Internal friction of R-phase and B19
martensite in equiatomic
TiNi shape memory alloy under isothermal conditions
S.H. Chang, S.K. Wu
∗Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan Received 6 May 2006; received in revised form 19 July 2006; accepted 19 July 2006
Available online 6 September 2006
Abstract
The intrinsic internal friction IFIof R-phase and B19martensite are composed of static internal friction IFSand dynamic internal friction IFD.
The tanδ values of IFRSand IF B19
S are both proportional toσ0/υ1/2and are related to the stress-assisted motions of twin boundaries. The tanδ values
of IFR
Sare higher than those of IF B19
S is owing to the softer storage modulus E0in R-phase. The tanδ values of IFB19
D are linearly proportional to
˙
T /υ1/2. The occurrence of relaxation peak at≈−60◦C is found to come from the IFB19
S , instead of the IF B19 D .
© 2006 Elsevier B.V. All rights reserved.
Keywords: Shape memory alloy; Thermal (dynamic mechanical) analysis; Internal friction; Martensite
1. Introduction
TiNi alloys are known as important shape memory alloys (SMAs) because of their functional properties such as shape
memory effect and superelasticity[1]. Many reported studies
revealed that TiNi SMAs exhibit a high internal friction peak associated with a shear modulus minimum during martensitic transformation and thus are suitable for the energy dissipation
applications[2–9]. The damping characteristics of internal
fric-tion peak during martensitic transformafric-tion are associated with
experimental parameters such as temperature rate ˙T , frequency
υ and amplitude σ0. It is also reported that both R-phase
pre-martensite and B19martensite in TiNi SMAs perform a high
damping property due to the easy movement of their twin
bound-aries in between the variants [5]. Besides, the occurrence of
R-phase can strongly soften the storage modulus E0and thus
promotes the TiNi SMAs’ damping capacity[10]. In addition to
the internal friction peaks in TiNi SMAs, there is also a relax-ation peak appearing at temperature around 200 K. Iwasaki and
Hasiguti[2]proposed that this relaxation peak is thermally
acti-vated and originates from dislocations.
It has been proposed that the internal friction of a first-order
phase transformation can be decomposed into three terms: IFTr,
∗Corresponding author. Tel.: +886 2 2363 7846; fax: +886 2 2363 4562. E-mail address:[email protected](S.K. Wu).
IFPTand IFI[11–17]. The first term IFTris the transitory
inter-nal friction which appears only at low υ and non-zero ˙T . It
depends on external parameters such as ˙T , υ, σ0 and volume
fraction transformed per unit time. The second term IFPTis the
internal friction due to the phase transformation, but it does not
depend on ˙T . The third term IFIis the intrinsic internal friction
of austenitic or martensitic phase measured at constant ˙T and
strongly dependent on microstructure properties such as dislo-cations, vacancies and twin boundaries. In the low frequency range, the internal friction peak observed during
transforma-tion is mainly ascribed to the first term IFTr. In equiatomic
TiNi SMA, Chang and Wu[18]reported that the inherent
inter-nal friction (IFPT+ IFI) measured under isothermal conditions
during B2→ R and R → B19 martensitic transformation are
linearly proportional toσ0/υ1/2but independent of ˙T . The
damp-ing mechanism of the inherent internal friction (IFPT+ IFI) is
mainly generated from the stress-assisted martensitic transfor-mation and stress-assisted motions of twin boundaries. However, all the reported studies focus on the damping characteristics of
transitory and inherent internal friction (IFTr, IFIor IFPT+ IFI)
during martensitic transformation. The damping characteristics of the single phase in TiNi SMAs, such as B2 parent phase,
R-phase premartensite and B19 martensite, under isothermal
conditions have not been systematically studied before. In this
study, the damping capacity tanδ values of a Ti50Ni50 SMA
which exhibits a two-stage B2→ R → B19 martensitic
trans-formation during cooling are measured by dynamic mechanical
0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.07.092
S.H. Chang, S.K. Wu / Journal of Alloys and Compounds 437 (2007) 120–126 121
analyzer (DMA) under isothermal conditions at different tem-peratures. Thereafter, the isothermal damping characteristics of
each single phase: B2, R-phase and B19 martensite are
dis-cussed.
