Download Report

Available online at www.sciencedirect.com
Acta Materialia 58 (2010) 2652–2665
www.elsevier.com/locate/actamat
The deformation of Gum Metal through in situ compression
of nanopillars
E.A. Withey a,*, A.M. Minor a, D.C. Chrzan a, J.W. Morris Jr. a, S. Kuramoto b
a
Department of Materials Science and Engineering, University of California, Berkeley, CA, USA
b
Toyota Central R&D Laboratory, Nagakute, Aichi 480-1192, Japan
Received 24 August 2009; received in revised form 19 December 2009; accepted 29 December 2009
Available online 25 January 2010
Abstract
The name “Gum Metal” has been given to a set of b-Ti alloys that achieve exceptional elastic elongation and, with appropriate preparation, appear to deform by a dislocation-free mechanism triggered by elastic instability at the limit of strength. We have studied the compressive deformation of these materials with in situ nanocompression in a quantitative stage in a transmission electron microscope. The
samples studied are cylindrical nanopillars 80–250 nm in diameter. The deformation pattern is monitored in real time using bright-ﬁeld
microscopy, dark-ﬁeld microscopy or electron diﬀraction. Interesting results include the following: (i) nanopillars approach, and in several
examples appear to reach, ideal strength; (ii) in contrast to conventional crystalline materials, there is no substantial “size eﬀect” in pillar
strength; (iii) the deformation mode is ﬁne-scale with respect to the sample dimension, even in pillars of 100 nm size; (iv) shear bands (“giant
faults”) do form in some tests, but only after yield and plastic deformation; and (v) a martensitic transformation to the base-centered orthorhombic a00 phase is sometimes observed, but is an incidental feature of the deformation rather than a signiﬁcant cause of it.
Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Compression test; Titanium; TEM; Gum Metal
1. Introduction
Several years ago, the Toyota Central R&D Laboratory
announced the development of a class of Ti–Nb–Zr–O alloys
with a most unusual set of mechanical properties [1]. The
alloy composition was adjusted to produce a very low shear
modulus and the alloy was severely worked to cold-form bars
with pronounced h1 1 0i texture. When the cold-worked
material was tested in tension, it deformed elastically until
the stress approached the previously predicted value of the
ideal strength (the stress that causes elastic instability of the
crystal lattice) [1–4]. Following yield, the material underwent
a signiﬁcant plastic deformation with little or no evidence of
dislocation motion. Rather, the deformation seemed to
involve the formation of severely distorted nanodomains [5]
*
Corresponding author. Tel.: +1 5106433547.
E-mail address: [email protected] (E.A. Withey).
and the development of extended shear bands (“giant faults”)
[1]. To our knowledge, this mechanical behavior is unique
among the crystalline materials studied to date.
The possibility that a bulk alloy might resist plastic deformation until elastic instability intrudes (ideal strength) is
exciting from a fundamental perspective, and has generated
research in a number of laboratories. Theoretical work that
demonstrated the possibility of attaining ideal strength in a
Ti–V (or Ti–Nb) alloy adjusted to have a small shear modulus and densely decorated with dislocation pinning points [6]
seemed to support the idea that Gum Metal can reach “ideal
strength”. Further support came from experimental studies
of deformation in and around nanoindentation pits [7] that
showed the absence of ordinary dislocation plasticity within
the pit and nanoscale pinning of the dislocations that did
form in the pit peripheries.
However, other research questioned both the “ideal
strength” of Gum Metal and its apparently anomalous
deformation mechanism. Particularly probative issues were
1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.actamat.2009.12.052
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
raised by Talling et al. [8], who measured the elastic constants of an example of the alloy and found values that
placed the alloy yield strength at no more than one-half
the ideal value. This yield strength level is very high, but
is low enough that non-ideal yield mechanisms are suspected. Moreover, they showed that atleast some examples
of Gum Metal undergo a deformation-induced transformation during tensile tests, introducing the a00 martensitic
phase that is found in a number of b-Ti alloys. This result
suggests that the strength-limiting mechanism in Gum
Metal may be a conventional transformation-induced plasticity rather than elastic instability. Other investigators
have found evidence of the x phase in chemically thinned
transmission electron microscopy (TEM) specimens [9].
More recently, Takesue et al. [10] measured the elastic
moduli and reinvestigated the transformation behavior of
Gum Metal by growing and testing single crystals. On the
basis of their measured elastic constants, the ideal shear
strength of Gum Metal [3] should be sm 0.11Gh111i 1.7–
2.0 GPa, which is about twice the value measured at yield in
bulk samples of the severely cold-worked material. Concerning the deformation-induced transformation to the a00 phase,
they found that its occurrence was very sensitive to crystal orientation. Crystals that were pulled in tension in a h1 1 0i direction transformed extensively and reversibly prior to general
yield, while crystals pulled along the h1 0 0i or h1 1 1i directions did not.
While the work by Takesue et al. was underway,
researchers in this laboratory were conducting compression
tests of nanopillars of Gum Metal in situ [11] using an
instrumented transmission electron microscope indentation
stage (Hysitron PicoIndenterÒ) [12]. This instrument permits the compression of pillars with diameters as small as
80–100 nm while continuously monitoring the evolution
of the pillar structure in bright-ﬁeld, dark-ﬁeld or diﬀraction modes. The sample geometry and instrument allow
us to combine the microcompression test methodology that
has proven useful to study the mechanics of small samples
[13,14] with the ability of in situ nanoindentation in TEM
to observed nanomechanical mechanisms in real time
2653
[15,16]. Preliminary results of these tests have been published [11]. While these tests are ongoing, we now have a
suﬃcient body of data and analysis to comment, in some
detail, on the questions of the alloy strength, the deformation mode and the role of deformation-induced phase
transformations, atleast under compressive load. The present paper reports these results.
