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
R Busch, J Schroers, WH Wang: MRS Bulletin 32 (2007) 620.
STRONG
FRAGILE
HOT COLD
GLASS LIQUID
The fragility of metallic glass-forming liquids
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 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
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.
Metallic glasses for structural applications
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)
Metallic glasses for structural applications
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)
Metallic glasses for structural applications
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)
Metallic glasses for structural applications
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)
Strain →
Str
es
s →
Within the elastic (reversible) regime ―
y
E
area = 2/2E = elastic energy
stored per unit volume
Metallic glasses for structural applications
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.
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)
Metallic glasses for structural applications
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.
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)
Metallic glasses for structural applications
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.
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)
Metallic glasses for structural applications
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.
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)
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)
Resilience and loss coefficient for metallic glasses and for 1507 conventional metals, alloys and metal-matrix composites.
Mechanical damping in metallic glasses
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.
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)
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
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.
JJ Lewandowski, WH Wang & AL Greer, “Intrinsic plasticity or brittleness of
metallic glasses”, Philos. Mag. Lett. 85 (2005) 77.
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
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
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.
typical trade-off
between y and Kc
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.
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.
JJ Lewandowski, WH Wang & AL Greer, “Intrinsic plasticity or brittleness of
metallic glasses”, Philos. Mag. Lett. 85 (2005) 77.
anisotropy
range
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.
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 —
Y Zhang, WH Wang, AL Greer: Nature Mater. 5 (2006) 857.
Conventional glasses are
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
Y Zhang, WH Wang, AL Greer: Nature Mater. 5 (2006) 857.
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.
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
— free volume decrease
— /B increase
— embrittlement
Cold-work
— rejuvenation
— free volume increase
— /B decrease
— plasticity (expect improvement)
Elastic loading
— monotonic seems analogous to
cold-work
— cyclic can be analogous to
annealing
Annealing
— relaxation
— free volume decrease
— /B increase
— embrittlement
Cold-work
— rejuvenation
— free volume increase
— /B decrease
— plasticity (expect improvement)
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
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)
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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