Comportement mécanique des verres métalliques massifs - Effet dune cristallisation partielle Sous la direction de : Jean-Jacques Blandin Sébastien Gravier

Comportement mécanique des verres métalliques massifs

-Effet d’une cristallisation partielle

Sous la direction de :

Jean-Jacques Blandin

Sébastien Gravier

http://www.gpm2.inpg.fr/pres.html

Mechanical behavior of bulk metallic glasses-

Impact of the partial crystallization

Supervised by :

Jean-Jacques Blandin

Sébastien Gravier

http://www.gpm2.inpg.fr/pres.html

3

Cooling a metal Crystallization

Temperature

Vol

ume

Tm

Liquid stateSolid state

Conventional solidification

4Production of a metallic glass

Cooling a metal Crystallization

Temperature

Vol

ume

Tm

Liquid stateSupercooled Liquid Region(SLR)

To avoid crystallization Rapid cooling

Tg

Glassy state

Metallic glass

Limited size !

More complex compositions to have Bulk metallic glasses

5Aim of the work

Temperature

Vo

lum

eSupercooled Liquid Region

Glassy state Tg

Crystallization

Effects ?

Room temperature : RT(T << Tg)

High temperature : HT(T>Tg)

Tg Nanocrystals

100 nm

brittleness large strain

5 mm

6

Aim: effect of crystallisation on mechanical properties at RT and HT

Room Temperature High Temperature

compression

DMAnanoindentation

compression

How the crystallisation modify the plasticity characteristics ?

How the crystals contribute to change the mechanical response ?

(rheology, elementary mechanism of deformation, reinforcement...)

Validation for the amorphous alloy

Mechanicalcharacterisation

methods

7




compression

DMAnanoindentation

compression

Microstructural characterisation

DSC TEMXRD

Crystal volume fraction ?





methods

8


High Temperature

DMA

compression


DSC TEMXRD






compression

nanoindentation


methods

Room Temperature

9Room temperature

Elements Zr Ti Cu Ni BeAtomic % 41.2 13.8 12.5 10 22.5

BMG studied in this thesis

Vit1 (Tg = 365 °C )

10

E ≈ corresponding crystalline alloys

+

f = 1830 MPa ( 1 %)

elast ≈ 0.02

Macroscopic brittleness

Compression tests at room temperature on a BMG

Macroscopic brittleness but local plasticity

Ef

Room temperature

elast

BMG studied in this thesis

Vit1 (Tg = 365 °C )Elements Zr Ti Cu Ni BeAtomic % 41.2 13.8 12.5 10 22.5

20 µm20 µm

Microscopic plasticity

Fracture surface

11

0

50

100

150

200

250

300

350

0 500 1000 1500

Depth "h" (nm)

Lo

ad "

L"

(mN

)

Nanoindentation loading and unloading curves

Room temperature

L

h

Loading curve : L = C h2

Unloading curve:

( Irreversible Work ratio ) RW = Wirr / Wtot

Collaboration: L. Charleux ( INP-Grenoble )

12

Loading curve : L = C h2

Unloading curve:


0

50

100

150

200

250

300

350

0 500 1000 1500

Depth "h" (nm)

Lo

ad "

L"

(mN

)


Wtot

Wirr

Room temperature

> Silica Glass ≈ 40 %

< Aluminium ≈ 100 %

Suggest many dissipative events !

= 67 %

13

0

50

100

150

200

250

300

350

0 500 1000 1500

Depth "h" (nm)

Lo

ad "

L"

(mN

)


Wtot

Wirr

5 µm

21 2d

eqc

SEE

A

Materials Science and Engineering A (2006)

Sd

Room temperatureLoading curve :

L = C h2

Unloading curve:


> Silica Glass ≈ 40 %

< Aluminium ≈ 100 %

Suggest many dissipative events !

