Effect of Pre Strain on Transformation and Deformation Behavior in Ti–50 at%Ni Shape Memory Alloy

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Eﬀect of Pre-Strain on Transformation and Deformation Behavior

in Ti–50 at%Ni Shape Memory Alloy

*

Toshio Sakuma

1

, Yuji Mihara

2

, Yasuo Ochi

3

and Kiyoshi Yamauchi

4

1

Department of Human Welfare Engineering and Assistive Technology, Oita University, Oita 870-1192, Japan

2_{Piping Engineering Center, Chiyoda Co., Yokohama 230-8601, Japan}

3_{Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, Tokyo 182-8585, Japan}

4_{Biomedical Engineering Research Organization, Tohoku University, Sendai 980-8579, Japan}

In many cases that shape memory alloys are applied to engineering and medical ﬁelds, it is necessary to deform them in martensitic phase and after that, to recover them by heating. However, if a slip-deformation occurs, a shape recovery does not occur completely even if heated up above a reverse transformation ﬁnish temperatureAf. It is reported that transformation temperatures are changed by pre-deformation and in

constrained strain condition. Therefore, it is important to investigate the relationship between the pre-deformation and the deformation and transformation characteristics such as the recovery stress, the transformation temperatures and so on. The purpose of this paper is to clarify the inﬂuence of the pre-deformation on the recovery strain, the recovery stress and the transformation temperatures in a Ti–Ni shape memory alloy. The material used in this study is Ti–50 at%Ni alloy annealed at 1103 K for 60 s. The variation of the recovery strain, the recovery stress and the transformation temperatures by the pre-straining are investigated experimentally, and also the variation of the transformation and deformation characteristics by the pre-straining is discussed in relation to the volume fraction of slip-deformed martensite.

(Received October 14, 2005; Accepted December 15, 2005; Published March 15, 2006)

Keywords: shape memory alloy, titanium–nickel alloy, pre-strain, recovery stress, recovery strain, transformation temperature, volume fraction of slip-deformed martensite

1. Introduction

In many new materials, which have been developing nowadays, shape memory alloys (SMAs) are remarkably noticed for using as machine elements by means of their functional characteristics. Especially, a Ti–Ni based SMA has superior mechanical property and corrosion resistance, and so on, then, they are used practically in ﬁelds of engineering and medicine.1–3)_{In cases that those SMAs are}

applied for using the recovery deformation and the recovery force by their shape memory eﬀects, it is necessary to deform them in martensitic phase, and after that, to recover them by heating, then, to use their recovery functions with the reverse transformation. However, when the SMAs are deformed, the slip-deformation occurs in the alloys, the shape recovery does not occur completely even if they are heated up to the reverse transformation ﬁnish temperature ofAf. And also, it has been

reported that the recovery stress and the reverse trans-formation start and ﬁnish temperatures of As and Af are

eﬀected by deformation conditions in the martensitic phase.4–10)Therefore, in order to apply the SMAs to use as functional materials for actuators and other devices, it is important to investigate the relationship between the pre-deformation and the pre-deformation, the transformation char-acteristics such as the recovery stress, the transformation temperatures and so on.

When the SMAs are loaded at a little higher temperature than the reverse transformation start temperature ofAs, the

martensitic phase of the SAMs preferentially occurs slip deformation.11) _{The slip-deformed martensitic phase does}

not transfer to the parent phase by heating, and remains locally in the parent phase. Authors have deﬁned the remained fraction of martensitic phase in the parent phase

as the volume fraction of slip-deformed martensite , and have clariﬁed that the value ofcan be used as a criterion of pre-strain induced dislocation.12,13) And also, elastic strain energy is stored in the materials by the martensitic deforma-tion, and the energy promotes the reverse transformadeforma-tion, then it acts to restrain the martensite from transforming.7–10) Therefore, if the elastic strain energy is released by the deformation of the martensitic phase, the transformation temperature increases.

In this study, the Ti–50 at%Ni SMA is loaded with various pre-strains and heated after the unloading tests under conditions of constrained strain and stress free. And then, it is the purpose of the paper to clarify the eﬀect of pre-strain on the recovery strain, the recovery stress and the transformation temperature. Also, the variation of the transformation and deformation characteristics will be discussed in relation to the slip-deformed martensite.

