review: achieving superplasticity in metals processed by high-pressure torsion
TRANSCRIPT
ULTRAFINEGRAINED MATERIALS
Review: achieving superplasticity in metals processedby high-pressure torsion
Megumi Kawasaki • Terence G. Langdon
Received: 24 January 2014 / Accepted: 26 March 2014
� Springer Science+Business Media New York 2014
Abstract It is now well established that processing by
equal-channel angular pressing (ECAP) leads to grain
refinement and produces materials having the potential for
exhibiting extensive superplastic flow at elevated tempera-
tures. High-pressure torsion (HPT) is also an effective pro-
cedure for refining the grain sizes of polycrystalline metals to
the submicrometer or even the nanometer level, and recent
results show that this processing method also gives materials
that exhibit excellent superplastic characteristics. This report
examines the various publications describing superplasticity
in metallic alloys processed by HPT. A comprehensive
tabulation is presented listing all of the results to date
showing true superplastic elongations of at least 400 % after
processing by HPT. Examples of superplastic elongations
are described for tensile tests conducted using specimens cut
from either disk or ring samples. An analysis shows that the
flow behavior of various Al and Mg alloys is in good
agreement with the predicted flow behavior for conventional
superplastic materials.
Introduction
When a polycrystalline metal is pulled in a laboratory in
tensile testing, it generally breaks at a relatively low strain.
However, under some testing conditions at elevated tem-
peratures, it is possible to achieve exceptionally high
elongations prior to failure. Superplasticity is defined for-
mally as the ability of a material to exhibit a tensile
elongation of at least 400 % before breaking, where this is
accompanied by a measured strain rate sensitivity, m (= qln r/q ln _e), of *0.5, where r is the flow stress and _e is the
strain rate [1]. The ability of some metallic alloys to pull
out to very high elongations forms the basis for the
superplastic forming industry where sheet metals are
formed into complex shapes and curved parts for use in
applications ranging from aerospace to automotive and
architectural [2].
It is now well established that there are two basic
requirements for achieving superplastic elongations in
polycrystalline materials [3]. First, the grain size must be
very small and, typically, this means a value \10 lm.
Second, since superplastic flow is a diffusion-controlled
process, the testing temperature must be relatively high and
generally at or above *0.5 Tm, where Tm is the absolute
melting temperature of the material. Since grain growth
occurs at elevated temperatures in pure metals and simple
solid solution alloys, superplastic metals are usually two-
phase alloys or they contain a fine dispersion of a second
phase to act as a grain refiner.
Detailed analysis has established that the physical flow
process characterizing superplasticity is grain boundary
sliding in which the individual grains of a polycrystalline
matrix flow over each other in response to the applied
stress [4]. In practice, however, sliding cannot occur in
isolation without opening up cavities in the material, and
M. Kawasaki (&)
Division of Materials Science and Engineering, Hanyang
University, Seoul 133-791, South Korea
e-mail: [email protected]
M. Kawasaki � T. G. Langdon
Departments of Aerospace & Mechanical Engineering and
Materials Science, University of Southern California,
Los Angeles, CA 90089-1453, USA
T. G. Langdon
e-mail: [email protected]
T. G. Langdon
Materials Research Group, Faculty of Engineering and the
Environment, University of Southampton,
Southampton SO17 1BJ, UK
123
J Mater Sci
DOI 10.1007/s10853-014-8204-5
this means that the sliding is accommodated by slip within
the adjacent grains so that ultimately the rate-controlling
step is the climb of these intragranular dislocations into the
adjacent grain boundaries. Direct experimental evidence is
available to confirm the movement of intragranular dislo-
cations during superplastic flow through measurements of
the densities of dislocations trapped in coherent twin
boundaries in a Cu-based alloy [5], from measurements of
the intragranular strains in a Pb–62 % Sn eutectic alloy [6]
and through the use of a Zn–22 % Al eutectoid alloy
containing a nanometer-scale dispersion of particles [7].
A theoretical model was developed for superplastic flow
based on grain boundary sliding accommodated by intra-
granular slip [8]. This model predicts a steady-state strain
rate, _e, which is given by a relationship of the form
_e ¼ ADgbGb
kT
b
d
� �2 rG
� �2
; ð1Þ
where A is a dimensionless constant having a value of
*10, Dgb is the coefficient for grain boundary diffusion,
G is the shear modulus, b is the Burgers vector, k is
Boltzmann’s constant, T is the absolute temperature and
d is the grain size.
