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The properties of two-phase Ni–Al–Fe shape memory alloys in the virgin and shape-memory-cycled states
Materials Science and Engineering A273 – 275 (1999) 420 – 424 www.elsevier.com/locate/msea
The properties of two-phase Ni–Al–Fe shape memory alloys in the virgin and shape-memory-cycled states N. Ono a,*, A. Tsukahara a, R. Kainuma b, K. Ishida b a
Department of Mechatronics and Precision Engineering, Graduate School of Engineering, Tohoku Uni6ersity, Aramaki-Aoba, Aoba, Sendai 980 -8579, Japan b Department of Materials Science, Graduate School of Engineering, Tohoku Uni6ersity, Aramaki-Aoba, Aoba, Sendai 980 -8579, Japan
Abstract Five polycrystalline Ni–Al–Fe alloys with 14–26 (at.)% Al and 16 – 26% Fe were made and heat-treated to have b and g dual phases with from 87% to less than 1% of b phase and to exhibit Ms temperatures at about 300 K. Depending on the b phase fraction and prestraining temperature, the alloys showed pseudoelastic strain recovery ratio from 1 – 2 up to 35% and shape memory strain recovery ratio from over 10–90% after prestraining by up to 1%. In the alloy with 87% b phase, the latter ratio reached 100% against 0.8% prestrain after a few cycles of shape memory training. Observed results were analyzed based on a model that assumed a simple linear mixture of the properties of the b and g phases. The results of the analysis suggest that the g phase after the training in certain conditions is almost elastic and thus acts as a bias spring. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Shape memory alloys; Ni–Al–Fe alloys; Dual phases; Shape memory cycling
1. Introduction It has been reported that a variety of ductile b (B2) Ni–Al base shape memory (SM) alloys can be fabricated with the conventional casting-hot working method by introducing the ductile g (A1) phase and controlling its morphology [1,2]. One would expect that the g phase in these alloys may impair the inherent SM performance of the b phase. This paper describes the results of experiments concerning the influence of the g phase on the SM effect in a series of Ni – Al – Fe alloys with from 0–87% of the b phase in virgin state and also after a few cycles of SM training. While most of the previous studies on Ni – Al base SM alloys were made with bending [1– 6], the present experiments were carried out in tension and, therefore, more detailed observations of deformation and SM properties were possible. Based on good linear dependence of various characteristics of the alloys on the b phase volume fraction, pseudo-elastic and SM properties of the alloys were analyzed with a simple linear mixture model. The * Corresponding author. Fax: +81-22-2177027. E-mail address: [email protected] (N. Ono)
analysis suggests that the g phase can be made almost elastic in certain conditions of SM training. The g phase as such acts as a bias spring and does not affect the SM capability of the alloys.
2. Experimental procedures Five alloy ingots as listed in Table 1 were prepared by induction melting in an argon atmosphere and hotrolled to sheets with a thickness of about 1.5 mm. Tensile specimens were laser-cut from the sheets in the rolling direction. They were annealed at 1100°C for 1800 s and quenched into ice water. After this treatment, the structure of alloy 1 consisted of b phase grains and g phase that formed continuous grain boundary precipitates and a small amount of coarse particles in the grain interior as reported in [2]. Alloy 6 with 22% Fe was virtually g single phase. Alloys from 2 to 4 with intermediate Fe contents showed b/g-duplex structures. The volume fractions of the b phase and grain sizes in these alloys are included in Table 1. Because grains in these alloys were elongated in the rolling direction, the grain size measurements were
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 3 1 0 - X
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421
Table 1 Compositions and other characteristics of alloys Alloy no.
1 2 3 4 6
Composition (at.%)
b Phase volume fraction
Grain size (mm)
Transformation temperatures (°C)
Ni
Al
Fe
f (%)
b
g
Ms
Mf
As
Af
Bal.
