Constrained thermoelastic martensitic transformation studied by modulated DSC

Acta Materialia 51 (2003) 5467–5475 www.actamat-journals.com

Constrained thermoelastic martensitic transformation studied by modulated DSC Yanjun Zheng a,∗, Jan Schrooten b, Lishan Cui a, Jan Van Humbeeck b b

a Department of Materials Science and Engineering, University of Petroleum, Changping, Beijing 102249, China Department of Metallurgy and Materials Engineering, KU Leuven, Kasteelpark Arenberg 44, B-3001 Leuven, Belgium

Received 17 April 2003; received in revised form 18 July 2003; accepted 19 July 2003

Abstract The constrained thermoelastic martensitic transformation of TiNiCu wires embedded in an epoxy matrix was studied by modulated differential scanning calorimetry (MDSC). Results showed that the non-reversing heat flow (NHF) signal of TiNiCu wires in a free condition is quite small whether the wires are pre-strained or not, while the NHF signal of the TiNiCu wires embedded in the epoxy matrix increases significantly with increasing level of pre-strain. Analysis showed that this significant increase of the NHF value is related to a term which is a function of the stress rate (ds/dT). If the interface is perfectly bonded, this term contributes to the reversing heat flow (RHF) signal, while if the interface is debonded, this term contributes to the NHF signal.  2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Shape memory alloy; Modulated differential scanning calorimetry (MDSC); Martensitic phase transformation

1. Introduction Martensitic transformations are typical first order transformations. According to their kinetics, martensitic transformations can be classified into two groups: athermal and isothermal transformations. The former transformations have a welldefined martensitic transformation starting temperature (Ms) and the martensitic volume fraction is independent of time, while the latter one does not have a definite Ms and the martensitic volume fraction is a function of time [1]. Corresponding author. Tel.: +86-108-973-3200; fax: +86106-974-4849. E-mail address: [email protected] (Y. Zheng). ∗

In the categories of athermal transformation, thermoelastic martensitic transformation is of particular interest because it is the basis of the shape memory effect and pseudoelasticity of shape memory alloys (SMAs). The martensitic phase in SMAs usually appears as plate-like twins, growing on cooling and shrinking on heating. If an SMA is pre-strained to a level of several percent in the martensitic state, reorientation occurs and the reverse transformation (disappearing of martensitic twins) reverses the deformation until total recovery. Due to this unique property, SMAs are now being used or expected to be used in various applications such as pipe couplings, medical stents, actuators in smart composites, etc. [2].

1359-6454/$30.00  2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00412-9

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If the pre-strained SMA is prevented from shape recovery, as in many applications, reverse transformation will lead to the creation of recovery stresses. Due to the stress, the constrained thermoelastic martensitic transformation is different from that in a free condition. Many researchers have investigated this topic [3–5], and a commonly accepted conclusion of its physical process is schematically illustrated in Fig. 1. A pre-strain will transform the self-accommodating martensite (denoted by SAM in Fig. 1a) into preferentially oriented martensite (denoted by POM in Fig. 1b). If the SMA is constrained and heated to above the reverse transformation starting temperature (As), recovery stresses are gradually built up and part of the POM transforms into parent phase (denoted by P in Fig. 1c). Due to the recovery stress, the POM cannot totally transform to parent phase even when the temperature is higher than the reverse transformation finishing temperature (Af) [3–5]. In the following cooling process, the parent phase cannot transform back into POM. Instead, the parent phase transforms into SAM (shown in Fig. 1d) [3–5].

Fig. 1. Constrained thermoelastic martensitic transformation during thermal cycling. SAM is the self-accommodating martensite, POM is the preferentially oriented martensite and P is parent phase.

There is always some POM retained in the SMA, but its volume fraction may vary according to the heating temperature. According to Fig. 1, the transformation behaviour in the first thermal cycle is always different from that in the following thermal cycles. From the second thermal cycle onwards, the constrained transformation behaviour is repeatable. Several experiments and calculations [3,6,7] have confirmed this.

