j m a t e r r e s t e c h n o l . 2 0 1 5;4(1):100–107

www.jmrt .com.br

Available online at www.sciencedirect.com

Review Article

Creep in amorphous metals�

Michael E. Kassner ∗, Kamia Smith, Veronica Eliasson

Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, United States

a r t i c l e i n f o

Article history:

Received 28 March 2014

Accepted 5 November 2014

Available online 2 January 2015

Keywords:

Bulk metallic glasses

a b s t r a c t

This paper reviews the work on creep behavior of amorphous metals. There have been, over

the past several years, a few reviews of the mechanical behavior of amorphous metals. Of

these, the review of the creep properties of amorphous metals by Schuh et al. though oldest

of the three, is particularly noteworthy and the reader is referred to this article published

in 2007. The current review of creep of amorphous metals particularly focuses on those

works since that review and places the work prior to 2007 in a different context where new

developments warrant.

Amorphous alloys

Creep

Time-dependent plasticity

© 2014 Brazilian Metallurgical, Materials and Mining Association. Published by Elsevier

Editora Ltda. All rights reserved.

Michael E. Kassner graduated with aBachelor in Science-Engineering fromNorthwestern University in 1972, and anMS and PhD in Materials Science and Engi-neering from Stanford University in 1979and 1981. Kassner accepted a position atLawrence Livermore National Laboratoryin 1981 and was employed there until 1990where he was Head of the Physical Metal-lurgy and Welding Section. He accepted afaculty position in the Mechanical Engi-

neering Department at Oregon State University in 1990 wherehe was Northwest Aluminum Professor of Mechanical Engi-

neering. He received the College of Engineering OutstandingSustained Research Award in 1995. He moved in 2003 to accepta position as Chairman, Mechanical and Aerospace Engineer-ing Department at the University of Southern California (USC).

� Paper presented in the form of an abstract as part of the proceedinJuly 21st to 25th 2014.

∗ Corresponding author.http://dx.doi.org/10.1016/j.jmrt.2014.11.0032238-7854/© 2014 Brazilian Metallurgical, Materials and Mining Associa

He is also a Professor of Materials Science at USC. He iscurrently Choong Hoon Cho Chair and Professor. He is cur-rently active in pursuing research at USC on creep, fracture,fatigue and thermodynamics. Most recently, he was assignedto Washington, DC, as the Director of Research at the Officeof Naval Research (ONR). He assumed the position in Octo-ber 2009 until October 2012. He was responsible for overseeingthe nearly one billion-dollar basic-research budget for the USNavy. He was awarded the Navy’s Meritorious Public ServiceMedal for his tenure at ONR. He has published three books,one on the fundamentals of creep plasticity in metals, hotdeformation of aluminum and aluminum alloys and anotheron phase diagrams and has authored or co-authored over 220

gs of the Pan American Materials Conference, São Paulo, Brazil,

published articles. He is a Fellow of American Society of Metals(ASM), a Fellow of the American Society of Mechanical Engi-neers (ASME) and a Fellow of the American Association for theAdvancement of Science (AAAS).

tion. Published by Elsevier Editora Ltda. All rights reserved.

o l . 2 0 1 5;4(1):100–107 101

udplimt

i

1

AirmatacaOpasptbtTsp

tstipi

1

00 1

Time

Amorphous

Crystalline

Tem

pera

ture

T`

Tg

Fig. 1 – A time–temperature-transformation diagram thatillustrates the important temperature regions of BMGs from

j m a t e r r e s t e c h n

Kamia Smith graduated from WheatonCollege in Norton, Massachusetts in 2011with a Bachelor of Arts degree in Chem-istry. Smith then pursued graduate levelstudies at the University of SouthernCalifornia. She completed her Masters ofScience in Materials Science and Engi-neering in 2013 and is now currentlypursuing her PhD in the same field. Herresearch, under Dr. Michael Kassner, stud-ies the mechanical behaviors of materials

nder various stress conditions. During her first year as aoctorate student, Smith accepted a fellowship position in arogram called Body Engineering Los Angeles GK-12. As a fel-

ow, she worked in a Downtown Los Angeles middle schooln which she taught her research to students in order to spark

ore engineering interest in younger generations. Smith lookso complete her studies by 2016.

Veronica Eliasson is an Assistant Pro-fessor at the Aerospace and MechanicalEngineering Department at University ofSouthern California. She graduated with aPhD in Mechanics from the Royal Instituteof Technology, Sweden, in 2007 and thenheld a postdoctoral appointment until2009 at the Graduate Aerospace Labora-tories, California Institute of Technology.Her research interests are in the area ofexperimental mechanics with particular

nterest in high-speed visualization techniques.