2. Experiment

2.1 Material and specimen

The material used in this study is Ti–50 at%Ni shape memory alloy, and it is performed by solid solution treatment at 1103 K for 60 s after cold extension working. The specimen is a wire with 1.0 mm in diameter and 70 mm in length. The transformation temperatures measured by DSC (Diﬀerential Scanning Calorimeter) and elastic moduli of martensitic phase and parent phase obtained by tensile tests are listed in Table 1, respectively. In the tensile tests obtained both elastic moduli, the tests were carried out at the ﬁxed temperature of Afþ20K for the modulus of parent phase,

and at the ﬁxed temperature ofAs20K after cooling down

to Mf30K for the modulus of the complete martensitic

phase. Where, temperaturesAsandAf show the start and the

ﬁnish temperatures of reverse transformation, respectively, andMsshows the martensite start temperature.

*_{This Paper was Originally Published in Japanese in J. Jpn. Inst. Met.}₆₉

(2005) 568–574.

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2.2 Experimental procedure

2.2.1 Heating test under stress free condition

Figure 1(a) shows a schematic diagram of stress–strain curve in the heating test under the stress free condition. After the specimen was cooled to the martensitic phase at Mf

30K, it was loaded to a given pre-strain "pr at the ﬁxed

temperature ofAs20K and unloaded (O–A–B). And then,

the specimen was heated under the stress free condition (B–C). The start temperature As0 and the ﬁnish temperature

Af0of the reverse transformation after the pre-strain loading

and unloading were obtained by the strain-temperature curve [see Fig. 1(b)], respectively. The percentage of recovery strain"Rby heating to"pris deﬁned as the strain recovery

rateRR¼"R="pr100(%), and the percentage of residual

strain"Reafter heating to"pris deﬁned as the strain residual

rateRp¼"Re="pr100(%). Where,"Reis the residual strain

after heating.

Moreover, the specimen was loaded again (C–D) after heating to Af0þ20K, and an apparent elastic modulusEL

was obtained from the stress–strain curve (C–D). Then, the volume fraction of slip-deformed martensite with various pre-strains was deﬁned as the eq. (1),12,13)where,EAandEM

are elastic moduli of parent phase and martensitic phase, respectively.

¼EMðEAELÞ ELðEAEMÞ

ð1Þ

2.2.2 Heating test under constrained strain condition

Figure 2(a) shows a schematic diagram of stress– strain curve in the heating test under the constrained strain condition. After the specimen was cooled to the temperature at Mf30K, it was loaded to a given pre-strain"pr at the

ﬁxed temperature of Tc¼As20K, and unloaded (O–A–

B). And then, the specimen was heated and cooled under the constrained strain condition (B–C–B0). From the stress– strain curve and the stress-temperature relation during heating-cooling process [see Fig. 2(b)], the recovery stress

R, the start and the ﬁnish temperature of reverse

trans-formation As0,Af0 and the martensite start temperatureMs0

after the pre-strain loading and unloading were obtained, respectively.

Moreover, the specimen was unloaded in the condition of re-heating to the temperature atAf0þ20K (B–C–D) after the

pre-strain loading and unloading, and an apparent elastic modulusELwas obtained from the stress–strain curve during

unloading process. Then, the volume fraction of slip-deformed martensitewas evaluated from the eq. (1). And, the recovery strain during unloading"RRwas deﬁned as the

amount of recovery strain under the constrained strain condition.

(b) Strain-temperature curve. (a) Stress-strain curve.

Fig. 1 Schematic drawing of experimental procedure of stress free test.

(b) Stress-temperature curve. (a) Stress-strain curve.

Fig. 2 Schematic drawing of experimental procedure of constrained strain test.

Transformation temperatures (K) Young’s moduli (GPa)

Mf Ms As Af EM EA

[image:2.595.311.537.66.420.2] [image:2.595.52.538.74.456.2] [image:2.595.49.285.80.453.2]

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3. Results and Discussion

3.1 Eﬀects of pre-strain on recovery strain and residual strain

Figure 3 shows the relationship between the recovery and the residual strain "R, "Re and the pre-strain "pr in the

heating tests under the stress free condition. Both of strains increased with an increase in"pr, but"Rhas a tendency to

saturate over 12% of"pr.