2. Experimental procedure Unidirectional SMA composites were produced using Strafil G-EPI-140/142 glass fibre epoxy prepreg supplied by Hexcel Composites. The glass fibre content of the prepreg was 58%. A ternary Ti–Ni–12wt%Cu alloy wire of 0.15 mm diameter was obtained from SMA Inc., USA. The transformation temperatures of this wire determined by differential scanning calorimetry (DSC) were: Ms = 320 K, Mf = 311 K, As = 324 K and Af = 341 K. The composites were cured in an autoclave at 413 K for 20 min with a heating rate of 2.7 K/min. A frame, designed by EPFL, Switzerland, was used to align the SMA wires with an adjustable, constant spacing, pre-strain and to hold the wires at constant strain during the curing process. The wires were sandwiched between two layers of prepreg, resulting in samples of dimension of 150 × 10 × 0.3 mm3. By adjusting the spacing between the wires, different SMA volume fractions could be achieved. In this study, the SMA volume fraction was 11.8%. SMA composites with wire prestrain levels ranging from 0% to 7% were produced. The dimensional change of the composites was measured using a DuPont 943 Thermomechanical Analyser (TMA) with a heating/cooling rate of 2 K/min. It is quite interesting to compare the differences in transformation behaviour between wires with and without the presence of the constraining matrix. For studying wires without the interference of resin matrix, some wire ends of the composite materials, which were not covered by the prepreg, were tested. During the autoclave run, the wires were held by the frame all the way from heating

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to cooling; therefore it is reasonable to assume that the wire ends had a history similar to those covered by the epoxy matrix. The wires were cut with a water-cooled slow speed diamond saw and each test sample consisted of six 4 mm segments placed in a sealed aluminium pan. The DSC composite samples were cut into approximately 5 × 5 mm2 using the diamond saw; then each sample was sealed into an aluminium pan. Because the samples were sufficiently thin, it was found that the characteristics of the DSC curve are practically unaffected by a heating rate between 5 and 15 K/min. A TA 2920 DSC (TA Instruments) was selected, the underlying heating rate was 5 K/min, the oscillation period of the sinusoidal modulation was 60 s and the amplitude was ±1 K. The oscillation amplitude and period were selected in such a way that at least four modulation cycles could be performed during the transformation.

3. Results 3.1. DSC–SMA transformations Fig. 1 is the base for interpreting various experimental results of the constrained thermoelastic martensitic transformation. Fig. 2 schematically

Fig. 2. Hypothetical DSC results for a SMA (a) and its composites (b–d): (a) SMA in a free condition, (b) the SMA component has no pre-strain, (c) the SMA is pre-strained to a moderate pre-strain level, and (d) pre-strained to its maximum recoverable strain level.

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shows the hypothetical DSC results for a SMA and its composites. For SMA composites with a wellbonded interface, experimental DSC curves are similar to those of Fig. 2 [3,4]. A reverse transformation in a free condition from the martensitic phase to the parent phase shows an endothermic peak on the DSC curve, as shown by curve (a) in Fig. 2. If the SMA is not pre-strained, embedding the SMA wire into a matrix does not notably affect the transformation behaviour (provided that the internal stress caused by the mismatch of coefficient of thermal expansion (CTE) between SMA and the matrix is not too large), as shown by curve (b) [8]. If the SMA is pre-strained, the martensite will be divided into two groups after one thermal cycle, that is, SAM and POM [3–5], as discussed in Fig. 1. Only the SAM shows an endothermic peak on the DSC curve without inducing any increase of recovery stress. The reverse transformation of POM is accompanied by linear increase of recovery stress, and thus is quite slow and covers a large temperature range, which could not be detected by DSC. The fraction of SAM and POM will decrease and increase, respectively, with increasing pre-strain. As a result, the area of the endothermic peak (proportional to the volume fraction of SAM) will decrease with increasing prestrain level, as shown by curve (c) in Fig. 2. If the pre-strain reaches the maximum level (about 6% for TiNiCu12), the endothermic peak will be reduced to almost zero, because there is almost no SAM left [3,4], as shown by curve (d) in Fig. 2. However, in practice, due to limited interfacial strength, the DSC results of SMA composites are not always so straightforward. The complexity comes from two possibilities: the characteristic temperatures of the endothermic peak (if any) shift, or more than one peak appears on the DSC curve. Conventional DSC cannot identify the different origins of these complex DSC peaks, and other complementary methods should be used to clarify the issue [6]. The development of the modulated DSC (MDSC) in the early 1990s seems to offer significant advantages over conventional DSC. By superimposing a small temperature oscillation on the normal heating/cooling rate, the heat flow signal can be deconvoluted into the reversing and non-