The issues that are speciﬁcally addressed below include the
following: (i) strength: whether the strength of the alloy
approaches the ideal, whether it shows conventional size
eﬀects, and how sensitive it is to prior processing; (ii) deformation mode: whether the compressive deformation mode
involves conventional dislocation plasticity, and to what
extent it involves or is governed by shear band formation
and nanodomain reconﬁgurations; and (iii) transformations:
what deformation-induced transformations occur during
nanocompression and their role in strength and deformation.
2. Experimental
Gum Metal with a composition of Ti–35.9Nb–2Ta–
2.7Zr–0.3O (wt.%) (Ti–23Nb–0.7Ta–2Zr–1.2O (at.%)) was
obtained from Toyota Central R&D Laboratories, Nagoya,
Japan in the form of two rods of 4 mm diameter, one solution-treated and the other 90% cold-swaged, and one rod of
7 mm diameter that had been 21% cold-swaged. Each rod
had been processed from elemental powders and prepared
according to the procedure described in Ref. [17].
Sections with 500 lm thickness were cut from each rod.
These sections were mechanically thinned to 20 lm and
attached to a metal substrate machined to ﬁt in a Hysitron
PicoIndenterÒ ﬁtted with a ﬂat-punch tip. They were then
machined in a FEI 235 dual focused ion beam (FIB) using
an annular pattern and a low current (10 pA) to produce
cylindrical pillars 100–200 nm in diameter. Each pillar
had a side-wall taper of 2–5°, deﬁned by the angle of the
side-wall with respect to the axis of the pillar, and a length
of up to 1 lm. The ﬁnal pillar structure after the FIB is
shown in Fig. 1. Note that the pillars have several steps,
rings and ridges, moving from the tip to the base. The plas-
Fig. 1. Scanning electron microscope images of (a) several pillars in a set and (b) a single pillar before compression after FIB fabrication.
2654
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
tic deformation studied here is conﬁned to the near-tip
region, above these geometrical features.
The metal substrate with the attached Gum Metal pillars was placed in a PicoIndenterÒ stage in a JEOL 3010
transmission electron microscope located in the National
Center for Electron Microscopy at the Lawrence Berkeley
National Laboratory. The PicoIndenterÒ is described in
some detail in Ref. [12]. It was equipped with a borondoped diamond ﬂat-punch tip with an area much larger
than the contact areas of the pillars. The nominal load
and displacement resolutions of the PicoIndenter were
0.1 lN and 0.5 nm, respectively.
The in situ compression tests reported here were done in
one of three diﬀerent modes. The ﬁrst (bright-ﬁeld) mode
provides a real-time bright-ﬁeld record of the compression
test. With the pillar oriented in a two-beam condition, the
changes in pillar shape and the movement of visible defects
within it can be observed, and are recorded as they occur.
In the second (dark-ﬁeld) mode, the same conditions are
used to record the evolution of a dark-ﬁeld view of the pillar utilizing a selected diﬀraction spot. In this mode
changes in crystallographically distinct domains, or other
coherent features, can be followed during the test, but with
less ability to see the overall shape change of the pillar. In
the third (diﬀraction) mode, the diﬀraction pattern of the
pillar is recorded in real time during the compression. In
order to gain useful information from this method, the pillar must be oriented on a low-index zone axis. This can be
diﬃcult, since the PicoIndenter has only single-tilt capability. To perform a compression test in diﬀraction mode, a
selected-area-aperture is placed over the pillar, just below
the lowest point that the ﬂat-punch will reach along the pillar axis. The diﬀraction pattern is then displayed and
recorded frame-by-frame during compression.
In each of these modes the load–displacement data are
measured and plotted in real time. Since the frame-rate
of the recorded video is known, the load and displacement
associated with each frame can be identiﬁed, and the point
to which a particular frame pertains can be located along
the load–displacement curve.
Before each test, diﬀraction patterns were taken from
several locations on the pillars to characterize the initial
microstructure and orientation. The tests were then performed under displacement control at an eﬀective strain
rate on the order of 102 s1 in bright-ﬁeld, dark-ﬁeld or
diﬀraction modes, as described. The compressions were
recorded in real time at 30 frames s1 by a camera within
the microscope. Load–displacement data were measured
continuously throughout each test by a feedback loop in
the indentation stage, and matched frame-by-frame with
the digital movie of the test.
The yield strength of the pillar was measured from the
load associated with the ﬁrst signiﬁcant change in the slope
of the load–displacement curve. Since there is some “noise”
in the elastic portion of the loading curve, the identiﬁcation
of this point does require some judgement on the part of the
experimenter. As we shall see, however, yielding is usually
well-deﬁned, and the load–deﬂection curves are preserved
if there is need for further review. In the current work, stress
was measured as the “engineering stress” at the tip, the load
per unit area on the tip of the pillar, determined from its
diameter pre-compression. Since the tip of the pillar is the
narrowest region of the pillar, due to the side-wall taper,
the stress reported is the highest stress applied to the pillar.
There is, of course, the possibility that the side-wall taper
may aﬀect the measured yield strength [18,19]. As we shall
show below, there does not appear to be any signiﬁcant eﬀect
over the range of taper angles in these specimens.
As the pillars deform during the course of the test, the
combination of pillar taper and “mushrooming” at the pillar tip has the consequence that the engineering stress is an
increasingly inaccurate measure of the true stress on the
sample. It is not yet clear how this inaccuracy can be
removed. However, our primary interest here is in the yield
strength, which is reasonably represented by the engineering stress at the tip, and also in the signiﬁcant load excursions that sometimes occur in subsequent plastic
deformation, which are atleast qualitatively apparent from
the behavior of the engineering stress.