= 67 %

AFM measurements : reduced Young modulus : Eeq

14

0.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

1.1 1.15 1.2 1.25 1.3

C/Eeq

Rw

Von Mises

Amorphous

Room temperature

In this plane

Von Mises criterion : y

Line in this plane

Plasticity map extracted from nanoindentation curves: gives plastic properties independently of elastic behavior

15

0.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

1.1 1.15 1.2 1.25 1.3

C/Eeq

Rw

Von Mises

Amorphous

> 0

< 0

Room temperature

Drucker Pragger criterion :

y and α (pressure sensitivity)

Upper part : > 0

Lower part : < 0

In this plane


Line in this plane


16

0.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

1.1 1.15 1.2 1.25 1.3

C/Eeq

Rw

Von Mises

Amorphous

> 0

< 0


Both values of y in agreement with compression

in agreement with

Vaidyanathan 2001

Patnaik 2004Nanoindentation: Fruitful technique to study deformation at room temperature (in particular pressure sensitivity)

Room temperature

Drucker Pragger criterion :

y and α (pressure sensitivity)

Upper part : > 0

Lower part : < 0

In this plane


Line in this plane

17


Room Temperature

compression

nanoindentation


DSC TEMXRD






High Temperature

DMA

compressionMechanicalcharacterisation

methods

18

1,E+08

1,E+09

1,E+10

1,E+11

1,E+12

1,E+13

1,E-05 1,E-04 1,E-03 1,E-02 1,E-01

Strain rate (s-1)

Vis

cosi

ty (

Pa.

s)

Room temperature fracture stress

T decreases

Tg - 10 °C

Tg + 40 °C

Viscosity as function of strain rate / compression

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8Strain

Str

ess

(MP

a)

5.10-3 s-1

5.10-4 s-15.10-4 s-1

T = Tg + 10 °C

Large strains

3

High temperature

Compression tests at Tg + 10 °C, various strain rates

Viscoplastic deformation in

steady state

19

1,E+08

1,E+09

1,E+10

1,E+11

1,E+12

1,E+13

1,E-05 1,E-04 1,E-03 1,E-02 1,E-01

Strain rate (s-1)

Vis

cosi

ty (

Pa.

s)

Room temperature fracture stress

T decreases

Tg - 10 °C

Tg + 40 °C

Confirmation of usual deformation behaviour in SLR

Newtonian regimeHigh temperature / low strain rate

Non Newtonian regimeLow temperature / high strain rate

Viscosity as function of strain rate / compression

Newtonian

Non Newtonian

High temperature

20

0.01

0.1

1

10

1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10N

/

N

Tg - 10°C

Tg + 50°C

Creation of a unique master curve for various temperatures

High temperature

effect of T : just translation

0 exp( )N

Q

RT Suppose:

Q = 440 kJ/mol

Complex multiatomic mechanism (activation volume ≈ 20 atoms)in large strain …

(strong temperature sensitivity)

Sensitivity to temperature:

Newtonian viscosity

Ability to draw a master curve:

Sensibility of viscosity to strain rate independent of temperature

21

0.01

0.1

1

10

1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10N

/

N

Tg - 10°C

Tg + 50°C

Creation of a unique master curve for various temperatures

0 exp( )N

Q

RT Suppose:

Q = 440 kJ/mol

Complex multiatomic mechanism (activation volume ≈ 20 atoms)in large strain …

High temperature

Data obtained in steady state (large strain)

Is there a minimum strain to measure these features ?

effect of T : just translation

Sensitivity to temperature:

Newtonian viscosity

Ability to draw a master curve:

Sensibility of viscosity to strain rate independent of temperature

22

Dynamic Mechanical Analysis (DMA) : Sinusoidal small strain tests

0

0,05

0,1

0,15

0,2

0,25

0,3

0,01 0,1 1 10f (Hz)

G"/

Gu

Frequency scans at various fixed temperatures

T

High temperature

Collaboration: Jean–Marc Pelletier, INSA - Lyon

Dissipative part of the deformation :

Construction of a master curve

0

0,05

0,1

0,15

0,2

0,25

0,3

0,0001 0,01 1 100"Translated" f (Hz)

G"/

Gu

Phase difference between applied stress and strain

"G

Gu

23

Dynamic Mechanical Analysis (DMA) : Sinusoidal small strain tests

0

0,05

0,1

0,15

0,2

0,25

0,3

0,01 0,1 1 10f (Hz)

G"/

Gu

Frequency scans at various fixed temperatures

T

High temperature

Collaboration: Jean–Marc Pelletier GEMPPM, INSA

Dissipative part of the deformation :

Construction of a master curve

0

0,05

0,1

0,15

0,2

0,25

0,3

0,0001 0,01 1 100"Translated" f (Hz)

G"/

Gu

"G

Gu

Elementary mechanism of deformation independent of TApparent activation energy ~ 400-450 kJ/mol

Similar mechanical behaviours in the investigated conditions(T and both small and large strains)

DMA + Compression : Fruitful techniques to study deformation at HT in a large strain interval

Phase difference between applied stress and strain

24




compression

DMAnanoindentation

compression





DSC TEMXRD



methods

25

0 20 40 60 80 100

Annealing time (min.)

