theory guided and experimentally validated materials design · heat treatment: 1100 c, 30min...
TRANSCRIPT
COST is supportedby the EU Framework Programme Horizon 2020
Theory guided and experimentally validated Materials Design
Gamsjäger ERNST (Austria) Training School "Solutions for Critical Raw Materials in extreme conditions: from fundamental science to industrial innovations", Sofia, 6 - 8 February 2018
Solutions for Critical Raw Materials Under Extreme Conditions(CRM-EXTREME)
Lecture overview
• Motivation:Materials at extreme conditions Microstructural changes Material properties
Influence and possible substition of CRMs
• Thermodynamics and kinetics of microstructural changes Phase transformations and grain growth and coarsening.
• Experimental verification High temperature laser scanning confocal microscopy (HT-LSCM), Dilatometry, In-situ high temperature X-ray diffraction.
• Conclusions
Motivation: Materials at extreme conditions
EXTREME CONDITIONS:
Temperature: From mK to the melting point
Pressure: From vacuum to several GPa
Corrosion
Radiation (high level nuclear waste)
REQUIREMENTS:
Tensile Strength and impact strength,Creep resistance.
High hardness and yield strength
Good oxidation and corrosion properties
Leach resistance, pouring temperature,no formation of yellow phases (molybdates)
Motivation: Materials at extreme conditions I
Linepipe steels
turkstream.info
Motivation: Materials at extreme conditions II
Large steam turbines (e.g. high temperature exposed, creep-resistant steels)
http://www.imoa.info/molybdenum-uses/molybdenum-grade-alloy-steels-irons/high-temperature-steel.php
High speed steels(e.g. Böhler S290)
Tools used under extreme compressive stresses (e.g. Precision blanking tools for high-strength materials.)
2
1
1C
T
T
Critical raw materials for Europe
Heat treatment:1100C, 30min
Solidification of a high speed steel (S290)
Cooling rate: 0.08 K/s Cooling rate: 104 K/s (powder metallurgy)
Mass fractions in %: 2.0C, 0.3Mn, 0.4Si, 3.8Cr, 2.5Mo, 4.8V, 14.3W, 11.0Co.
Mechanical properties: excellent toughness & machinability
Improved heat treatment during tempering reduction of Co?
Grain growth (X80 linepipe steel)
Microstructures at high temperatures
t1 = 110s t2 = 610s
Lecture overview
Motivation: Materials at extreme conditions and CRMs
• Thermodynamics and kinetics of microstructural changes Phase transformations and grain growth and coarsening.
• Experimental verification High temperature laser scanning confocal microscopy (HT-LSCM), In-situ high temperature X-ray diffraction, Dilatometry
• Conclusions
Thermodynamic description of multi-particle systems
Ext
rem
alpr
inci
ples
Phase transformations
Maxima and Minima (subject to constraints: Lagrange multipliers)
Determine: Extremum of F(x1, x2, …, xN)m constraints gj(x1, x2, …, xN) = 0
j = 1,2, … , m ; (m < N)
Extremum ofBy Lagrange multipliers j:
1j
m
jj
F g
10; 1 ... ,
j
m
jji
F g i , Nx
N + m equationsfor m unknown j
N unknown xi
Lagrange: Théorie des Fonctions Analytiques (p. 198, 1797)
Phase equilibrium(binary system)
Phase equilibrium(binary system)
g g g gx x x x
01 1g g x x x
0x x
1g g g
Molar Gibbs energy of the system: g = g(x, x, )
Minimum!
0Constraint: 1x x x
G. R. Purdy, Y.J.M. Brechet, Acta Mater. 44 (1996) 4853-4864
Principle of maximum dissipation Q
The extremal principle asserts that the rates of the characteristicvariables correspond to a maximum of the Gibbs energy dissipation Q constrained by the energy balance and by m further constraints.Q G
Contact conditions at the sharp interface
Mass balance at the interface
Substitutional diffusion
Assumption: The amount of lattice vacancies is negligibly small, and so is the flux jva.
M
Contact conditions at the sharp interface
Fluxes of the substitutional components (i = 1, … , s)
E. Gamsjäger, “A concise derivation of the contact conditions at a sharp interface“, Phil. Mag Letters 88 (2008) 363-369.
Contact conditions at the sharp interface
Fluxes of the substitutional components (i = 1, … , s)
E. Gamsjäger, “A concise derivation of the contact conditions at a sharp interface“, Phil. Mag Letters 88 (2008) 363-369.
Contact conditions at the sharp interface
Fluxes (interstitial components i=s + 1, …, N)
Contact conditions at the sharp interface
Interface velocity v
Sharp-interface and Quasi-sharp interface
E. Gamsjäger, J. Svoboda, F.D. Fischer: Comput. Mater. Sci. 32 (2005) 360-369.E. Gamsjäger, M. Rettenmayr: Philos. Mag. 95 (2015) 2851-2865.