. Introduction

morphous metals are a relatively new class of alloy, orig-nating in about 1960 with the discovery of thin metallicibbons by splat cooling [1]. These are always alloys, and pure

etal glasses have not yet been produced. As these alloysre non-crystalline, they have no dislocations, at least inhe sense normally described in crystalline materials. Thus,morphous metals have yield stresses that are higher thanrystalline alloys. High fracture stress, low elastic moduli,nd sometimes-favorable fracture toughnesses are observed.ften, favorable corrosion properties were observed, as well,artly due to an absence of grain boundaries. Towards 1990,lloys with deep eutectics were developed that allowed liquidtructures to be retained in thicker sections in the amor-hous state on cooling to ambient temperature [2–13]. Withhis development, there has been fairly intensive study ofulk metallic glasses (BMG) for possible structural applica-ions. Most of the alloys in this chapter are relevant to BMGs.able 1 lists some of the short-term mechanical properties ofome BMGs taken from [14–34] and some of the impressiveroperties are listed.

Fig. 1, based on an illustration by [35], is a time–emperature-transformation (T–T-T) diagram that illustratesome of the important temperatures for metallic glasses. First,

here is the equilibrium liquid to solid transition at the melt-ng temperature Tm where, of course, multiple solid crystallinehases form on cooling. Below this temperature a T–T-T curve

s illustrated. Cooling below Tm must be sufficiently rapid to

Ref. [36].

avoid intersecting the “nose” of the curve. Also illustrated isthe glass transition temperature, Tg.

This is generally assigned to that temperature where thereis discontinuity in the change of a property (e.g. heat capac-ity, thermal expansion coefficient, etc.) with temperature. Theregion between Tm and Tg is generally referred to as the super-cooled liquid regime. Some values for various BMGs are listedin Table 2 [36–47].

The discussions in this chapter will be largely confined totemperatures above 0.7 Tg. As will be discussed subsequently,this is the regime in which homogeneous deformation isobserved. This review refers to this regime as a “creep regime”of amorphous metals. A practical importance of this regimeis that this is where forming of a metallic glass is fre-quently performed. This regime is contrasted by the regimeof lower temperatures where heterogeneous deformation orshear banding is often (but not always) observed.

2. Mechanisms of deformation

2.1. Overview

The suggested deformation mechanism has generally falleninto three categories: (a) Dislocation-like defects [48–50], (b)diffusion-type deformation [51], and (c) shear transformationzones (STZs) [52,53]. These are illustrated in Fig. 2, and are allearly explanations for plasticity, but it appears that the amor-phous metals community has generally embraced the third,STZ [12,13,54].

The essence of this latter mechanism is that there is a so-called “free volume” in amorphous metals. Free volume is a“concept” and it has no absolute definition. The starting stateis the baseline; only the difference has meaning, so a change indensity after deformation defines the free volume. The exactform and shape of these free volumes is not known. Increasingfree volume would be associated with decreased density. Esti-

mates for free volume for Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vitreloy1) is about 3% [54]. Free volume decreases (tighter packing)appear to increase ductility in homogeneous deformation

102 j m a t e r r e s t e c h n o l . 2 0 1 5;4(1):100–107

Table 1 – Mechanical properties of some glassy alloys from Ref. [13].

Material E (GPa) �y (MPa) �f (MPa) εy (%) εp (%) References

Co43Fe20Ta5.5B31.5 268 5185 2 [14]Cu60Hf25Ti15 124 2024 2088 1.6 [15](Cu60Hf25Ti15)96Nb4 130 2405 2.8 [16]Cu47Ti33Zr11Ni6Sn2Si1 1930 2250 [17]Cu50Zr50 84 1272 1794 1.7 6.2 [18]Cu64Zr36 92.3 2000 2.2 [19](Fe0.9Co0.1)64.5Mo14C15B6Er0.5 192 3700 4100 0.55 [20]Fe71Nb6B23 4850 1.6 [21]Fe72Si4B20Nb4 200 4200 2.1 1.9 [22]Fe74Mo6P10C7.5B2.5 3330 3400 2.2 [23][(Fe0.6Co0.4)0.75B0.2Si0.05]96Nb4 210 4100 4250 2 2.25 [24]Fe49Cr15Mo14C15B6Er1 220 3750 4140 0.25 [25]Gd60Co15Al25 70 1380 1.97 [26]Ni61Zr22Nb7Al4Ta6 3080 5 [27]Pd77.5Cu6Si16.5 1476 1600 11.4 [28]Pd79Cu6Si10P5 82 1475 1575 3.5 [29]Pt57.5Cu14.7Ni5.3P22.5 1400 1470 2 20 [30]Ti41.5Zr2.5Hf5Cu42.5Ni7.5Si1 95 2040 0 [31]Zr55Cu20Al20Ni5 1410 1420 [32]Zr41.25Ti13.75Cu12.5Ni10Be22.5 96 1900 1900 2 [33]Zr57Nb5Al10Cu15.4Ni12.6 86.7 1800 1800 2 [34]