Conventional superplastic metals are usually produced
by thermo-mechanical processing and have grain sizes
within the range of *3–5 lm. However, it is now known
that the processing of metals through the application of
severe plastic deformation (SPD) leads to exceptional
grain refinement so that the grain sizes typically lie within
the submicrometer or even the nanometer range. It is
reasonable to anticipate that these SPD materials will
exhibit excellent superplastic properties. In practice, sev-
eral SPD processing methods are now available [9], but
the two most important techniques, and the procedures
most widely used, are equal-channel angular pressing
(ECAP) [10] and high-pressure torsion (HPT) [11]. A
comprehensive review published in 2007 tabulated the
large numbers of results available at that time describing
superplasticity in metals processed by ECAP [12]. More
recently, numerous publications have also become avail-
able describing the occurrence of superplastic flow in
metals processed by HPT. Thus, the objective of this
report is to examine the fundamental characteristics of
superplastic flow in materials processed by HPT and to
provide a comprehensive tabulation of the results avail-
able to date. Accordingly, the following section summa-
rizes the historical development of superplasticity in SPD
processing, the next sections describe some of the prin-
ciple results obtained using disk and ring samples, and the
final section tabulates the data and examines the flow
process in terms of the fundamental mechanism for
superplasticity in conventional materials.
Historical developments for superplasticity using SPD
techniques
An early report, published over 25 years ago, sets the scene
for establishing SPD processing as a major tool in producing
materials that exhibit excellent superplastic properties. In a
paper entitled ‘‘Low-temperature superplasticity of metallic
materials,’’ Valiev et al. [13] used an Al–4 % Cu–0.5 % Zr
alloy, processed the alloy by HPT and then obtained an
elongation of 250 % at the very low temperature of 493 K.
Although the latter elongation is not within the current def-
inition of superplasticity, nevertheless the result raised
considerable interest because of the high elongation that was
achieved at an unusually low temperature [14]. Thus, this
early result prompted additional experiments on samples
processed by ECAP [15] and, when two review articles were
published describing extensive results in SPD processing
[16, 17], interest in the field developed further so that pro-
cessing by SPD methods became a regular feature of many
materials laboratories around the world.
As demonstrated by Eq. (1), the strain rate varies
inversely with the grain size raised to a power of two in
conventional superplasticity and it was first noted in 1996
that provided the ultrafine grain sizes were reasonably
stable at elevated temperatures, materials produced by SPD
techniques may exhibit excellent superplasticity with the
high elongations occurring at very rapid strain rates [18]. In
the following year, in 1997, superplasticity was achieved in
two commercial aluminum alloys with elongations up to
[1000 % at a strain rate of 10-2 s-1 [19]. This strain rate
is generally defined as the point of transition to high strain
rate superplasticity [20].
For many years, the development of superplasticity in
SPD materials was devoted almost exclusively to metals
processed by ECAP. The reason is due to the relatively
large samples that are easily produced using the ECAP
method. Typically, ECAP samples are in the form of bars
or rods with dimensions of the order of 10 9 10 mm2 and
lengths of at least 65 mm. These large sizes mean that it is
a simple procedure to machine tensile specimens from the
as-processed samples. Processing by HPT is advantageous
because it produces materials generally having smaller
grain sizes and higher fractions of high-angle boundaries
than in ECAP [21–23]. Nevertheless, the processing gen-
erally uses thin disks and these samples are not directly
amenable to conventional tensile testing.
An additional problem is that the equivalent von Mises
strain imposed on an HPT disk, eeq, is given by the rela-
tionship [24–26]
eeq ¼2pNr
hffiffiffi3p ; ð2Þ
J Mater Sci
123
where r and h are the radius and height (or thickness) of the
disk, respectively, and N is the number of HPT turns. It
follows from Eq. (2) that the imposed strain varies from
zero at the disk center to a maximum at the periphery. In
practice, however, extensive experiments show that there is
a gradual evolution toward a reasonable homogeneity after
a large number of turns [27, 28]. Because of the problems
associated with inhomogeneities in the centers of the disks,
it has become a standard practice to machine two tensile
specimens from each HPT disk using off-center positions,
as illustrated schematically in Fig. 1 where the central
point of each specimen is located at 2 mm from the center
of the disk [29]. It is then possible to pull these specimens
in tension at an elevated temperature in order to evaluate
the superplastic properties after HPT processing. Numer-
ous results are now available confirming the feasibility of
using miniature specimens cut from HPT disks to measure
the mechanical properties of materials after processing by
HPT [30, 31].
