Internal friction of B2 → B19′ martensitic transformation of Ti50Ni50 shape memory alloy under isothermal conditions

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Internal friction of B2

→ B19

martensitic transformation of

Ti

50

Ni

50

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 7 September 2006; received in revised form 7 November 2006; accepted 23 November 2006

Abstract

The inherent internal friction (IFPT+ IFI)B2→B19of cold-rolled and annealed Ti50Ni50alloy that exhibits B2→ B19martensitic transformation

is studied under isothermal conditions. The tanδ value of (IFPT+ IFI)B2→B19is proportional toσ0/ν1/2and its damping mechanism is thus related to

stress-assisted martensitic transformation and stress-assisted motion of twin boundaries. The tanδ value of (IFPT+ IFI)B2→B19is smaller than those of (IFPT+ IFI)B2→Rand (IFPT+ IFI)R→B19because the former shows no R-phase. The obliterated dislocations and defects after sufficient annealing can lower the tanδ value of the relaxation peak at about −60◦C.

Keywords: TiNi shape memory alloy; Martensitic transformation; Internal friction; Dynamic mechanical analysis

1. Introduction

TiNi-based alloys exhibiting a thermoelastic martensitic transformation are known as very important shape memory alloys (SMAs) with a good shape memory effect (SME) and superelasticity [1]. Many reported studies revealed that TiNi SMAs perform a high level of mechanical damping and are suit-able for energy dissipation applications[2–10]. Near equiatomic TiNi SMAs exhibit high internal friction peaks in the tempera-ture range of martensitic transformation and the magnitude of these internal friction peaks are associated with experimental parameters, such as temperature heating/cooling rate ( ˙T ), fre-quency (ν) and amplitude (σ0) [3]. In addition to the internal

friction peaks associated with martensitic transformation, the high damping property is also obtained in the R-phase and B19 martensite due to the easy movement of their own twin bound-aries [5]. Moreover, it has also been reported that a suitable control of the annealing conditions of cold-rolled TiNi SMAs can acquire a rather good damping capacity[10].

The internal friction of a first-order phase transformation is proposed to be decomposed into three terms: IFTr, IFPT and

IFI[11–14]. The first term IFTris a transitory internal friction,

which appears only at lowν and non-zero ˙T . The second term

∗_{Corresponding author. Tel.: +886 2 2363 7846; fax: +886 2 2363 4562.}

E-mail address:[email protected](S.K. Wu).

IFPTis the internal friction due to phase transformation, but it

does not depend on ˙T . The third term IFIis the intrinsic internal

friction of austenitic or martensitic phase and depends strongly on microstructure properties, such as dislocations, vacancies and twin boundaries.

All the aforementioned reports focus on the studies involving damping characteristics of transitory internal friction (IFTr);

however, only a few works discuss the inherent internal friction (IFPT+ IFI) during martensitic transformation and/or the

intrinsic internal friction (IFI) of a single phase measured under

isothermal treatment in TiNi-based SMAs. Chang and Wu[15]

reported that the inherent internal friction during B2→ R and R→ B19martensitic transformation, i.e., (IFPT+ IFI)B2→Rand

(IFPT+ IFI)R→B19, are both linearly proportional toσ0/ν1/2and

their damping mechanism is mainly generated from the stress-assisted martensitic transformation and stress-stress-assisted motions of twin boundaries. They also showed that the intrinsic internal friction IFIof the R-phase and B19martensite is composed of

static internal friction (IFS) and dynamic internal friction (IFD) [16]. The tanδ values of IFSin both R-phase and B19martensite

are proportional toσ0/ν1/2and are related to the stress-assisted

motions of twin boundaries. However, the damping character-istic of TiNi SMAs exhibited one-stage B2→ B19martensitic transformation under isothermal conditions has not been sys-tematically investigated. In this study, equiatomic TiNi SMA was severely cold-rolled and then annealed at 650◦C for 30 min to obtain a one-stage B2→ B19 transformation in cooling.

