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Mechanical Properties of Metallic Glasses

A. L. Greer

Dept. of Materials Science & Metallurgy University of Cambridge

Res Metallica 2013

Aula van de Tweede Hoofdwet

KU Leuven, 8 May 2013

How to make a glass?

• a glass forms if crystallization is avoided on cooling

• the density of the glass depends on cooling rate

The Glassy State

— is found for all classes of material:

• oxide (e.g. SiO2)

• ionic (e.g. ZnF2)

• polymeric

• metallic

• chalcogenides (Se, Te ….)

• carbohydrates

CA Angell: Science 267 (1995) 1924.

gTTg TTd

dm

))/(

log( 10

Fragility

R Busch, J Schroers, WH Wang: MRS Bulletin 32 (2007) 620.

STRONG

FRAGILE

HOT COLD

GLASS LIQUID

The fragility of metallic glass-forming liquids

R Busch, J Schroers, WH Wang: MRS Bulletin 32 (2007) 620.

STRONG

FRAGILE

HOT COLD

GLASS LIQUID

Metallic Glasses

• metals and alloys are naturally crystalline

• pure metals cannot form glasses — their simple structure

crystallizes too easily on cooling the liquid

• liquid metals have a low viscosity, very similar to that of water

• alloying can stabilize the liquid, and aids glass

formation (“confusion principle”)

• for a binary alloy such as Fe80B20 (atomic %), the critical cooling

rate for glass formation is

105 to 106 K s–1

Bulk Metallic Glasses

• multicomponent compositions aid glass formation

• the critical cooling rate is much lower (~1 K s–1)

• glasses can be formed in bulk

Bulk metallic glasses ― at the cutting edge of metals research

AL Greer and E Ma,

MRS Bulletin 32 (2007) 611-615.

from The Times Higher Education Suppl. 3 Feb. 2006

John Desmond Bernal

1901-1971

The dense random packing model for

the structure of liquids.

Close packing of discs in 2D ―

DB Miracle, WS Sanders & ON Senkov, Philos. Mag. 83 (2003) 2409.

Close packing of spheres in 3D

preferred radius ratios ―

DB Miracle, WS Sanders & ON Senkov,

Philos. Mag. 83 (2003) 2409.

“Thermodynamics and kinetics of bulk metallic glass”

R Busch, J Schroers & WH Wang,

MRS Bulletin 32 (2007) 620-623.

“Thermodynamics and kinetics of bulk metallic glass”

R Busch, J Schroers & WH Wang,

MRS Bulletin 32 (2007) 620-623.

0

ST

G

ST

G

Elastic limit y and density r for metallic glasses and for 1507 conventional metals, alloys and metal-matrix composites.

Metallic glasses for structural applications


Elastic limit y and density r for metallic glasses and for 1507 conventional metals, alloys and metal-matrix composites. The contours show the specific strength y/r.

Ce70Al10Cu20 — Tg = 338 K, Tx = 390 K

B Zhang, DQ Zhao, MX Pan, WH Wang & AL Greer:

Amorphous metallic plastic, Phys. Rev. Lett. 94 (2005) 205502.

The world’s smallest motor


Elastic limit y and Young’s modulus E for metallic glasses and for 1507 conventional metals, alloys and metal-matrix composites. The contours show the elastic strain limit y/E.

M.F. Ashby & A.L. Greer: Scripta Materialia 54 (2006) 321.

(in Viewpoint Set on Mechanical Behavior of Metallic Glasses, edited by T.C. Hufnagel)

Pressure Sensors

Diaphragms

Annual production now nearly 50 million units

Strain →

Str

es

s →

Within the elastic (reversible) regime ―

y

E

area = 2/2E = elastic energy

stored per unit volume

Strain →

Str

es

s →

to increase the elastic stored energy ―

E

increase the yield stress, y

Strain →

Str

es

s →

E

decrease the Young modulus, E

to increase the elastic stored energy ―


Elastic limit y and Young’s modulus E for metallic glasses and for 1507 conventional metals, alloys and metal-matrix composites. The contours show the resilience y

2/E.





Resilience and loss coefficient for metallic glasses and for 1507 conventional metals, alloys and metal-matrix composites.

