L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
397–405
FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97
Al-Li ALLOY
ANALIZA OMEJITEV PREOBLIKOVANJA SUPERPLASTI^NE
Al-Li ZLITINE 2A97
Li Jia
1
, Xueping Ren
1*
, Yanling Zhang
2
, Hongliang Hou
2
1
School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China
2
Aviation Industry Corporation of China (AVIC) Manufacturing Technology Institute, Beijing 100024, P. R. China
Prejem rokopisa – received: 2019-10-09; sprejem za objavo – accepted for publication: 2019-12-23
doi:10.17222/mit. 2019.240
The superplastic formability of the as-rolled 2A97 Al-Li alloy was studied under various stress states with the use of both tensile
tests and bulge tests deformed at 350–430 °C. The flow stress curves of the 2A97 alloy at the test temperature with an initial
strain rate ranging from 1×10
–3
s
–1
to 3×10
–2
s
–1
were characterized by the modified Hooke equation and the Grosman equation.
The bulge tests were performed under four different strain paths, ranging from equi-biaxial to approaching plane strain. The
effects of temperature and bulge-tool aspect ratio on the dome height, forming pressure, thickness distribution, and cavitation
were investigated. Dome height and forming pressure appear to be more sensitive to tool ratio than temperature. Increasing the
temperature in bulge forming was found to improve the thickness distribution in the formed parts, but it may lead to excessive
cavitation. The results of the forming-limit diagram show significant scatter in terms of failure strain. It indicates that a
determination of the forming limits of superplastic 2A97 cannot be represented with a simple forming-limit diagram and
additional metrics for internal cavitation need to be considered.
Keywords: superplasticity, 2A97 Al-Li alloy, forming limit, cavitation
Avtorji tega prispevka so {tudirali superplasti~no preoblikovanje Al-Li zlitine 2A97 v valjanem stanju pri razli~nih napetostnih
stanjih z uporabo nateznega in vle~nega preizkusa ter deformacijo materiala pri temperaturah med 350 °C in 430 °C. Krivulje
te~enja zlitine 2A97 pri izbranih temepraturah so deformirali z za~etno hitrostjo deformacije med 1×10
–3
s
–1
in 3×10
–2
s
–1
ter
jih okarakterizirali z modificiranima ena~bama Hooka in Grosmana. Preizkus vle~enja so izvajali na {tiri razli~ne na~ine v
obmo~jih od ekvivalentne dvo-osne do ravninske deformacije. Ugotavljali so vpliv temperature, deformacijskega razmerja,
dobljenega pri testu vle~enja (vi{ine deformirane polkrogle), tlaka preoblikovanja, porazdelitve debeline in kavitacije. Ugotav-
ljajo {e, da sta stopnja deformacije in tlak preoblikovanja bolj odvisna od geometrije orodja kot od temperature. Z nara{~anjem
temperature in tlaka vle~enja, se ob~utljivost na geometrijsko razmerje orodja pove~uje bolj kot na temperaturo preizkusa.
Povi{evanje temperature preizkusa vle~enja izbolj{uje porazdelitev debeline preoblikovanega preizku{anca, toda to lahko
privede do pove~ane kavitacije. Rezultati diagrama omejitev preoblikovanja ka`ejo pomemben raztros podatkov glede na
deformacijo, pri kateri pride do odpovedi (poru{itve) materiala. To ka`e na to, da mej preoblikovanja superplasti~ne zlitine
2A97 ne moremo predstaviti z enostavnim diagramom preoblikovanja, zato bodo morali avtorji izvesti {e dodatne analize
meritev interne kavitacije.
Klju~ne besede: superplasti~nost, Al-Li zlitina 2A97, omejitve preoblikovanja, kavitacija
1 INTRODUCTION
Nowadays, weight reduction is a crucial aspect of
aircraft design.
1
For most transport aircraft, including the
Airbus A380, aluminum alloys account for about 60 %
of the structural weight.
2
The density of aluminum (Al)
alloys can be lowered by 3 % with a 1 w/% addition of
lithium (Li).
3
There is a notable trend toward using
aluminum–lithium (Al–Li) alloys to replace conventional
aluminum alloys as structural materials. This is due to
their relatively low density, high elastic modulus, high
specific strength and other good properties.
4
However,
there are plenty of difficulties during cold forming, such
as low formability, high notch sensitivity and crack
formation. The superplastic forming (SPF) process opens
up a new direction for solving the complex forming of
Al-Li alloy sheet.
5
This work is primarily concerned with the super-
plastic forming of specially processed 2A97 Al-Li alloys
for SPF. As a novel damage-tolerant alloy newly deve-
loped in China, 2A97 exhibits excellent fracture
toughness and malleability, in addition to the benefits of
normal Al-Li alloys. The 2A97 Al-Li alloy has attracted
much research interest as an alloy with moderate
strength, corrosion resistance and weldability,
5–16
which
has opened up potential applications in the aerospace,
aviation and military industries. However, less research
work has been carried out on the superplastic forming
properties of 2A97 Al-Li alloy. Accurately predicting the
fracture behavior of the 2A97 alloy in SPF has important
significance for engineering applications.
The forming limit is an important performance index
for the fracture behavior of sheet metal forming, and
reflects the maximum amount of deformation that can be
reached before the plastic deformation of the material is
unstable during the forming process.
17
The Forming
Limit Diagram (FLD), is a band region or curve formed
Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405 397
UDK 67.017:620.1:669.715 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 54(3)397(2020)
*Corresponding author's e-mail:
rxp33@ustb.edu.cn (Xueping Ren)

