Various stages in stress–strain curve of Ti–Al–Nb
alloys undergoing SIMT
Archana G. Paradkar a,∗ , S.V. Kamat a , A.K. Gogia b , B.P. Kashyap c
a
Defence Metallurgical Research Laboratory, Hyderabad 500058, AP, India
Project Office (Materials), Kaveri Engine Programme, Hyderabad 500058, AP, India
c Indian Institute of Technology, Department of Metallurgical Engineering and Material Science, Mumbai 400076, Maharashtra State, India
b
Abstract
Ti–Al–Nb alloys in the present range of composition were found to exhibit a typical four-stage behaviour observed in alloys undergoing stressinduced martensitic transformation (SIMT) in ␤ as well as ␣2 –␤ heat-treated condition. Intermittent unloading–reloading during tensile test was
used to measure the apparent modulus at regular strain intervals. This coupled with the observation of microstructure of the samples from tensile
tests interrupted at each of the four stages was used to identify the operative mechanism of each stage.
Keywords: Ti–Al–Nb alloys; Apparent modulus; Stress-induced martensitic transformation (SIMT)
1. Introduction
Stress-induced martensitic (SIM) transformations in steels
and shape memory alloys are studied extensively [1–4]. Alloy
undergoing SIM transformation exhibits a typical stress-plateau
in the tensile stress–strain curve (Fig. 1). The curve delineates
four distinct stages and the numbers in Fig. 1 denote these stages
during deformation. Several investigations [1,5–14] have been
carried out to clarify the nature of each stage in Ni–Ti and
the results of these studies are summarized in the following.
Stage 1 is the initial linear elastic region. In this stage, the parent phase undergoes an elastic deformation [5,6]. Stage 2 or
stress plateau region corresponds to stress-induced transformation of metastable parent phase to martensite or reorientation of
martensite present in initial microstructure [1,5,7]. In case the
reorientation of martensite is responsible for deformation strain,
the stress plateau is flat, but, when stress-induced martensite contributes to deformation strain, this stage is reported to exhibit
gradual increase in stress with increase in strain [8] resulting in
a rising stress plateau.
The mechanism of the deformation in stage 3 is not well
established. Some authors [1,9] have suggested that the defor-
mation in stage 3 is an elastic deformation of the martensite
phase formed in stage 2. Similar observations are also reported
by Vaidyanathan et al. [6]. However, transmission electron
microscopy observations by Melton and Mercier [10] revealed
an intersecting array of martensite laths in some part and dislocations in another part in a specimen deformed into stage 3.
However, their observation is limited to a small region of stage
3. Miyazaki et al. [11], on the other hand, reported that in Ni–Ti
alloy, this stage corresponds to the mixed processes of elastic deformation of stress-induced martensite formed in stage 2
and reorientation of martensite in combination with the further
stress-induced transformation of the parent phase.
Mohamed and Washburn [1] made an electron microscopy
observation of specimens elongated by 8% and found heavy
irregularity of martensite boundaries. Thus, they suggested that
slip occurred at the stage 4 in Ni–Ti alloy. Michel [12] and
Tadaki and Wayman [13] also made the electron microscopy
observation of heavily cold-rolled (∼30%) specimens, which
roughly corresponded to stage 4 in tensile tests. They both found
high density of dislocations and the segmentation of martensites.
These results are clear evidence to show that slip occurs in stage
4. Stage 4 defines the plastic deformation of oriented martensite
or martensite and retained parent phase, if any, depending upon
the initial microstructure. Similar four-stage stress–strain curves
are also reported in Cu–AI–Ni single crystals in specific orientations [14]. While the first two stages are similar to those seen
293
Table 2
Solutionising temperatures for various alloys
S/N
1
2
3
4
Fig. 1. Typical stress–strain curve for an alloy undergoing SIM (numbers denote
various stages during tensile testing).
in Ni–Ti alloy, the deformation modes in stages 3 and 4, in this
case, are proved unambiguously to be due to the elastic deformation of a martensite and martensite-to-martensite transformation,
i.e. successive stress-induced transformation, respectively [14].
Thus, it is seen that the operative mechanisms during the various
stages of stress–strain curve are dependent on the alloy system.
SIM in Ti alloys is well reported in literature [15–24].
