Inherent internal friction of B2
! R and R ! B19
0
martensitic
transformations in equiatomic TiNi shape memory alloy
S.H. Chang and S.K. Wu
*Department of Materials Science and Engineering, National Taiwan University, 1 Roosevelt Rd. Sec. 4, Taipei 106, Taiwan, ROC Received 15 March 2006; revised 19 April 2006; accepted 28 April 2006
Available online 26 May 2006
The inherent internal frictions IFB2!R
PT þ IFI and IFR!B19
0
PT þ IFI of Ti50Ni50alloy are studied under isothermal conditions. The
tan d values of IFB2!R
PT þ IFI and IFR!B19
0
PT þ IFI are both proportional to r0/t1/2and thus the damping mechanism of IFB2!RPT þ
IFI and IFR!B19
0
PT þ IFI is related to the stress-assisted martensitic transformation and stress-assisted motions of twin boundary.
The tan d value of IFR!B19PT 0þ IFIis larger than that of IFB2!RPT þ IFIbecause of the larger transformation strain and the greater twin
boundaries associated with the R! B190transformation.
2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Shape memory alloys (SMA); Martensitic phase transformation; Internal friction; Dynamic mechanical analysis
TiNi-based alloys exhibiting a thermoelastic mar-tensitic transformation are known as the most impor-tant shape memory alloys (SMAs) with a good shape memory effect and superelasticity [1]. It has also been reported that TiNi SMAs perform a high level of mechanical damping and are suitable for energy dissipa-tion applicadissipa-tions [2–9]. The high damping obtained in
both R-phase and B190 martensite of TiNi SMAs is
attributed to the movement of their twin boundaries
[5]. In addition, the occurrence of R-phase can signifi-cantly soften the storage modulus E0and thus promote
the damping capacity of TiNi SMAs[10].
It has been proposed that the internal friction of a first-order phase transformation can be decomposed into three terms: IFTr, IFPT, and IFI [11–14]. The first
term IFTris a transitory internal friction which appears
only at low frequency and non-zero heating/cooling rates. The second term IFPTis the internal friction due
to phase transformation, but it does not depend on the heating and cooling rates. The third term IFI is the
intrinsic internal friction of the austenitic or martensitic phase.
All of the aforementioned reports focus on studies involving IFTr characteristics; however, the inherent
internal friction (IFPT+ IFI) of TiNi SMAs associated
with the phase transformation under isothermal
condi-tions has not been systematically investigated. In this study, equiatomic TiNi SMA was severely cold-rolled and then annealed at 650C for 2 min to obtain a
two-stage B2! R ! B190 transformation during cooling.
The damping capacity tan d values of B2! R ! B190
martensitic transformation were measured using a dynamic mechanical analyzer (DMA) under isothermal conditions at different temperatures. The isothermal damping characteristics of B2! R and R ! B190
trans-formations are discussed.
Equiatomic Ti50Ni50 alloy was prepared by
conven-tional vacuum arc remelting. The as-melted ingot was hot-rolled at 850C into a 2 mm thick plate and then the plate was solution-treated at 850C for 2 h followed by quenching in water. Then, the plate was cold-rolled at room temperature along the hot-rolling direction and reached a final 30% thickness reduction. No anneal-ing was conducted duranneal-ing cold-rollanneal-ing so as to avoid the occurrence of recrystallization. Subsequently, the cold-rolled plate was cut into test specimens, sealed in an evacuated quartz tube and annealed at 650C for 2 min. Transformation temperatures of cold-rolled and annealed specimens were determined by differential scanning calorimetry (DSC) using TA Q10 DSC equip-ment. The weight of the specimen used in DSC was about 30 mg and the heating and cooling rates were
set at 10C/min. Specimens for DMA experiment were
cut to the dimensions 40· 5 · 1.26 mm3along the roll-ing direction to eliminate the influence of rollroll-ing texture
[15]. Tan d and storage modulus E0were measured by
1359-6462/$ - see front matter 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2006.04.044
* Corresponding author. Tel.: +886 2 2363 7846; fax: +886 2 2363 4562; e-mail:skw@ntu.edu.tw
Scripta Materialia 55 (2006) 311–314
TA 2980 DMA equipment using various cooling rates, amplitudes and frequencies. The inherent damping char-acteristics of the specimens were also investigated by DMA, but tested under isothermal conditions. The de-tailed procedure for the isothermal DMA test was con-ducted as follows. The specimen was initially cooled at a constant cooling rate, starting from 150C, and was kept isothermally for 30 min at the set temperature. After this, the specimen was heated to 150C to ensure it had returned to the B2 parent phase. Then, the spec-imen was cooled to another temperature and kept isothermally at that temperature for 30 min, and so on. During the isothermal conditions, the set
tempera-ture was chosen to be in between +80C and 80 C
in which the B2! R ! B190 two-stage martensitic
transformation can be covered.