Note: E, Young’s modulus; �y, yield strength; �f, fracture stress; εy, elongation at yielding; εp, plastic elongation. All the tests were conductedunder compression, generally, at strain-rates from (1–5) × 10−4 s−1.

Table 2 – Deformation data of some BMGs in the super-cooled liquid region from Ref. [78].

Alloys (in at%) Tg (K) Tx (K) m value Ductilitya References

La55Al25Ni20 480 520 1.0 1800 (T) [36]Zr65Al10Ni10Cu15 652 757 0.8–1.0 340 (T) [37]Zr52.5Al10Ti5Cu17.9Ni14.6 358 456 0.45–0.55 650 (T) [38]Zr55Cu30Al10Ni5 683 763 0.5–1.0 N/A (C) [39]La60Al20Ni10Co5Cu5 451 523 1.0 N/A [40]Pd40Ni40P20 589 670 0.5–1.0 0.94 (C) [41]Zr65Al10Ni10Cu15 652 757 0.83 750 (T) [42]Zr55Al10Cu30Ni5 670 768 0.5–0.9 800 (T) [43]Ti45Zr24Ni7Cu8Be16 601 648 N/A 1.0 (T) [44]Cu60Zr20Hf10Ti10 721 766 0.3–0.61 0.78 (C) [45]Zr52.5Al10Cu22Ti2.5Ni13 659 761 0.5–1.0 >1.0 (C) [46]Zr41.25Ti13.75Ni10Cu12.5Be22.5 614 698 0.4–1.0 1624 (T) [47]

a

Table 3 – Activation energies for creep of selectedmetallic glasses ([6,52,56,59]).

Composition Tg (K) Ttest (K) �Q (kJ/mol)

Al20Cu25Zr55 740 573 230.12Cu40Zr60 677 543 218.82Cu56Zr44 727 573 217.57Cu60Zr40 750 573 228.45Pd80Si20 673 546 191.63Zr55Cu30Al10Ni5 410

“T” and “C” stand for tension and compression, respectively.

at ambient temperature [55]. With an applied stress, groupsof atoms (e.g. few to 100 [2,54,56]), under an applied shearstress, �, move and perform work. This constitutes an STZ.Argon et al. [51,52] considered that the STZ operation takesplace within the elastic confinement of a surrounding glassmatrix, and the shear distortion leads to stress and strainredistribution around the STZ region [2,51,52]. When the STZsexist throughout the alloy we have homogeneous deforma-tion. STZs also occur in shear bands leading to heterogeneousdeformation. STZs have been observed to create free volumeduring homogeneous deformation [57,58]. Steady-state flowwithin the homogeneous regime can be considered a case

where there is a balance between free volume creation andannihilation [77].

Fig. 2b illustrates the STZ mechanism. Argon et al.described the activation energy for this process and Schuh

Au49Ag5.5Pd2.3Cu26.9Si16.3 103Zr44Ti11Cu10Ni10Be25 625/632 366

et al. estimated the predicted activation energy, Q, as100–500 kJ/mol. Table 3 [52,56,59,60] lists some of the exper-imentally observed activation energies which are consistentwith Argon’s predictions.

j m a t e r r e s t e c h n o l . 2 0 1 5;4(1):100–107 103

Burgers vector Burgers vector

Dislocation line

τ τ

a

b c

Fig. 2 – (a) Two-dimensional representation of a dislocation line in crystalline (left) and amorphous (right) solids, atomisticdeformation of amorphous metals in the form of (b). Shear transformation zones (STZ), and (c). Local atomic jump.Figure adapted from [12].

rf

�

wdivb

N

�

s

�

ri(s

iisapp

The equations that have been used to describe the creep-ate based on STZ have used the classic rate equationormalism leading to [2]:

˙ = �o�o�o · exp(

− Q

kT

)sinh

(�V

kT

), (1)

here ˛о is a constant that includes the fraction of materialeforming by activation, �о is an attempt frequency, and �о

s the characteristic strain of an STZ, and V is the activationolume. The hyperbolic sine function arises, as there can beoth a forward and reverse “reaction”.