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reversing quantities, and thus provide some information that may not be available from conventional DSC. MDSC has so far been proven to be quite useful in the research of glass transition, relaxation processes and the measurement of heat capacity [9]. It has also been shown that MDSC can be used in the research of first order transformations [10], enabling one to obtain valuable insight into transformation processes and their kinetics. The objective of this paper is to examine the behaviour of the total, reversing and non-reversing heat flow signals of the constrained thermoelastic martensitic transformation of TiNiCu alloy wires embedded in a glass/epoxy composite, and the origin of the complex endothermic peaks on the DSC curves. 3.2. TiNiCu wires For a better understanding of the results for the composites, preliminary knowledge of plain TiNiCu wires is quite necessary. Fig. 3a and b show the MDSC results of plain TiNiCu wires with prestrain levels of 0% and 7%, respectively. The RHF value is almost equal to the total heat flow (THF) value, leaving the NHF quite small. It was shown that the magnitude of RHF is closely related to the inherent characteristics of the martensitic transformation [11,12]. If the martensitic transformation is not thermoelastic, for example the ⑀→γ transformation in ferrous SMAs, the RHF exhibits no evident endothermic peak during the reverse transformation. Only the thermoelastic martensitic transformation has an RHF peak that is equivalent to the THF peak [11,12]. One can see two important characteristics in Fig. 3. One is that the transformation of the pre-strained wire shifted towards higher temperatures after prestrain, in other words, the martensite phase was stabilised by deformation. Note that the epoxy– glass fibre matrix is not present here; thus the stabilisation is not caused by recovery stresses. This characteristic has been discussed in several papers [13–16]. The other important characteristic seen in Fig. 3 is that the NHF signal remains small even after a pre-strain higher than its maximum recovery strain (6%). In earlier studies on SMA by MDSC [11,12],

Fig. 3. MDSC result of TiNiCu wires in free conditions. (a) The pre-strain level is 0%, and (b) the pre-strain level is 7%.

the NHF signal was proposed to include not only the irreversible frictional work dissipated during the transformation, but also the contribution of the large hysteresis of the thermoelastic martensitic transformation. From Fig. 3, one can see that the pre-strain of 7% stabilises the martensite and elevates the peak temperature of the reverse transformation by about 15 K. We can conclude that as predicted by Refs. [11,12], the hysteresis, as well as the pre-strain level, does not affect the NHF signal significantly.

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3.3. TiNiCu composites As described in Fig. 2, a constrained martensitic transformation with a perfect interface will show only a moderate thermal peak for a moderate prestrain level, or almost no perceivable thermal peak for the maximum recoverable pre-strain level. However, in practice, as shown in Fig. 4, the composite DSC curves are quite complicated. In fact, in the temperature window from As to Af, the grey coloured endothermic peaks in Fig. 4 do show a tendency as predicted in Fig. 2. The difference is that a peak at temperatures higher than Af appeared on the DSC curve. It is quite reasonable to assume that the interface of the composite samples debonded at a certain temperature above Af, and the constraint effect that the matrix has on the embedded wires was weakened or even disappeared. Accordingly, the recovery stress decreased because of the disappearance of constraint, and resulted in the reverse transformation of the retained POM. Therefore, a large endothermic peak corresponding to POM appeared on the DSC curve. The higher the pre-strain level, the larger will be the volume fraction of POM and therefore also the endothermic peak area (above Af). A comparison between the DSC and TMA results, as shown in Fig. 5, can be regarded as direct evidence of the above assumption. Some micrograph evidence and mechanical analysis can

Fig. 4. The DSC curves of TiNiCu/epoxy composites with different pre-strain levels.