by the local instability limit of sheet metal under
different strain paths, which can fully reflect the local
forming limit of sheet metal under unidirectional and
biaxial tension stress.
18–20
It is an essential tool to assess
the sheet-metal formability in metal-forming ope-
rations.
21,22
The FLD lays the foundation for a qualitative
and quantitative study of the local forming properties of
sheet metal. At present, FLD is often used in the
finite-element method (FEM) simulation in most of the
sheet forming.
To better predict the fracture behavior of 2A97 alloy
sheet during the SPF process, it is necessary to perform a
comprehensive study of the tensile properties, forming
limit, and cavitation evolution. Cavitation occurs during
the superplastic deformation of high-strength aluminum
alloys, resulting in the development of small inter-
granular voids during straining.
23
The cavities formed
during superplastic forming can induce premature failure
of superplastic materials during processing,
24–26
and
affect the subsequent service properties (ambient tempe-
rature tensile and fatigue) of superplastically formed
parts.
27
Therefore, FLD is not the only criterion for
evaluating superplastic-forming performance. It is
necessary to perform a comprehensive study of the
cavitation behavior and FLD to establish the practical
criteria for evaluating the superplastic forming limit of
2A97 alloy sheet.
In this paper, experiments were conducted on 2A97
Al-Li sheet alloys using both the uniaxial tensile test and
biaxial tension bulge test at 350 °C–430 °C. The FLD
was determined from specimens that were deformed by a
pneumatic bulge test with tool ratios of 1:1, 4:3, 2:1, and
8:3. The shape of the forming-limit curves was found to
be different from that of traditional room-temperature
forming-limit curves. In order to determine the influence
of temperature on cavitation, samples from the formed
parts were studied using optical microscopy.
2 MATERIALS AND EXPERIMENTAL
PROCEDURE
2.1 Materials
The material in this paper is an Al-Cu-Li alloy
supplied by Southwest Aluminum (Group) Co., Ltd.,
China, referred to as 2A97 alloy. The nominal chemical
composition of the sheet was Al–3.8Cu–1.4Li–0.5Mg–
0.5Zn–0.3Mn–0.2Ti–0.2Si–0.1Zr–0.06Fe–0.006Be
(w/%). The material used is 2.5-mm-thick warm-rolled
plates, and was specifically thermomechanically treated
for superplastic forming. After casting and homo-
genizing, the alloy is hot rolled to 25 mm in thickness to
break down the as-cast structure. The material is solution
treated at 520 °C for2htotakemost of the copper into
solid solution, and aged at 400 °C for 48 h to obtain the
uniform distribution and a larger volume fraction of the
second-phase particles.
5
And then the plate is warm
rolled to the as-received state with intermediate
annealing to avoid rolling cracking.
12
2.2 Experimental procedure
2.2.1 Tensile test
The tensile tests were conducted on a SK10-70×300
universal testing machine equipped with a three-zone
heating furnace with temperature control accuracy of
±3 °C. Four K-type thermocouples were used to monitor
the temperature: three for the furnace and one for the
specimen. Tests were initiated following equilibration of
the testing temperature and samples were held at the
target temperature for 30 min prior to tension. The
tensile experiments were carried out at temperatures of
350–430 °C with an initial strain rate ranging from
1×10
–3
s
–1
to 3×10
–2
s
–1
without any atmosphere protec-
tion. The dog-bone tensile samples were cut along the
RD with a gauge length of 10 mm and 6 mm in width.
2.2.2 Bulge forming
The schematic diagram of the bulge forming die is
shown in Figure 1. It was fixed within a 300-ton SPF
press and equipped with a heating furnace of 50 kW.
Integral heating was adopted for superplastic forming
heating. The forming temperature was maintained by
heaters arranged on four sides of the furnace. The holes
were reserved in the upper die shown in Figure 1 so that
the thermocouple can be placed in to monitor the tem-
perature of the sample in real time. The edge of the sheet
was pressed by the blank holder and the lower die to
ensure sealing. Samples were pre-heated for 30 min to
achieve the target temperature before the press was
closed and the blank sealed between the lower and upper
die halves. The loading rate of the gas pressure is 0.04
MPa/min. Circular samples with a diameter of 100 mm
for the bulging experiment were fabricated by laser
cutting from the as-received sheet.
The circular grid patterns with a diameter of 2 mm
were electrochemically etched on the surface of the
samples prior to the forming. Both sides of the blank and
the inner wall of the die were coated with a SPF lubri-
cant containing boron nitride. The lubricant was received
in water-based suspensions to allow spraying appli-
cations. The lubricant was allowed to dry in air, leaving
only the solid components on the surface. The lubricant
L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
398 Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405
Figure 1: Schematic diagram of bulge testing apparatus

