Transformational behaviour of constrained shape memory alloys

Acta Materialia 50 (2002) 3535–3544 www.actamat-journals.com

Transformational behaviour of constrained shape memory alloys K.A. Tsoi a,∗, R. Stalmans b, J. Schrooten a a

Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, B-3001 Leuven, Belgium b FLEXMET, Rillaarsebaan 233, B-3200 Aarschot, Belgium Received 9 November 2001; received in revised form 12 April 2002; accepted 15 April 2002

Abstract The transformational behaviour of shape memory alloy (SMA) wires embedded into a fibre reinforced epoxy composite was investigated and is discussed in this article. The effects on the transformational temperatures, and heats of the embedded SMA wires and the generation of recovery stresses within the composites on heating are shown to be related to the reversible martensitic transformation of the SMA wires. This article details the effects of the constraining matrix on the transformations of self-accommodating and preferentially oriented martensite. It was found that there is little change in the transformation temperatures of the constrained SMA wires with increasing pre-strain, but that the measurable transformation heats decrease significantly with increasing pre-strain. It is concluded that the transformation of self-accommodating martensite is nearly not affected by the constrained matrix, whereas the transformation of the preferentially oriented martensite is suppressed.  2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Re´sume´ Cet article porte sur l’e´tude du comportement a` la transformation de fils en alliage a` me´moire de forme (AMF) inse´re´s dans un mate´riau composite en re´sine epoxy renforce´ par fibres. On montre dans cet article que les diffe´rents effets sur les tempe´ratures et les chaleurs de transformation des fils AMF inse´re´s dans la matrice, ainsi que la ge´ne´ration de contraintes de relaxation lors du chauffage au sein du mate´riau composite sont lie´s a` la transformation martensitique re´versible des fils AMF. Cet article de´taille les effets de la matrice induisant de la contrainte sur les transformations de la martensite auto accomodante et celle a` orientation pre´ferentielle au sein des fils AMF. Les tempe´ratures de transformation des fils AMF sous contrainte sont sensiblement modifie´es en fonction de l’augmentation de la pre´de´formation, alors que les chaleurs de transformation mesureables diminuent de fac¸on significative avec l’augmentation de cette pre´de´formation. Cette e´tude permet de conclure que la transformation de la martensite auto accomodante n’est quasiment pas affecte´e par la pre´sence de la matrice induisant de la contrainte, alors que la transformation de la martensite a` orientation pre´fe´rentielle disparaıˆt.  2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Shape memory; Composites; Phase transformation

1359-6454/02/$22.00  2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 2 ) 0 0 1 4 5 - 3

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1. Introduction The functional properties of shape memory alloys (SMAs) and SMA-composites are based on the shape memory effect, i.e. the reversible transformation from a martensitic to an austenitic state due to the application of heat or stress on the SMAs. One of the most important aspects derived from the shape memory effect is the ability of the SMAs to generate recovery stresses. If a prestrained SMA is constrained during the transformation from martensite to austenite, large recovery stresses of up to 800 MPa are generated [1–4]. There has been an increased interest in adaptive composites, in which embedded SMA wires or fibres act as actuators. These fibre reinforced matrices with embedded SMAs are called SMA-composites. These composites can be used as actuating surfaces in structures, to reduce vibration [5–9], enhance impact damage resistance [10,11] and crash worthiness of structures, or for shape control. However, the functional properties of the SMAcomposites need to be well understood before they can be considered for industrial applications. The functional properties of the SMA-composites are directly related to the constraining behaviour that the composite matrix has on the SMA wires. SMA wires that are pre-strained and embedded in a constraining matrix, when heated, act against the constraining nature of the matrix. Recovery stresses are gradually generated within the wires during heating and the strain recovery is delayed. This phenomenon can be used as a basis for adaptive composites. Recently, researchers [8,12–18] have looked at embedding SMA actuators into polymeric composites, either as strips or ribbons, concentrating, in particular, on the possibilities of producing new materials, which are capable of modifying the frequency or damping the modes of structures [5,19] ∗

Corresponding author. Present address: Department of Metallurgy and Materials Engineering, School of Aerospace, University of Sydney, DSTO, 506 Lorimer Street, Fishermens Bend, Victoria 3207, Australia. Tel.: +61-3-9626-7597; fax: +61-3-9626-7089. E-mail address: [email protected] (K.A. Tsoi).

as well as for shape control [15]. However, it is interesting to note that in the literature there has been little done with respect to the transformational behaviour of SMA-composites. Only the effects that time and temperature have on the thermal stability of SMAs have been discussed, as well as the resulting effects that this has on the SMA-composite, [20]. Initial investigations by the authors into the recovery stresses of SMA-composites [21] and into their functional properties [22] have been completed. The results have been combined with theoretical predictions into the SMA-composite behaviour [23,24], showing very good correlation between theory and experiment. The transformational behaviour of the SMA wires embedded in a polymer composite matrix is investigated more extensively in this article.