En

do

the

rmic

he

at

flo

w (

a.u

.)_

Crystallization / Microstructure

Isothermal annealing DSC at Tg + 50 °CAmorphous : transformed fraction Ft = 0%

100 nm100 nm

~ 30 nmFt = 10 %

10 min.

100 nm100 nm

Φ ~ 35 nmFt = 60 %

30 min.

100 nm100 nm

Φ ~ 30 nmFt = 45 %

20 min.

100 nm100 nm

Crystallite average size Φ ~ 35 nmFt ≈ 100 %

60 min.

100 nm100 nm

Φ ~ 35 nmFt = 80 %

45 min.

Various heat treatments

26

0 20 40 60 80 100


En

do

the

rmic

he

at

flo

w (

a.u

.)_

Crystallization / Microstructure

Isothermal annealing DSC at Tg + 50 °CAmorphous : transformed fraction Ft = 0%

100 nm100 nm

~ 30 nmFt = 10 %

10 min.

100 nm100 nm

Φ ~ 35 nmFt = 60 %

30 min.

100 nm100 nm

Φ ~ 30 nmFt = 45 %

20 min.

100 nm100 nm

Crystallite average size Φ ~ 35 nmFt ≈ 100 %

60 min.

100 nm100 nm

Φ ~ 35 nmFt = 80 %

45 min.

Various heat treatments

Spherical crystallites + constant average size

27Crystallization / volume fraction

Direct measurements through TEM imaging

100 nm

100 nmd

100 nmd

100 nm

Dark field observation Thickness measurement

Bright field observation

Crystal superposition and lack of contrast in bright field

Dark field measurements of volume fraction

Collaboration: P. Donnadieu (LTPCM – INPG)

28

To calculate the real volumefraction we need to have onlyone crystal type :

Crystallite sizeCrystallite nature

Crystallization / volume fraction

annealing time ≤ 30 min.

Direct measurements through TEM imaging

100 nm

100 nmd

100 nmd

100 nm

Dark field observation Thickness measurement

Bright field observation

Crystal superposition and lack of contrast in bright field

Dark field measurements of volume fraction

0 min. 10 min. 20 min. 30 min.

Fv (%) 0 4 1 17 4 26 5

TEM volume fraction of crystals depending on annealing time at Tg + 50 °C

Collaboration: P. Donnadieu (LTPCM – INPG)

29Crystallization / volume fraction

Crystals randomly oriented

Density constant

(d / d < 1 %)

Direct measurements through XRD analysis

0,751,251,752,252,75dhkl (A)

Cou

nts

Amorphe

10mn

45mn

30mn

60mn

20mn

XRD curves for the various samples

30

20 30 40 50 60 70 80

angle (2q)

Co

un

ts

Separation of the amorphous and crystalline contributions.

Amorphous

60 min.

Volume fraction of crystals


Crystals randomly oriented

Density constant

(d / d < 1 %)

Direct measurements through XRD analysis

Crystallized part

Amorphous part

31

Amorphous 10 min. 20 min. 30 min.

Volume fraction

(%)

TEM 0 4 1 17 4 26 5

XRD 0 7 3 17 3 27 3

Equivalent values with the two methods :

Validation of the measurement methodsXRD analysis is an accurate way to measure Volume fraction of crystals (even for small crystallites)

Validation of the method


32

Amorphous 10 min. 20 min. 30 min. 45 min. 60 min.

Volume fraction

(%)

TEM 0 4 1 17 4 26 5 ? ?

XRD 0 7 3 17 3 27 3 32 3 45 5





33

Amorphous 10 min. 20 min. 30 min. 45 min. 60 min.

Volume fraction

(%)

TEM 0 4 1 17 4 26 5 ? ?