Figure 1(a) and (b) shows the DSC and DMA curves, respectively, of 30% cold-rolled Ti50Ni50alloy annealed
at 650C for 2 min. InFigure 1(a), there are two trans-formation peaks, i.e. B2! R and R ! B190, in the
forward transformation and one B190! B2
transforma-tion peak in the reverse.Figure 1(b) illustrates the tan d and storage modulus E0curves of the specimen of
Fig-ure 1(a). Only the cooling curves with _T ¼ 1C=min,
t= 1 Hz and amplitude of r0= 5 lm are shown in
Figure 1(b) for clarity. Two peaks also appear in the
tan d curve which correspond to the B2! R and
R! B190 transformation peaks observed in the DSC
curve shown inFigure 1(a). The peak temperatures mea-sured by DSC and DMA tests show a small shift due to different cooling rates and specimen sizes. Except for the aforementioned tan d transformation peaks, an extra broad peak is also observed in Figure 1(b) at about 65 C. This extra peak is known as the relaxation peak
[4], but it is not observed in the DSC curve.
Figure 2plots the tan d values vs. isothermal interval (0–30 min) ofFigure 1specimen under isothermal con-ditions. In Figure 2, tan d values of both the B2! R and R! B190transformations decrease with increasing
isothermal intervals and reach a steady value after 10–
15 min. From the B2! R and R ! B190 peaks, the
decayed tan d values during isothermal conditions repre-sent the aforementioned transitory internal friction IFTr
which is associated with the magnitude of _T , and the steady tan d values after 15 min of isothermal conditions are the inherent internal friction IFPT+ IFI during
phase transformation which is independent of _T . At
the same time, the IFTr of the B2! R transformation
under isothermal conditions, say IFB2!RTr , will collapse much faster than the IFR!B19Tr 0 of the R! B190
transfor-mation.
In order to investigate the inherent internal friction
for the B2! R and R ! B190 transformations, DMA
tan d tests under 30 min of isothermal conditions were conducted at different temperatures and the results are exhibited in Figure 3. The tan d curve of Figure 1(b)
24.3J/g 24.6J/g -1.2°C 24.4°C 50.4°C -0.6 -0.4 -0.2 0.0 0.2 0.4 H e a t flow (W/g) -150 -100 -50 0 50 100 150 Temperature (°C) Exo Up Universal V3.5B TA Instruments 30000 40000 50000 60000 70000
Storage modulus (MPa)
0.00 0.02 0.04 0.06 0.08 Tan delta -150 -100 -50 0 50 100 150
Temperature (°C) Universal V3.7A TA Instruments
R←B2 B19’ ←R cooling R←B2 B19’←R (a) (b)
Figure 1. (a) DSC curves measured at _T¼ 10C=min, (b) tan d and storage modulus E
0curves measured at _T¼ 1C=min, t = 1 Hz and r0= 5 lm
for 30% cold-rolled Ti50Ni50alloy annealed at 650C for 2 min.
0 5 10 15 20 25 30 35 0.00 0.02 0.04 0.06 0.08 0.10 B2->R transformation peak(23 o C) R->B19′ transformation peak (-2.5o C) Ta n δ
Isothermal interval (min)
IFTrB2→R
IFPTB2→R+IFI
IFPTR→B19’+IFI IFTrR→B19’
Figure 2. Tan d values vs. isothermal interval forFigure 1 specimen measured at t = 1 Hz, r0= 5 lm and isothermally at 23C (B2 ! R
martensitic transformation) and 2.5 C (R ! B190 martensitic
transformation). -150 -100 -50 0 50 100 150 0.00 0.02 0.04 0.06 0.08 0.10 -150 -100 -50 0 50 100 150 0.00 0.02 0.04 0.06 0.08 0.10 cooling at 1o C/min 1Hz 5μm T an δ Temperature (o C)
isothermal after 30 min
IFTrB2→R
IFPTB2→R+IFI IFTrR→B19’
IFPTR→B19’+IFI
Figure 3. Tan d values vs. temperature forFigure 1specimen measured at t = 1 Hz, r0= 5 lm. The solid curve is measured at _T¼ 1C=min
and the empty circle curve is the data of the specimen kept isothermally for 30 min.