Figure 4 shows the relationship between the recovery ratio and the residual ratio of strainRR,Rpand"pr.RRdecreases

and Rp increases with an increase in "pr, respectively.

Therefore, the shape memory function degrades with an increase in"pr. The slip deformation occurs in the martensitic

phase with an increase in the pre-strain. It is considered that the internal damage in material subjected to the slip

deformation increases with an increase in the pre-stain. As it is assumed that the shape memory function of martensitic phase is lost by the slip deformation, the martensitic phase with the shape memory possibility decreases with an increase in the slip deformation, and then, the shape memory recovery function decreases. Therefore, in this study, we discussed with using the volume fraction of slip-deformed martensite

as an index of the internal damage induced by the pre-strain. Figure 5 shows the relationship between and"prin the

case of the heating test under constrained strain and stress free conditions after the pre-strain loading. The values of

increase linearly with an increase in"prin both cases, and the

values of in the case of constrained strain condition are larger than those in the case of the stress free condition. In the latter condition, the internal damage in material occurs in the process of only pre-strain loading. In the former condition, the recovery stress is generated by the reverse transformation with an increase in temperature. Since there exist both of the parent phase and the martensitic phase in material during the process of the reverse transformation, the martensitic phase having the lower critical stress occurs the slip deformation by the recovery stress.11) Therefore, in the former condition adding the internal damage by the pre-strain loading to slip deformation by the recovery stress with heating,becomes larger than that in the latter condition.

Figure 6 shows the relationship between residual strain"Re

after heating under the stress free condition, the residual strain "Re after unloading under the constrained strain

condition and the volume fraction of slip-deformed marten-site. From the ﬁgure, in spite of diﬀerence in the condition, the relation between them shows the same linear relationship and the values of"Reincrease linearly with an increase in.

As the residual strain can be taken macroscopic damage in material, it is considered that it shows a factor of shape memory function released by plastic deformation, and then, the value ofis an index for evaluating generally the internal damage of material in spite of diﬀerence in the strain conditions at heating tests.

0

2

4

6

8

10

0

3

6

9

12

15

Recovery and Residual strain,

R

,

ε

Re

(%)

Pre-strain, (%)

Recovery strain,

∆ε

R

Residual strain,

ε

Re

∆ε

ε

Pr

Fig. 3 Variation of recovery and residual strain"R,"Re with pre-strain

"pr.

0

20

40

60

80

100

0

3

6

9

12

15

Recovery and Residual ratio,

R

, R

P

(%)

Recovery ratio, R_R

Residual ratio, R

P

Pre-strain, (%)

ε

_Pr

Fig. 4 Variation of recovery and residual ratioRR,Rpwith pre-strain"pr.

0

10

20

30

40

50

0

3

6

9

12

15

Volume fraction of

slip-deformed

martensite,

ξ

(%)

Constrained strain

Stress free

Pre-strain, (%)

ε

_Pr [image:3.595.57.283.70.285.2] [image:3.595.313.540.75.275.2] [image:3.595.57.284.341.552.2]

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3.2 Eﬀects of pre-strain on recovery stress

Figure 7 shows the relationship between the recovery stressRand the pre-strain"prin the heating tests under the

constrained strain condition.Rincreases with an increase in

"prup to about 9%, but it shows maximum in the

neighbor-hood of 9–12% of"prand then after that it decreases with an

increase in "pr. In order to increase the amount of shape

recovery with an increase in"pr(see Fig. 3), it is considered

that the recovery stress also increases. Therefore, the slip-deformed portion increases with an increase in"pras shown

in Fig. 5, then it is assumed that the recovery stress decreases above 12%"pr. Figure 8 shows the relationship between the

recovery stressRand the amount of recovery strain"RRin

the heating test under the constrained strain condition. Since the residual strain increases with an increase in slip deformation in material, it is considered that the amount of the recovery strain becomes larger with a decrease in the internal damage of material. As the larger"RRis, the higher

Ris from Fig. 8, it is clear that the specimen has the higher

recovery stress as showing in the lower internal damage of material.

