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Inherent internal friction of B2 → R and R → B19′ martensitic transformations in equiatomic TiNi shape memory alloy

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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

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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.

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(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.

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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.

[1] C.M. Wayman, T.W. During, in: T.W. During, K.N. Melton, D. Sto¨ckel, C.M. Wayman (Eds.), Engineering Aspects of Shape Memory Alloys, Butterworth-Heine-mam, London, 1990, pp. 3–20.

[2] K. Iwasaki, R. Hasiguti, Trans. JIM 28 (1987) 363. [3] O. Mercier, K.N. Melton, Y. De Pre´ville, Acta Metall. 27

(1979) 1467.

[4] S.K. Wu, H.C. Lin, T.S. Chou, Acta Metall. 38 (1990) 95. [5] H.C. Lin, S.K. Wu, M.T. Yeh, Metall. Mater. Trans. A

24 (1993) 2189.

[6] K. Sugimoto, T. Mori, K. Otsuka, K. Shimizu, Scripta Metall. 8 (1974) 1341.

[7] Y. Liu, J. Van Humbeeck, R. Stalmans, L. Delaey, J. Alloys Compd. 247 (1997) 115.

[8] B. Coluzzi, A. Biscarini, R. Campanella, L. Trotta, G. Mazzolai, A. Tuissi, F.M. Mazzolai, Acta Mater. 47 (1999) 1965.

[9] S.K. Wu, H.C. Lin, J. Alloys Compd. 72–78 (2003) 355. [10] S.H. Chang, S.K. Wu, Key Eng. Mater. 319 (2006) 9. [11] J.F. Delorme, R. Schmid, M. Robin, P. Gobin, J. Phys.

32 (1971) C2-101.

[12] W. Dejonghe, R. De Batist, L. Delaey, Scripta Metall. 10 (1976) 1125.

[13] J.E. Bidaux, R. Schaller, W. Benoit, J. Phys. 46 (1985) C10-601.

[14] J. Van Humbeek, J. Stoiber, L. Delaey, R. Gotthardt, Z. Metalkd. 86 (1995) 1976.

[15] S.H. Chang, S.K. Wu, Scripta Mater. 50 (2004) 937.

數據

Figure 2. Tan d values vs. isothermal interval for Figure 1 specimen measured at t = 1 Hz, r 0 = 5 lm and isothermally at 23 C (B2 ! R martensitic transformation) and 2.5 C (R ! B19 0 martensitic transformation)
Figure 5. Tan d values of IF B2!R PT þ IF I and IF R!B19 PT 0 þ IF I obtained in Figure 4 as a function of (a) _T , (b) t (c) 1/t 1/2 and (d) r 0 .

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