26.0 23.6 21.2 18.8 14.0
16.0 18.0 20.0 22.0 26.0
87 71 51 38 B1
19.4 11.5 7.2 4.7 –
– 4.8 6.2 9.5 105
24–32 21–27 26–36 28–30 –
0–13 4–7 16–24 7–9 –
10–27 15–24 24–33 12–27 –
40–58 33–51 53–63 46–58 –
made in the transverse section along the lines at 45° to the tensile axis. Individual specimens were attached to a laboratorymade gear-servo tensile testing machine controlled to zero load and subjected to heating – cooling – reheating cycling between− 80 and 120°C and then cooled to respective intended prestraining temperatures. During this temperature cycling, electric resistance across the gauge part of the specimens was monitored in order to measure transformation temperatures. The scatter of the measured transformation temperatures among a heat of specimens was within a few K as summarized in Table 1. After the temperature cycling, the specimens were stretched to prescribed plastic strains and unloaded to observe pseudoelastic behavior. Following this, they were heated to 120°C and cooled to respective prestraining temperatures at zero load. SM strain recovery was evaluated based on the crosshead positions before and after this heating – cooling cycle. Some specimens were subjected further to the repetition of the above stretching–unloading – heating – cooling cycle several times to observe the effect of SM training.
The results of SM strain recovery measurements for alloys 1–4 are summarized in Fig. 3 in terms of the percentage of overall recovery strain DoSR against the amount of prestrain DoP. In the all alloys, the largest strain recovery was observed when specimens were prestrained at Ms. At this temperature, DoSR/DoP exceeded 90% in alloy 1 but decreased with decreasing f. The dependence of DoSR on temperature and f as such may be due to plastic deformation of the g phase. This will be larger when the applied stress is larger and its influence will be larger when f is smaller. Specimens stretched at temperatures below Ms showed spontaneous elongation when they were cooled across Ms and Mf after the shape recovery heating due to the two-way SM effect [3]. This makes DoSR values below Ms smaller. As shown with an example in Fig. 4, some specimens after the SM test in the virgin state were stretched again to the maximum plastic strain the same as that in the first SM test. The pseudo-elastic strain recovery and SM effect were observed by unloading and heating– cooling temperature cycling, respectively. The same procedure was repeated several times. In this cycling
3. Experimental results Fig. 1 shows some of observed stress – plastic strain curves. Pseudo-elastic strain recovery DoPE increased with increasing prestraining temperature and with increasing b phase volume fraction, f. Even in alloy 1 prestrained at 50°C above Ms, however, DoPE was only a third of given prestrain DoP. Observed yield stresses at different test temperatures are plotted against f in Fig. 2. The yield stresses of the alloys with b phase showed good linear relations with f: sY = fs bY + (1− f )s gY Here, the yield stress of g phase, s gY, was larger than that of the b phase, s bY. It was independent of temperature while s bY exhibited a positive temperature dependence above Ms. Observed yield stresses of alloy 6 were far smaller than s gY in the above relation. This is apparently because this alloy had a grain size far larger than other alloys (see Table 1).
Fig. 1. Effects of temperature and b phase volume fraction on pseudo-elastic behavior.
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Fig. 2. Effect of b phase volume fraction on the yield stress at various temperatures.
Fig. 4. Pseudo-elastic loops of alloy 1 at Ms 60 K during shape memory training.
4. Linear mixture model scheme, DoP decreases with the number of cycles until 100% SM strain recovery is attained. In this example, this occurred between fourth and fifth cycles where DoP was still as large as 0.5%. The relations between DoP and DoSR/DoP for individual cycles are presented in Fig. 5 for alloy 1 and alloy 2. The alloy 1 specimen cycled at Ms showed DoSR/DoP larger than 95% with prestrain range of about 0.8%. Other specimens cycled at higher and lower temperatures attained similar or even larger recovery ratios, but with smaller remaining prestrain ranges. In alloy 2, DoP decreased more rapidly and DoSR/DoP values were smaller than corresponding values in alloy 1. These features were more pronounced in alloys with smaller f.
As seen in Fig. 2, for example, certain properties of the present alloys show good proportionality with f. Based on this, it was attempted to simulate experimental results with a simple linear mixture model. In the model, the applied stress on a specimen s is given as the volumetric average of those in b and g phases, s b and s g,, respectively: s = fs b + (1− f )s g
(1)
The sum of elastic and plastic strains is the same in the b and g phases. If we write the latter as o bp and o gp, respectively, and let E b and E g denote Young’s moduli of respective phases, this equality is expressed as follows o=s b/E b + o bp = s g/E g + o gp
(2)
To describe the deformation and strain recovery behavior of the b and g phases, simplified parallelogramic
Fig. 3. Shape memory strain recovery at various prestraining temperatures.