At low stresses (� � kT/V), this equation reduces to theewtonian:

˙ = �o�o�oV

kT· exp

(− Q

kT

)�, (2)

ince “reverse” deformation is irrelevant.Conversely, at stresses, � � kt/V,

˙ = 12

�o�o�o · exp(

−Q − �V

kT

), (3)

Schuh et al. [2] point out that Eq. (1) suggests a Newtonianegion followed by, with increasing stress, continual increasen stress exponent. Examples of BMGs that have evinced Eqs.1)–(3) behaviors are illustrated in Figs. 3 and 4, which plot theteady-state creep behavior of several BMGs [2,36].

The figures on steady-state behavior illustrate that withncreasing strain-rate and/or decreasing temperature theres a breakdown in Newtonian behavior and the apparent

tress-exponent increases. Generally, this has been regardeds a natural consequence of Eq. (2), the rate equation thatredicts Newtonian behavior at low stresses (higher tem-erature and lower strain-rates) but increased exponents

with higher stresses (low temperatures and higher strain-rates). This explanation does not appear to be unanimouslyembraced [36]. For some, an important question is whether thenon-Newtonian homogeneous deformation region is actuallya reflection of nano-crystallization.

These equations suggest that free volume is largely respon-sible for plastic flow; larger free volumes would appear to moreeasily lead to regions of plastic flow. Schuh et al. point out thatatomic simulations have suggested that other variables suchas short-range chemical ordering can affect plasticity as well,which is not explicitly included in the above equations [61–64].The pressure sensitivity of these equations was addressed bySun et al. [65].

Nieh and Wadsworth [36] found that nano-crystallizationoccurred in Zr10Al5Ti19.9Cu14.6Ni BMG coincident with thedeviation from Newtonian behavior. Nieh rationalized thenano-crystalline precipitates as akin to dispersion strengthen-ing. Suryanarayana and Inoue [66] appear to suggest that thestress exponent increases due to second phase strengthen-ing of the nanoparticles by a straightforward rule of mixturesfor the flow strength. Schuh et al. [2] referenced the Nieh andWadsworth work and certainly acknowledged the observationthat deformation can induce crystallization (as have others[66–69]) but appear to favor the rate equation as an expla-nation for the deviation from Newtonian behavior at higherstresses. Wang et al. [70] found only non-linear creep behaviorin Vitreloy 1 if some crystallization occurred. Whereas Newto-nian conditions led to elongations in La55Al25Ni20 in excessof 20,000% [36], those at higher rates with non-Newtonianbehavior exhibited dramatically reduced values. Many authors

[2,12,13] proposed metallic glass deformation maps, similarto the construct by Ashby and Frost for crystalline mate-rials. A metallic glass deformation–map is illustrated inFig. 5.

104 j m a t e r r e s t e c h n o l . 2 0 1 5;4(1):100–107

5000

500

50

51.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00

Strain-Rate (s-1 )

Str

ess

(MP

a)

Zr41.2Ti13.8Cu12.5Ni10Be22.5

683 K663 K

643 K

623 K

613 K

603 K

593 K

573 K

Fig. 3 – Steady-state homogeneous flow data for Zr41.2Ti13.8Cu12.5Ni10Be22.5 metallic glass at elevated temperatures, fromthe work of Lu et al. [53].Figure based on [2].

1000

100

100.0001 0.001 0.01

Strain-Rate (s-1 )

Str

ess

(MP

a)

Zr10AI5Ti 17.9Cu 14.9Ni

T = 683 K

m = 1

Fig. 4 – Stress–strain rate curve for a Zr10Al5Ti17.9Cu14.6Niglassy alloy shows Newtonian flow at low strain rates butnon-Newtonian at high strain rates (data from Ref. [37]).

Figure based on [36].

Newtonian deformation appears to reflect a fully amor-phous alloy, but at least in other regions, including hetero-geneous deformation, nano-crystallization may be occurring[66–69].

Furthermore, as will be discussed in a subsequent section,homogeneous deformation may extend to low temperature,in at least some cases.