Characteristics of superplasticity after HPT processing
of disks
Equation (1) delineates the strain which is imposed on the
disk when processing by HPT. In practice, the strain
increases with additional torsional revolutions, but ulti-
mately a stable microstructure is attained, usually after a
relatively small number of turns, and thereafter there is
little or no additional grain refinement with increasing
straining. Figure 2 shows the elongations achieved in a Zn–
22 % Al eutectoid alloy after processing by HPT at room
temperature under an applied pressure of 6.0 GPa with a
rotational speed of 1 rpm [32]. The tensile tests were
conducted at 473 K using an initial strain rate of
1.0 9 10-1 s-1, the upper specimen is untested, and the
other three specimens were processed through 1, 3 and 5
turns, respectively. Inspection shows that all specimens in
Fig. 2 are superplastic but the maximum elongation of
1800 % was attained after a total of N = 5 turns.
There is also a significant dependence on the testing
strain rate as shown in Fig. 3 where specimens of the Zn–
22 % Al alloy were processed through 5 turns in HPT and
then pulled to failure at initial strain rates from 1.0 9 10-3
to 1.0 s-1 [32]. These results show that, as in conventional
superplastic materials not processed by SPD techniques,
superplasticity occurs over a limited range of strain rates,
and there are decreases in the elongations to failure at both
faster and slower strain rates [33]. The behavior visible in
Fig. 3 corresponds to the three regions of flow in super-
plasticity where region II is true superplasticity with high
Fig. 1 Procedure for cutting miniature tensile specimens from off-
center positions in disks processed by HPT [29]
Fig. 2 The variation of the elongations to failure with the numbers of
revolutions applied in torsional straining for a Zn–22 % Al alloy
tested at a strain rate of 1.0 9 10-1 s-1 at 473 K [32]
Fig. 3 The variation of the elongations to failure with the imposed
strain rates for a Zn–22 % Al alloy tested at a temperature of 473 K
[32]
J Mater Sci
123
elongations at intermediate strain rates, region III corre-
sponds to a transition to conventional dislocation creep at
faster strain rates, and region I represents a regime of flow
which is impurity dependent at the slowest strain rates [34].
It is important to note that the maximum elongation of
1800 % appears to represent the highest elongation
achieved to date in any material processed by HPT. Fur-
thermore, this specimen exhibits the fundamental charac-
teristics of true superplastic flow including uniform
deformation without any evidence for necking within the
gauge length and with failure occurring by pulling down to
a point [35].
An important question concerns the relative values of
the elongations that may be achieved in the same alloy
when processing either by HPT or ECAP. In principle,
HPT produces a smaller grain size, and this should displace
the superplastic region II to faster strain rates and at the
same time produce larger elongations to failure. This
comparison is shown in Fig. 4 using HPT data for the Zn–
22 % Al alloy after processing through 5 turns [32] and
ECAP data for the same alloy processed through 8 passes
at 473 K [36]. For the ECAP processing, the billets were
pressed through a die with a channel angle of 90� using
processing route BC, in which the ECAP billet is rotated in
the same sense by 90� between each pass [37]. The mea-
sured grain sizes in the Zn–Al alloy were *900 nm after
ECAP and *350 nm after HPT so that the HPT specimens
are anticipated to show a peak ductility at a faster strain
rate and with elongations which are larger than after
ECAP. Inspection of Fig. 4 shows, however, that the HPT
datum points are correctly displaced to faster rates but the
maximum elongation in HPT is lower than in ECAP.
The reason for this apparent discrepancy lies in the
dimensions of the two sets of tensile specimens. For ECAP
the initial cross-sectional areas of the specimens were
3 9 2 = 6 mm2, whereas in HPT the specimens had a
width of 1 mm from Fig. 1 and a thickness of *0.8 mm so
that the cross-sectional areas were *0.8 mm2. Various
experiments have shown that the elongations achieved in
tensile testing are dependent upon the cross-sectional areas,
and specifically the measured elongations increase when
using samples having larger cross-sectional areas [38–40].