Fig. 5. Changes in prestrain range and shape memory strain recovery with training cycles.
N. Ono et al. / Materials Science and Engineering A273–275 (1999) 420–424
423
Fig. 6. Assumed stress–strain relations for b and g phases.
stress–strain relations as depicted in Fig. 6 were assumed. Young’s moduli, yield stresses and work hardening rates for respective phases were evaluated by extrapolating observed linear relations between these properties and f. A small temperature dependence of work hardening rates for both phases was ignored for simplicity. The reverse yield stress of g phase, s gYR, was assumed to be the reverse of the forward yield stress, s gY, ignoring work hardening in prestraining and the Bauschinger effect. The magnitude of the stress hysteresis in the pseudo-elastic loop of b phase, Dsh, could not be determined directly because the present alloys did not exhibit clear pseudo-elastic strain recovery even at 50 K above Ms. Therefore, this value was assumed to be independent of temperature and determined in a trial-and-error manner to obtain the best possible agreement between the predictions of the model and experimental observations on pseudo-elastic loops and SM behavior. The temperature dependence of yield stress in a SM alloy is generally represented with the Clausius– Clapeyron equation, sY =(T −Ms)DS/Do*, where Do* is the transformation strain. Because we assume that Dsh is independent of temperature, to heat a prestrained specimen by DT amounts to shifting the pseudo-elastic segments of the stress-strain relation in Fig. 6 by Dt =DTDS/Do*. The shape recovery behavior of the b phase is thus calculated by substituting s b in Eqs. (1) and (2) with s b −Dt. Parameters used in the calculations are summarized in Table 2. Table 2 Characteristics of stress–strain relations for b and g phases used in the analysis with the linear mixture model Phase Young’s Modulus E (Gpa) Yield stress sY (MPa) Work hardening rate u (Gpa) Stress hysteresis Dsh (MPa) a
s bY = 77+4.54(T−Ms).
b
g
42 a
4.8 280
95 560 2.5 –
Fig. 7. Pseudo-elastic curves calculated for alloy 1 at Ms and 50 K above Ms in comparison with experimental results.
As shown in Fig. 7, calculated stress–strain relations for alloy 1 during a stretching-unloading cycle show good agreement with corresponding experimental results. At Ms, op in the b phase is much larger than that in the g phase so that residual internal stresses produced with this cycle are compressive and tensile in the b and g phases, respectively. The latter is in the direction to help pseudo-elastic strain recovery but its magnitude is not sufficient for this to actually take place. At 50 K above Ms, pseudo-elastic strain recovery occurs in the b phase. Plastic strain in the g phase is larger than that in the b phase firstly because the yield stress of the b phase is now closer to that of the g phase and also because the Young’s modulus of the g phase is larger than that of the b phase. Because of this, a tensile internal stress develops in the b phase and it suppresses the strain recovery of the b phase that otherwise could be more extensive at this temperature. In heating, o bp decreases when s bYR0 B s b − Dt Bs bYR. The stress–strain responses to this in the individual phases and the specimen as a whole can be calculated by solving Eq. (1) and Eq. (2) simultaneously with a prescribed value of Dt and s= 0. The model duly predicts that the plastic strain in the b phase recovers completely by heating and produces a compressive stress in the g phase. During this, however, the g phase is purely elastic and shows only a small reverse plastic strain when prestrained at Ms and 50 K above Ms, respectively, resulting in considerable remaining overall strain and tensile internal stress in the b phase. The latter causes a lower yield stress and a higher plastic slope in the second prestraining as in fact observed experimentally. In the third cycle, the g phase is mostly elastic and almost perfect strain recovery to the value at the start of this cycle is achieved. In reality, the prestrained g phase itself should exhibit some amount of
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strain hysteresis during stress cycling so that the observed change in shape recovery behavior is less clearcut than this. But the analysis explains the quick increase in strain recovery ratio with the SM training.