XRD 0 7 3 17 3 27 3 32 3 45 5

DSC Ft (%) 0 10 45 60 80 100


Large difference with predicted DSC transformed fraction(while sometimes used as crystalline fraction…)




34



High Temperature

compression

DMAnanoindentation

compression


DSC TEMXRD



Room Temperature



methods

Crystal volume fraction : OK

35



High Temperature

compression

DMAnanoindentation

compression


DSC TEMXRD




Room Temperature



methods

36Effect of crystallization / room temperature

Fracture stress increases slightly and then falls !

Journal of Alloys and Compounds (2006)

Fracture stress as a function of annealing time

Nanoindentation is even more interesting to study plasticity

Change in fracture mechanism :

Fragmentation rather than shear fracture for Fv > 30 %

500

700

900

1100

1300

1500

1700

1900

2100

0 10 20 30 40 50 60

Fv (%)

Fra

ctu

re s

tres

s (M

Pa)

_

37

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5

C/Eeq

Rw

Effect of crystallization / room temperature

Journal of Materials Research (2007)

Plasticity map extracted from nanoindentation curves

Al

Silica

Amorphous

38

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5

C/Eeq

Rw

Effect of crystallization / room temperature

Journal of Materials Research (2007)

Plasticity map extracted from nanoindentation curves

Al

Silica

At room temperature:

Effect on fracture rather than on deformation mechanisms

Effect of crystallization

(Fv < 0.5)

Very limited variations of Rw and C/Eeq

Still sensitive to pressure

39



Room Temperature

compression

DMAnanoindentation

compression


DSC TEMXRD



High Temperature




methods

40Effect of crystallization / high temperature

Two main effects of crystallization

Increase of viscosity

Promotion of non Newtonian behaviour

The reinforcement for a given temperature depends on strain rate

Viscosity depending on strain rate

Deformation ability is maintained up to large Fv

1,E+09

1,E+10

1,E+11

1,E+12

1,E+13

1,E-05 1,E-04 1,E-03 1,E-02Strain rate (s-1)

Vis

cosi

ty (

Pa.

s)

amorphous

Fv = 7 %

T = Tg + 20°C

Increase of the viscosity

decrease oflim itFv = 32 %

Fv = 27 %

Fv = 17 %

Fv = 45 % : brittle behaviour


Similar mechanical behaviours in the investigated conditions(Fv, T and large strains)

Viscosity curves : all temperatures and annealing times / translated along the two axes

"Translated" strain rate

"Tra

nsl

ated

" V

isco

sity

~ 25 compression tests Still ability to draw master curves

Strain rate dependence of viscosity is the same for the various temperatures and Fv

Effect of T : still just translation


DMA curves : all temperatures and annealing times / translated along the two axis

0

0,05

0,1

0,15

0,2

0,25

0,01 1 100 10000 1000000frequency "translated" (Hz)

G"

"tra

nsl

ated

"

THERMEC (2006)

~ 200 curves

Again able to draw master curves

Same elementary mechanism of deformation for the various temperatures and Fv


Reinforcement depends on strain rate…

Comparison performed in Newtonian regime

( )VF

NAmorphousN

R Fv

Similar mechanical behaviours in the investigated conditions(Fv, T and both small and large strains)

Prediction of the reinforcement factor ( ) ?VF

Amorphous

The amorphous matrix seems responsible for the deformation

44

1

10

100

1000

0 10 20 30 40 50 60Fv (%)

Rei

nfo

rcem

ent

fact

or

: R

Effect of crystallization / high temperature / reinforcement

Prediction of R from mechanical models ?

Hard sphere dispersion in a viscous media : Krieger model

T = Tg + 30 °C( )VF

NAmorphousN

R Fv

Reinforcement factor for various Fv (less than 30 %)

45

1

10

100

1000

0 10 20 30 40 50 60Fv (%)

Rei

nfo

rcem

ent

fact

or

: R


Underestimate the reinforcement !!



T = Tg + 30 °C

Krieger model

( )VF

NAmorphousN

R Fv

Reinforcement factor for various Fv (less than 30 %)

46

1

10

100

1000

0 10 20 30 40 50 60Fv (%)

Rei

nfo

rcem

ent

fact

or

: R


Reinforcement factor for various Fv (less than 30 %) and temperatures

Underestimate the reinforcement !!