Ti–Al–Nb alloys containing 15–18 at.% Al and 8–12 at.% Nb
are also reported to undergo SIM in ␤ WQ condition [25].
The present investigation is aimed at studying the operative mechanisms during the tensile deformation of Ti–Al–Nb
alloys undergoing stress-induced transformation for various heat
treatments resulting in either fully single-phase ␤ microstructure or (␤ + ␣2 ) microstructure with different volume fraction
of ␣2 . Three alloys, viz. Ti–15Al–8Nb, Ti–15Al–12Nb and
Ti–18Al–8Nb were selected for this purpose.
2. Experimental work
Ingots of Ti–15Al–8Nb, Ti–15Al–12Nb and Ti–18Al–8Nb
alloys were melted by consumable vacuum arc melting process.
The nominal composition of the alloys is listed in Table 1.
The ␤ transus temperatures of the alloys were found to
be 1000, 950 and 1060 ◦ C for Ti–15Al–8Nb, Ti–15Al–12Nb
and Ti–18Al–8Nb, respectively. The ingots were first forged in
single-phase ␤ region and hot rolled at a temperature 100 ◦ C
below the ␤ transus to 14 mm thick plates in several passes.
Few samples were ␤ solution treated and water-quenched to get
single-phase ␤ structure. The volume fraction of ␣2 is varied
%␣2
0
∼10
∼20
∼40
Solution treatment temperature (◦ C)
Ti–15Al–12Nb
Ti–15Al–8Nb
Ti–18Al–8Nb
970
920
880
840
1010
965
926
886
1080
1026
985
941
by heat-treating in ␣2 –␤ region at different temperatures so as
to obtain different volume fractions of ␣2 , viz. 10, 20 and 40%
(Table 2) and then water quenched.
The tensile samples of 4 mm diameter and 10 mm gage length
(parallel to the rolling direction) were machined and stress
relieved after machining and pickled so as to avoid masking
of the true flow behaviour of the alloy [25]. The tensile tests
were carried out using strain gauges on a servo-hydraulic Instron
Universal Testing Machine at a crosshead speed of 1 mm/min.
A set of specimens in ␣2 –␤ and ␤ water-quenched condition for all the three alloys were loaded, unloaded and reloaded
several times at regular strain intervals during the tensile deformation with holding time of 2 min after each loading and
unloading. The apparent modulus was measured by taking the
average of the unloading and reloading stage. Few samples
of Ti–15Al–8Nb alloy, as a representative case, were electropolished and the tensile test was interrupted at each stage for
SEM observations.
3. Results and discussions
Microstructures of all the alloys in ␣2 –␤ and ␤ waterquenched condition are similar and representative micrographs
for Ti–15Al–8Nb in ␤ and ␣2 –␤ heat-treated conditions are
shown in Figs. 2 and 3, respectively. The microstructure shows
single-phase structure (Fig. 2), in ␤ water-quenched condition
and a two-phase structure in ␣2 –␤ (Fig. 3a–c) water-quenched
condition, which is confirmed by XRD (Figs. 2b and 3d) to be
␤ and ␤ + ␣2 , respectively.
Ti–Al–Nb alloys in the present range of composition,
show typical four-stage behaviour in both ␤ and (␣2 –␤)
water-quenched condition during the tensile test, similar to
observations in Ni–Ti alloy [5], and representative σ–ε curves for
Ti–15Al–8Nb are shown in Fig. 4. In the present case, however,
the stress-plateau is slightly rising. This indicates that the transformation strain in the present case is due to the stress-induced
transformation of ␤ to martensite [8].
In Ti alloys, the elastic modulus of orthorhombic martensite
(␣ ) is significantly different than that of ␤ phase. The phase
Table 1
Nominal composition of the alloys
Alloy
Al, wt.% (at.%)
Nb, wt.% (at.%)
O (wt.%)
N (wt.%)
Ti
Ti–15Al–8Nb
Ti–15Al–12Nb
Ti–18Al–8Nb
8 (14.4)
7.8 (14.5)
10.10 (17.9)
15.75 (8.23)
21.90 (11.82)
15.9 (8.18)
0.0450
0.0415
0.0450
0.0085
0.0100
0.009
Balance
Balance
Balance
294
Fig. 2. (a) Optical micrograph and (b) XRD of the Ti–15Al–8Nb alloy in ␤ water-quenched condition showing ␤ phase.
change from bcc to orthorhombic martensite during the deformation would then be reflected by a change in the elastic modulus.