5. Conclusion It is generally expected that the mixing of a nonshape-memory second phase in a SM alloy would deteriorate the inherent SM capability of the alloy. This is supported by the experimental observations, such as the limited pseudo-elastic strain recovery, and the linear degradation of SM recovery strain with increasing g phase fraction. The present experimental results and their analysis with a linear mixture model suggest that this drawback of two-phase SM alloys may be avoided by training. In certain combinations of the factors, such as the yield stress and volume fraction of the second phase, the temperature and strain range of prestraining etc., we can produce, with a few cycles of SM training, an internal state where the second phase is mostly elastic and thus does not affect the inherent SM capability of the alloy. In this stable state, the second phase is stressed in the direction of the forward deformation. The elastic second phase thus acts like a bias spring in a usual SM device and enhances the two-way SM effect.
.
In regard to the combinations of training conditions, the present study covers only a small part of them. For example, we have not studied the effect of prestraining at pseudo-elastic region on the SM effect when the specimen is strained at Ms or lower temperatures. The linear mixture model described here will be useful in the planning of such experiments on two-phase SM alloys and also in interpreting their results.
Acknowledgements The authors would like to thank the support from The Sound Technology Promotion Foundation.
References [1] K. Ishida, R. Kainuma, N. Ueno, T. Nishizawa, Metall. Trans. 22A (1991) 441. [2] R. Kainuma, N. Ono, K. Ishida, MRS. Symp. Proc. 360 (1995) 467. [3] S. Furukawa, A. Inoue, T. Masumoto, Mater. Sci. Eng. 98 (1988) 515. [4] M. Wallin, P. Johansson, S. Savage, Mater. Sci. Eng. A133 (1991) 307. [5] C.T. Liu, C.J. Sparks, J.A. Horton, E.P. George, M.-Y. Kao, H. Kunsmann, MRS Symp. Proc. 246 (1991) 169. [6] C.Y. Xie, L.W. Sen, T.Y. Hsu, Scripta. Mater. 35 (1996) 345.
The properties of two-phase Ni–Al–Fe shape memory alloys in the virgin and shape-memory-cycled states N. Ono a,*, A. Tsukahara a, R. Kainuma b, K. Ishida b a
Department of Mechatronics and Precision Engineering, Graduate School of Engineering, Tohoku Uni6ersity, Aramaki-Aoba, Aoba, Sendai 980 -8579, Japan b Department of Materials Science, Graduate School of Engineering, Tohoku Uni6ersity, Aramaki-Aoba, Aoba, Sendai 980 -8579, Japan
Abstract Five polycrystalline Ni–Al–Fe alloys with 14–26 (at.)% Al and 16 – 26% Fe were made and heat-treated to have b and g dual phases with from 87% to less than 1% of b phase and to exhibit Ms temperatures at about 300 K. Depending on the b phase fraction and prestraining temperature, the alloys showed pseudoelastic strain recovery ratio from 1 – 2 up to 35% and shape memory strain recovery ratio from over 10–90% after prestraining by up to 1%. In the alloy with 87% b phase, the latter ratio reached 100% against 0.8% prestrain after a few cycles of shape memory training. Observed results were analyzed based on a model that assumed a simple linear mixture of the properties of the b and g phases. The results of the analysis suggest that the g phase after the training in certain conditions is almost elastic and thus acts as a bias spring. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Shape memory alloys; Ni–Al–Fe alloys; Dual phases; Shape memory cycling
1. Introduction It has been reported that a variety of ductile b (B2) Ni–Al base shape memory (SM) alloys can be fabricated with the conventional casting-hot working method by introducing the ductile g (A1) phase and controlling its morphology [1,2]. One would expect that the g phase in these alloys may impair the inherent SM performance of the b phase. This paper describes the results of experiments concerning the influence of the g phase on the SM effect in a series of Ni – Al – Fe alloys with from 0–87% of the b phase in virgin state and also after a few cycles of SM training. While most of the previous studies on Ni – Al base SM alloys were made with bending [1– 6], the present experiments were carried out in tension and, therefore, more detailed observations of deformation and SM properties were possible. Based on good linear dependence of various characteristics of the alloys on the b phase volume fraction, pseudo-elastic and SM properties of the alloys were analyzed with a simple linear mixture model. The * Corresponding author. Fax: +81-22-2177027. E-mail address: [email protected] (N. Ono)
analysis suggests that the g phase can be made almost elastic in certain conditions of SM training. The g phase as such acts as a bias spring and does not affect the SM capability of the alloys.