T decreases

Tg

Tg + 30°C

Reinforcement depends on strain rate and temperature(simple mechanical models are not adapted)



Various T

Krieger model

( )VF

NAmorphousN

R Fv

47

ISMANAM (2006)

0 exp( )N

Q

RT

Still able to use an Arrhenius law

Activation energies in SLR measured by two ways

0

100

200

300

400

500

0 10 20 30 40 50 60

Fv (%)

Ap

par

ent

acti

vati

on

en

erg

y (k

J/m

ol)

_

compressionDMA


Temperature

New

ton

ian

vis

cosi

ty

Glass

Partially crystallized

48

0 exp( )N

Q

RT

Still able to use an Arrhenius law

ISMANAM (2006)


Reinforcement increases with temperature because:Decrease of viscosity is less rapid when crystals are present

0

100

200

300

400

500

0 10 20 30 40 50 60

Fv (%)

Ap

par

ent

acti

vati

on

en

erg

y (k

J/m

ol)

_

compressionDMA


Temperature

New

ton

ian

vis

cosi

ty

Glass

Partially crystallized

49Effect of crystallization / high temperature / activation energies

• Direct change in composition of the residual glass ?

Three possible reasons to explain the decrease of activation energy

ISMANAM (2006)

NO( ∆ Tg < 4 °C )

NO( TEM observationsafter deformation > 1.5 )

• Direct contribution of crystal deformation ?


• Direct change in composition of the residual glass ?

• Direct contribution of crystal deformation ?

• Influence of the coupling between matrix and crystals ?

Three possible reasons to explain the decrease of activation energy

Matrix layer perturbed by the proximity of crystals

Small “flow channels” between crystallites

d

Modification of matrix activation energy at crystal neighborhood


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50Fv (%)

Rat

io "

per

turb

ated

am

orp

ho

us

/ to

tal r

emai

nin

g a

mo

rph

ou

s"

1 nm

3 nm

5 nm

Fraction of amorphous matrix perturbed because of proximity of crystals

Effect of various interface thickness

coupling between matrix and crystals (crystal size ≈ 30 nm) ?


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50Fv (%)

Rat

io "

per

turb

ated

am

orp

ho

us

/ to

tal r

emai

nin

g a

mo

rph

ou

s"

Fraction of amorphous matrix perturbed because of proximity of crystals

Nanometer crystallites Large fraction of the remaining amorphous matrix can be disturbed by crystal proximity

coupling between matrix and crystals (crystal size = 30 nm) ?

1 nm

3 nm

5 nm

Distance between crystallites effect

Visualization of the small distances between

crystals : Fv = 30 %

30 nm

Effect of various interface thickness

53

Validation of new methods

- compression / nanoindentation

fracture vs. plasticity calculation of both the pressure sensitivity and the yield stress

- compression / DMA

large strain interval deformation mechanism at small strains vs. large strain mechanism

- TEM / XRD

Measurements of the volume fraction of crystals

Main conclusions

54Main conclusions

Open questions on the effect of crystallization

- At room temperature: Does the crystals modify the plasticity characteristics ?

Modify the fracture (fragmentation for Fv > 30 %) Limited modification of the plastic mechanism

Small variation of RwStill a pressure sensitivity

- At high temperature: How the crystals contribute to change the mechanical response ?

Deformation mechanism seems similar whatever Fv (< 50 %), the strain or the temperature Promotion of non Newtonian behavior Reinforcement effect depends on temperature

55Perspectives / scientific

Modelling the high temperature deformation

Similarity between deformation mechanisms for small strain and large strain

Interest of the definition of the elementary mechanism of deformation


Modelling the high temperature deformation

Similarity between deformation mechanisms for small strain and large strain

Need to go from elementary deformation to macroscopic deformation

Flow defect concentration

Interest of the definition of the elementary mechanism of deformation

Elementary shear mechanism of Argon

Flow defect


Study of the size effect of nanocrystals

One comparison point already achieved:

Fv = 16% + Mean crystallite size = 7 nm

Fv = 17% + Mean crystallite size = 30 nm

and

No differences observed … … up to now !!