In all of the cases that we shall discuss here, the pillar tips
were cut from a single grain, so, atleast initially, the tips
deform as single crystals. It follows that their strengths
should be determined by the critical resolved shear stress
on some favored slip system. We therefore computed the critical resolved shear stress for slip (sc) by multiplying the nominal compressive stress at yield by the maximum Schmid
factor for {1 1 0}h1 1 1i, {1 1 2}h1 1 1i, or {1 2 3}h1 1 1i slip
in the crystallographic orientation of the pillar. These are the
slip systems that provide the minimum values of the ideal
shear strength of a body-centered cubic (bcc) crystal.
3. Results
3.1. Strength
The compressive yield and critical resolved shear strengths
of the pillars are plotted in Fig. 2a and b, respectively, as a
function of initial pillar diameter. Each point on the plots in
Fig. 2a and b refers to a single compression test. The symbol
type used indicates the sample processing – solution-treated
(ST) (circles), 21% cold-swaged (21CW) (diamonds), or 90%
cold-swaged (90CW) (squares). Some points have numbers
attached to them. Each of these numbers refers to the ﬁgure
in the following text that contains the load–deﬂection curve
and other pertinent data from that particular test. Several
of the pillars were compressed more than once. Fig. 2c plots
the yield strengths of these pillars as a function of the measured taper angle of the pillar. Fig. 2d plots the yield strength
as a function of the compression number.
There are several signiﬁcant features of the strength data.
First, the pillars have strengths that closely approach the
ideal value, sm 1.8 GPa. As shown in Fig. 2b, atleast one
pillar from each processing condition (ST, 21CW, 90CW)
has sc P 1.4 GPa, and one pillar reached sc = 1.7 GPa.
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
2655
Fig. 2. (a) Pillar yield strength and (b) critical resolved shear stress vs. initial pillar diameter for all preparations of Gum Metal. The particular
compression tests that are discussed below are labeled with the number of the ﬁgure in which they ﬁrst appear. (c) The yield strength plotted against taper
angle for all of the pillars tested. (d) The strength vs. number of compression for several pillars, which were compressed multiple times. Each set of circles
or squares represents one solution-treated or cold-worked pillar, respectively.
Fig. 3. The stress–displacement curve of the 90CW sample labeled “3” in Fig. 2 with bright-ﬁeld images labeled to correspond with the labeled points on
the curve.
2656
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
The average value of sc for all of the samples tested was
850 MPa, which is roughly half of the ideal strength. Given
the free surfaces, internal defects and minor misalignments
that may induce yielding at values well below sm in these tiny
columns, the observed strengths are very high, and suggest
that atleast the stronger of these pillars do yield at ideal
strength.
Second, the strength is relatively insensitive to pillar
diameter; there is little or no “size eﬀect”. While the strongest pillars are among those with the smallest diameters,
there is no clear trend of strength with size, and certainly
no dramatic increase of the Hall–Petch type (sc d1/2)
such as is found in the compression of micropillars of other
metals [13,14,20,21].
Third, there is no obvious dependence of the strength on
the sample processing. The strengths of pillars with diﬀerent processing are intermixed. This observation contrasts
with the results of tensile tests on polygranular specimens,
which show a signiﬁcant change with sample preparation
[1]. Signiﬁcantly, the pillars tested in these experiments
had diameters much smaller than the typical grain size,
which ranged from 50 to 100 lm for the solution-treated
material to 10 lm after 90% cold work; most of the pillar
tips compressed were crystals from the interiors of single
grains. The insensitivity of their strength to preparation is
strong evidence that the sharp dependence of strength on
the processing of bulk Gum Metal is a polygranular eﬀect.
Fourth, as documented in Fig. 2c, there is no obvious
dependence of the yield strength on the taper angle over
the range of small taper angles sampled. This independence
is, we believe, a consequence of the fact that our pillar tips
are single crystals that yield locally and abruptly. The published models that predict a strong inﬂuence of the taper
angle assume gradual yielding, as in polycrystalline plasticity [18], or yielding by a non-local process that samples a
length of the tapered column [19]. As will become apparent
below, neither assumption applies in our case.
Another unusual feature of the strength data is illustrated in Fig. 2d. The strengths of the pillars decreased with
repeated compression; a second and third compression of
the same pillar produced yield at smaller values of the stress.
This behavior contrasts with that which is often observed in
pillars of conventional metals, such as Ni [12]. The conventional behavior is commonly attributed to “defect exhaustion” [12], as pre-existing dislocations are driven from the
sample by the compression. The present result appears to
show that in Gum Metal the defects that promote plastic
deformation are produced during compression and are
retained in the sample. Lee et al. [22] found similar behavior
in the ex situ compression of larger pillars of single crystal
Au; these samples retained deformation-induced defects,
and the strength decreased with pre-straining.
3.2. Patterns of deformation
We next consider the patterns of deformation in the
compressed pillars, relying on information contained in
the real-time test records, which include tests performed
in bright-ﬁeld, dark-ﬁeld and diﬀraction modes.
3.2.1. High-strength deformation
Of the pillars that exhibited the highest yield strengths,
two were tested in the bright-ﬁeld mode, allowing their
deformation patterns to be followed in real time. The ﬁrst
pillar we shall describe was solution-treated and had a
compressive yield strength of 3.6 GPa. Its data point is designated “3” in Fig. 2a and b. The pillar axis was along a
h4 5 5i direction of the bcc crystal; hence, the critical
resolved shear stress at yield was sc 1.4 GPa. Fig. 3
includes the stress–displacement curve along with several
frames extracted from the real-time digital movie of the
test. Pre- and post-compression images and diﬀraction patterns of the pillar are given in Fig. 4.