Fig. 5. A comparison between the DSC results and TMA results of TiNiCu/glass fibre/epoxy composites with a pre-strain level of 3%.

also be found elsewhere [6]. From Fig. 5, one can see that the composite shows a positive expansion coefficient if the temperature is lower than As, where no martensitic transformation takes place. From As on, the reverse martensitic transformation starts and the composite begins to contract. Also, an endothermic peak appears on the DSC curve. The reverse transformation of POM is quite slow and does not show perceivable thermal peaks; therefore the small endothermic peak corresponds mainly to the reverse transformation of SAM. When the temperature reaches a certain temperature T1 that is higher than Af, the interface begins to debond gradually. The SMA wires are not fully constrained anymore and therefore the accumulated compressive strain on the matrix is released gradually, as indicated by the expansion of the composite. At the same time, accompanied by the disappearance of the constraining effect of the matrix, the retained POM transforms rapidly into parent phase under the decreased recovery stress and high temperature, resulting in a broad endothermic peak on the DSC curve. After the end point of the endothermic peak of POM (T2), some accumulated compressive strain will further be released until eventually the composite expands at a rate equal to that below As, indicating total failure of the composite (T3). However, there is more information in the large endothermic peak in Fig. 4 than just a delayed

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reverse martensitic transformation of POM. Fig. 6 shows the MDSC results of composites prestrained to 1% and 7%, respectively. In contrast to plain wires, the NHF signal of the composite increases significantly with increasing pre-strain level. For a composite with 7% pre-strained wires, as shown in Fig. 6b, the NHF quantity is even larger than the RHF quantity. The variation of NHF and RHF with pre-strain level can be clearly seen in Fig. 7. For composites with 0% and 1% pre-strain, the RHF value is almost equal to THF and leaves RHF to be quite small. However, RHF increases significantly for 2% and 3% pre-strained Fig. 7. The ratio of reversing heat flow (RHF) and non-reversing heat flow (NHF) to total heat flow (THF) as a function of the pre-strain level.

samples and increases further but relatively slower for pre-strains higher than 3%. In fact, when the pre-strain is 3%, the NHF quantity is already larger than RHF. Results on plain wires have confirmed the validity of the experimental parameters used in this study.

4. Discussion 4.1. TiNiCu wires For a first order transformation, such as the melting of a crystal, the enthalpy is a function of temperature T and the volume fraction of the product phase x at constant pressure H ⫽ H(T,x)

(1)

Thus, the differential of H is dH ⫽

冉 冊

冉 冊

∂H ∂H dT ⫹ dx ∂T x ∂x T

(2)

where the subscripts x and T refer to constant phase composition and temperature, respectively. The heat flow dH / dt can be given from Eq. (2) as

Fig. 6. The MDSC results of TiNiCu/epoxy composites. (a) Pre-strain level is 1%, and (b) pre-strain level is 7%.

冉 冊

冉 冊

∂H dT ∂H dx dH ⫽ ⫹ dt ∂T x dt ∂x T dt

(3)

The component (∂H / ∂T)x is in fact the heat

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capacity of the sample, and can be expressed by the term cp, where the subscript p refers to constant pressure. The component dT / dt is the heating rate b. The second term on the right hand side in Eq. (3) is a function of both temperature and time scale; therefore Eq. (3) can be rewritten as

dH ⫽ HFrev ⫹ HFnon-rev dt

dH ⫽ cpb ⫹ f(T,t) dt

HFrev ⫽

(4)