For example, tensile tests at room temperature on ultrafine-
grained Cu samples produced by ECAP processing showed
that the overall strains increased significantly as the spec-
imen thickness was increased from 250 lm to 1.0 mm
[41]. In addition, a later study used miniature tensile
specimens of various sizes and geometries and compared
the experimental data with predictions derived from finite
element modeling [42]. The general conclusions from an
examination of these earlier experiments are that the lower
elongations recorded for the superplastic HPT specimens in
Fig. 4 are a direct consequence of the very small cross-
sectional areas available in these specimens prior to testing.
Figure 5 shows another example of superplastic elon-
gations after HPT where specimens of an Al–33 % Cu
eutectic alloy were tested in tension at 723 K: a detailed
description of these results was given earlier [43]. These
results are similar to the Zn–Al alloy in Fig. 3 except that
the maximum elongation in this alloy occurs at a slower
initial strain rate and there is no evidence for high strain
rate superplasticity.
The testing temperature also affects the measured
elongations to failure and this can be seen in Fig. 6 where
all specimens of the AZ61 magnesium alloy were pulled at
Fig. 4 A comparison of superplasticity in a Zn–22 % Al alloy
processed by either HPT [32] or ECAP [36] and then tested at a
temperature of 473 K
Fig. 5 The variation of the elongations to failure with the imposed
strain rates for an Al–33 % Cu alloy tested at a temperature of 723 K
[43]
J Mater Sci
123
the same initial strain rate of 3.3 9 10-3 s-1 over a range
of temperatures from 373 to 523 K [44]. The results show
an optimum elongation of 620 % at 473 K and smaller
elongations at both lower and higher testing temperatures.
A careful microstructural analysis showed that the decrease
in elongation at 523 K was due to grain growth at this
higher temperature.
Characteristics of superplasticity after HPT processing
of rings
The preceding results were obtained for HPT specimens
cut from conventional thin disks using the specimen con-
figurations shown in Fig. 1. However, it is also possible to
conduct HPT processing using ring samples. This approach
was adopted many years ago in experiments using very low
pressures [45, 46] but more recently ring samples were
used to evaluate the potential for achieving superplastic
elongations in an Al–3 % Mg–0.2 % Sc alloy [47].
The tests were conducted using rings with widths of
3 mm and outer diameters of 40 mm. After processing
through 1 turn under a pressure of 1.25 GPa, the rings were
used to provide both disks having diameters of 3 mm for
inspection using transmission electron microscopy (TEM)
and tensile specimens having gauge widths and lengths of
1 mm where these dimensions are identical to the disk
specimens as shown in Fig. 1: the procedure for cutting
TEM and tensile samples is shown schematically in Fig. 7
[47]. The tensile specimens were pulled to failure at a
temperature of 573 K at two different strain rates and the
result is shown in Fig. 8 where it is apparent that these
miniature specimens exhibit excellent superplastic prop-
erties including an elongation of[1000 % in the regime of
high strain rate superplasticity [47]. It follows, therefore,
that superplastic specimens may be achieved using both
disk and ring configurations.
The flow process in superplastic HPT specimens
The preceding sections on disk and ring samples show that
excellent superplastic properties can be achieved in
metallic alloys processed by HPT. Several superplastic
results are now available for HPT specimens, and a com-
prehensive summary is given in Table 1. In this Table, the
HPT processing conditions are listed in columns 2–4 as the
maximum numbers of turns, the applied pressure and the
processing temperature, column 5 gives the grain sizes
achieved by HPT, details of the superplastic tests are given
in columns 6–8 including the testing temperature, imposed
strain rate and the maximum reported elongation to failure,
Fig. 6 The variation of the elongations to failure with the testing
temperature for an AZ61 magnesium alloy tested at a strain rate of
3.3 9 10-3 s-1 [44]
Fig. 7 Procedure for cutting TEM samples and miniature tensile
specimens from rings processed by HPT [47]
Fig. 8 The variation of the elongations to failure with the imposed
strain rates for an Al–3 % Mg–0.2 % Sc alloy processed as rings by
HPT and tested at a temperature of 573 K [47]
J Mater Sci
123
Table 1 Reports of superplasticity in ultrafine-grained materials
Alloy or
composition
(wt%)
HPT Grain
size (nm)
Superplasticity Reference
Number
of turns
Pressure
(GPa)
Temperature
(K)
Testing
temperature
(K)
Strain rate
(s-1)
Maximum
elongation (%)
Al1420a 3n 1.2 RT 100 523 1.0 9 10-2 440 Mishra et al. [48]
573 1.0 9 10-1 775
Al1421b ? 6 293 1080 623 1.0 9 10-2 537 Islamgaliev et al. [49]
393 700–1000 508
573 1160 489
613 930 664
643 570 1030
Al1570c 5 6 RT 120 573 1.0 9 10-1 580 Perevezentsev et al.