Here, we proposed a two-phase model considering of the parent phase and the martensitic phase connected in series as shown in Fig. 9. It is assumed that the specimen is applied by tensile loading of"RRby means of the constrained strain at

heating. Then,Ris expressed by following eq. (2) using the

apparent elastic modulusELand"RRafter heating,

R¼EL"RR ð2Þ

where, the apparent elastic modulus EL is obtained by

following eq. (3) using the values of obtained by experi-ments,

EL¼

EAEM

ð1ÞEMþEA

ð3Þ

0

5

10

0

10

20

30

40

50

Residual strain, (%)

Volume fraction of

slip-deformed martensite,

ξ

(%)

Stress free Constrained strain

ε

Re

Fig. 6 Relationship between residual strain"Re and volume fraction of

slip-deformed martensite.

0

50

100

150

200

250

300

350

400

0

3

6

9

12

15

Recovery stress, / MPa

σ

R

Calculation

Pre-strain, (%)

ε

_Pr

Fig. 7 Variation of recovery stressRwith pre-strain"prof constrained

strain condition.

0

100

200

300

400

0

0.2

0.4

0.6

0.8

1

Recovery stress, /

MPa

RR

(%)

ε

σ

R

∆

Fig. 8 Relationship between recovery stressRand recovery strain"RRof

constrained strain condition.

[image:4.595.62.283.70.307.2] [image:4.595.316.539.76.295.2] [image:4.595.309.543.352.467.2] [image:4.595.61.283.363.574.2]

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"RRcan be expressed approximately by following eq. (4)

as a function of"prresulted from the Fig. 10,

"RR¼ 4:8103"prþ0:1"prþ0:2 ð4Þ

Robtained from the eq. (3) are shown in Fig. 7 as the solid

curve. The curve expresses well the relation betweenRand

"pr.

3.3 Eﬀect of pre-strain on transformation temperature

Figure 11 shows the relationship between the start temper-ature As0, the ﬁnish temperature Af0 of the reverse

trans-formation after pre-straining and the pre-strain "pr by the

heating test under the stress free condition. Figure 12 also shows the relationship betweenAs0,Af0and"prby the heating

tests under the constrained strain condition. Both of the transformation temperatures increase with an increase in"pr

under both conditions, and these results suggest that the elastic strain energy stored in material is released by loading of"pr. Moreover, the increasing rate ofAf0for"prin the case

of the heating test under the constrained strain condition is larger than that under the stress free condition.

Heating under the constrained strain condition generates the recovery stress. Since the recovery stress acts as the reverse force against the shape recovery of specimen, it acts as the resistance for the reverse transformation. Therefore, there needs a large driving force in order to ﬁnish the reverse transformation, and then, the reverse transformation ﬁnish temperature ofAfincreases remarkably under the constrained

strain condition.

Figure 13 shows the relationship between the temperature changes Ms (¼Ms0Ms) of the martensite start

temper-0

0.2

0.4

0.6

0.8

1

0

3

6

9

12

15

RR

(%)

∆

ε

[image:5.595.60.283.68.286.2]

Pre-strain, (%)

ε

_Pr

Fig. 10 Variation of"RRwith pre-strain"pr.

0

3

6

9

12

15

300

330

360

390

420

450

A

s

', A

f

' / K

Af

A_s '

'

[image:5.595.311.540.76.284.2]

Pre-strain, (%)

ε

_Pr

Fig. 11 Variation of transformation temperaturesAs0 andAf0 with

pre-strain"prof stress free condition.

300

330

360

390

420

450

0

3

6

9

12

15

A

s

', A

f

' / K

A

f'

A

s'

[image:5.595.57.283.328.545.2]

Pre-strain, (%)

ε

_Pr

Fig. 12 Variation of transformation temperaturesAs0 andAf0 with

pre-strain"prof stress free condition.

0

3

6

9

12

15

0

20

40

60

80

100

∆

M

s

/ K

s

'

∆

M

s

∆

M

Pre-strain, (%)

ε

_Pr [image:5.595.317.538.343.559.2]

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atureMsand"prunder the constrained strain conditions. The

value ofMs increases with an increase in"pras similar as

the other transformation temperatures, but it saturates above 6% of "pr. It has been reported from the study of the cold

worked SMAs that the transformation temperatures of SMAs decrease by inducing of dislocation.1)Therefore, the value of

is used as a criterion of dislocation density induced by"pr.