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measured by the dynamic mechanical analyzer (DMA) under isothermal conditions at different temperatures. Thereafter, the isothermal damping characteristic of (IFPT+ IFI)B2→B19 at

one-stage B2→ B19 martensitic transformation is compared with those of (IFPT+ IFI)B2→R and (IFPT+ IFI)R→B19 at

two-stage B2→ R → B19martensitic transformation.

2. Experimental procedures

Equiatomic TiNi SMA was prepared by conventional vac-uum arc re-melting. The as-melted ingot was hot-rolled at 850◦C into a 2-mm-thick plate and the plate was subsequently solution-treated at 850◦C 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 reduction of 30% thickness. No annealing was conducted during cold-rolling so to avoid the occurrence of recrystallization. Thereafter, the cold-rolled plate was cut into test specimens, sealed in an evacuated quartz tube and annealed at 650◦C for 30 min. Transformation temperatures of cold-rolled and annealed specimens were determined by dif-ferential scanning calorimetry (DSC) test using TA Q10 DSC equipment. The weight of the specimen used in DSC was about 30 mg and the heating and cooling rates were set at 10◦C/min. Specimens for DMA experiment were cut to the dimension of 40 mm× 5 mm × 1.26 mm along the rolling direction to elimi-nate the influence of rolling texture[17]. tanδ and E0values were

measured by TA 2980 DMA equipment with ˙T = 3◦C/ min,

ν = 1 Hz and σ0= 5␮m. The inherent damping characteristics

of the specimens were also investigated by DMA, but now measured under isothermal conditions at different temperatures. The detailed procedure for the isothermal DMA test was con-ducted as follows. The specimen was initially cooled starting from 150◦C at a cooling rate of 3◦C/min and was kept isother-mally for 30 min at the set temperature. After being isothermal for 30 min, the specimen was heated to 150◦C to ensure that it had returned to the B2 parent phase. Then, the specimen was cooled to another set temperature and kept isothermally at that temperature for 30 min, and so on. Under the isother-mal condition, the set temperature was chosen within the range of +80 to−80◦C.

3.1. DSC and DMA measurements at constant ˙T

Fig. 1(a and b) shows DSC and DMA curves, respectively, of 30% cold-rolled Ti50Ni50 alloy annealed at 650◦C for 30 min.

As seen inFig. 1(a), there is a B2→ B19transformation peak in the forward transformation and a B19→ B2 one in the reverse.Fig. 1(b) illustrates the tanδ and E0curves of the

spec-imen ofFig. 1(a). Only the cooling curves with ˙T = 3◦C/ min,

ν = 1 Hz and σ0= 5␮m are shown in Fig. 1(b). There is also

a B2→ B19internal friction peak appearing in the tanδ curve which corresponds to the observed peak in the DSC curve shown in Fig. 1(a). Also seen in Fig. 1(b), the E0 curve decreases

gently in the B2 parent phase, and then reaches a minimum during B2→ B19martensitic transformation. After B2→ B19 martensitic transformation is completed, the E0value in B19

martensite increases with decreasing temperature. The peak tem-peratures measured by DSC and DMA tests show a small shift due to different cooling rates and specimen sizes. Except for the aforementioned tanδ transformation peak, an extra broad peak is also observed inFig. 1(b) at about−75◦C. This extra peak is known as the relaxation peak[4], and is not observed in the DSC curve.

3.2. DMA measurement under isothermal conditions

Fig. 2plots the tanδ values versus isothermal interval when the specimen of Fig. 1 is isothermal-treated at 80◦C (B2 parent phase), 20◦C (B2→ B19 transformation peak) and −80◦_{C (B19} _{martensite) for 0–30 min. In} _{Fig. 2}_{, the tan}_δ

value measured at B2→ B19 transformation decreases dras-tically with increasing isothermal interval and reaches a steady value after 10–15 min. The decayed tanδ value as a result of isothermal treatment represents the transitory internal friction of B2→ B19 transformation, (IFTr)B2→B19, which is associated

with the magnitude of ˙T . The steady tan δ value after 15 min of isothermal treatment shown inFig. 2indicates the inherent internal friction (IFPT+ IFI)B2→B19 during phase

transforma-tion which is independent of ˙T . Moreover, as seen in Fig. 2, the measured tanδ values of the B2 parent phase are almost the same throughout the entire isothermal duration, while the