Grain growth in a polycstalline material
Grain boundary motion decrease the total energy of grain boundaries in the system. https://www.youtube.com/watch?v=J_2FdkRqmCAh
2b
1
1 42
n
kk
G r
2 2
1b
1 42
n
k kk
Q r rM
Constraints:
Lagrange:
3
1
4 const.3
nk
k
rV
2
14 0
n
k kk
V r r
G Q
2
1
0 ( 1,..., )n
l llk
Q G Q r r k nr
crit
1 12 0, ( 1,..., )k b bk
r M k nr r
J. Svoboda, F.D. Fischer, Acta Mater. 55 (2007) 4467–4474
Chemisches Potential in small systems
2surf. 4U r
3
vol. mm
43rU UV
surf. m
vol. m
3 1U VU U r
d d d d d d d dU T S p V n T S p V n
m2d d d d dVU T S p V n nr
m2 Vr
Ostwald-ripeningA process driven by diffusion
Materials at high temperatures
Stable microstructure.Grain coarsening should be a very slow process.
Example 1: Y2O3-precipitates in steels.Beispiel 2: Automotive and aerospace industry:
Welding connections close to hot parts.
03 3 m8 ( )
9D T V xR R t
RT
, , (as small as possible)D x
Lecture overview
Motivation: Materials at extreme conditions and CRMs
Thermodynamics and kinetics of microstructural changes Phase transformations and grain growth and coarsening.
• Experimental verification High temperature laser scanning confocal microscopy (HT-LSCM), Dilatometry, In-situ high temperature X-ray diffraction.
• Conclusions
HT-LSCMHigh temperature laser scanning confocal microscopy
Temperatures up to 1650C,heating rates up to 50 K/s,15 frames per second dynamic processes.
Crucible on sample holder
Gold coated double elliptic furnace chamber
Gaseinlass
Gas inlet (Ar)
Suction pump
Laser beam (405 nm) Objective
Gas cooledhalogen bulb
Cover glass
Radiography Jördis Rosc/ÖGI
Dilatometry
Migrating austenite / ferrite interface (LSCM and dilatometry)
Mass fractions in %: 0.06C,1.7Mn, 0.034Nb, 0.012Ti, 0.24Mo.
Grain growth by HTLSCM I
t = 185s = 1006°C
30m
Grain growth by HTLSCM II
Modeling the kinetics of a triple junction
F. D. Fischer, J. Svoboda, K. Hackl: Acta Mater. 60 (2012) 4704 4711.
T
sin( ) sin( ) ik k i l l i i i
M
M
, , ... = 1, 2, 3 and , , i j k i k i l k l
3
1
T, Tcos
x i ii
v M
3
1
T, Tsin
y i ii
v M
Motion of grain boundaries at triple junctions I
Triple junction motion at = 1205°C within t = 8s:
M1 = 2, M2 = 0.267, M3 = 2.67, MT = 0.067.
See bachelor thesis: Daniel Marian Ogris (2018)
Motion of grain boundaries at triple junctions II
Triple junction motion within t = 8s:
M1 = 0.33, M2 = 6.710-5, M3 = 0.267, MT = 0.033.
See bachelor thesis: Daniel Marian Ogris (2018)
Future project IExperimental and theoretical grain growth investigationswith different amounts of alloying elements (e.g. Nb).
Grain size distribution as a function of T and composition.
Motion of triple junctions as a function of T and composition.
Motion of whole structures as a function of T and composition.
In situ high temperature XRD
o Motivation Mechanical properties: What are the underlying microstructural changes during
processing?
o In-situ X-ray diffraction Experimental setup X-ray diffractograms and their numerical analysis Microstructural changes in martensitic stainless steel Microstructural changes in high speed steel
o Noisy diffractograms Levenberg Marquardt versus Bayes-Theorem Microstructural changes by means of global optimization
o Comparison of the numerical results
o Conclusions
Mechanical Properties:What are the underlying microstructural changes during processing?
C Si Mn Cr Mo Ni0.04 0.40 0.40 15.4 0.9 5.30
Mass fraction 100
Martensitic stainless steel
Experimental setupIn situ high temperature X-ray diffraction (HT-XRD)
X-ray tubewith a Göbel mirror to select Cr Kα1 and Kα2, parallel beam optic.