(measured at _T ¼ 1C=min) is also plotted inFigure 3
for the purposes of comparison. When the isothermal temperature is set at about 30C, as indicated by the arrow, an inherent tan d peak corresponding to the B2! R transformation, say IFB2!RPT þ IFI, appears with
a tan d value of 0.018. The temperature shift between the IFB2!RPT þ IFIpeak ofFigure 3and the B2! R
transfor-mation peak of Figure 1(b) is due to the cooling rate effect. When the isothermal temperature is set at about 5C, as indicated by the double arrow, another inherent internal friction peak corresponding to the R! B190
transformation, i.e. IFR!B19PT 0þ IFI, appears with a tan d
value of 0.024.
Figure 4(a)–(c) shows the inherent tan d curves mea-sured under isothermal conditions at different _T , t and r0, respectively. As shown inFigure 4(a), all the
damp-ing behaviors durdamp-ing phase transformation are similar when measured at different _T .Figure 5(a) plots the tan d values of IFB2!RPT þ IFIand IFR!B19
0
PT þ IFIas a function
of _T measured inFigure 4(a). This figure shows that the magnitudes of IFPT+ IFI measured at different _T are
almost the same for the B2! R and R ! B190
transfor-mations. It indicates that both IFB2!RPT þ IFI and
IFR!B19PT 0þ IFIare independent of _T . Additionally, from
Figure 4(b) and (c), the tan d values of IFB2!RPT þ IFIand
IFR!B19PT 0þ IFI decrease with increasing t but increase
with increasing r0.Figure 5(b) plots the tan d values of
IFB2!RPT þ IFI and IFR!B19
0
PT þ IFI as a function of t
measured inFigure 4(b). It makes clear that the relation between IFPT+ IFIand t is non-linear; however, a
lin-ear relation between IFPT+ IFI and 1/t1/2 for both
IFB2!RPT þ IFIand IFR!B19
0
PT þ IFIis observed and shown
in Figure 5(c). Figure 5(d) plots the tan d values of IFB2!RPT þ IFI and IFR!B19
0
PT þ IFI as a function of r0
measured inFigure 4(c). InFigure 5(d), the magnitudes of both IFB2!RPT þ IFI and IFR!B19
0
PT þ IFI are linearly
proportional to r0. Also inFigure 5, note that the tan d
values of IFR!B19PT 0þ IFI are always larger than those of
IFB2!RPT þ IFI measured at various parameters.
As shown inFigure 1(b), for cold-rolled and annealed Ti50Ni50SMA, there are two internal friction peaks
cor-responding to B2! R and R ! B190 transformations
when the DMA test is conducted at constant _T . After the specimen is isothermal-treated (i.e. _T ¼ 0) at peak temperatures of the B2! R and R ! B190
transforma-tions, however, the tan d values decrease and only IFPTB2!R+ IFI and IFR!B19
0
PT þ IFI linger, as shown in
Figure 3. In Figure 5(a), both IFB2!RPT þ IFI and
IFR!B19PT 0þ IFI are independent of _T and hence their
damping mechanisms cannot be explained by Delorme’s model[11]. As illustrated inFigure 5(c) and (d), both the
-20 0 20 40 60 0.00 0.01 0.02 0.03 0.04 Tan δ Temperature (°C) cooling at 1°C/min cooling at 3°C/min cooling at 5°C/min -20 0 20 40 60 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Tan δ Temperature (°C) 0.05Hz 0.1Hz 1Hz 10Hz -20 0 20 40 60 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Tan δ Temperature (°C) 1μm 5μm 10μm 15μm (b) (a) IFPTB2→R+IFI IFPTR→B19’+IFI IFPTB2→R+IFI IFPTR→B19’+IFI (c) IFPTB2→R+IFI IFPTR→B19’+IFI
Figure 4. The inherent tan d curves measured under isothermal conditions at (a) t = 1 Hz and r0= 5 lm with different _T , (b) at _T¼ 1C=min and
r0= 5 lm with different t and (c) at _T¼ 1C=min and t = 1 Hz with different r0.