Fig. 1. (a) DSC curves measured at ˙T = 10◦C/ min and (b) tan δ and storage modulus E0 curves measured at ˙T = 3◦C/min,ν = 1 Hz and σ0= 5␮m for 30%

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Fig. 2. tanδ values vs. isothermal interval for Fig. 1 specimen measured at ν = 1 Hz, σ0= 5␮m and isothermal at 80◦C (B2 parent phase), 20◦C

(B2→ B19 transformation peak) and−80◦C (B19 martensite phase) for 0–30 min.

measured tanδ values of B19martensite decrease with increas-ing isothermal interval and reaches a steady value after 10 min. As illustrated in Fig. 2, the tanδ value of B19 martensite is composed of a dynamic term IFDB19

, which diminishes during isothermal condition and a static term IFB19_S , which is the steady value measured after 30 min of isothermal treatment[16].

In order to investigate the damping characteristics of (IFPT+ IFI)B2→B19, DMA test under 30-min isothermal

treat-ment at different temperatures was conducted and the results are indicated inFig. 3. The tanδ curve ofFig. 1(b) (measured at

˙

T = 3◦_{C/min) is also plotted in}_{Fig. 3}_{for comparison. When the}

isothermal temperature is set at about 30◦C, an inherent internal friction peak of (IFPT+ IFI)B2→B19 appears with a tanδ value

of 0.013. The temperature shift between the (IFPT+ IFI)B2→B19

peak of Fig. 3 and the B2→ B19 internal friction peak of

Fig. 1(b) is due to the cooling rate effect. This cooling rate effect can be considered as a technical effect which corresponds to the large specimen and big furnace size used in DMA.Fig. 4(a and b) shows the measured tanδ values of (IFPT+ IFI)B2→B19peak

under isothermal conditions at differentσ0andν, respectively.

As illustrated in Fig. 4, the tanδ value of (IFPT+ IFI)B2→B19

peak is linearly proportional toσ0and 1/ν1/2when the applied

Fig. 3. tanδ values vs. temperature forFig. 1specimen measured atν = 1 Hz, σ0= 5␮m. The solid curve is measured at ˙T = 3◦C/ min and the empty circle

curve is the data of the specimen kept isothermal for 30 min.

ν and σ0are within 10 Hz and 15␮m, respectively. This feature

is similar to the damping characteristics of (IFPT+ IFI)B2→R

and (IFPT+ IFI)R→B19 at two-stage B2→ R → B19

marten-sitic transformation[15]. Therefore, the damping mechanism of (IFPT+ IFI)B2→B19can also be attributed to the stress-assisted

martensitic transformation and stress-assisted motions of the twin boundary in B19 martensite. As shown in Fig. 2, the tanδ value of static internal friction in B19martensite (IFB19_S ) is much higher than that in the B2 parent phase (IFB2_S ). IFB2_S exhibits a rather small tanδ value because it comes only from the dynamic/static hysteresis of lattice defects. On the other hand, IFB19_S has a higher tanδ value because of its abundant twin boundaries in between the variants which can be easily moved by the external stress to accommodate the applied strain[16]. With further isothermal treatment at lower temperatures, the tanδ value of intrinsic internal friction also exhibits a relaxation peak at around−60◦C, as shown inFig. 3.

3.3. Comparison of damping characteristics between B2→ B19and B2→ R → B19martensitic transformation

Fig. 5(a and b) shows the tanδ and E0 values,

respec-tively, of the specimens annealed at 650◦C for 2 min [15]

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Fig. 5. (a) tanδ and (b) E0values of the specimen annealed at 650◦C for 2 min[15]and 30 min measured after isothermal 30 min at different temperatures.