2. Materials and methods Two commercially available SMA wires were used in this work. A binary NiTi-wire was obtained from SMA, Inc. (USA). The martensitic transformation in this binary alloy is preceded by an R-phase transformation. A ternary NiTiCu-wire with a single transformation was obtained from Memry (USA). All wires were supplied in the straight annealed condition and had a diameter of 0.15 mm. The transformation temperatures of the wires in the as-supplied condition are given in Table 1. The subscripts s, p and f stand for the start, peak and finish temperatures, respectively, of the martensitic (M), austenitic (A) and R-phase (R) transformations. To produce SMA-composites with pre-strained SMA wires a frame was designed and made by EPFL, Switzerland. It enabled SMA wires to be wound around comb-like pins, 500 µm apart, situated at both ends of the frame. One of these combs could be moved in order to pre-strain and then hold the wires at the required pre-strain value during curing. The maximum number of wires possible was 2 wires/mm. The frame is shown in Fig. 1. The SMA-composites consisted of two layers of aramid fibre pre-preg and one layer of SMA wires. The pre-preg was supplied by the Advanced Com-

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Table 1 The transformation temperatures (°C) and heats (J/g) of the as-received NiTi and NiTiCu wires as measured with DSC

NiTi NiTiCu

Ms

Mp

Mf

⌬HM

As

Ap

Af

⌬HA

Rs

Rp

Rf

⌬HR

39.8 46.8

38.2 43.1

29.7 38.3

14 15

74.4 55.6

77.9 60.7

81.7 64.2

23.1 14.4

61.2

60.1

58

7.2

Fig. 1. SMA-composite frame, designed and made by EPFL, used to make the SMA-composites (photo courtesy EPFL, Switzerland, 1999).

posites Group, UK, and contained 60 vol% Kevlar 29 fibre and an epoxy resin system LTM217. This pre-preg was chosen for several reasons: (i) the curing temperature is sufficiently low, (ii) this prepreg can be used in general aerospace applications and (iii) the Young’s modulus is sufficiently close to that of the SMA wires used. The glass transition temperature (Tg) of the cured composite was found to be around 160 °C [25]. The wires were prestrained to different values ranging from 0 to 8% for NiTi and from 0 to 5% for NiTiCu. The curing cycle of the composites consisted of 12 h at 70 °C followed by a post cure of 1 h at 140 °C. An example of the resulting composites can be found in Fig. 2. To investigate the transformation temperatures and heats of the SMA-composite with differential scanning calorimetry (DSC; TA Instruments DSC 2920) the composites were cut into 0.5 × 0.5cm2 pieces using a low speed diamond saw, in order to retain an intact interface and to minimise the effects of stress and deformation along the edges of the specimens. The SMA-composite samples used for the DSC

Fig. 2. Examples of SMA-composite specimens used in this investigation (photo courtesy EPFL, Switzerland, 1999).

measurements weighed approximately 7 mg. The temperature and energy flow were calibrated using an indium reference standard and the specimens were placed directly into the cell with helium gas flowing through the chamber. A composite without SMA wires, which consisted of a matrix sample with similar weight to the matrix fraction of the specimen, was used as a reference. All specimens were initially cooled at a rate of 5 °C/min to 0 °C, then heated to 120 °C at a rate of 5 °C/min (first heat cycle), cooled to ⫺30 °C, reheated to 120 °C (second heat cycle) and cooled to 0 °C. The transformation temperatures were determined using a standard line crossing technique, as shown in Fig. 3(a) and the transformation heats were determined by calculating the area bounded by the heat peak and the baseline, as shown in Fig. 11(a). 3. Results As discussed in Section 1, the amount of heat flowing from the SMA-specimen gives an indi-

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Fig. 3. DSC curves for composite specimens with embedded NiTi-wires for different pre-strains showing the heating curve. (a) 0% pre-strain, (b) 2% pre-strain, (c) 5% pre-strain, (d) 8% pre-strain.

cation of the martensitic transformation properties of the material. The energy required for the forward transformation to proceed is important in order to determine the amount of energy the system requires to undergo a transformation. Fig. 4 shows a DSC curve of the complete thermal cycle obtained for a NiTi SMA-composite with no pre-strain. The forward curve (cooling)