2. Experimental procedures Five alloy ingots as listed in Table 1 were prepared by induction melting in an argon atmosphere and hotrolled to sheets with a thickness of about 1.5 mm. Tensile specimens were laser-cut from the sheets in the rolling direction. They were annealed at 1100°C for 1800 s and quenched into ice water. After this treatment, the structure of alloy 1 consisted of b phase grains and g phase that formed continuous grain boundary precipitates and a small amount of coarse particles in the grain interior as reported in [2]. Alloy 6 with 22% Fe was virtually g single phase. Alloys from 2 to 4 with intermediate Fe contents showed b/g-duplex structures. The volume fractions of the b phase and grain sizes in these alloys are included in Table 1. Because grains in these alloys were elongated in the rolling direction, the grain size measurements were
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 3 1 0 - X
N. Ono et al. / Materials Science and Engineering A273–275 (1999) 420–424
421
Table 1 Compositions and other characteristics of alloys Alloy no.
1 2 3 4 6
Composition (at.%)
b Phase volume fraction
Grain size (mm)
Transformation temperatures (°C)
Ni
Al
Fe
f (%)
b
g
Ms
Mf
As
Af
Bal.
26.0 23.6 21.2 18.8 14.0
16.0 18.0 20.0 22.0 26.0
87 71 51 38 B1
19.4 11.5 7.2 4.7 –
– 4.8 6.2 9.5 105
24–32 21–27 26–36 28–30 –
0–13 4–7 16–24 7–9 –
10–27 15–24 24–33 12–27 –
40–58 33–51 53–63 46–58 –
made in the transverse section along the lines at 45° to the tensile axis. Individual specimens were attached to a laboratorymade gear-servo tensile testing machine controlled to zero load and subjected to heating – cooling – reheating cycling between− 80 and 120°C and then cooled to respective intended prestraining temperatures. During this temperature cycling, electric resistance across the gauge part of the specimens was monitored in order to measure transformation temperatures. The scatter of the measured transformation temperatures among a heat of specimens was within a few K as summarized in Table 1. After the temperature cycling, the specimens were stretched to prescribed plastic strains and unloaded to observe pseudoelastic behavior. Following this, they were heated to 120°C and cooled to respective prestraining temperatures at zero load. SM strain recovery was evaluated based on the crosshead positions before and after this heating – cooling cycle. Some specimens were subjected further to the repetition of the above stretching–unloading – heating – cooling cycle several times to observe the effect of SM training.
The results of SM strain recovery measurements for alloys 1–4 are summarized in Fig. 3 in terms of the percentage of overall recovery strain DoSR against the amount of prestrain DoP. In the all alloys, the largest strain recovery was observed when specimens were prestrained at Ms. At this temperature, DoSR/DoP exceeded 90% in alloy 1 but decreased with decreasing f. The dependence of DoSR on temperature and f as such may be due to plastic deformation of the g phase. This will be larger when the applied stress is larger and its influence will be larger when f is smaller. Specimens stretched at temperatures below Ms showed spontaneous elongation when they were cooled across Ms and Mf after the shape recovery heating due to the two-way SM effect [3]. This makes DoSR values below Ms smaller. As shown with an example in Fig. 4, some specimens after the SM test in the virgin state were stretched again to the maximum plastic strain the same as that in the first SM test. The pseudo-elastic strain recovery and SM effect were observed by unloading and heating– cooling temperature cycling, respectively. The same procedure was repeated several times. In this cycling
3. Experimental results Fig. 1 shows some of observed stress – plastic strain curves. Pseudo-elastic strain recovery DoPE increased with increasing prestraining temperature and with increasing b phase volume fraction, f. Even in alloy 1 prestrained at 50°C above Ms, however, DoPE was only a third of given prestrain DoP. Observed yield stresses at different test temperatures are plotted against f in Fig. 2. The yield stresses of the alloys with b phase showed good linear relations with f: sY = fs bY + (1− f )s gY Here, the yield stress of g phase, s gY, was larger than that of the b phase, s bY. It was independent of temperature while s bY exhibited a positive temperature dependence above Ms. Observed yield stresses of alloy 6 were far smaller than s gY in the above relation. This is apparently because this alloy had a grain size far larger than other alloys (see Table 1).