and 30 min (fromFig. 3) after 30-min isothermal treatment at different temperatures. The experimental parameters used for these two specimens inFig. 5are ν = 1 Hz and σ0= 5␮m. As

seen in Fig. 5(a), the specimen annealed at 650◦C for 2 min exhibits B2→ R and R → B19inherent internal friction peaks, (IFPT+ IFI)B2→R and (IFPT+ IFI)R→B19, while the specimen

annealed at 650◦C for 30 min shows only a single B2→ B19 inherent internal friction peak, (IFPT+ IFI)B2→B19, in

cool-ing. Meanwhile, as shown in Fig. 5(a), tanδ values of both (IFPT+ IFI)B2→R and (IFPT+ IFI)R→B19 are higher than that

of (IFPT+ IFI)B2→B19. As shown in Fig. 5(b), the E0 value

of the specimen annealed at 650◦C for 2 min decreases drasti-cally and shows a deep minimum (about 33,000 MPa) associated with B2→ R transformation and a shallow minimum (about 37,500 MPa) related to R→ B19transformation. On the other hand, the E0 value of the specimen annealed at 650◦C for

30 min also decreases at B2→ B19martensitic transformation but shows a E0minimum value of about 42,300 MPa. The lower E0 minimum value in B2→ R and R → B19 transformations

than that in B2→ B19implies that the specimen becomes more softened as the R-phase is formed. This feature indicates that the formation of R-phase can induce easier movement of twin boundaries and more dissipated energy under constant stress amplitude[10], thus exhibiting a higher tanδ value of IFI.

Con-sequently, the tanδ value of (IFPT+ IFI)B2→B19 is smaller than

those of (IFPT+ IFI)B2→R and (IFPT+ IFI)R→B19 because the

R-phase is not formed in the former.

In addition to inherent internal friction, the static internal friction IFB19_S of the specimen annealed at 650◦C for 2 min is also larger than that annealed at 650◦C for 30 min, as shown inFig. 5(a). However, as shown inFig. 5(b), the E0values of

B19 martensite in these two specimens are not significantly different. This phenomenon reveals that the difference in tanδ values of IFB19_S between these two specimens is not due to the different mobility of twin boundaries in B19 martensite, but comes from the different magnitude of the relaxation peak. As shown inFig. 5(a), the specimen annealed at 650◦C for 2 min shows a transformation sequence of B2→ R → B19 because this specimen has abundant residual tangled dislocations and defects which induce the formation of the R-phase. On the other hand, the specimen annealed at 650◦C for 30 min has tangled

dislocations and defects to be annihilated and only B2→ B19 transformation can be obtained[18–20]. It has been reported that the relaxation peak in TiNi alloys near 200 K is originated from the movement of dislocations that have been pinned by point defects [2,21]. Therefore, the lower tanδ value of the relax-ation peak in the specimen annealed at 650◦C for 30 min can be expected owing to the obliterated dislocations and defects after sufficient annealing in this specimen.

4. Conclusions

The tanδ value of inherent internal friction (IFPT+

IFI)B2_→B19 corresponding to B2→ B19 transformation of

Ti50Ni50 SMA is linearly proportional to σ0/ν1/2 when the

applied ν and σ0 are within 10 Hz and 15␮m, respectively.

This characteristic explicates that the damping mechanism of (IFPT+ IFI)B2→B19is mainly generated from the stress-assisted

martensitic transformation and stress-assisted motion of twin boundaries. IFB19_S have higher tanδ values than those of IFB2_S because of the abundant twin boundaries present in between the B19 variants, which can be easily moved by the external stress to accommodate the applied strain. The

E0 minimum values of B2→ R and R → B19 martensitic

transformations under isothermal treatment are lower than those of B2→ B19transformation. At the same time, the tanδ values of (IFPT+ IFI)B2→R and (IFPT+ IFI)R_→B19 are higher

than those of (IFPT+ IFI)B2_→B19. These features come from

the fact that the R-phase is not formed in the latter. The lower tanδ value of the relaxation peak in the specimen annealed at 650◦C for 30 min than that in the specimen annealed at 650◦C for 2 min is attributed to the obliterated dislocations and defects after sufficient annealing of the former.

Acknowledgement

The authors gratefully acknowledge the financial support for this research provided by the National Science Coun-cil (NSC), Taiwan, Republic of China, under Grants Nos. NSC95-2221-E002-164.

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