Thus, the measurement of the apparent modulus can be used as
a tool for tracking the SIM transformation in these alloys and
hence identifying the various stages in the tensile stress–strain
curve. The term “apparent modulus” is used here as the modulus obtained on unloading and reloading is not the true modulus
of mixture since secondary deformation mechanisms such as
stress-induced transformation and martensite reorientation are
also operative [5].
Representative stress–strain curves for Ti–15Al–8Nb alloy,
tested with intermittent unloading–reloading condition, in ␤ and
␣2 –␤ (10% ␣2 ) heat-treated conditions are shown in Fig. 5. Similar curves are obtained for other alloys in various microstructural
conditions.
Hysteresis is absent in stage 1. However, beyond this stage,
hysteresis is seen and it decreases with increase in strain.
The hysteresis seen during unloading and reloading (Fig. 5)
can be attributed to mechanical reversibility of stress-induced
martensite or partial reversibility of martensite reorientation
[26].
Figs. 6–8 depict the measured values of the apparent elastic
modulus plotted as a function of strain during different stages
of tensile deformation for the three alloys. It is seen from these
figures that the apparent modulus is high initially (see Table 3)
and does not change in stage 1. The modulus starts to decrease
as stage 2 commences and attains a stable value (Figs. 6–8) at
the end of stage 2, which is significantly lower than the corresponding initial modulus values (Table 3). The value does not
change subsequently in stages 3 and 4.
The microstructures of the specimens during each of the
four stages are also examined. Microstructure of the tensile
specimen of Ti–15Al–8Nb alloy interrupted at stage 1 (Fig. 9a)
shows that there is no change in the microstructure as a result
of loading to stage 1. This coupled with the observation that
the elastic modulus does not change in stage 1 indicates that
Fig. 3. SEM micrographs of alloy Ti–15Al–8Nb in: (a) (␤ + 10% ␣2 ) WQ, (b) (␤ + 20% ␣2 ) WQ, (c) (␤ + 40% ␣2 ) WQ condition and (d) XRD pattern showing
presence of ␣2 and ␤.
295
Fig. 4. Tensile stress–strain curves in ␤ and ␣2 –␤ water-quenched condition: (a) 1040 ◦ C/1 h/WQ, (b) 965 ◦ C/1 h/WQ, (c) 926 ◦ C/1 h/WQ and (d) 886 ◦ C/1 h/WQ
for Ti–15Al–8Nb alloy.
Table 3
Initial modulus of the alloys from σ–ε curves
Fig. 5. Intermittent loading unloading curves in: (a) ␤ WQ condition and (b)
␣2 –␤ heat-treated condition (10% ␣2 ) for Ti–15Al–8Nb alloy.
Alloy
10% ␣2
20% ␣2
40% ␣2
Ti–15Al–12Nb
Ti–15Al–8Nb
Ti–18Al–8Nb
74.68
78.89
90.68
79.81
83.45
96.54
89.04
92.96
104.06
Fig. 6. Variation of apparent modulus of elasticity vs. engineering strain for
Ti–15Al–12Nb alloy in various heat-treated conditions.
296
Fig. 7. Variation of apparent modulus of elasticity with engineering strain for Ti–15Al–8Nb alloy in various heat-treated conditions.
this stage corresponds to elastic deformation of the starting
microstructure.
The stress-induced martensite in Ti alloys is known to
have orthorhombic structure [27]. A representative micrograph
(Fig. 9b) of the Ti–15Al–8Nb alloy in ␤ heat-treated condition,
in the beginning of stage 2, shows a small volume fraction of
orthorhombic martensite (␣ ) needles along with retained ␤.
The microstructure at the end of stage 2 shows a considerably
higher volume fraction of ␣ needles along with some retained
␤. There is no significant change in the microstructure in stage
3 (Fig. 9c). The point to note is that no slip lines are observed
in the micrograph either in stage 2 or 3. However, the micrograph
Fig. 8. Variation of apparent modulus of elasticity with engineering strain for Ti–18Al–8Nb alloy in various heat-treated conditions.