0 1 2 3 4 5 6 0.00 0.02 0.04 0.06 0.08 0.10 IFPT B2->R+IF I IFPT R->B19'+IF I Tan δ
Cooling rate (oC/min)
0 2 4 6 8 10 12 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Tan δ Frequency (Hz) IFPT B2->R+IF I IFPT R->B19'+IF I 0 1 2 3 4 0.00 0.02 0.04 0.06 0.08 0.10 Tan δ 1/υ1/2(1/Hz1/2) IFPT B2->R +IFI IFPT R->B19' +IFI Linear Fit of IFPT B2 ->R +IFIR=0.969 Linear Fit of IFPT R->B19' +IFIR=0.981 0 5 10 15 20 0.00 0.02 0.04 0.06 0.08 0.10 Tan δ σ0(μm) IFPTB2> R+IF I IFPT R> B19'+IF I Linear Fit of IFPT B2> R+IF IR=0.993 Linear Fit of IFPT R> B19'+IF IR=0.992 (a) (b) (d) (c)
Figure 5. Tan d values of IFB2!RPT þ IFIand IFR!B19
0
PT þ IFIobtained inFigure 4as a function of (a) _T , (b) t (c) 1/t 1/2
and (d) r0.
tan d values of IFB2!RPT þ IFIand IFR!B19
0
PT þ IFIare
line-arly proportional to r0/t1/2 when the applied t and r0
are within 10 Hz and 15 lm, respectively. This feature is closely related to the formation of abundant twin
boundaries and phase interfaces during the B2! R !
B190 martensitic transformation. The amplitude of
stress-assisted martensitic transformation can increas-ingly correspond with increasing r0 and hence lead to
a higher energy dissipation of IFPT. This characteristic
corresponds with Dejonghe’s model[12]which proposed that the tan d value of IFPT is linearly proportional to
the r0 measured at _T ¼ 0. Besides, the tan d value of
IFIin R-phase and B190martensite which is
correspond-ing to the stress-assisted motions of twin boundary also increases with increasing r0. Consequently, we conclude
that tan d values of IFB2!RPT þ IFIand IFR!B19
0
PT þ IFIare
linearly related to r0/t1/2 and independent of _T . This
indicates that the damping mechanism of IFPT+ IFI
is mainly generated from stress-assisted martensitic transformation and stress-assisted motions of twin boundary during martensitic transformation but not from thermal-induced martensitic transformation.
Meanwhile, as illustrated inFigures 4 and 5, the tan d values of IFR!B19PT 0þ IFIare always larger than those of
IFB2!RPT þ IFI under the same conditions. This is owing
to the transformation strain of R! B190 being larger
than that of B2! R transformation [5]. Moreover, it is well known that there is an abundance of twin bound-aries in the R-phase and B190martensite of TiNi SMAs.
These twin boundaries can self-accommodate the strain which comes from the stress-induced movement of twin boundaries between the variants of R-phase or B190
martensite. Both R-phase and transformed B190
martensite subsist during the R! B190transformation,
while only transformed the R-phase appears during
the B2! R transformation. Accordingly, more twin
boundaries result in a greater dissipation of energy and a higher tan d peak during the R! B190
transfor-mation.
In conclusion, both tan d values of inherent internal friction IFB2!RPT þ IFI corresponding to the B2! R
transformation and IFR!B19PT 0þ IFI corresponding to
the R! B190 transformation are linearly proportional
to r0/t1/2 but independent of _T . The damping
mecha-nism of IFB2!RPT þ IFI and IFR!B19
0
PT þ IFI is mainly
generated from the stress-assisted martensitic transfor-mation and stress-assisted motions of twin boundary, but not from thermal-induced martensitic transforma-tion. The tan d values of IFR!B19PT 0þ IFIare always larger
than those of IFB2!RPT þ IFIdue to the larger
transforma-tion strain and the greater amount of twin boundaries associated with R! B190transformation.
The authors gratefully acknowledge the financial support for this research provided by the National Science Council (NSC), Taiwan, Republic of China, under Grants Nos. NSC93-2216-E002-003.
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