2. Experimental procedures
Equiatomic Ti50Ni50alloy was prepared by conventional vacuum arc remelt-ing. The as-melted ingot was hot-rolled at 850◦C into a 2 mm thick plate and then the plate was solution-treated at 850◦C for 2 h followed by quench-ing in water. Then, the plate was cold-rolled at room temperature along the hot-rolling direction and reached a final 30% thickness reduction. Subse-quently, the cold-rolled plate was cut into test specimens with the dimension of 40 mm× 5 mm × 1.26 mm, sealed in an evacuated quartz tube and annealed at 650◦C for 2 min. The detailed procedure for preparing specimen is demon-strated in another paper[18].
Transformation temperatures of cold-rolled and annealed specimen were determined by differential scanning calorimetry (DSC) test using a TA Q10 DSC equipment with a constant cooling rate of 10◦C/min. Specimen for DMA experiment was cut along the rolling direction to eliminate the influence of rolling texture[19]. The tanδ and storage modulus E0were measured by a TA 2980 DMA equipment using a constant cooling rate of 3◦C/min. The isothermal damping characteristics of B2, R-phase and B19martensite were also investi-gated by DMA but tested under isothermal conditions using various amplitudes and frequencies. The detailed procedure for the isothermal DMA test was con-ducted as follows. The specimen was initially cooled starting from 150◦C at a constant cooling rate (1, 3 or 5◦C/min) and was kept isothermally for 30 min at the set temperature. After being isothermal for 30 min, the specimen was heated up to 150◦C to ensure it had returned to B2 parent phase. Then, the specimen was cooled to another set temperature and kept isothermally at that temperature for 30 min. During the isothermal conditions, the set temperature was chosen in between +80◦C and−80◦C in which B2, R-phase and B19martensite are all included.
3. Experimental results
3.1. DSC and DMA measurements at constant ˙T
Fig. 1shows the DSC and DMA curves of 30% cold-rolled Ti50Ni50alloy annealed at 650◦C for 2 min. As shown inFig. 1, there are two transformation peaks, i.e. B2→ R and R → B19obtained in DSC cooling curve. There are also two transformation peaks appearing in the tanδ curve which correspond to B2→ R and R → B19transformation peaks in DSC curve. Except the afore-mentioned tanδ transformation peaks, an extra broad peak which is not observed in DSC curve appears at about−65◦C in tanδ curve. This extra broad peak is
Fig. 1. DSC curve measured at ˙T = 10◦C/min and DMA curves measured at ˙T = 1◦C/min, υ = 1 Hz and σ0= 5m for 30% cold-rolled Ti50Ni50alloy annealed at 650◦C for 2 min.
Fig. 2. The tanδ values vs. isothermal interval forFig. 1specimen measured at υ = 1 Hz, σ0= 5m. The selected isothermal temperatures are 60◦C (B2 phase), 12.5◦C (R-phase) and−60◦C (B19martensite).
known as the relaxation peak[2,4]. Also fromFig. 1, the E0 curve declines gently in B2 parent phase while cooling, then drops drastically and exhibits a deeper minimum during B2→ R transformation and a shallower minimum dur-ing R→ B19transformation. After R→ B19transformation completes, the E0 value of B19martensite increases quickly with decreasing temperature.
3.2. DMA measurement under isothermal conditions
Fig. 2plots the tanδ values versus isothermal interval when the specimen of
Fig. 1is tested by DMA under isothermal treatment at 60◦C (B2 parent phase), 12.5◦C (R-phase) and−60◦C (B19 martensite) for 0–30 min. As shown in
Fig. 2, the measured tanδ values of B2 parent phase are almost the same in the whole isothermal conditions. However, both the measured tanδ values of R-phase and B19martensite decrease with increasing isothermal intervals and reach a steady value after 10–15 min. As illustrated inFig. 2, the tanδ values of R-phase and B19martensite are composed of a dynamic term IFDwhich diminishes during isothermal conditions and a static term IFSwhich is the steady value measured after 30 min of isothermal interval.