297
Fig. 9. SEM micrographs of electro-polished tensile sample interrupted at various stages: (a) elastic region in stage 1, (b) at the beginning of stage 2 showing SIMT
of ␤ to ␣ , (c) in stage 3 showing absence of slip lines and (d) beginning of stage 4 showing slip lines for Ti–15Al–8Nb alloy in ␤ treated condition.
(Fig. 9d) in stage 4 clearly indicates the presence of slip lines.
The observation of the apparent modulus variation with strain
as well as the microstructure in the different stages confirmed
that the behaviour is similar in ␣2 –␤ heat-treated specimens.
The only difference is the presence of ␣2 in addition to ␤.
Stress-induced ␣ produced at the beginning of stage 2 in ␣2 –␤
Fig. 10. Similar stages are observed for alloy in ␣2 –␤ heat-treated condition.
Microstructure shows the presence of an additional phase primary ␣2 . SEM
micrographs of electro-polished tensile sample interrupted at the beginning of
stage 2 showing SIMT of ␤ to ␣ are seen for (20% ␣2 + ␤).
Fig. 11. XRD of Ti–15Al–8Nb alloy after deformation in: (a) ␤ WQ and (b)
␣2 –␤ WQ condition.
298
of the initial microstructural constituents. The stress-induced
martensitic transformation commences in the beginning of stage
2 and whatever transformation has to occur is completed by the
end of stage 2. Stage 3 corresponds to the elastic deformation
of retained ␤ + ␣ structure prevailing at the end of stages 2
and 4 corresponds to plastic deformation of this mixture. Thus,
the change in apparent modulus with strain can be used as an
excellent tool to track the different stages of tensile deformation.
The change in apparent modulus with strain can also be used
to estimate the volume fraction of martensite (␣ ) if one knows
the modulii of ␤ and ␣2 phases. This method could overcome the
limitation of measurement of volume fraction of martensite by
optical method which is not only time consuming and tedious but
also may not be very accurate due to the uncertainties associated
in resolving smaller martensitic laths.
4. Summary
The tensile curves for all the three alloys in both, ␤ and
␣2 –␤, solution-treated and water-quenched conditions depict
four-stage behaviour. It is established that stage 1 represents
the elastic deformation of the phases present in initial structure, stage 2 corresponds to stress-induced transformation of ␤
to martensite (␣ ), stage 3 represents the elastic deformation of
all the constituent phases and stage 4 corresponds to the plastic
deformation of the constituent phases.
Acknowledgements
Fig. 12. TEM micrographs of Ti–15Al–8Nb alloy after deformation in: (a) ␤
WQ (1040 ◦ C/1 h/WQ) and (b) ␣2 –␤ WQ (925 ◦ C/1 h/WQ) conditions, showing
presence of ␣ .
heat-treated condition for Ti–15Al–8Nb alloy for (␤ + 20% ␣2 )
is shown in Fig. 10.
The transformation of retained ␤ to orthorhombic martensite
(␣ ) during the tensile deformation is also clearly evident from
a representative XRD patterns of the Ti–15Al–8Nb alloy after
deformation as depicted in Fig. 11. All the alloys exhibit presence of an additional phase, i.e. orthorhombic martensite (␣ )
after deformation.
TEM micrographs of all the alloys after deformation, both in
␤ and ␣2 –␤ solution treatment and water-quenched conditions,
also indicate the presence of an additional phase, orthorhombic martensite (␣ ) as shown in representative micrograph of
the Ti–15Al–8Nb alloy after deformation (Fig. 12). This further
corroborates the results of XRD studies (Fig. 11).
The observation of the change in apparent modulus with the
strain as well as microstructure at each stage clearly indicates
that in the present alloys stage 1 represents elastic deformation
The authors like to thank all the members of Titanium group
for melting, members of rolling and forging group for processing
and members of SFSG group for characterization of the alloys.
Authors thank Dr. Vikas Kumar for his help during the experimentation and for helpful discussions. The authors would like to
thank DRDO, India, for providing funding and facilities for carrying out this work. The authors would also like to thank Director
DMRL, Hyderabad, for permission to publish this work.
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