Mechanical damping in metallic glasses

Golf clubs …. and tennis-racket frames, baseball bats, skis …

Photo: courtesy of Dr K. Georgarakis (SIMaP, Grenoble; WPI-AIMR, Sendai)

0

500

1000

1500

2000

2500

0 0.01 0.02 0.03 0.04 0.05 0.06

True Strain

Tru

e S

tres

s [M

Pa]

Vitreloy

0.1 MPa Hydrostatic Pressure

Yield/Fracture Strength = 1986 MPa

f = 0%

JJ Lewandowski

― can perform mechanical tests on bulk samples

― in tension, samples always appear macroscopically brittle

― but there is extensive local deformation in the shear bands

Adiabatic shear bands in

conventional (polycrystalline) engineering alloys

a-b titanium alloy

S.P. Timothy & I.M. Hutchings (1984)

martensitic steel

R. Dormeval (1987)

How to understand the thickness of shear bands in

metallic glasses?

TEM studies consistently suggest a shear-band thickness of ~10 nm

Y. Zhang & A.L. Greer: “Thickness of shear bands in metallic glasses”, Appl. Phys.

Lett. 89 (2006) 071907.

M. Chen, A. Inoue, W. Zhang & T. Sakurai: “Extraordinary plasticity of ductile bulk

metallic glasses”, Phys. Rev. Lett. 96 (2006) 245502.

N.P. Bailey, J. Schiøtz & K.W.

Jacobsen, Phys. Rev. B 73

(2006) 064108.

Molecular-dynamics simulations

— also show a shear-band thickness of ~10 nm

Q.-K. Li & M. Li, Appl. Phys. Lett. 88

(2006) 241903.

PG Saffman & GI Taylor, Proc. Roy. Soc. Lond. A 245 (1958) 312‒329.

A.S. Argon & M. Salama, Mater. Sci. Eng. 23 (1976) 219.

The vein pattern is formed by

Saffman-Taylor fingering of air into a

liquid-like layer of thickness 2-20

times the vein spacing.

Heating at Shear Bands in Metallic Glasses

TEM shows that the shear is sharply localized —

— thickness of shear band = 10 to 20 nm

The origins of localization remain controversial — structural change, or

temperature rise?

Measurements of temperature rise 0.4 K to 1000 K

Predictions of temperature rise 40 K to 1000 K

B. Yang, P.K. Liaw, G. Wang, M. Morrison, C.T. Liu, R.A. Buchanan & Y. Yokoyama:

“In-situ thermographic observation of mechanical damage in bulk-metallic glasses

during fatigue and tensile experiments”, Intermetallics 12 (2004) 1265.

Average measured

temperature rise in

shear bands = 0.4 K

(for observed width of

0.15 mm)

J.J. Lewandowski & A.L. Greer

Test of method on Vitreloy 1 (Zr41.25Ti13.75Ni10Cu12.5Be22.5)

JJ Lewandowski & AL Greer: “Temperature rise at shear bands in metallic

glasses” Nature Materials 5 (2006) 15.

A tin coating applied to a Zr-based BMG melts when shear

bands form on bending.

0

500

1000

1500

-2 -1 0 1 2

Te

mp

era

ture

Ris

e,

T

(K

)

Distance, x ( m)

H = 0.4 kJ m-2

H = 2.2 kJ m-2

7

50

1

0.2

10

50

167

1000

T = 207 K

Minimum observed

melting half-width

= 200 nm

Observed melting

half-width = 1 m

H = 0.4 kJ m–2 H = 2.2 kJ m–2

Distance, x (m)

Half-profiles of

temperature at a typical

shear band evolving over

time (in nanoseconds)

― calculated from

independently measured

thermal diffusivity

Profile when tin coating is

melted to maximum width

Shear steps scale

with sample size

and machine

stiffness.

Serrated flow

without significant

temperature rise can

become unstable,

leading to significant

heating and a

runaway instability

S. Braeck & Y.Y. Podladchikov, “Spontaneous thermal runaway as an ultimate failure

mechanism of materials”, Phys. Rev. Lett. 98 (2007) 095504, and later work.

numerical

approach

gives the highest

temperature increases

Conventional glasses are

brittle —

What about metallic glasses?

Fracture toughness and Young’s modulus for metals, alloys,

ceramic, glasses, polymers and metallic glasses. The contours

show the toughness Gc in kJ m–2.

MF Ashby & AL Greer: Scripta Materialia 54 (2006) 321.