Supposing that the super cooling rate TPMð¼AfMsÞ

needed for the martensitic transformation is constant being independent on "pr, the temperature change Ms0 are

obtained as the following eq. (5).

Ms0¼Af0TPMMs ð5Þ

Ms0obtained by the eq. (5) is shown as the broken curve in

Fig. 13. Figure 14 shows the relationship between the change (Ms0Ms) and. From the ﬁgure, they show the linear

relation and the decreased change of Ms increases linearly

with an increase in . Therefore, the increase of the martensite start temperature Ms is restrained with an

increase inby increasing of"pr.

Figure 15 shows the relationship between the transforma-tion hysteresis (Af0Ms0) and"pr by heating test under the

constrained strain condition. It is clear that the hysteresis increases linearly with an increase in"pr. The temperatureAf0

increases remarkably with an increase in "pr, however, the

temperature Ms0 saturates above 6% of "pr as mentioned

before. Then, the transformation hysteresis (Af0Ms0)

increases constantly with an increase in"pr.

In cases of using the shape recovery and the recovery stress of SMAs, the smaller the heating quantity needed for finishing the reverse transformation is, the more the temper-ature responsive property increases. Figure 16 shows the relationship between the heating temperature difference (Af0As0) needed for finishing the reverse transformation

and"pr. From the ﬁgure, the value of (Af0As0) decreases

with an increase in"pr. The smaller the value of (Af0As0) is,

the smaller the driving force needed for ﬁnishing the reverse transformation is, and it is considered that the larger the"pris,

the more superior the temperature responsive property is. Therefore, the temperature responsive property increases with an increase in"prin both cases of the constrained strain

and stress free conditions. And also, there needs the larger heating temperature under the constrained strain condition than that under the stress free condition, and it is clear that the temperature responsive property becomes lower in that case. That is because of remarkable increase inAf0 in the case of

the constrained strain condition as shown in Fig. 12.

4. Conclusion

In this study, the eﬀect of pre-strain "pr on the

trans-0

10

20

30

40

0

5

10

15

20

25

30

Volume fraction of

slip-deformed martensite,

ξ

(%)

s

'-s

/ K

∆

M

∆

[image:6.595.59.282.71.304.2]

M

Fig. 14 Relationship between the (Ms0Ms) and the volume fraction

of slip-deformed martensite.

0

10

20

30

40

50

0

3

6

9

12

15

Hysteresis, (A

f

'-M

s

') / K

Constrained strain

Pre-strain, (%)

ε

_Pr

Fig. 15 Variation of transformation hysteresis (Af0Ms0) with pre-strain

"prof constrained strain condition.

0

10

20

30

40

50

0

3

6

9

12

15

A

f

'-A

s

' / K

Constrained strain

Stress free

[image:6.595.312.541.75.290.2]

Pre-strain, (%)

ε

_Pr [image:6.595.312.538.348.563.2]

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formation and the deformation characteristics were inves-tigated in the Ti–50 at%Ni shape memory alloy. And we discussed by using the volume fraction of slip-deformed martensiteas the fraction of remained martensitic phase in the parent phase by pre-straining. The results obtained are summarized as the followings,

(1) Both of the recovery strain under the stress free condition and the recovery stress under the constrained strain condition increase with an increase in "pr to the

values of 9–12% and after that they decrease with"pr.

(2) Both of the start and the ﬁnish temperatures of the reverse transformation increase with an increase in"pr

in both cases of the constrained strain and the stress free conditions. The reverse transformation ﬁnish temper-ature increases larger in the case of the constrained strain condition than that in the case of stress free condition.

(3) The martensite start temperature also increases with an increase in "pr; however, the increase is restrained

above 6%"prdue to the increase in.

(4) The heating temperature diﬀerence (Af0As0) from

the start temperature to the ﬁnish one of the reverse transformation decreased with an increase in "pr, and

the temperature responsive property increases with in"pr.

(5) The changes of the transformation and the deformation characteristics with the pre-strain are explained qual-itatively by using as a criterion of slip-induced dislocation density in material.

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