Fig. 4. DSC curves for composite specimens with embedded NiTi-wires for 0% pre-strain showing cooling and heating.

shows that the martensitic transformation is preceded by an R-phase transformation, and the reverse (heating) curve shows one austenitic transformation. Fig. 3(a)–(d) shows the reverse austenitic transformations for 0, 2, 5 and 8% pre-strained NiTi SMA-composites. The effect that increasing the pre-strain of the SMA wires has on the measured transformation heats can be clearly seen. Fig. 3(c) and (d) shows jagged endothermic peaks at more elevated temperatures. These have been determined to be an indication of debonding between the wire and matrix interface and the details of this are discussed in Ref. [26] and will not be further explained here. However, this indication means that after the first heat cycle, there is a limited amount of debonding occurring between the wires and the matrix. It also means that any influence of the specimens during preparation, such as edge effects, are annealed out. Thus, during the second heat cycle the specimen becomes stable and it has been shown through thermomechanical cycling that the amount of debonding in the wires does not increase (see Fig. 5). Fig. 6 shows the change in transformation tem-

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Fig. 5. Stress vs. temperature chart showing stable thermal cyclic behaviour for an SMA-composite embedded with NiTiCu wires pre-strained to 3% (four cycles are shown). The composite was heated and cooled in an oil bath to 140 °C while in a constant strain condition.

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peratures with increasing pre-strain for embedded NiTi and NiTiCu wires. From these it can be seen that there are no significant changes in the transformation temperatures with increasing pre-strain value. Fig. 7 shows the changes in the transformation heats as a function of pre-strain for both the first, (a) and (c), and second heat cycles, (b) and (d). From these figures it is clear that the measured transformation heats decrease significantly with increasing pre-strain value. Fig. 7(a) and (b) shows that the transformation heats for NiTi wires for both forward transformations (austenite to R-phase and R-phase to martensite) and for the reverse martensite to austenite transformation reach 0 near 8% pre-strain. This value is close to the maximum shape memory strain for the NiTi wires ([27] and from experiment). Fig. 7(c) and (d) shows that the transformation heats for the NiTiCu wires also decrease, however, they do not reach 0 at 6% pre-strain, being the maximum shape memory strain for NiTiCu ([28– 30] and from experiment). The fact that the transformation heats do not reach zero at the prescribed maximum pre-strain value and that the transformation temperature charts in Fig. 6 contain a variation in transformation temperature for specimens with the same percent pre-strain, can be accounted for. A problem encountered, particularly with the NiTiCu wire, is that extra (plastic) deformation could be induced during the winding of the wire onto the frame. This is related to the stress–strain behaviour of these wires (Fig. 8). Also, plastic strains might have been induced during the curing by the combination of high stresses and strains at relatively high temperatures. As such, the wires may have a slightly different pre-strain than theoretically intended. This error was minimised as much as possible by the careful winding of the wires onto the frame.

4. Discussion

Fig. 6. Transformation temperatures as function of pre-strain for embedded (a) NiTi and (b) NiTiCu wires. NB. No austenite transformation peaks for 8% pre-strain for NiTi were observed.

Fig. 9 shows the recovery stress build-up for a NiTiCu SMA wire, pre-strained to 3% and constrained during thermal cycling up to 120 °C. The strain was kept constant and a recovery stress of

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Fig. 7. The measured transformation heats during heating vs. the pre-strain for composite samples with (a) NiTi wires during the first heat cycle, (b) NiTi wires during the second heat cycle, (c) NiTiCu wires during the first heat cycle, and (d) NiTiCu wires during the second heat cycle.

Fig. 8. wires.

Stress vs. strain curves for NiTi and NiTiCu SMA

around 400 MPa was obtained at 110 °C. It is correct to assume that the wires in the SMA-composite are in a similarly constrained condition. Researchers [25,26] have investigated the interfacial properties between the SMA wires and the

Fig. 9. The recovery stress build-up and heat flow vs. temperature for a constrained shape memory wire (NiTiCu, 3% prestrain, two cycles shown). The recovery stress of the wire was obtained by heating and cooling in an oil bath up to 110 °C while in a constant strain condition.