The most obvious feature of the deformation pattern is
its relative uniformity. While the plastic deformation is
Fig. 4. (a) Pre- and (b) post-compression bright-ﬁeld images of the
solution-treated pillar compressed in Fig. 3. The top diﬀraction pattern in
(b) corresponds to the deformed tip of the pillar and the bottom to the
base of the pillar.
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
2657
Fig. 5. The stress–displacement curve of the 90CW sample labeled “5” in Fig. 2 with bright-ﬁeld images labeled to correspond with the labeled points on
the curve.
conﬁned to the tip of the pillar, the deformation within the
plastic region is generally homogeneous, with no obvious
shear banding or isolated defects. There is some ﬁne-scale
heterogeneity; the compression appears to generate a series
of diﬀuse, transverse bands across the diameter of the specimen. Reference to the stress–displacement curve shows
that the formation of each band is associated with a step
in the curve that involves a 10–20 nm compressive displacement under a slightly decreasing ﬂow stress. These diﬀuse
bands are visible in the post-compression image (Fig. 4b),
running nearly parallel to the top edge of the pillar. Their
internal structure could not be resolved, and remains
unclear, beyond the observation that they appear mottled
on the nanometer scale.
The initial condition of the pillar includes some ﬁne
defects that are visible in Fig. 4a and are apparently residual
defects from the FIB machining of the pillar. It is probable,
though not entirely clear, that these are dislocations that are
very tightly pinned by microstructural barriers. Nonetheless,
the diﬀraction pattern from the tip region is sharp; it shows
no evidence of signiﬁcant internal strain. The population
of nanodefects increases during the deformation leading to
the mottled appearance of the compressed pillar that is seen
in Fig. 4b. The spots in the diﬀraction pattern of the compressed pillar are broadened, showing that there are crystallographic rotations on the nanoscale. Similar rotations are
observed in the deformed periphery of nanoindentation pits
in Gum Metal which were characterized at higher resolution
in Ref. [5]; these appear to be associated with nanodomains
rather than with linear defects.
To compare samples with diﬀerent processing conditions at high strength, the next pillar we will describe is
the 90CW specimen designated as “5” in Fig. 2a and b.
It had a compressive yield strength of 2.95 GPa with a pillar axis very close to h0 1 1i, hence sc 1.4 GPa. The
stress–deﬂection curve is presented in Fig. 5g along with
bright-ﬁeld images from the selected, labeled points along
the curve in Fig. 5a–f. Pre- and post-compression images
and diﬀraction patterns are shown in Fig. 6.
While the axis of the undeformed pillar was approximately parallel to h0 1 1i, it contained multiple domains
through its diameter and along its length, as shown by
the diﬀraction patterns in Fig. 6a. A small lobe formed
when the sample yielded (Fig. 5c), and increased in size
with further compression. After signiﬁcant deformation
to the point labeled “d” in the ﬁgure, a deﬁnite boundary
had formed from the point where the lobe intersected the
rest of the pillar to the right corner of the pillar tip
(Fig. 5d). As deformation continued from point “d” to
point “e”, the lobe stopped growing and the deformation
shifted to the material beneath it on the pillar. This is evidenced by the development of dark contours below the
lobe in these images. Based on the diﬀraction patterns in
Fig. 6b, the material at the top of the pillar had signiﬁcant
residual stress after deformation, but the material in the
mid-section of the pillar was not signiﬁcantly aﬀected.
While the boundary of the lobe observed in this test is
angled across the pillar, it does not appear to be a shear
band or “giant fault” of the sort observed in Ref. [1] or
in the test described below; rather, it appears to be the
boundary of a region that has deformed internally, as indicated by the spreading of the spots in the diﬀraction pattern taken from the lobed region of the tip after the test
(Fig. 6b, top right).
2658
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
The compression experiments described in Figs. 3 and 5
had several common features. First, the compressive
strengths of the pillars were 75% of the predicted ideal
strength of Gum Metal. Second, the deformation was diffuse on a very ﬁne scale. It did not involve any obvious dislocation slip or form any pronounced shear bands (“giant
faults”). Third, it does not appear that a00 martensite
formed to any signiﬁcant degree in these tests since no a00
diﬀraction spots were detected and no planar features suggesting a00 were seen in the bright-ﬁeld images.
Fig. 6. (a) Pre- and (b) post-compression bright-ﬁeld images of the pillar
compressed in Fig. 5 with corresponding diﬀraction patterns. The top
diﬀraction patterns were taken from the tip and the bottom diﬀraction
patterns were taken from the middle of the pillar.
3.2.2. Shear band formation
While well-developed shear bands did not form in the
highest strength pillars, they were observed in pillars of lower
strength, suggesting that the formation of shear bands might
be a strength-limiting mechanism. To investigate that possibility we examine the deformation of the pillar marked “7” in
Fig. 2a and b. This was a 90CW pillar with a strength of
1.92 GPa and an axis near h1 1 2i, thus sc 0.79 GPa. The
stress–deﬂection curve is presented in Fig. 7g along with
selected bright-ﬁeld micrographs in Fig. 7a–f. Pre- and
post-compression images are given along with diﬀraction
patterns taken along the pillar in Fig 8. The upper and lower
diﬀraction patterns in Fig. 8a were taken from the top and
middle domains, which extend through the diameter of the
pillar in a stacked formation. Each domain was oriented
slightly away from a h1 1 1i zone axis. As is clear from the
micrographs, a well-deﬁned shear band propagated across
the sample at an angle of 45° to the pillar axis.
When this pillar yielded in compression, a dark contour
formed, and a diﬀuse boundary developed between the
deformed and undeformed regions (Fig. 7b). After macro-
Fig. 7. The stress–displacement curve of the 90CW pillar marked “7” in Fig. 2. Bright-ﬁeld images taken at the corresponding points along the curve
showing the formation of and deformation along a well-deﬁned shear band after yield has taken place.