can reduce the oxidation of the sheet in the forming
process, effectively preventing the sheet from sticking to
the die, and playing the role of typing agent in the
process of parts extraction. In the experiment, the long
axis of the die is parallel to the rolling direction of the
sample.
In actual production, the material deformation in
sheet-metal forming processes is often not in the equi-
biaxial stress state. It requires different die geometries to
obtain different stress and strain states. One set of lower
dies, with a length of 60 mm and different widths of (60,
45, 30, and 22.5) mm were designed, in which each die
represents one strain path on the FLD. The entry radius
of 5 mm is designed on the lower die to prevent the
pattern from breaking due to local thinning. All the test
samples were formed until failure.
3 RESULTS AND DISSCUSSION
3.1. Constitutive model
Figure 2 shows the specimens before and after the
superplastic tensile test. It can be seen that the elongation
and the section shrinkage of the specimens increase
significantly with decreasing strain rates and increasing
deformation temperature. The maximum elongation of
the 2A97 alloy at 350 °C, 390 °C, and 430 °C was
337 %, 446 %, and 470 %, respectively. The optimum
strain rate decreases with the increase of the temperature.
The constitutive equation is a mathematical model
that describes the flow stress during the deformation
process. The constitutive model is mainly divided into
two categories.
28
The first group of the model directly
describes the influence of deformation conditions such
as the temperature and strain rate on the flow stress.
These models usually do not take into account the
deformation history. They describe correctly the flow
stress in cases when strain hardening is the dominant
factor that determines the state of the materials. The
model parameters mainly include the work-hardening
coefficient, the strain-rate sensitivity index and the
temperature. The second group embraces models in
which the deformation history affects the internal state of
a material, determined primarily by its structure,
29
and in
which the actual response of the material to the defor-
mation conditions depends on its internal state. Because
the superplasticity experiment temperature is low and the
original structure is a lath structure, the hardening stage
accounts for a relatively high proportion in the tensile
curve, so the first group of the model is adopted in this
paper. The Grossman equation in the first model can
describe three states of deformation: work hardening,
softening, and flow-stress steady state. The tensile
process can be divided into two ordinal phases: elastic
deformation phase and ductile deformation phase. The
modified Hooke equation and the Grossman equation
describe the elastic and plastic stages, respectively, as
shown in Equations (1) and (2).
elastic deformation phase:
 
e
=ET (,
 ) (1)
ductile deformation phase:
  
 p
= K
nmB
 (2)
Where  e
and  p
represent the flow stress in the
elastic and plastic stages, respectively, E is the elastic
modulus, K is the material coefficient, m is strain-rate-a
sensitive coefficient, n is a strain-hardening coefficient,
and B is a strain-softening coefficient.
The elastic modulus is obtained by calculating the
slope of the stress-strain curve in the elastic deformation
stage. It was found that the E-value is different under
different strain rates and temperatures. The relationship
between the elastic modulus and the temperature and
strain rate is obtained using the least-squares method,
shown as Equation (3):
ETT
T
=−+−+
+−
11053589 18206 241191 256677
0006 1
2
..
 .
 .

