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 crm-extreme@univpm.it 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)