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
Fig. 8. (a) Pre- and (b) post-compression bright-ﬁeld images of the coldworked pillar shown in Fig. 7 along with corresponding diﬀraction
patterns. The upper diﬀraction patterns were taken from the top domain
and the deformed tip of the pillar, respectively. The lower diﬀraction
patterns were taken from the middle domain of the pillar.
2659
scopic yield, local deformation continued in the tip above the
contour and the loading curve evolved in a somewhat jerky
fashion (Fig. 7g). Just prior to point “d” on the stress–deﬂection curve the load dropped quickly and dramatically. The
dark area at the tip of the pillar, above the boundary between
the two initial domains, slid along the diagonal boundary,
creating the shear band that is apparent in Fig. 7d. While
the instability associated with this shear caused a signiﬁcant
drop in strength, the ﬂow stress stabilized and recovered. The
remaining deformation occurred through a series of loaddrops and increased as the tip of the pillar continued to slide
jerkily along the shear band.
While the appearance of a well-deﬁned shear band is
clearly associated with a drop in the strength of this specimen, the shear band did not form until well after plastic
deformation began, and hence was not responsible for
the relatively low strength of the pillar. Both visual observation of the deformation pattern and the diﬀraction patterns of the tip region above the shear band taken after
the test reveal a substantial degree of plastic deformation.
The bright-ﬁeld images in Fig. 7a–c show that this deformation preceded the formation of the band. Moreover,
while the shear across the band increased signiﬁcantly during further deformation, showing that atleast a major part
of the deformation was concentrated in the band, the ﬂow
stress remained relatively constant. Even after a welldeﬁned shear band formed there was strong resistance to
shear displacements on its plane.
This deformation pattern, plastic compression with discrete shear band formation and multiple load-drops, was
observed in several of the pillars. In every case the shear
band formed after general yielding and ﬁne-scale plastic
Fig. 9. The stress–displacement curve of the 90CW pillar marked “9” in Fig. 2. h1 1 0i Dark-ﬁeld images taken at the corresponding points along the curve
show the evolution of domains during the test. The arrow in (d) locates an incipient shear band that never fully developed.
2660
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
deformation at the pillar tip. The shear band did not determine the yield strength in any of the cases studied; shear
banding was a consequence of the deformation rather than
its cause. This result means that, while giant faults may
contribute to plasticity in Gum Metal, they are not ordinarily the initiating cause of it.
The detailed mechanism of shear band formation is not
clear from the research done to date. It is also unclear
which geometric or crystallographic characteristics cause
shear bands to appear in some samples but not in others.
We have noticed a tendency for shear bands to form in
cold-worked specimens that have distinguishable domains
along the axis of the pillar, but do not yet know if this is
a necessary precondition for shear banding in these nanopillars. Well-deﬁned shear bands do appear in the compression of micropillars of larger diameter, which are
presumably polygranular [13].
3.2.3. Domain evolution during compression
Prior work on nanoindentation pits in Gum Metal suggests that nanodomain formation and rotation play a significant role in the deformation of this material [7]. Some
further information on that process was obtained during
the deformation of the pillar marked “9” in Fig. 2a and b.
This was a 90CW pillar with a 145 nm diameter. Its yield
strength was 2.19 GPa and its orientation was near
h2 5 11i, giving sc 1.08 GPa. The sample contained four
distinct domains, two of which were suﬃciently close in orientation to light up in a h1 1 0i dark-ﬁeld image. The evolution of these domains was monitored as the pillar was
compressed in the dark-ﬁeld mode.
The load–deﬂection curve is presented in Fig. 9g along
with frames extracted from the digital movie in Fig. 9a–f.
The pre- and post-compression bright-ﬁeld images and diffraction patterns are given in Fig. 10. Two of the four
domains in the undeformed pillar appear as the bright areas
in Fig. 9a and the other two can be recognized in Fig. 10a as
the light area and part of the darker area in the TEM view.
As the pillar was compressed from its original state
(Fig. 9a), the two bright domains grew toward each other
(Fig. 9b). At the point of compressive yield (Fig. 9c), the
two domains coalesced. Plastic deformation continued at a
roughly constant ﬂow stress until the load drop at point
“d”. Fig. 9d shows the domain conﬁguration at this point,
and has atleast three interesting features. First, the two
domains remain joined. Second, a lobe has started to form
at the left tip corner of the pillar, which continued to grow
through subsequent serrations of the load–deﬂection curve.
Third, a weak shear band, indicated by the arrow in the ﬁgure, appears to extend from the left side of the pillar tip
upward toward the centerline of the pillar. Subsequent deformation did not cause this shear band to grow across the pillar.
Instead, a small domain aligned with the shear band broke
away from the large, coalesced domain. The incipient shear
band grew through to the boundary of the newly formed
domain. On subsequent deformation, another new domain
appeared at the left edge of the pillar tip and grew to join this
Fig. 10. (a) Pre- and (b) post-compression bright-ﬁeld images of the 90%
cold-worked pillar compressed in Fig. 9. The diﬀraction pattern shown in
(a) was taken from below the dark area at the very tip of the pillar. In (b),
the top diﬀraction pattern corresponds to the dark domain on the top lobe
of the pillar and bottom diﬀraction pattern to the less deformed area of the
pillar below the dark lobe.
domain, which had broadened into a more blocky shape, as
shown in Fig. 9f. At the base of the aggregated domain was
a well-deﬁned, straight discrete boundary that separated
the deformation lobe from the body of the pillar.
After compression, the diﬀraction pattern of the material in the lobe had circumferentially broadened diﬀraction
spots, indicating that a signiﬁcant amount of deformation
had taken place and signiﬁcant local nanorotations
remained. The area below the lobe also produced broadened diﬀraction spots, but the streaks were much shorter,
consistent with a smaller degree of deformation.
