ/m2 31 mJ/m2 28 mJ/m2
Fe-22Mn-0.6C15
µm2 24 94
233 34 mJ/m2 28 mJ/m2 25 mJ/m2
SFE ValuesK
373 47 mJ/m2 40 mJ/m2 37 mJ/m2SFE > 20 mJ/m2
296
3
37 mJ/m2 31 mJ/m2 28 mJ/m2
No possibility for
Fe-22Mn-0.6C16
µm2 24 94
233 34 mJ/m2 28 mJ/m2 25 mJ/m2
No possibility for TRIP mechanism!
9
Flow Curves
233 K 296 K
373 K
2 µm, 24 µm, 94 µm17
Flow Curves
296 K18
10
Microstructures (Fe-22Mn-0.6C)
µm2 24 94
As Received19
µ
X-Ray Patterns
94 µm – 373 K
94 µm – 296 K
94 µm – 233 K
94 µm – No Def.
24 µm – 373 K
24 µm – 296 K
24 µm – 233 K
Before and After Deformation20
24 µm – 233 K
24 µm – No Def.
11
Different Stages of Work Hardening
Work Hardening Rate (WHR)21
Work Hardening Rate (WHR) Diagrams
Method:Using a software for the first derivative of the flow curve!
Fe-22Mn-0.6C22
12
WHR Diagrams – Onset of Twinning?
Fe-22Mn-0.6C23
Stress and Strain for Onset of Twinning
Larger grain size is usually favorable for twinning!Grain size may affect the capacity for dislocation pile up in the
Grain Size and Temperature Dependency24
Grain size may affect the capacity for dislocation pile up in theneighbouring grains before the onset of twinning (activation phase)!Increasing temperature generally increases the required twinning stress.As seen here, temperature has a different effect when working at low SFE range!
competetivephenomena?
13
EBSD Results at Different Strains
ε= 0.02 ε= 0.02
Grain Size ↑
24 µm, 94 µm (296 K)25
24 µm 94 µm
Strain for the Onset of Twinning
= 0.
043
67<Δε
=
Δε
= 0.
06<Grain Size and Temperature Dependency
26
14
EBSD Results at Different Strains
ε= 0.10ε= 0.10
Grain Size ↑
24 µm, 94 µm (296 K)27
24 µm 94 µm
Strain for the Onset of Twinning
Grain Size and Temperature Dependency28
TEM Measurements at ε = 0.02
15
Some Selected TEM Results at ε = 0.02
Indexed pattern still must be measuredmeasured
24 µm (233 K)29
Some Selected TEM Results at ε = 0.02
24 µm (373 K)30
16
Hardness Variations of Twinned Structure
Fe-22 Mn – 0.6 CHadfield Steel
Finding a Suitable Hardness Criteria31
Hardness Mapping
300 µm
Machine and Pattern32
Indentation point
17
Calculations
If hardness = ~ 600 HV1.0 Kg:
For the grain size of 2 µm ~ 800 grains per indentationFor the grain size of 2 µm 800 grains per indentationFor the grain size of 24 µm ~ 5 grains per indentationFor the grain size of 94 µm ~ 3 indentations per grain
HV1.0 Kg Hardness Mapping Machine
Indentation Size33
Hardness Maps
~ 10 mm
~ 3 mm
Selection of the Specimen34
mountingHardness Mapping
18
Hardness Maps (Fe-22Mn-0.6C)
K73
> 600 HV1.0 < 600 HV1.0
Tens
ile
Dire
ctio
n
296
3
44% HT
91% HT
67% HT
53% HT
74% HT
62% HT
Finding the Heavily Twinned (HT) Fraction35
µm2 24 94
233
87% HT 62% HT 94% HT
Strain for the Onset of Twinning
Trend of Variations36
19
Strain for the Onset of Twinning
?
Trend of Variations37
Strain for the Onset of Twinning
Trend of Variations38
20
EBSD Results of 94 µm Grain Size
94 µm
233 K, 296 K, 373 K39
233 K94% HT
296 K62% HT
373 K74% HT
HT fractions were calculated by hardness mapping!
EBSD Results of 94 µm Grain Size
94 µm
233 K, 296 K, 373 K40
233 K94% HT
296 K62% HT
373 K74% HT
HT fractions were calculated by hardness mapping!
21
EBSD Results of 24 µm Grain Size
24 µm
233 K, 296 K, 373 K41
233 K62% HT
296 K53% HT
373 K67% HT
HT fractions were calculated by hardness mapping!
EBSD Results of 24 µm Grain Size
24 µm
233 K, 296 K, 373 K42
233 K62% HT
296 K53% HT
373 K67% HT
HT fractions were calculated by hardness mapping!
22
EBSD Results of 2 µm Grain Size
le!
le!
2 µm
Not
Avai
lab
Not
Avai
lab
233 K, 296 K, 373 Kof Variations43
233 K87% HT
296 K91% HT
373 K44% HT
HT fractions were calculated by hardness mapping!
EBSD Results of 2 µm Grain Size
le!
le!
2 µm
Not
Avai
lab
Not
Avai
lab
233 K, 296 K, 373 K44
233 K87% HT
296 K91% HT
373 K44% HT
HT fractions were calculated by hardness mapping!
23
Hall-Petch Equation2/1
0−+= dK yTTyT σσ
yKTemperature
dependency?!
233 K, 296 K, 373 K45
Source: M. R. Barnett: Scripta Mater., 2008, vol. 59, pp. 696-698.
Hall-Petch Equation and Twinning
Onset of twinning follows a Hall-Petch –type
equation ?!
233 K, 296 K, 373 K46
equation ?!
24
Future Plans
Finding out new techniques to calculate the twins density
Checking the consistency of the room temperature SFE calculations with the TEM based techniques
Further EBSD observations after the interrupted tensile tests to look for the changes of the microstructure
Adding more influential parameters like strain rate to study their effects in conjunction with temperature (SFE variations) and grain size to define the deformation mechanism and twinnability!
Evaluation of the effects of the PLC bands initiation, movement, and
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variations by changing the grain size and temperature on the mech. prop.
Looking for a possible scalar value to integrate the mentioned parameters for a rather consistent prediction of mechanical properties
SFB 761 „Stahl ab initio“
THANK YOU!Quantum-mechanics guided design
of new Fe-based materials