2.2. Homogeneous flow at very low temperatures

Recent work [57,71–73] shows that, given sufficient time,homogeneous deformation can be detected under “electro-static” (i.e. at a stress less than the yield stress, �y) loading atroom temperature (RT). The stress exponent was not assessed,

so it was unclear whether Newtonian flow was observed.Alloys include Zr46.75Ti8.25Cu7.5Ni10Be27.5, Ni62Nb38, Cu50 Zr50,Cu57 Zr43 and Cu65 Zr35. Of course, some BMGs, such asZn20Cu20Tb20(Li0.55Mg0.45)20, may have low Tg (323 K) allow-ing homogeneous deformation at RT [74]. Alloys with higherpacking densities exhibit greater plastic strain during homo-geneous deformation at room temperature, but show lessglobal plasticity during inhomogeneous deformation in a typ-ical compression test [55]. Park et al. [57] suggest deformationinduced structural disordering by molecular dynamic simu-lations, although others [73] imply STZ as the mechanism.Compression tests on Pd77Si23 with cylindrical samples ofdiameters 8 �m and 140 nm showed that as the sample sizedecreased to the submicron range, homogeneous deformationoccurs and was suggested to occur due to the necessity of acritical size volume for shear bands [75]. Similar results werenoted by others [76].

2.3. Anelasticity

In the above discussion of the so-called “electrostatic” regime,a substantial fraction of the (small) non-elastic strain isanelastic. It should be noted that the STZ model naturally pre-dicts some anelasticity. An isolated STZ, by the Argon model,is elastically constrained during activation. This implies thateven at a low applied stress (where backflow, according toEq. (2), is negligible), there is, nonetheless, a back stress thaton unloading leads to anelastic back flow. It was additionallypointed out by Ke et al. [72] that there is a range of atomic envi-ronments in a glass such that some atoms reside in regions

where the local topology is unstable. In these regions, theresponse to shear stress may include not only atomic dis-placements but also an anelastic reshuffling of the atomicnear-neighbors (i.e. an anelastic STZ operation). Even though

j m a t e r r e s t e c h n o l . 2 0 1 5;4(1):100–107 105

0.1

0.01

0.0010.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

0.3

0.03

T/Tg

Nor

mal

ized

str

ess

(τ/μ

)S

hear stress at 300 K (G

Pa)

ShearLocalization

(Inhomogeneous deformation)

Non-Newtonian

Homogeneousdeformation

Newtonian

Elasticdeformation

Applied pressure:0.01µ (0.4 GPa)

Applied pressure:0µ (0 GPa)

Fig. 5 – Deformation mechanism maps for metallic glass plotted in (a) normalized stress versus normalized temperature.The absolute stress values indicated in the figure are for the Zr41.2Ti13.8Cu12.5Ni10Be22.5 metallic glass.Adapted from [2,12].

ttm[

2fl

SbefbaiboFmis

3

Tsawtin

2000

1800

1600

1400

1200

1000

800

600

400

200

00 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Strain

Str

ess

(MP

a)

0.1 (1/s)0.032 (1/s)

0.005 (1/s)

0.0002 (1/s)

Fig. 6 – Effect of strain rate on the uniaxial stress–strainbehavior of Vitreloy 1 at 643 K and strain rates of 1.0 × 10−1,

he fraction of atoms involved in these events may be small,he local strains are large enough that their cumulative effect

akes a significant contribution to the macroscopic strain72].

.4. Primary and transient creep (non-steady-stateow)

teady-state flow has principally been discussed. So far, it haseen presumed that STZs create free volume (leading to soft-ning) and that recovery processes involve the annihilation ofree volume (leading to hardening). Therefore, steady state haseen regarded as a balance between free volume creation andnnihilations. Other hardening effects such as chemical order-ng have not been explicitly considered for steady state. It haseen suggested that there can be a net free volume increaser decrease during deformation that precedes a steady state.ig. 6 from Lu et al. [53] shows hardening at the onset of defor-ation that continues beyond the eventual steady state. The

nterpretation of this peak stress followed by softening to ateady state is unclear.

. Summary

his review of creep (above 0.7 Tg) in amorphous alloys empha-izes a variety of conclusions. First, the mechanism of creepppears to largely be explained by shear transformation zones

here deformation is homogeneous. The descriptive equa-

ion for STZs suggests a Newtonian region followed by, withncreasing stress, a continual increase in the stress expo-ent. It is not clear, as some suggest, that the non-Newtonian

3.2 × 10−2, 5.0 × 10−3 and 2.0 × 10−4 s−1 [55].

behavior is due to nano-crystallization. Second, homogeneousdeformation at room temperature has recently been observed.Third, a substantial fraction of the small non-elastic strain atroom temperature is anelastic. Fourth, during primary creep,STZs create free volume, leading to softening. Furthermore,recovery processes or annihilation of free volume leads tohardening.

Conflicts of interest

The authors declare no conflicts of interest.

n o l

r

106 j m a t e r r e s t e c h

Acknowledgment

Support by the US Defense Threat Reduction Agency undergrant HDTRA1-11-1-0067 is appreciated.

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