[50]623 1.8 9 10-1 800
673 1.0 9 10-2 1460
673 1.0 600
Al2024d,j 5 6 293 140 673 1.7 9 10-3 570 Dobatkin et al. [51]
673 290 450
Al2024d,k 293 160 410
673 300 440
Al7034e 5 4 RT (293) *600 673 1.0 9 10-2 550 Xu et al. [52]
703 1.0 9 10-2 750
473 *800 673 1.0 9 10-3 550
703 1.0 9 10-2 650
Al7075f 5 6 RT *250 623 1.0 9 10-4 *700 Sabbaghianrad et al.
[53]10 1.0 9 10-3 *570
1.0 9 10-4 *680
Al–33Cu 5 6 RT *3000 723 3.3 9 10-5 *1250 Kawasaki et al. [43]
10 1.0 9 10-4
Al–3 Mg–0.2Sc 5 6 RT *150 673 3.3 9 10-2 500 Sakai et al. [54]
Al–3 Mg–0.2Sc 2 1 RT *130 573 3.3 9 10-3 *1600q Horita and Langdon
[55]
Al–3 Mg–0.2Sc 1 1.25 623 *220 573 3.3 9 10-2 1030r Harai et al. [47]
3.3 9 10-3 1510r
AZ61g 5 3 423 230 473 3.3 9 10-3 620 Harai et al. [44]
ZK60h 5 2 RT (296) 900–1000 473 1.0 9 10-3 415 Torbati-Sarraf and
Langdon [56]523 477
573 508
Mg–9All 5 3 RT (298) 210 473 1.0 9 10-3 600 Kai et al. [57]
423 330 5.0 9 10-3 550
1.0 9 10-3 620
5.0 9 10-4 810
Mg–9Alm 423 370 1.0 9 10-3 590
Mg–10Gd 5 6 RT *100 673 1.0 9 10-2 470 Kulyasova et al. [58]
1.0 9 10-3 580
Ni3Ali 7o 7 RT *50 998 1.0 9 10-3 560 Mishra et al. [59],
Valiev et al. [60]
Ti–6Al–4 V 5p 2.2 RT (293) 100-200 923 1.0 9 10-4 530 Sergueeva et al. [61]
5 1.0 9 10-3 575
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123
and finally the reference for each report is listed in the last
column. The results summarized in Table 1 cover only
those investigations where the measured elongations to
failure fulfill the requirement of a tensile elongation of at
least 400 % for superplastic flow: reports of tensile elon-
gations less than 400 % are not included. Additional
information is provided after the Table 1 on the composi-
tions of the various alloys and there are also notes on the
HPT processing.
The results documented in this report show that excel-
lent superplastic properties may be achieved in HPT sam-
ples and it is appropriate to consider whether these
specimens exhibit flow properties which are consistent with
the theoretical model for conventional superplasticity [8].
An earlier report examined data for superplastic Al and Mg
alloys after processing by ECAP and showed that for both
sets of materials there was excellent agreement, to within
an order of magnitude of strain rate, with the theoretical
model as given by Eq. (1) [65].