Fig. 1. Effects of temperature and b phase volume fraction on pseudo-elastic behavior.
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Fig. 2. Effect of b phase volume fraction on the yield stress at various temperatures.
Fig. 4. Pseudo-elastic loops of alloy 1 at Ms 60 K during shape memory training.
4. Linear mixture model scheme, DoP decreases with the number of cycles until 100% SM strain recovery is attained. In this example, this occurred between fourth and fifth cycles where DoP was still as large as 0.5%. The relations between DoP and DoSR/DoP for individual cycles are presented in Fig. 5 for alloy 1 and alloy 2. The alloy 1 specimen cycled at Ms showed DoSR/DoP larger than 95% with prestrain range of about 0.8%. Other specimens cycled at higher and lower temperatures attained similar or even larger recovery ratios, but with smaller remaining prestrain ranges. In alloy 2, DoP decreased more rapidly and DoSR/DoP values were smaller than corresponding values in alloy 1. These features were more pronounced in alloys with smaller f.
As seen in Fig. 2, for example, certain properties of the present alloys show good proportionality with f. Based on this, it was attempted to simulate experimental results with a simple linear mixture model. In the model, the applied stress on a specimen s is given as the volumetric average of those in b and g phases, s b and s g,, respectively: s = fs b + (1− f )s g
(1)
The sum of elastic and plastic strains is the same in the b and g phases. If we write the latter as o bp and o gp, respectively, and let E b and E g denote Young’s moduli of respective phases, this equality is expressed as follows o=s b/E b + o bp = s g/E g + o gp
(2)
To describe the deformation and strain recovery behavior of the b and g phases, simplified parallelogramic
Fig. 3. Shape memory strain recovery at various prestraining temperatures.
Fig. 5. Changes in prestrain range and shape memory strain recovery with training cycles.
N. Ono et al. / Materials Science and Engineering A273–275 (1999) 420–424
423
Fig. 6. Assumed stress–strain relations for b and g phases.
stress–strain relations as depicted in Fig. 6 were assumed. Young’s moduli, yield stresses and work hardening rates for respective phases were evaluated by extrapolating observed linear relations between these properties and f. A small temperature dependence of work hardening rates for both phases was ignored for simplicity. The reverse yield stress of g phase, s gYR, was assumed to be the reverse of the forward yield stress, s gY, ignoring work hardening in prestraining and the Bauschinger effect. The magnitude of the stress hysteresis in the pseudo-elastic loop of b phase, Dsh, could not be determined directly because the present alloys did not exhibit clear pseudo-elastic strain recovery even at 50 K above Ms. Therefore, this value was assumed to be independent of temperature and determined in a trial-and-error manner to obtain the best possible agreement between the predictions of the model and experimental observations on pseudo-elastic loops and SM behavior. The temperature dependence of yield stress in a SM alloy is generally represented with the Clausius– Clapeyron equation, sY =(T −Ms)DS/Do*, where Do* is the transformation strain. Because we assume that Dsh is independent of temperature, to heat a prestrained specimen by DT amounts to shifting the pseudo-elastic segments of the stress-strain relation in Fig. 6 by Dt =DTDS/Do*. The shape recovery behavior of the b phase is thus calculated by substituting s b in Eqs. (1) and (2) with s b −Dt. Parameters used in the calculations are summarized in Table 2. Table 2 Characteristics of stress–strain relations for b and g phases used in the analysis with the linear mixture model Phase Young’s Modulus E (Gpa) Yield stress sY (MPa) Work hardening rate u (Gpa) Stress hysteresis Dsh (MPa) a
s bY = 77+4.54(T−Ms).
b
g
42 a
4.8 280
95 560 2.5 –
Fig. 7. Pseudo-elastic curves calculated for alloy 1 at Ms and 50 K above Ms in comparison with experimental results.