Position sensitive detector
Oven (Anton Paar)
Analysis of X-ray diffractograms I(e.g. powder-metallurgically processed high speed steel)
Rietveld methode combined with a
Fundamental Parameter model(instrumental influence on thediffractogram)
Double Voigt-model (crystallite size and lattice straindue to dislocations)
- Measurement- Model- Difference
Martensite
Austenite
DiffractogramPeak areas → Phase fractions
Peak positions → Lattice parameters
Width of Peaks → → Crystallite size & lattice strain
Dislocation density from microstrain e:
Analysis of X-ray diffractograms II(Determination of dislocation densities in the phases)
20 e
0 0
0
0 0 0
d d d
a a
02
20
1 2 41 1 2
0
0
2 a
a
M. Wiessner, E. Gamsjäger, S. van der Zwaag, P. Angerer: ”Effect of reverted austenite on tensile and impact strength in a martensitic stainless steel − An in-situ X-ray diffrac-tion study”, Materials Science & Engineering A 682 (2017) 117–125.
Analysis of X-ray diffractogramsMass fraction of carbon
DiffractogramC in austenite (relative shift lattice parameter)thermal expansion has to be corrected.
C in martensite (tetragonality)Temperature independent
C1 0.045( 100) **c wa
**
hkl: (002) hkl: (020)
hkl: (022)
4C9.5 10 100 (nm) *a z *
** J. W Christian: Mater Trans, JIM (1992) 208–214.
* L. Cheng, A. Böttger, Th.H. de Keijser, E.J. Mittemeijer: Sripta Metallurgicaet Materialia, (1990) 509–514.*
Mass fraction of austenite & dislocation density I
M. Wiessner, E. Gamsjäger, S. van der Zwaag, P. Angerer: ”Effect of reverted austenite on tensile and impact strength in a martensitic stainless steel − An in-situ X-ray diffrac-tion study”, Materials Science & Engineering A 682 (2017) 117–125.
Mass fraction of austenite & dislocation density II
M. Wiessner, E. Gamsjäger, S. van der Zwaag, P. Angerer: ”Effect of reverted austenite on tensile and impact strength in a martensitic stainless steel − An in-situ X-ray diffrac-tion study”, Materials Science & Engineering A 682 (2017) 117–125.
Mass fraction of austenite & dislocation density III
M. Wiessner, E. Gamsjäger, S. van der Zwaag, P. Angerer: ”Effect of reverted austenite on tensile and impact strength in a martensitic stainless steel − An in-situ X-ray diffraction study”, Materials Science & Engineering A 682 (2017) 117–125.
Impact strength versus mass fraction of austenite anddislocation density
M. Wiessner, E. Gamsjäger, S. van der Zwaag, P. Angerer: ”Effect of reverted austenite on tensile and impact strength in a martensitic stainless steel − An in-situ X-ray diffraction study”, Materials Science & Engineering A 682 (2017) 117–125.
Diffractograms and their numerical analysisLow signal-to-noise ratio: Numerical solutions?
Global optimization: Bayesian Statistics applied to the Rietveld Method
measurement D (XRD dataset), hypothesis space H
2
calc,22
1
1| const exp22
ni i i
i ii
D DL D
(D | ) ( | H)( , D)(D | H)i i
iL pp
p
PRIOR distributionof the model parameters i
Likelihood
POSTERIOR distributionof the model parameters i
EVIDENCENormalization factor
Local optimization versus global optimization
Residual sum of squares
Austenite fraction after tempering before cooling
Austenite fraction during tempering
Dislocation density martensite at 25°C (before tempering) and after tempering (650°C) before cooling
Dislocation density of martensite(tempering process 650°C )
Dislocation density austenite complete tempering process
Heat treatmentHSS
C Si Mn Cr Mo V W Co2.0 0.44 0.27 3.7 2.4 5.1 14.1 11.0
Mass fraction 100
Lattice parameter a in austenite &Change of mass fraction of carbon in austenite
-
HSS
Tetragonality c/a &Mass fraction of carbon in martensite
HSS
Change of the mass fraction of carbon in austenite &Mass fraction of carbon in martensite
HSS
Lattice parameter in austenite, dislocation density in martensite & Hardness (HRC)
HSS
Conclusions and Outlook
HT-XRD for in-situ evaluation of process conditions:
o Relations between evolving microstructure and mechanicalproperties.
o Treatment of noisy diffractograms by global optimization.
Results:
o Microstructural evolution from high quality diffractograms (LM)o Microstructural evolution from noisy diffractograms (MCMC)
Future goal:
o Evaluation of diffractograms obtained during faster in-situprocesses.
Future project IIHeat treatment:a) Co-reduced HSS ? b) Cr-reduced MSS ? Material e.g. from Boehler Company.
Mechanical tests for different steel grades.
High temperature X-ray diffraction and evaluation.
Thank you for your attention!
Assoz. Prof. Ernst Gamsjäger
Institut für MechanikMontanuniversität LeobenFranz-Josef-Str. 18A-8700 Leoben
Tel.: ++43 3842 402 4006Fax: ++43 3842 46048
CRM-EXTREME [email protected] www.crm-extreme.euhttp://www.cost.eu/COST_Actions/ca/CA15102
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Solutions for Critical Raw Materials Under Extreme Conditions(CRM-EXTREME)