In order to investigate the damping characteristics of IFSand IFDfor B2, R-phase and B19martensite under isothermal conditions, DMA tanδ tests under 30 min isothermal interval at different temperatures were conducted with various
˙
T , υ, σ0and the results are exhibited inFigs. 3–5, respectively.Fig. 3(a)–(c) show the tanδ curves (empty mark curves) measured after 30 min isothermal interval at different temperatures when the specimen is conducted at the cooling rate ˙T of 1, 3 and 5◦C/min, respectively, before it reaches the set isothermal temperature. The solid lines inFig. 3(a)–(c) represent the tanδ curves measured at constant ˙T of 1, 3 and 5◦C/min, respectively.Fig. 4(a)–(c) show the tanδ curves measured after 30 min isothermal condition (empty mark curves) at differentυ of 0.1, 1 and 10 Hz, respectively.Fig. 5(a)–(c) are the tanδ curves measured after 30 min isothermal condition (empty mark curves) at differentσ0of 5, 10 and 15m, respectively. InFigs. 4 and 5, the tanδ curves measured at constant ˙T (solid line curves, ˙T = 1◦C/min) are also plotted for comparison. As shown inFigs. 3–5, all the tanδ values of B2 parent phase measured after isothermal conditions, i.e. IFB2
S , are quite low and approximately same as those measured at constant ˙T (IFB2
I ). The tanδ values of R-phase measured after isothermal conditions, i.e. IFR
S, are much higher than those of IFB2I . However, the tanδ values of B19 martensite measured after isothermal conditions, i.e. IFB19S , decline quickly after R→ B19transformation completes. With further isothermal treatment at lower temperatures, the tanδ values of IFB19S also exhibit a relaxation peak at around−60◦C.Fig. 6enlarges the diagram of B19martensite region inFig. 3(a) so to describe the decayed and steady tanδ values measured under isothermal conditions. As illustrated inFig. 6, the intrinsic internal friction IFIB19of B19 martensite measured at constant ˙T is composed of IFB19
S and IF B19 D .
Fig. 3. The intrinsic tanδ curves measured under isothermal conditions at υ = 1 Hz and σ0= 5m with different cooling rates of (a) ˙T = 1◦C/min (empty circle curve); (b) ˙T = 3◦C/min (empty triangle curve); and (c) ˙T = 5◦C/min (empty diamond curve).
4. Discussion
4.1. IFSof B2 parent phase, R-phase and B19martensite
From the DMA results exhibited inFigs. 3–5, all the internal
friction of IFB2S are very low and their tanδ values associated
Fig. 4. The intrinsic tanδ curves measured under isothermal conditions at ˙T = 1◦C/min and σ0= 5m with different frequencies of (a) υ = 0.1 Hz (empty circle curve); (b)υ = 1 Hz (empty triangle curve); and (c) υ = 10 Hz (empty diamond curve).
with ˙T , υ and σ0are inconspicuous to investigate. Thus, only
the effects of ˙T , υ and σ0on IFRSand IFB19S are discussed in the
following.Fig. 7(a) plots the tanδ values of IFRS and IFB19S as
a function of ˙T measured at 20◦C and−20◦C, respectively, in
Fig. 3. FromFig. 7(a), both the tanδ values of IFRS and IFB19S
fea-S.H. Chang, S.K. Wu / Journal of Alloys and Compounds 437 (2007) 120–126 123
Fig. 5. The intrinsic tanδ curves measured under isothermal conditions at ˙
T = 1◦C/min and υ = 1 Hz with different amplitudes of (a) σ0= 5m (empty circle curve); (b)σ0= 10m (empty triangle curve); and (c) σ0= 15m (empty diamond curve).
ture indicates that the tanδ values of IFRS and IFB19S are both
independent of ˙T .Fig. 7(b) and (c) plot the tanδ values of IFRS
and IFB19S as a function of 1/υ1/2 andσ0 measured at 20◦C
and−20◦C, respectively, inFigs. 4 and 5. As seen inFig. 7,
both IFRS and IFB19S are linearly proportional to σ0/υ1/2 but
independent of ˙T when the applied υ and σ0 are in between
Fig. 6. Enlarged diagram of B19martensite region inFig. 3(a).