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kevlar epoxy matrix and found that the interface strength between the wire and the matrix is stronger than the matrix itself. Therefore, it leads to the fact that the recovery stress build-up in the NiTiCu wires pre-strained to 3% and embedded in a kevlar epoxy matrix will be comparable to that observed in Fig. 9, taking into account the stiffness of the matrix. Comparing the recovery stress with the heat flow in Fig. 9, it is clear that in the temperature range between 70 and 110 °C, where recovery stresses are generated, no indication of a transformation is observed. This indicates that the recovery stress generation is not associated with one or more transformation peaks and vice versa. This observation can be explained by the difference in selfaccommodating martensite (SAM) and preferentially oriented martensite (POM), both martensitic variants that can be present in an SMA. When there is no stress applied to the alloy and a forward transformation occurs, SAM-variants are formed. The strain of one SAM variant is compensated by the surrounding variants so that as the variants grow and shrink, the net strain is zero [31,32]. When applying a stress to an SMA with SAM-variants, these are transformed into POM-variants and a net strain is present [32]. Thus, in a first approximation, a specimen containing 100 vol% SAM can be transformed into 100 vol% POM, resulting in the maximum shape memory strain of the alloy. Further straining will induce plasticity. When heated in a non-constrained condition, the SMA will undergo a reverse transformation of SAM and POM into austenite and recover the induced shape memory strain. The vol% POM is directly proportional to the amount of shape memory strain, eSMA, and the first approximation can be written as Vol%POM ⫽

eSMA × 100% emax

(1)

where emax is the maximum shape memory strain for the alloy, being 8% for NiTi and 6% for NiTiCu. In a constrained condition, the reverse transformation of SAM is not impeded by the matrix because no macroscopic shape change occurs during the transformation of SAM. Thus, the constraint has no influence on this transformation. The

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transformation of POM will be impeded because it generates a net strain that will be constrained. As a result, recovery stresses are generated. The speed at which the recovery stresses build up is independent of the %POM. From this reasoning the following hypothesis can be made: the heat peak measured by the DSC during the reverse transformation corresponds only to the transforming SAM. Fig. 6 shows that the reverse transformation temperatures are nearly not affected by the pre-strain. This confirms that the SAM experiences no effects from the matrix. The amount of SAM within the specimen can be derived from the measured transformation heat, ⌬HSAM, with ⌬Href, the heat measured in the case of 0% prestrain Vol%SAM

⫽

⌬HSAM × 100% ⌬Href

(2)

⫽ 100%⫺Vol%POM Combining Eqs. (1) and (2) it follows that the amount of SAM decreases linearly with prestrain, reaching zero at emax. From Eq. (2) it follows that the measured transformation heat (⌬HSAM), as a result of the transformation of SAM, will also decrease linearly with the pre-strain, reaching zero at emax. Thus, for NiTi wires with 8% pre-strain (i.e. Vol%SAM ⫽ 0, eSMA ⫽ emax), no heat peak is observed, as shown in Fig. 7(a). This confirms the above hypothesis that the heat peak is related completely to the SAM-transformation. The results shown in Fig. 7(b) indicate that the transformation heat of SAM does not drop, as would be expected, to zero at 6% pre-strain, which is the maximum shape memory strain for NiTiCu. A plausible explanation is that for the NiTiCuwires, which have a lower ‘reorientation’ yielding than NiTi, (see Fig. 8) it is easier for unwanted pre-strains to be induced during the wire winding and the sample curing at 140 °C. Thus, the actual shape memory strain is below the applied prestrain shown in the abscise of Fig. 7(c). It should also be noted from Fig. 7 that the transformation heats for the NiTi do not change between the first and second cycles, however, the NiTiCu shows a large change from the first and

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the second cycle. This is most probably related to the differences in the SMA wire/matrix interface. It has been found from pullout tests, [33], that the NiTiCu wire/matrix interface has an average intrinsic shear stress of 5 ± 1MPa. Due to this low interfacial shear strength decohesion of the prestrained NiTiCu wires could appear during the first heat cycle, resulting in a less constrained wire. Thus, during the subsequent cooling more SAM will be formed. Hence, a larger transformation peak will be visible during cooling and during the subsequent cycles. The reason that this effect is not seen in NiTi is that the wire/matrix interface is much stronger (24 ± 1MPa) [33]. Therefore, after the first heat cycle the majority of the interface remains intact. Further investigations were carried out with regard to the interface between the wires and matrix during heating and the results can be found in Ref. [26]. It will be explained subsequently in more detail why POM, in a constrained condition, does not give rise to a detectable heat peak in DSC measurements. The total strain of the SMA wires, indicated by eS, can always be divided into a recoverable shape memory strain eSMA, a thermal expansion, eSA and an elastic strain eSE eS ⫽ eSMA ⫹ eSA ⫹ eSE ⫽ eSMA ⫹ aS (T⫺T0) ⫹