The microstructural evolution illustrated in Figs. 9 and
10 suggests that local plastic deformation proceeds through
a combination of local shears and the reconﬁguration of
local domains. As noted in previous research, structural
boundaries resist shear band propagation [1]. In the pillar
specimens, if the boundary cannot reach from one free surface to another, discrete deformation along the shear band
either does not occur or is so minute that it goes unnoticed.
When discrete deformation is not possible, the applied load
is shed into adjacent nanovolumes of the pillar, where the
microstructure again governs whether deformation pro-
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
ceeds through local shear, rotation or reconﬁguration of
local domains.
Similar deformation patterns were observed in other
cold-worked pillars that had multiple domains through
the diameter. Deformation lobes also formed on solutiontreated single-crystal pillars that were slightly misaligned
from the ﬂat-punch compression tip.
3.3. Deformation-induced phase transformation
It is possible to monitor changes that occur in the crystal
structure of the pillars during a test by using the “diﬀraction mode” in which a selected-area-aperture is placed over
the region just below the lowest point the ﬂat-punch will
reach. When the pillars were compressed in this mode, it
was possible to determine whether there was a measurable
deformation-induced transformation to the orthorhombic
a00 martensite, as had been observed by Talling et al. [8]
through X-ray diﬀraction during tensile tests of Gum
Metal, and by Takesue et al. [10] in tensile tests of a
h1 1 0i-oriented single crystal.
To monitor the phase transformation, it was necessary
to estimate the diﬀraction pattern of the a00 phase that
should appear in the bcc Gum Metal. Both the results of
2661
Ref. [8] and unpublished diﬀraction studies done at the
Toyota Central R&D Laboratory show that the a00 has
an orthorhombic cell, space group Cmcm, with the usual
orientation relations to the bcc (b) phase:
a1 ¼ ½1 0 0a00 jj½1 0 0b
a2 ¼ ½0 1 0a00 jj½0 1 1b
a3 ¼ ½0 0 1 00 jj½0 1 1
a
ð1Þ
b
where the ai are the orthogonal edges of the a00 unit cell.
Following Ref. [8], we take a1 = 0.325 nm, a2 = 0.485 nm
and a3 = 0.474 nm, while the bcc cell has an edge length
a = 0.335 nm.
3.3.1. Transformation in a low-strength sample
We ﬁrst consider the behavior of the pillar marked “11”
in Fig. 2a and b, which was compressed in the diﬀraction
mode. This was a solution-treated pillar with a strength
of 1.7 GPa and an orientation near h2 4 7i, giving
sc 0.64 GPa. The low value of sc suggested that the phase
transformation might limit its strength.
Fig. 11g shows the load–displacement curve and Fig. 11a–
f the evolution of the diﬀraction pattern during the compression of pillar “11”, while Fig. 12 contains pre- and post-com-
Fig. 11. The stress–displacement curve of the ST pillar marked “11” in Fig. 2. The labeled diﬀraction patterns were taken at the corresponding points
along the curve. Arrows indicate diﬀraction spots that correspond to the a0 0 phase.
2662
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
ever, the relatively small intensity of the diﬀraction spots
suggests that the fraction of a00 is small.
Fig. 12. (a) Pre- and (b) post-compression bright-ﬁeld images of the ST
pillar compressed in Fig. 11 with the corresponding diﬀraction patterns.
The top diﬀraction pattern in (b) is from the deformed tip of the pillar and
the bottom pattern from the very dark region just below the deformed tip.
pression bright-ﬁeld images and diﬀraction patterns. During
the elastic portion of the stress–displacement curve (Fig. 11g)
the pattern only contained spots associated with the [0 1 2]
zone axis of the bcc structure. Then, at the point designated
“c” in the load–displacement curve, well after the sample had
yielded in compression, two new spots appeared in the [0 1 2]
zone axis pattern (Fig. 11c). These can be matched with a00
martensite. As was observed in prior work [8], the intensity
of the new spots, and therefore the volume of a00 , increased
as deformation continued (Fig. 11d). Further compression
also led to the appearance of a second pair of diﬀraction
spots that are also associated with a00 (Fig. 11d). When the
load was fully released (Fig. 11f), the spots associated with
a00 decreased in intensity but did not disappear entirely, suggesting that the transformation was partially reversible.
The signiﬁcant observation from this experiment is that,
while some transformation occurred, it did not happen
until well after yield. Hence, the a00 transformation did
not determine the strength and did not inﬂuence the elastic
modulus prior to yielding. It was not possible to estimate
the volume fraction of a00 from the diﬀraction data or to
identify a00 phase in the post-test bright-ﬁeld image. How-
3.3.2. Transformation in a high-strength sample
The second sample tested in diﬀraction mode that will be
discussed here was the 21CW specimen that is labeled “13”
in Fig. 2a and b. This sample had a strength of 3.48 GPa
with an h0 1 2i orientation, giving sc 1.7 GPa, which
was the highest strength measured and is essentially equal
to the ideal strength. The load–displacement curve is
shown in Fig. 13 along with selected diﬀraction patterns.
The pre- and post-test bright-ﬁeld images and diﬀraction
patterns are presented in Fig. 14. It should be noted that
the low modulus region in the ﬁrst 20 nm of compression
in Fig. 13 was due to a slight bending of the pillar to make
full contact with the ﬂat-punch.
As documented in the diﬀraction patterns in Fig. 13,
this pillar also experienced a partial transformation to
a00 during the test. In this case the initial a00 transformation occurred before the sample reached its yield strength,
at point “b” on the loading curve (Fig. 13b and c). Weak
a00 spots appeared in the diﬀraction pattern (Fig. 13c), and
there was a small jog in the load–displacement curve that
is presumably due to the transformation strain. However,
the transformation stopped immediately after this small
increment. The intensity of the transformation spots did
not increase, no new spots appeared and the load–displacement curve resumed its monotonic climb to eventual
yield at the peak just before point “d”, where we ﬁrst
noticed the deformation-induced broadening of the diffraction spots.