(in Viewpoint Set on Mechanical Behavior of Metallic Glasses, edited by TC Hufnagel)

• the plastic flow stress in shear is proportional to the elastic shear

modulus — thus the shear modulus is a measure of the difficulty of

plastic flow

• similarly the bulk modulus is a measure of the difficulty of cracking

• thus high values of the shear-to-bulk modulus ratio /B should favour

brittleness and vice versa

• proposed by Pugh in 1954, and developed by others —

S.F. Pugh, Philos. Mag. 45 823 (1954).

A. Kelly, W.R. Tyson and A.H. Cottrell, Philos. Mag. 15 567 (1967).

J.R. Rice and R. Thomson, Philos. Mag. 29 73 (1974).

A.H. Cottrell, in Advances in Physical Metallurgy, edited by J.A. Charles and

G.C. Smith (Institute of Metals, London, 1990), pp. 181–187.

Metals: Plasticity or Brittleness?

• For polycrystalline metals there is a scale from ductile, low /B (Ag,

Au, Cd, Cu) to brittle, high /B (Be, Ir)

• for fcc metals (/B)crit = 0.43-0.56 or 0.32-0.57

• for hcp metals (/B)crit = 0.60-0.63

• for bcc metals (/B)crit = 0.35-0.68

• thus critical modulus ratio (/B)crit is not very well defined even for

one structure type

• (/B)crit is affected by anisotropy

• most detailed theory for (/B)crit concerns dislocation emission from a

crack tip

What will happen for metallic glasses?

— no anisotropy

— no dislocations

— no clearly different structures

With BMGs, good data are now available

Fracture data are presented in terms of the energy of fracture

G = K2/E(1 – n2)

where K is the toughness (stress intensity at fracture) and n is Poisson’s ratio

All the data superposed, together with data on oxide glasses for

comparison. Overall, (/B)crit = 0.41-0.43

JJ Lewandowski, WH Wang & AL Greer, “Intrinsic plasticity or brittleness of

metallic glasses”, Philos. Mag. Lett. 85 (2005) 77.

The same data presented in terms of Poisson’s ratio. The critical

value corresponding to (/B)crit = 0.41-0.43 is ncrit = 0.31-0.32.



Alloy design To avoid intrinsic brittleness and to have greater resistance to annealing-induced embrittlement — • we need to choose component elements with small /B or, equivalently, high n (ideally n should tend towards 0.5, which is the value for liquids)

Au

Nb

Pd

Pt

Hf

Al

Cu

Zr

Ti

Ni

Ca

Co

Fe

Mg

Nd

La

Pr

Y

Tb

Gd

Ce

Be

/B

0.12

0.22

0.24

0.27

0.27

0.35

0.35

0.39

0.42

0.43

0.44

0.45

0.48

0.49

0.50

0.52

0.52

0.54

0.57

0.58

0.61

1.02

n

0.44

0.40

0.39

0.38

0.37

0.34

0.34

0.33

0.32

0.31

0.31

0.30

0.29

0.29

0.28

0.28

0.28

0.26

0.26

0.26

0.25

0.03

plastic brittle

/B

n

CA Angell: Science 267 (1995) 1924.

gTTg TTd

dm

))/(

log( 10

Fragility

GP Johari: Philos. Mag. 86 (2006) 1567.

gTTg TTd

dm

))/(

log( 10

Angell’s “fragility” of liquid:

plasticity brittleness

“fragility”

“strength”

plasticity

“strength” brittleness

“fragility”

better

glass-forming

ability

The better the glass-forming ability, the more likely to be brittle!

A Damage-Tolerant Glass MD Demetriou, ME Launey, G Garrett, JP Schramm, DC Hofmann,

WL Johnson, RO Ritchie: Nature Materials 10 (2011) 123-128.

Define: f =

(probability of shear activation event)/(probability of cavitation event)

Then derive: logf = (Tg/T)[(B/G) − 1]

Study the BMG Pd79Ag3.5P6Si9.5Ge2 (rods, critical diameter = 6 mm)

n= 0.42 plastic zone size = 6 mm

Comparison:

y (MPa) Kc (MPa m1/2)

low-C steel < 500 > 200

silicates up to 3000 < 1

MGs in general 500−5000 1−100

Pd79Ag3.5P6Si9.5Ge2 1490 200

MD Demetriou et al., A damage-tolerant glass, Nature Mater. 10 (2011) 123-128.


AL Greer, Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.

contour of

constant yKc



typical trade-off

between y and Kc



highest known

product of y

and Kc

AL Greer: Damage tolerance at a price, Nature Mater. 10 (2011) 88-89.