0.1–10 Hz and 1–15m, respectively. This behavior is same
as the damping characteristic of the inherent internal friction
IFPT+ IFIof B2→ R and R → B19martensitic transformations
which is also linearly proportional toσ0/υ1/2and independent
of ˙T [18]. Therefore, the inherent internal friction IFPT+ IFIof
B2→ R and R → B19martensitic transformations and IFS of
the single R-phase and B19martensite may originate from the
similar damping mechanism. Since the inherent internal friction
IFPT+ IFI is mainly generated from stress-assisted martensitic
transformation and stress-assisted motions of twin boundaries
[18], the damping mechanism of IFRS and IFB19S is proposed to
be contributed by the stress-assisted movements of twin
bound-aries in between the variants of R-phase and B19 martensite,
respectively.
From Figs. 3–5, all the measured tanδ values of IFB2S are
quite low and very close to those of IFB2I . This feature indicates
that IFB2I is mainly contributed by the IFB2S while IFB2D is
insignificant in B2 parent phase. Also from Figs. 3–5, both
tanδ values of IFRS and IFB19S are much higher than those of
IFB2S . IFB2S exhibits a rather small intrinsic internal friction
because its tanδ only comes from the dynamic/static hysteresis
of lattice defects [5]. On the other hand, from DMA results
shown inFigs. 3–5, both IFRSand IFB19S have higher tanδ values
than those of IFB2S due to their abundant twin boundaries in
between the variants which can be easily moved by the external stress to accommodate the applied strain. This characteristic indicates that the effect of twin boundaries on internal friction is more dominant than that of the lattice defects/dislocations introduced by cold-rolled and annealed treatment. Since the
internal friction of IFRS and IFB19S are mainly contributed
by stress-assisted motions of twin boundaries, the effect of defects/dislocations due to thermal/mechanical process on damping behavior can be neglected in this study. Furthermore,
Figs. 3–5 also show that the tanδ values of IFRS are always
higher than those of IFB19S measured at the same experimental
parameter. This feature comes from the fact that the lower
storage modulus E0 in R-phase, as shown inFig. 1, leads to
the easier movement of twin boundaries in R-phase and hence
Fig. 7. The tanδ values of IFRSand IFB19S measured inFigs. 3–5at 20◦C and −20◦C as a function of (a) ˙T ; (b) 1/υ1/2; and (c)σ
0.
4.2. IFDof B19martensite
As illustrated inFig. 6, when the specimen is kept
isother-mally at B19martensite, the decayed tanδ value represents the
Fig. 8. The tanδ values of IFB19
D vs. temperature obtained at (a) different ˙T in
Fig. 3; (b) differentυ inFig. 4; and (c) differentσ0inFig. 5.
IFB19D . The damping behavior of IFRDis suggested to be similar
to that of IFB19D , but IFRD damping is difficult to measure due
to the R-phase having a narrow existing temperature range, as
shown inFig. 1. As a result, only IFB19D is discussed in detail in
S.H. Chang, S.K. Wu / Journal of Alloys and Compounds 437 (2007) 120–126 125
Fig. 9. The tanδ values of IFB19
D measured inFig. 8(a) and (b) at−20◦C, −30◦C,−40◦C and−50◦C as a function of (a) ˙T and (b) 1/υ1/2.