289064
2
 (3)
Based on the unidirectional tension data of the 2A97
Al-Li superplastic alloy, the differential evolution
method was used for a regression analysis of Equation
(2). It was found that the strain rate had little effect on K
and B in the plastic stage, so it only considered the effect
L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405 399
Figure 2: Macrophotograph of some specimens before and after the tensile test

of temperature on them here. The relationship curves
between K, B, n, m and T,
 are established. The re-
gression analysis is carried out by using the least-squares
method and MATLAB, and the following Equations (4),
(5), (6), and (7) are obtained.
K
TT
=− +
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 35422566 10805034
100
812792
100
...
2
(4)
B
TT
=−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 70307 21336
100
1591
100
2
.. . (5)
m
TT
=− +
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 4211 12526
100
0086
100
2
.. . (6)
n
TT
=−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ +
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 9660 2632
100
6415
100
.. .

  −
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − 0185
100
1017642
2
..
 T
  (7)
Figure 3 depicts the relationships between the para-
meters of the 2A97 superplastic alloy and the tem-
perature and strain rate. Seen from Figure 3a, the elastic
modulus decreases with the increase of the temperature
and the decrease of the strain rate. The effect of tem-
perature on elastic modulus is greater than that of the
strain rate. With an increase of the temperature, the
strain-rate sensitivity index increases, the strain-soften-
ing factor decreases first and then increases, and the
material coefficient increases first and then decreases, as
seen from Figure 3b. The strain-hardening factor
decreases with an increase of the temperature and a
decrease of the strain rate, as shown in Figure 3c.
The comparison between the experimental and fitted
curves under different strain rates at 410 °C is shown in
Figure 4. The theoretical stress-strain curves are in good
agreement with the actual ones. It can be seen that the
flow curve could be divided into three stages in the
tensile test. At the first stage, the flow stress increases
with the increase of the strain. At the second stage, the
curves of different strain rates can be divided into two
types: softening and steady state. Within the range of
high strain rates (> 0.001 s
–1
), the flow stress tends to be
stable during the deformation process, indicating a dyna-
mic balance between strain hardening and softening. In
the range of low strain rate (< 0.001 s
–1
), the flow stress
decreases continuously with the strain. The strain hard-
ening behavior was mainly caused by sub-grain growth.
Since the stacking-fault energy of an aluminum alloy is
relatively low, the softening behavior might be attributed
to two factors: the decreasing true strain rate and the
dynamic recrystallization.
30
At the third stage, the flow
stress rapidly decreases, and the localized necking occurs
at the specimens until fracture. The fitting curve accur-
ately reveals this flow behavior. Therefore, the consti-
tutive equation can represent the flow stress of the 2A97
alloy for the temperature range of 350–430 °C with the
strain rate of 0.001 s
–1
to 0.03 s
–1
, and could be used for
the theoretical computation of the forming limits.
L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
400 Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405
Figure 4: Comparison between the experimental and fitted curves
under different strain rates at 410 °C
Figure 3: Diagrams of the relationships between the parameters, the
temperature and the strain rate

3.2. Forming-Limit diagram
In order to establish the FLD of the superplastic
2A97 Al-Li alloy, the superplastic bulging tests with
different die ratios were carried out at (350, 390, and
430) °C. According to the constitutive equation men-
tioned above, the forming process was fitted by ANSYS
software, and the bulging pressure rate corresponding to
the initial strain rate of 1× 10
–3
s
–1
was 0.04 MPa/min. All
the bulging experiments were carried out until the
specimens failed. Figure 5 shows the macroscopic view
of the specimens after bulging with different dies ratios
at 390 °C.
The forming pressure and peak height of the bulge
samples deformed at different temperatures with diffe-
rent tool aspect ratios are plotted in Figures 6a and 6b.It
can be seen from Figure 6a that increasing temperature
generally reduces the forming pressure and increases the
dome height. When the die ratio is 4:3, the forming
pressure is 3.4 MPa and the dome height is 34.12 mm at
350 °C. While the temperature increase to 430 °C, the
forming pressure and dome height are 1.96 MPa and
35 mm, respectively. The effect of temperature on the
forming pressure is greater than that on the bulging
height. It can be concluded from Figure 6b that the
forming pressure increases and the bulging height
decreases with the increase of the tool aspect ratio at the
same temperature. At 390 °C, the forming pressure is
only 1.66 MPa and the dome height is 40.2 mm with the
die ratio of 1:1. When the die ratio is increased to 8:3,
the forming pressure is increased to 4 MPa and the dome
height is 26.96 mm. The forming pressure and dome
height appear to be sensitive to the die ratios. The
thickness distribution is an important index to measure
the uniformity of the superplastic bulging. In order to
investigate the thickness distribution of deformed parts,
specimens were cut along the 0 and 45° section. A
thickness gauge was used to measure the thickness along
the cross-section and thickness reduction was calculated
and plotted as a function of the location along the
cross-section, as shown in Figure 6c. It shows that the
thickness distribution of the parts after superplastic
bulging at (350, 390 and 430) °C with the die ratio of
1:1. The thickness reduction appears to decrease with
increasing temperature. The maximum thickness reduc-
tion at (350, 390 and 430) °C are (86.3, 85, and 84.1) %,
respectively.
In order to calculate the superplastic forming limit of
the 2A97 Al-Li alloy, the grids near the fracture zone of
the deformed specimen were selected to measure with
the single-grid method. The principal and secondary
strains of each grid were calculated and the FLD was
drawn. Figure 7a shows the FLD of the 2A97 Al-Li
alloy with different die ratios at 390 °C. It can be seen
that the data points obtained under different die ratios are
L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405 401
Figure 6: Forming pressure and dome height plotted as a function of:
a) temperature and b) tool ratio for tests performed at 390 °C, c) thick-
ness distribution plotted as a function of distance along the section
Figure 5: Superplastic bulge specimens with different die ratios at
390 °C