Photo

: M

axim

ilien E

. Launey

At a notch, cracks of several 100 m are stable. The shear

bands are very finely spaced.

Pd79Ag3.5P6Si9.5Ge2 BMG

L. Addadi et al., “Mollusk shell formation: A source of new concepts for

understanding biomineralization processes,” Chem. Eur. J. 12 (2006) 980.

0.5 m thick layers of aragonite

separated by organic sheets of chitin with fibroin surfaces

organic components ~ 2 wt% of total

Uniaxial compression was used to

induce anisotropy:

• cylindrical samples, 3 mm diameter

• length to diameter 2:1

• compressed at a constant strain rate

(104 s1)

• tests stopped at total strains of 2%,

4%, 11%, 20%

• 548 K (Tg = 586 K)

• after the tests a heat treatment of 4 h

at 548 K was used to measure the

anelastic strain recovery.

A Concustell, S Godard-Desmarest,

MA Carpenter, N Nishiyama & AL Greer

Induced elastic anisotropy in a bulk metallic glass

Scripta Mater. 64 (2011) 1091-1094.

creep under

compression at

548 K

then RUS under

zero stress at

room temp.

Fracture energy as a function of Poisson’s ratio for several metallic

glasses (and states of relaxation). The critical value distinguishing

plasticity and brittleness is ncrit = 0.31-0.32.



anisotropy

range



highest known

product of y

and Kc

anisotropy?

Effects of shot-peening on BMGs

• introduction of shear bands

(softening)

• surface compressive stress

• obtain material that is generally

deformed (without distinct

shear bands)

Residual stresses give improved plasticity in bending —

Y Zhang, WH Wang, AL Greer: Nature Mater. 5 (2006) 857.

Residual stresses give improved plasticity in compression —



brittle —

— but metallic glasses can

show considerable plasticity:


brittle —

— but metallic glasses can

show considerable plasticity:

— can deformation processing be used (as for conventional alloys)

to obtain new structures and properties?

Shear bands in a thin plate of

Pd77.5Cu6Si16.5 glass.

H. Kimura, PhD Thesis (1978) Tohoku Univ.

At room temperature, the flow

is localized in very thin shear

bands —

— so the material that is

affected by the deformation is

a very small volume fraction

of the sample

Ce70Al10Cu20 — Tg = 338 K, Tx = 390 K

B Zhang, DQ Zhao, MX Pan, WH Wang, AL Greer:

“Amorphous metallic plastic”, Phys. Rev. Lett. 94 (2005) 205502.

At elevated temperature,

above Tg, plastic flow is

homogeneous.

But the structural effects

of the flow are mostly

annealed out (structural

relaxation)

Structure and property changes at shear bands

Preferential etching of a

polished surface:

CA Pampillo, HS Chen, Mater. Sci. Eng. 13 (1974) 181-188.

Effects of cold-rolling on BMGs

Extensive results show that cold-rolling increases the plasticity of

metallic glasses. It can lead to softening or hardening.

It always leads to greater inhomogeneity in properties:

Cu47.5Zr47.5Al5 BMG

(a) as-cast

(b) cold-rolled to

thickness

reduction of 2.9%.

KK Song, S Pauly, Y Zhang, S Scudino, P Gargarella, KB Surreddi, U

Kühn, J Eckert, Intermetallics 19 (2011) 1394-1398.

microhardness maps

The peened layer

is ~ 80 m thick

and shows work-

softening


Cold-working: Swaging of Pd77.5Cu6Si16.5 rod

Original rod, 2 mm diameter

Have prepared 2 types of

sample:

• swaged at room temp.

to 15% reduction in area (RA)

• swaged at liq. nitrogen temp.

to 31% RA

(C33－C11)/C33 (C13－C12)/C13 (C66－C44)/C66

Crept sample (εinel = 2%) －3.68% －2.42% 0.60%

Crept sample (εinel = 4%) －3.40% －2.14% －0.03%

Crept sample (εinel = 11%) －0.50% 0.00% 0.08%

Crept sample (εinel = 20%) 2.83% 2.16% -1.47%

LT-swaged sample (S3) 14.10% 8.96% -2.44%

Swaging treatments

― as well as creep, can induce elastic anisotropy

in BMG samples:

Pd77.5Cu6Si16.5

creep data from Concustell et al., Scripta Mater. (2011)

3

2 1

Yonghao Sun, Cambridge (unpublished)

Elastostatic Loading

Lee et al. (2008):

— uniaxial compression can induce structural rejuvenation

• 1.5-mm-diameter rods of Ni62Nb38 metallic glass

• compressed at 0.95 y for 30 hours at room temperature

• creep

• decrease in density (from electron diffraction and calorimetry)

• increase in compressive plasticity (from zero to 5.2% after loading)

SC Lee, CM Lee, JW Yang, JC Lee, Scripta Mater. 58 (2008) 591-594.