Well after yielding, the initially observed a00 spots disappeared and new a00 spots appeared. The additional transformation was noticed at point “e” (Fig. 13e), where it seems to
be associated with a noticeable load drop, and at point “f”
(Fig. 13f), where it has no obvious eﬀect on the load curve.
As with the solution-treated pillar in Fig. 11, some a00 spots
remained after the load was removed.
Since this pillar had the highest resolved shear strength
of the pillars tested, it is clear that its strength was not
determined by the phase transformation. A slight transformation occurred both before and after plastic yield, with
only an incremental eﬀect on the load–displacement curve.
The transformation is an incidental feature of the deformation rather than a determinant of it.
We also found evidence of stress-induced martensitic
transformations in other pillars, with the same general
characteristics. In those cases where the transformation
point could be identiﬁed or estimated on the load–displacement curve, the transformation happened well after yield.
Interestingly, in pillars where the transformation was evident the a00 spots did not appear to grow signiﬁcantly during deformation and their intensities were always much less
than those from the bcc structure. In shorter pillars the
transformation appeared to be only partially reversible.
No evidence for transformation to the x phase was
found in any of these tests.
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
2663
Fig. 13. The stress–displacement curve of the 21CW pillar marked “13” in Fig. 2. The labeled diﬀraction patterns were taken at the corresponding points
along the curve. Arrows indicate diﬀraction spots that correspond to the a0 0 phase.
4. Discussion and conclusion
The present work was undertaken with three particular
issues in mind: (i) the compressive strength of Gum Metal
and its relation to the ideal shear strength and the sample
size; (ii) the deformation mechanism and, in particular, the
role of mobile dislocations, shear bands and domain reconﬁgurations; and (iii) the occurrence and signiﬁcance of deformation-induced phase transformations during the test.
4.1. Strength
The strength of the samples tested is shown in Fig. 2.
The samples reach exceptionally high values of sc before
yielding; in several cases the value closely approaches or
reaches the ideal strength. The plots in Fig. 2a and b show
little, if any, size eﬀect, and are surprisingly insensitive to
processing.
The high strength is consistent with the results obtained
with bulk samples in Ref. [1]. The insensitivity to sample
size suggests that strength is controlled on a microstructural scale that is even smaller than the nanoscale of the
samples tested here. This result is consistent with our prior
results on nanoindentation pits [7], which shows disloca-
tion pinning on the nanoscale, and with the analytic theory
[6] of what must happen if a sample is to reach ideal
strength with some residual ductility.
4.2. Deformation mechanism
The results of these tests support the conclusion that
mobile dislocations do not govern the strength or plasticity
of these samples. No signiﬁcant dislocation motion was
observed in any of the samples. This result is in keeping
with the results of tests on larger samples, but was not
obvious until the tests were done.
We note that our sample set included single crystal
samples of solution-treated material. Solution-treated
material is believed to have atleast some dislocation activity in bulk, which is reﬂected in its lower strength. In our
tests the strength of the ST material is equal to that of
CW material, and close to ideal strength. This is consistent with the absence of evident dislocation activity, and
suggests that dislocation activity in the bulk requires grain
boundaries or “soft spots” in the microstructure that are
spatially infrequent and unlikely to be captured in a nanopillar. In other bcc metals, the residual FIB damage
appears suﬃcient to initiate dislocation plasticity at stres-
2664
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
observations reinforce similar observations on the deformation associated with nanoindentation pits [7]. The nature and evolution of the nanodomain structure are
clearly important subjects for further work, but require
atomic resolution microscopy, which is not practical with
the nanopillar geometry.
The results of these tests do not reveal the mechanism of
the relatively homogeneous nanoscale deformation that is
observed in the strongest samples other than to reconﬁrm
that this mechanism operates on a very ﬁne scale. The
strength is apparently inﬂuenced by internal nanodefects,
as evidenced by the fact that the strength decreases on
sequential tests (Fig. 2c), during which the nanodefects
are presumably stored. The most likely candidates for these
nanodefects are the lattice “nanodisturbances” that have
been seen in atomic resolution images of deformed Gum
Metal [1,5]. We are currently investigating this issue.
Another very interesting result is the insensitivity of the
strength to prior processing. In particular, the solutiontreated material, which is signiﬁcantly weaker than the
90% cold-swaged material in bulk polycrystalline form, is
equally strong in these nanopillars. There are atleast two
possible explanations for this result: the relatively largegrained structure of the bulk solution-treated material
introduces mechanically weak sites that produce early
yielding or, conversely, the preparation of the nanopillars
has introduced nanodefects that dramatically raise its
strength. The FIB machining is a possible source of
strengthening defects that needs further investigation.
Fig. 14. (a) Pre- and (b) post-compression bright-ﬁeld images of the
21CW pillar compressed in Fig. 13 with the corresponding diﬀraction
patterns.
ses well below the ideal values [23]. The ST Gum Metal
pillars tested here were clearly decorated with FIB damage, but this did not promote deformation at low stress.
In fact, while the nanodefect population increased during
the compression tests, we saw no evidence that these
defects propagated after being formed. It remains possible, of course, that such does propagation does occur,
but this could not be resolved with the spatial and temporal resolution available in these tests.
The results of these tests also show that shear band formation does not ordinarily determine the strength. Welldeﬁned shear bands do not appear in the samples with
the highest strengths and, when they do appear, are a consequence of the deformation rather than a cause of it. Some
of the results of bulk mechanical tests suggest an important
role for shear bands (or “giant faults”). The present results
suggest that these striking features of the deformation may
be very important to plastic deformation after yield, but do
not determine the yield strength itself.