(3)

⫹ ⌬eSA ⫹ ⌬eSE The maximum values of the coefficients of thermal expansion of the SMA wires and of the kevlar fibre reinforced epoxy matrix (aM ⫽ ⫺3.6 × 10⫺6 / °C), ⌬eSA and ⌬eMA, and elastic deformations of the matrix, ⌬eME, are one order of magnitude smaller than ⌬eSMA and ⌬eSE. Therefore, Eq. (5) can be approximated by ⌬eS ⫽ ⌬eSMA ⫹ ⌬eSE⬇0

(6)

Thus, the total strain is almost constant. This means that when there is a change in the elastic deformation of the specimen, an equal (inverse) change of the shape memory strain must occur. Fig. 9 shows that when the total strain is kept constant, the recovery stresses (sr) increase linearly with temperature. Therefore, the elastic strain, eSE ( ⫽ sr / ESMA, Hooke’s law) (Fig. 10) also increases linearly, and the shape memory strain, eSMA, must decrease linearly with increasing temperature. Thus, the vol% POM decreases linearly with temperature, as derived from Eq. (1). Considering a stress increase from 0 to 400 MPa over a temperature range of 60 °C (see Fig. 9), a value of 50 GPa for ES, and a value of 6–8% for emax, the rate of transformation, d(vol%POM) / dT, is only about 0.2 vol%/K. This quantitative estimation points out that there is only a very slow,

sS ES

where T is the temperature and s, aS and ES are the stress, coefficient of thermal expansion and elasticity modulus of the SMA wires, respectively. Similarly, the total strain of the matrix, eM, can be divided into a thermal expansion, eMA and an elastic strain eME eM ⫽ eMA ⫹ eME ⫽ aM(T⫺T0) ⫹

sM EM

(4)

where sM, aM and EM are the stress, coefficient of thermal expansion and elasticity modulus of the matrix material, respectively. From the condition for strain equilibrium between the SMA wires and the surrounding matrix it follows that ⌬eS ⫽ ⌬eM ⫽ ⌬eMA ⫹ ⌬eME ⫽ ⌬eSMA

(5)

Fig. 10. Strain–temperature relationship of elastic and SMA wire strains with temperature.

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techniques. A comparison of the global baseline shift with pre-strain indicated no significant change (Fig. 11(b)), confirming that the POM-transformation rate is independent of the pre-strain.

5. Conclusions

Fig. 11. (a) DSC curve for NiTi 5% pre-strained SMA-composite, showing Global Baseline shift. The shaded area is the area used to calculate the heat flow and corresponds to the amount of SAM in the wire and (b) Global Baseline Shift for different pre-strain values.

almost constant, progress of the reverse transformation of POM during heating of the embedded SMA wires. Besides the limited and slow character of the POM transformation there is another reason why this linear transformation is not detected by DSC. In standard DSC-testing, the temperature rate, dT / dt, is kept constant and the heat flow dQ / dt is measured. As explained previously, the transformation rate, d(vol%POM) / dT, is not only small but is nearly constant. In this constrained condition, this transformation of POM at a constant rate results not in a transformation peak, but in a small, global shift of the baseline, because dHPOM / dt is constant and small (Fig. 11(a)). This global baseline shift cannot be quantified using standard DSC-

The results shown in this investigation have given a better indication of what is happening during the transformation of pre-strained SMA wires that are embedded in a constraining matrix. Due to the many similarities, these results are also valuable for understanding the generation of recovery stresses by pre-strained SMA elements in constrained conditions. It was determined that the transformation temperatures of the constrained SMA wires as measured by a DSC are almost not affected by prestraining. Transformation heats decrease substantially with increasing pre-strain. These observations have been explained in terms of the SAM and POM as well as the basic principles of the thermoelastic martensitic transformation. The results indicate that the remaining transformation of SAM is not significantly influenced by the process of pre-straining, embedding in the matrix, constraining and activation. On the other hand, the constraining matrix effectively suppresses the progress of the transformation of the POM, which is related to the generation of recovery stresses.

Acknowledgements This work has been completed under the framework of the ADAPT-project which is funded by the European Commission, in the Industrial and Materials Technologies research and technological programme. K.A.T. acknowledges the financial support of Zonta International through the Amelia Earhart Fellowship Award and Professor Y.-W. Mai, Dr S.C. Galea and Professor M. Wevers for their generous support during this research. R.S. acknowledges the F.W.O Vlaanderen for a grant as Postdoctoral Fellow.

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