KW Park, CM Lee, M Wakeda, Y Shibutani, ML Falk, JC Lee, Acta Mater. 56

(2008) 5440-5454.

HB Ke, P Wen, HL Peng, WH Wang & AL

Greer:

Homogeneous deformation of metallic glass

at room temperature reveals large dilatation”

Scripta Mater. 64 (2011) 966-969.

Zr46.75Ti8.25Cu7.5Ni10Be27.5 BMG

loaded at 80% of y at room temp.

direct measurement of density

decrease

the deformation leads to a volume

increase of roughly 100% at each

active STZ

consistent with rejuvenation

HB Ke, P Wen, HL Peng, WH Wang & AL

Greer:

Homogeneous deformation of metallic glass

at room temperature reveals large dilatation”

Scripta Mater. 64 (2011) 966-969.

Zr46.75Ti8.25Cu7.5Ni10Be27.5 BMG

loaded at 80% of y at room temp.

direct measurement of density

decrease

the deformation leads to a volume

increase of roughly 100% at each

active STZ

the bulk modulus decreases by more

than the shear modulus: /B

increases!

consistent with rejuvenation

Property changes after loading for 50 h

Plastic strain 0.023% (compressive)

Density −0.26%

Bulk modulus, B −0.7%

Shear modulus, −0.55%

Young modulus, E −0.55%

/B +0.15%

— quite large changes in properties given

that the strain is so small

— structural changes are well preserved in

this quasistatic RT treatment, not reduced by

self-annealing.

In internal equilibrium:

supercooled

liquid

thermal

treatments

• exploring states that can be related to the liquid

• intrinsically isotropic

Annealing

— relaxation

— free volume decrease

— /B increase

— embrittlement

Cold-work

— rejuvenation

— free volume increase

— /B decrease

— plasticity (expect improvement)

cold-work

• are annealing and cold-work simply opposite in their effects?

• are we just exploring states that can be related to the liquid?

• or, does mechanical treatment give access to states that could

never be attained by thermal treatments?

structural relaxation

on annealing

Annealing

— relaxation


— /B increase

— embrittlement

Cold-work

— rejuvenation


— /B decrease


Elastic loading

— monotonic seems analogous to

cold-work

— cyclic can be analogous to

annealing

Annealing

— relaxation


— /B increase

— embrittlement

Cold-work

— rejuvenation


— /B decrease


Elastic loading

— monotonic seems analogous to

cold-work

— cyclic can be analogous to

annealing

In all cases

Need to be concerned with both:

— average property change

— anisotropy



Fracture toughness and elastic limit for metals, alloys, ceramic,

glasses, polymers and metallic glasses. The contours show the

process-zone size d in mm.

T Fukushige & S Hata, J. Microelectro. Syst. (2005) 14, 243

MEMS Applications

A conical spring microactuator

with a long stroke of 200 m

normal to the substrate. The

spring is a 7.6 m thick film of

Pd76Cu7Si17 metallic glass.

J.H. Tregilgas, “Amorphous titanium

aluminide hinge”

Adv. Mater. Proc. 162 (Oct. 2004) 40.

MEMS Applications of Metallic Glasses

The Texas Instruments Digital

Light Processor (DLP) data

projector technology is based on

mirrors supported by amorphous

Ti-Al hinges. DLP devices with

>1.3 x 106 addressable mirrors

are in production, and the hinges

still show no fatigue failures after

1012 cycles.

Conclusions

Metallic glasses are non-crystalline, yet highly ordered.

Their high elastic limit and structural uniformity are very attractive for a

variety of applications, especially in small components.

Work softening and the associated shear-banding are the biggest

obstacles to a wider range of structural applications.

The conditions in operating shear bands are extreme, and much remains

to be understood.

A basis has been established for design of glasses with high toughness

— a low /B (or high Poisson ratio n) favours plasticity over brittleness.

Remarkably, a monolithic BMG shows the highest value of yKc

― damage tolerance higher than any other known material.

Anisotropy may be exploited to improve the mechanical properties.

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