The results document the importance of nanodomain
growth and reconﬁguration in the deformation process,
though the precise mechanisms remain unclear and the nature of the nanodomain boundaries remains obscure. These
4.3. Deformation-induced phase transformations
The possible structural phase transformations in this
alloy are martensitic transformations to the a00 or x phases.
Deformation-induced transformation to a00 was
observed in a number of samples, including sample “13”,
which had the highest sc value measured, at 1.7 GPa,
which is at or very near ideal strength. However, in all cases
the transformation appears to have been incidental to the
yield strength, occurring well after yield or, in the case of
sample “13”, before yield but in a small quantity that did
not propagate and had no apparent inﬂuence on the subsequent strength or deformation.
The formation of a00 under stress is very sensitive to
the orientation of the stress, as was strikingly demonstrated in recent work by Takesue et al. [10], who tested
single crystal Gum Metal in tension. A crystal oriented
along h1 1 0i transformed extensively, while crystals oriented along h1 0 0i and h1 1 1i showed no transformation
at all. The reason, which we shall explore in a companion paper [24], lies in the inﬂuence of stress on the elastic
energy of the a00 precipitate. A h1 1 0i tension couples
strongly to the a00 transformation strain, while tension
along h1 0 0i or h1 1 1i does not. The results for compressive stress show that a h1 0 0i compression strongly
promotes a00 , and stresses along h0 1 2i and h2 4 7i promote the formation of certain a00 variants. On the other
E.A. Withey et al. / Acta Materialia 58 (2010) 2652–2665
hand, h1 1 0i and h1 1 1i compressions do not strongly
promote the transformation. These results are generally
consistent with the present results: a00 appeared in sample
“11”, with its h2 4 7i orientation, and sample “13”, with
its h0 1 2i orientation, but not in the other very highstrength samples tested here, which had orientations near
h1 1 1i or h1 1 0i. It follows that the a00 transformation is
interesting, but ordinarily incidental to the properties of
Gum Metal.
While there have been periodic reports of x phase in
tested samples of Gum Metal, no evidence of x phase
was found in any of these in situ tests.
Acknowledgements
This research was supported by the National Science
Foundation under Grant DMR 0706554 and by Toyota
Motor Corporation under a grant to the University of California Berkeley. We also acknowledge support from NSF
through a graduate research fellowship. Research at the
National Center for Electron Microscopy was supported
by the Scientiﬁc User Facilities Division of the Oﬃce of Basic Energy Sciences, US Department of Energy under Contract # DE-AC02-05CH11231.
References
[1] Saito T, Furuta T, Hwang JH, Kuramoto S, Nishino K, Suzuki N,
et al. Science 2003;300:464.
[2] Morris Jr JW, Krenn CR, Roundy D, Cohen ML. In: Turchi PE,
Gonis A, editors. Phase transformations and evolution in materials. Warrendale (PA): TMS; 2000. p. 187.
[3] Roundy D, Krenn CR, Cohen ML, Morris Jr JW. Philos Mag A
2001;81:1725.
2665
[4] Krenn CR, Roundy D, Morris Jr JW, Cohen ML. Mater Sci Eng A
2001;A319–A321:111.
[5] Gutkin MY, Ishizaki T, Kuramoto S, Ovid’ko IA. Acta Mater
2006;54:2489.
[6] Li T, Morris Jr JW, Chrzan DC, Nagasato N, Kuramoto S. Phys Rev
Lett 2007;98:105503.
[7] Withey E, Jin M, Minor A, Kuramoto S, Chrzan DC, Morris JW.
Mater Sci Eng 2008;A493:26.
[8] Talling RJ, Dashwood RJ, Jackson M, Dye D. Acta Mater
2009;57:1188.
[9] Yano T, Murakami Y, Shindo D, Kuramoto S. Acta Mater
2009;57:628.
[10] Takesue N, Shimizu Y, Yano T, Hara M, Kuramoto S. J Cryst
Growth 2009;311:3319.
[11] Withey EA, Ye J, Minor AM, Kuramoto S, Chrzan DC, Morris JW.
Exp Mech 2010;50.
[12] Shan ZW, Mishra RK, Syed Asif SA, Warren OL, Minor AM.
Nature Mater 2008;7:115.
[13] Uchic MD, Dimiduk DM, Florando JN, Nix WD. Science
2004;305:986.
[14] Greer JR, Oliver WC, Nix WD. Acta Mater 2005;53:1821.
[15] Minor AM EA, Stach EA, Morris Jr JW. Appl Phys Lett 2001;79:625.
[16] Minor AM, Lilleodden ET, Stach EA, Morris Jr JW. J Mater Res
2004;19:176.
[17] Furuta T, Nishino K, Hwang JH, Yamada A, Ito K, Osawa S, et al.
In: Luetjering G, Albrecht J, editors. Titanium-2003 science and
technology. Weinheim: Wiley-VCH; 2003. p. 1519.
[18] Zhang H, Shuster BE, Wei Q, Ramesh KT. Scripta Mater
2006;54:181.
[19] Shuster BE, Wei Q, Hufnagel TC, Ramesh KT. Acta Mater
2008;56:5091.
[20] Dimiduk DM, Uchic MD, Parthasarathy TA. Acta Mater
2005;53:4065.
[21] Volkert CA, Lilleodden ET. Philos Mag 2006;86:5567.
[22] Lee SW, Han SM, Nix WD. Acta Mater 2009;57:4404.
[23] Bei H, Shim S, George EP, Miller MK, Herbert EG, Pharr GM.
Scripta Mater 2007;57:397.
[24] Kuramoto S, Hatashi Y, Hara M. Acta Mater, in press.