Fig. 8(a) plots the tanδ values of IFB19D versus.
tempera-ture in which IFB19D is calculated by subtracting IFB19
S from
IFIB19measured at different ˙T inFigs. 3 and 6. The temperature
deviation of IFB19S and IFIB19has been corrected by the peak
temperature shift of R→ B19transformation to eliminate the
influence of ˙T .Fig. 8(b) and (c) show the tanδ values of IFB19D as
a function of temperature at differentυ measured inFig. 4and at
differentσ0measured inFig. 5, respectively. As shown inFig. 8,
the tanδ values of IFB19D increase with ˙T but decreases with υ and
almost independent ofσ0.Fig. 9(a) and (b) plot the tanδ values of
IFB19D as a function of ˙T and 1/υ1/2, respectively, in which IFB19D
is measured at different temperatures (−20◦C,−30◦C,−40◦C
and−50◦C). As shown inFigs. 8(c) and 9, all the tanδ values of
IFB19D measured at different temperatures increase linearly with
increasing ˙T /υ1/2but independent ofσ0when the applied ˙T and
υ are in between 1–5◦C/min and 0.1–10 Hz, respectively. This
relationship is quite similar to that of IFRSand IFB19S except that
the termσ0is now replaced by ˙T . This feature demonstrates that
the damping mechanism of IFS is generated by stress-assisted
movements of twin boundaries while that of IFDis contributed
by thermal-assisted motions of twin boundaries. Furthermore,
Fig. 8 shows IFB19D does not exhibit a broad peak at around
−60◦C as IFB19
S shown inFigs. 3–5. This indicates the
occur-rence of relaxation peak only comes from the IFB19S , instead of
the IFB19D .
5. Conclusions
The intrinsic internal friction IFIof R-phase and B19
marten-site measured at constant ˙T is both composed of a static
term IFS which keeps steady after isothermal conditions and
a dynamic term IFD which diminishes during isothermal
con-ditions. Both tanδ values of IFRS and IFB19S are linearly
pro-portional toσ0/υ1/2when the appliedυ and σ0are in between
0.1–10 Hz and 1–15m, respectively. Consequently, the
damp-ing mechanism of IFRS and IFB19S is associated with
stress-assisted movements of twin boundaries in between the variants
of R-phase and B19 martensite, respectively. The tanδ value
of IFRS is higher than that of IFB19S because the R-phase has
softer storage modulus E0which leads to easier movement of
twin boundaries in R-phase and dissipates more energy
dur-ing dampdur-ing. The tanδ value of IFB19D increases linearly with
˙
T /υ1/2and is independent ofσ
0when the applied ˙T and υ are
in between 1–5◦C/min and 0.1–10 Hz, respectively. It implies
that the damping mechanism of IFRDis due to thermal-assisted
motions, instead of stress-assisted movements, of twin
bound-aries in B19 martensite. The occurrence of relaxation peak
at about −60◦C only comes from the IFB19S , instead of the
IFB19D .
Acknowledgement
The authors gratefully acknowledge the financial support for this research provided by the National Science Council (NSC), Taiwan, Republic of China, under Grants Nos. NSC94-2216-E002-030.
References
[1] C.M. Wayman, T.W. During, in: T.W. During, K.N. Melton, D. St¨ockel, C.M. Wayman (Eds.), Engineering Aspects of Shape Memory Alloys, Butterworth-Heinemam, London, 1990, pp. 3–20.
[2] K. Iwasaki, R. Hasiguti, Trans. JIM 28 (1987) 363.
[3] O. Mercier, K.N. Melton, Y. De Pr´eville, 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– C101.
[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–C601. [14] J. Van Humbeek, J. Stoiber, L. Delaey, R. Gotthardt, Z. Metallkd. 86 (1995)
1976.
[15] J.S. Zhu, R. Schaller, W. Benoit, Phys. Stat. Sol. A 108 (1988) 613.
[16] G. Gremaud, J.E. Bidaux, W. Benoit, Helv. Physica Acta 60 (1987) 947.
[17] J.E. Bidaux, R. Schaller, W. Benoit, Acta Metall. 37 (1989) 803. [18] S.H. Chang, S.K. Wu, Scripta Mater. 55 (2006) 311.