scattered, and the material is sensitive to the stress state.
Figure 7b shows the FLD of 2A97 alloy at different
temperatures. The deformation necking zone of the ma-
terial is shown in the shadows of the figure. The safety
zone is below the necking zone and the failure zone is
above the necking zone. It can be seen from Figure 7b
that the forming limit at 390 °C is obviously better than
that at 350 °C and 430 °C. This is consistent with the
tensile properties at this strain rate.
3.3. Cavitation
The intrinsic problem with the present methods of
superplastic forming is the nonuniform thickness ob-
served in the formed components. Cavity formation is
another disadvantage associated with superplasticity.
Thickness variation and cavitation affect the mechanical
properties of the superplastically formed components.
23
To measure the extent of cavitation in the deformed
regions, samples were extracted from the formed parts
and investigated with optical microscopy. The cavity
L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
402 Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405
Figure 8: Optical micrographs showing the cavitation of 2A97 deformed at 390 °Cwith a die ratio of 1:1 corresponding to different thinning
ratios (rolling direction is horizontal)
Figure 7: Forming-limit diagram of 2A97 alloy: a) at 390 °C with different tool ratios, b) at different temperatures with the tool ratios of 1:1 and
4:3

distribution at the different thinning ratios of the
deformed part at 390 °C with a die ratio of 1:1 is shown
in Figure 8. It can be concluded that with the increase of
the thinning ratio,  t
, the degree of cavitation increases.
Where the thinning ratio is 25 %, there are few voids; the
number of voids does not increase significantly at the
thinning ratio of 42 %. The density of the cavities
increases significantly where the thinning rate reaches
74 %. Some cavities interconnect and aggregate at the
bulging rupture ( t
= 85 %). There are not only a large
number of large cavities but also a large number of small
voids in this region, indicating that cavity nucleation and
growth coexist in the superplastic bulging process.
In order to quantitatively evaluate the cavitation be-
havior of the 2A97 Al-Li alloy after superplastic bulging,
the fraction of cavities is calculated. The volume fraction
of cavities, which can be approximated as the area
fraction of cavities, is the sum of the products of the
population and the size of the individual cavities.
18
Two-dimensional measurements of cavities on the
cutting planes were conducted via computer imaging
using the method discussed in
31
. Figure 9 depicts the
variation of the cavity area fraction with the thinning
ratio for equi-biaxial tension at 390 °C. As can be seen
from Figure 9, the cavity area fraction increases expo-
nentially with the thinning ratio. When  t
<4 0% ,t h e
cavity area fraction increases slowly with the thinning
ratio. While  t
> 40 %, the cavity area fraction increases
rapidly with deformation. This clearly shows that new
cavities were continuously nucleated with the increasing
strain. The increase of strain not only promotes the rapid
growth of cavities generated by low deformation, but
also promotes the nucleation of new cavities. It is
believed that cavity nucleation during superplastic
deformation (SPD) is caused by the stress concentration
at a particle or ledge in the grain boundary produced by
grain-boundary sliding (GBS).
23,32
Based on the existing
models, it appears that cavity nucleation is a result of the
stress concentration arising from incomplete accommo-
dations of the GBS. It can be assumed that both the
cavity growth and the nucleation of new cavities contri-
buted to the increasing cavity volume fraction. So, when
the thinning ratio reaches a certain degree, the cavity
area fraction will increase rapidly with the strain. It con-
firms that cavity growth is essentially strain-controlled
during superplastic deformation.
33
The effect of temperature on cavitation is presented
in Figure 10, from samples with a thinning ratio of
 85 % for the three test temperatures. Clearly, the speci-
mens deformed at the optimum superplastic temperature
of 390 °C exhibited the least cavitation. An increasing or
decreasing temperature resulted in an increase in the
cavity volume fraction for a given strain. At the lowest
test temperature of 350 °C, the size of cavity is small, but
the number is large. This may be due to the stress con-
centration caused by insufficient GBS at low temper-
ature, which promotes the cavity nucleation. At 430 °C,
the significant cavity coalescence and linkage lead to an
increase in the volume fraction of the cavities. The
deformed sample exhibits the highest ratio of large-size
cavities and the cavity volume fraction. This is attributed
to a more intense grain growth during higher-tempera-
ture exposure. In addition, the increase in the grain size
results in an increase in the cavitation tendency in the
superplastic materials.
34
Therefore, the size and volume
fraction of the cavities of 2A97 increase with increasing
temperature from 390 °C to 430 °C. The large-size
cavities are most harmful to the overall properties of the
superplastically formed components and healed with
difficulty by subsequent treatment. Therefore, the SPF of
L. JIA et al.: FORMING-LIMITS ANALYSIS OF THE SUPERPLASTIC 2A97 Al-Li ALLOY
Materiali in tehnologije / Materials and technology 54 (2020) 3, 397–405 403
Figure 10: Effect of temperature on cavitation of 2A97 for  t
= 85 % (rolling direction is horizontal)
Figure 9: Cavitation volume fraction plotted as a function of thinning
ratio for equi-biaxial tension at 390 °C