The same approach was adopted in the present analysis,
and Fig. 9 shows the results for aluminum-based alloys
where the temperature and grain size compensated strain
rate, ( _ekT/DgbGb)(d/b)2, is plotted against the normalized
stress, r/G, using data taken from reports on various Al
alloys [43, 47, 48, 50–54]. The experimental points were
plotted using the following values for all aluminum alloys:
Table 1 continued
Alloy or
composition
(wt%)
HPT Grain
size (nm)
Superplasticity Reference
Number
of turns
Pressure
(GPa)
Temperature
(K)
Testing
temperature
(K)
Strain rate
(s-1)
Maximum
elongation (%)
Ti–6Al–4 V 5p 5 RT (293) 100–200 923 1.0 9 10-3 568 Sergueeva et al. [62]
1.0 9 10-4 513
998 1.0 9 10-2 504
1.0 9 10-3 676
Zn–22Al 5 6 RT *600 473 1.0 1170 Kawasaki and
Langdon [32, 63]1.0 9 10-1 1800
1.0 9 10-2 1370
1.0 9 10-3 900
Zn–22Al 1 6 RT *770 473 1.0 9 10-2 1800 Cho et al. [64]
3 *650 1.0 9 10-1 1680
5 *600 1.0 9 10-1 1800
a Al1420: Al–5 Mg–2Li–0.1Zrb Al1421: Al–5.5 Mg–2.2Li–0.12Zr–0.2Scc Al1570: Al–5.6 Mg–0.4Mn-0.32Scd Al2024: Al–4.4Cu–1.5 Mg–0.6Mne Al7034: Al–11.5Zn–2.5 Mg–0.9Cu–0.2Zrf Al7075: Al–5.6Zn–2.5 Mg–1.6Cug AZ61: Mg–6.4Al–0.74Zn–0.35Mn-0.0012Ni-0.001Cu–0.001Fe-0.015Sih ZK60: Mg–5.5Zn–0.5Zri Ni3Al: Ni-8.5A1-7.8Cr-0.6Zr–0.02Bj The Al2024 was processed by HPT and annealed for 10 min at 673 K followed by air coolingk The Al2024 was processed by HPT and solution treated for 10 min at 768 K followed by quenching into waterl The Mg–9Al was cast prior to HPTm The Mg–9Al was cast and subsequently extruded prior to HPTn The total number of turns was calculated from the true logarithmic strain of 6 at a distance of 3 mm from the center of a disk with a diameter of
20 mm and a thickness of *0.5 mmo The total number of turns was calculated from the true logarithmic strain of 7 at a distance of 3 mm from the center of a disk with a diameter of
12 mm and a thickness of *0.3 mmp The total number of turns was calculated from the true logarithmic strain of 7 at a distance of 3 mm from the center of a disk with a diameter of
15 mm and a thickness of *0.5 mmq Samples were taken from the mid-section of a bulk HPT sampler Specimens were taken from ring HPT samples
J Mater Sci
123
b = 2.86 9 10-10 m [66], G (MPa) = (3.022 9 104) –
16T where the temperature is in degrees Kelvin [66],
Dgb = Do(gb) exp (-Qgb/RT) where R is the gas constant,
Do(gb) = 1.86 9 10-4 m2 s-1, Qgb = 86 kJ mol-1 [66], a
value for the dimensionless constant in Eq. (1) of A = 10
[8] and converting from the reported mean linear intercept
grain size, �L, to the spatial grain size, d, using the
expression d = 1.74 �L [67]. The prediction for the theo-
retical model is shown in Fig. 9 by the line labeled _esp
having a slope of n = 2 where n is the stress exponent.
Inspection of Fig. 9 shows that all of the experimental
points are mutually consistent and they are generally in
reasonable agreement with the theoretical model except
that, for any imposed strain rate, the measured stress levels
tend to be too high by about one-half order of magnitude on
the stress axis. This discrepancy is due to the use of
exceptionally small tensile samples.
A similar plot is shown in Fig. 10 for magnesium-based
alloys processed by HPT [44, 56–58] where
b = 3.2 9 10-10 m [68], G (MPa) = 1.92 9 104 -
8.6T [68], Do(gb) = 7.8 9 10-3 m2 s-1 [69], and
Qgb = 92 kJ mol-1 [69]. Again, all experimental points
are consistent with the theoretical model but they are dis-
placed to slightly higher stresses which is attributed to the
use of very small tensile specimens.
All of these results confirm that HPT processing, using
either disk or ring samples, is as effective as processing by
ECAP in producing specimens that exhibit excellent
superplasticity when pulled in tension at elevated temper-
atures. As anticipated from the very small grain sizes
attained in HPT, the peak superplastic flow tends to occur
at faster strain rates than when testing ECAP samples but
the total elongations are slightly lower due to the use of
specimens having very small cross-sectional areas.
Summary and conclusions
1. Samples processed by HPT exhibit excellent super-
plastic properties when tested in tension at elevated
temperatures. Several results are now available docu-
menting this behavior for both disks and rings and
these results are tabulated and described.
2. The strain rates inherent in superplastic flow provide a
reasonable match to the anticipated behavior from the
theoretical mechanism for conventional superplasticity.
However, the measured stresses tend to be slightly high
because of the use of very small tensile specimens.
Acknowledgements This work was supported in part by the
National Science Foundation of the United States under Grant No.
DMR-1160966 and in part by the European Research Council under
ERC Grant Agreement No. 267464-SPDMETALS.
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