As shown in Fig. 7, calculated stress–strain relations for alloy 1 during a stretching-unloading cycle show good agreement with corresponding experimental results. At Ms, op in the b phase is much larger than that in the g phase so that residual internal stresses produced with this cycle are compressive and tensile in the b and g phases, respectively. The latter is in the direction to help pseudo-elastic strain recovery but its magnitude is not sufficient for this to actually take place. At 50 K above Ms, pseudo-elastic strain recovery occurs in the b phase. Plastic strain in the g phase is larger than that in the b phase firstly because the yield stress of the b phase is now closer to that of the g phase and also because the Young’s modulus of the g phase is larger than that of the b phase. Because of this, a tensile internal stress develops in the b phase and it suppresses the strain recovery of the b phase that otherwise could be more extensive at this temperature. In heating, o bp decreases when s bYR0 B s b − Dt Bs bYR. The stress–strain responses to this in the individual phases and the specimen as a whole can be calculated by solving Eq. (1) and Eq. (2) simultaneously with a prescribed value of Dt and s= 0. The model duly predicts that the plastic strain in the b phase recovers completely by heating and produces a compressive stress in the g phase. During this, however, the g phase is purely elastic and shows only a small reverse plastic strain when prestrained at Ms and 50 K above Ms, respectively, resulting in considerable remaining overall strain and tensile internal stress in the b phase. The latter causes a lower yield stress and a higher plastic slope in the second prestraining as in fact observed experimentally. In the third cycle, the g phase is mostly elastic and almost perfect strain recovery to the value at the start of this cycle is achieved. In reality, the prestrained g phase itself should exhibit some amount of
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N. Ono et al. / Materials Science and Engineering A273–275 (1999) 420–424
strain hysteresis during stress cycling so that the observed change in shape recovery behavior is less clearcut than this. But the analysis explains the quick increase in strain recovery ratio with the SM training.
5. Conclusion It is generally expected that the mixing of a nonshape-memory second phase in a SM alloy would deteriorate the inherent SM capability of the alloy. This is supported by the experimental observations, such as the limited pseudo-elastic strain recovery, and the linear degradation of SM recovery strain with increasing g phase fraction. The present experimental results and their analysis with a linear mixture model suggest that this drawback of two-phase SM alloys may be avoided by training. In certain combinations of the factors, such as the yield stress and volume fraction of the second phase, the temperature and strain range of prestraining etc., we can produce, with a few cycles of SM training, an internal state where the second phase is mostly elastic and thus does not affect the inherent SM capability of the alloy. In this stable state, the second phase is stressed in the direction of the forward deformation. The elastic second phase thus acts like a bias spring in a usual SM device and enhances the two-way SM effect.
.
In regard to the combinations of training conditions, the present study covers only a small part of them. For example, we have not studied the effect of prestraining at pseudo-elastic region on the SM effect when the specimen is strained at Ms or lower temperatures. The linear mixture model described here will be useful in the planning of such experiments on two-phase SM alloys and also in interpreting their results.
Acknowledgements The authors would like to thank the support from The Sound Technology Promotion Foundation.
References [1] K. Ishida, R. Kainuma, N. Ueno, T. Nishizawa, Metall. Trans. 22A (1991) 441. [2] R. Kainuma, N. Ono, K. Ishida, MRS. Symp. Proc. 360 (1995) 467. [3] S. Furukawa, A. Inoue, T. Masumoto, Mater. Sci. Eng. 98 (1988) 515. [4] M. Wallin, P. Johansson, S. Savage, Mater. Sci. Eng. A133 (1991) 307. [5] C.T. Liu, C.J. Sparks, J.A. Horton, E.P. George, M.-Y. Kao, H. Kunsmann, MRS Symp. Proc. 246 (1991) 169. [6] C.Y. Xie, L.W. Sen, T.Y. Hsu, Scripta. Mater. 35 (1996) 345.