2A97 at lower temperatures is a practical requirement,
which at high temperature should be avoided.
The results of the bulge test in this paper show
significant scatter in terms of the forming-limit data.
This is closely related to the accumulated damage and
the final failure mode of high-strength aluminum alloy,
in which cavity coalescence eventually induces failure.
23
The nucleation, growth and aggregation of cavities or
voids occur during superplastic deformation. The da-
mage accumulation in the superplastic forming process
is a complicated, dynamic process in which a wide
variety of cavity formations can occur. The low-flow
stresses in the SPF make it possible for the material to
continue to form even though the material contains
significant cavitation.
19
The strain values obtained by
measuring the grids near the fracture zone cannot reflect
the real damage of the material. Therefore, the FLD is
not a perfect method for evaluating the forming perform-
ance of superplastic forming. The true criterion for
material failure should be considered to be when the
material has attained a certain extent of cavitation, rather
than when the material ruptures.
4 SUMMARY AND CONCLUSIONS
This work focuses on the failure modes of the
superplastic 2A97 alloy rolled sheet and considers the
metrics necessary to establish practical superplastic
forming limits. The superplastic tensile behavior, form-
ing limit, and cavitation are studied in this paper. Some
conclusions are summarized as follows:
1) The flow stresses of the 2A97 alloy in the tem-
perature range 350–430 °C with an initial strain rate
ranging from 1×10
–3
s
–1
to 3×10
–2
s
–1
, are accurately
characterized by the modified Hooke equation and
Grossman equation. The theoretical stress-strain curves
are in good agreement with the actual ones.
2) Results of the bulge tests show significant scatter
in terms of failure strain. The FLD is not a perfect me-
thod for evaluating the superplastic forming performance
of the 2A97 Al-Li alloy. But the dome height and thick-
ness reduction provide useful and quantifiable data that
may be applicable to establish a suitable criterion for
determining the practical forming limits when coupled
with proper consideration of the role of cavitation. Dome
height and forming pressure appear to be more sensitive
to tool ratio than temperature.
3) The cavity volume fraction should be specified as
the forming-limit index of the 2A97 alloy. Therefore, it
is necessary to study the cavitation during SPF. The
evolution of cavity volume is due to both nucleation and
the growth of cavities. Cavity growth is essentially
strain-controlled during superplastic deformation.
Acknowledgment
This research was carried out with funding from the
National Basic Research Program of China (973
Program, Grant No. 2011CB012804) and the National
Natural Science Funds of China (Grant No.
51605458,51334006,51405457). The authors would like
to acknowledge assistance of these programs for the
financial support.
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