58Perspectives / technological

Interest of bulk metallic glasses / metallic alloys composites

Patent in progress

10 mm

Advanced Engineering Materials (2006)

1 mm

Al-alloy

Vit1

Interesting mechanical properties…

Fracture stress + Plasticity + High interface shear stress

Co-deformed multimaterials designed thanks to the deformation ability of the glass in the SLR

Resistance of metallic glass + ductility of metallic alloy

Push out tests

1 mm

Al-alloy

Vit1

59

Merci à …

Ludovic CharleuxBéatrice Doisneau-CottigniesPatricia DonnadieuMarc FivelAlexandre MussiJean-Marc PelletierLuc SalvoJean-Louis SoubeyrouxMichel SueryAndré SulpiceMarc VerdierQing Wang

… pour leurs contributions à ce travail

60

61

62Conclusion and ….perspectives

Crystallites size effect (heat treatments at other temperatures)

Room temperatureYoung modulus

High temperatureModel of deformation based on the Argon model

Effect of the high temperature deformation on the crystallization

Point not aborded


63

Link between localized deformation and homogeneous flow ?

Characterization of the localized deformation

Influence of a temperature increase

Transition with homogeneous flow0

500

1000

1500

2000

0 0,05 0,1 0,15

Strain

Str

es

s (M

Pa)

Compression test at room temperature:Zr based BMG with plasticity (collaboration with Shanghai university)

plastic > 0.07

Perspectives / scientific

64

Poisson ratio … deformation mechanism

Yoshida et al., JMR 2005

Lewandowski et al., Phil. Mag. 2005

Pd

65Crystallisation

Three crystallization events may occur at higher temperature…

Analyze here the two first crystallization peaks

250 300 350 400 450 500 550Temperature (°C)

En

do

ther

mic

he

at f

low

(a.

u)

DSC scan at 10°/min. / amorphous sample

Tg ≈ 365 °C

Tp1 = 438 °C

Tp2 = 457 °C

Tp3 = 505 °C

Isothermal Annealing at 410°C

0 20 40 60 80 100


En

do

ther

mic

hea

t fl

ow

(a.

u.)

_

66DMA / Activation energy

Activation energy:

T<Tg : Q ≈ 100 kJ/mol

**

1' "J J iJ

G " 1J

Ju Maxwell

model 0ln( ) ln( )"

Ju Q

J RT and

Calculation of the activation energy in Small deformation

-5

-3

-1

1

3

5

1,3 1,35 1,4 1,45 1,5 1,55 1,6 1,65 1,7

1000/T (K-1)

ln(J

u/J

")

T = Tg

T > Tg T < Tg

Activation energy:

T > Tg : Q ≈ 450 kJ/mol

DMA / Temperature scan

67

1,E+09

1,E+10

1,E+11

1,E+12

1,E+13

340 350 360 370 380 390 400

temperature (°C)

N (

Pa

.s)

ISMANAM (2006)


Effect of crystallization : Newtonian Viscosity

Amorphous

Fv = 32 %

Influence of the temperature on the reinforcement

68Effect of the deformation on the crystallization


No visible influence of the deformation on the crystallization

Reinforcement factor as a function of time.Cristallisation proceed while deforming

69Effect of the deformation on the crystallization


DRX on two samples DSC on four samples


70

Deformed

Effect of the deformation on the crystallization



71High temperature Mechanism

Multiatomic approach of the high temperature deformation

Multiatomic deformation mechanism

High apparent activation energy

Shear model of Argon Resistance of the surrounding

i

i

ii

Qapparent = Q (interfacial shear resistance) + Q (mechanical resistance of the

surrounding)


Evolution of the activation energy

Température

En

erg

ie d

'ac

tiva

tio

n

Glassy state Supercooled liquid Liquid state

Tg Tf

Eact:T < Tg

Eact T > Tf

Eact T > Tg

Continuous decrease ?

Mechanical resistance of the surrounding is decreasing


Defect concentration evolution

0

0,05

0,1

0,15

0,2

0,25

0,3

-250 -50 150 350 550 750

température (°C)

De

fec

t c

on

cen

tra

tio

n Equilibrium defect concentration

Out of equilibrium concentration

1

1 exp( )exp( )

ed

f f

CH S

RT R

Hf = 14 kJ /mol

Sf = 6 J /mol/°C

74Co-extruded materials





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Comportement mécanique des verres métalliques massifs - Effet dune cristallisation partielle Sous la direction de : Jean-Jacques Blandin Sébastien Gravier