Eq. (4) is often adopted in many papers to interpret the mechanism of MDSC [9,17], where in Eq. (4) the first term on the right hand side is referred to as the reversing heat flow, or the heat capacity component, whereas the second term on the right hand side is referred to as the non-reversing heat flow, or the kinetic component. However, for thermoelastic martensitic transformations, where x is the volume fraction of martensite phase, this analysis is not valid anymore. In a thermoelastic martensitic transformation, x is a function of temperature T, but independent of time. Thus, the second term on the right hand side in Eq. (3) can be expressed as (∂H / ∂x)Tb(dx / dT), which is independent of time and not the non-reversing heat flow anymore. Therefore, a new approach is necessary to interpret the MDSC results of SMA. In fact, the transformation enthalpy of a thermoelastic martensitic transformation is the sum of three components, given by [18] m⫺p ⫹ Em⫺p Hm⫺p ⫽ ⌬Hm⫺p ch ⫺⌬Hel fr

(5)

for the reverse transformation, where the superscript (m–p) refers to the reverse transformation from martensite to parent phase, and the subscripts ch, el and fr refer to chemical enthalpy, elastic strain enthalpy change and the energy dissipated during the transformation, respectively. Here, the negative sign implies that the system releases heat or energy, and vice versa. The and Em⫺p components together are called ⌬Hm⫺p el fr non-chemical components, which enlarge the transformation hysteresis and resolve some irreversible contributions to the transformation [11,12]. Without these non-chemical components, the thermoelastic martensitic transformation would be ideally reversible. Therefore, Eq. (3) can be rewritten according to Eq. (5) as

(6)

where HFrev represents the reversing heat flow which originates from the chemical enthalpy change, as

冉 冊 冉 冊

dx ∂Hm⫺p ∂Hm⫺p ch ch b⫹ b ∂T x ∂x T dT

(7)

and HFnon-rev represents the non-reversing heat flow which comes from the non-chemical enthalpy change, as

冉

HFnon-rev ⫽ ⫹

冉

冊

∂(⫺Hm⫺p ⫹ Efrm⫺p) el b ∂T x

冊

(8)

dx ∂(⫺Hm⫺p ⫹ Em⫺p ) el fr b ∂x T dT

From the MDSC results shown in Fig. 3, we know that HFnon-rev is quite small whether the SMA was pre-strained or not. 4.2. TiNiCu composites For SMA embedded in a matrix, however, a new variable, the external stress s, should be considered in the thermoelastic martensitic transformation because recovery stresses are generated and act on the SMA wire. Therefore, Eq. (1) is now written as [9] H ⫽ H(T,s,x)

(9)

and the heat flow is expressed as

冉 冊 冉 冊

∂H dH ⫽ dt ∂T ⫹

∂H ∂s

冉 冊

dT ∂H ⫹ ∂x x,s dt

dx T,s dt

(10)

ds T,x dt

A new term, (∂H / ∂s)T,x ds / dt, expressed as (∂H / ∂s)T,xb ds / dT, is added to the equation. The value (ds / dT) is in fact the stress rate of recovery stress build-up. Fig. 8 shows the measured ds / dT values of the wires used in this research. The solid circle on each curve denotes the starting point of the heating process. Note that the recovery stress build-up during the first thermal

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Fig. 8. The stress rate (ds / dT) of TiNiCu wires during a constrained heating process.

cycle differs from that of the later thermal cycles. This is consistent with the mechanism shown in Fig. 1. One can also see from Fig. 8 that the recovery stress increased almost linearly with temperature, and the hysteresis is almost zero. This indicates that during a temperature-modulating period, the stress increases (or decreases) with increasing (or decreasing) temperature with instant reversibility. For simplicity, (∂H / ∂s)T,x ds / dt can be expressed as K⬘(∂H / ∂T)s,x dT / dt, where K⬘ is a constant. Then, Eq. (10) can be rewritten as

冉 冊

冉 冊

∂H dT ∂H dx dH ⫽K ⫹ dt ∂T x dt ∂x T dt

(11)

where (K = 1+K⬘). The physical meaning of Eq. (11) is that the stress component can be converted into the temperature component provided that the stress increases (or decreases) with increasing (or decreasing) temperature with instant reversibility. Eq. (11) is equivalent to Eq. (3), and the analysis for SMA wires in Section 4.1 is also valid for SMA composites here. Therefore, the equations of the reversing and non-reversing heat flow for SMA composites are the same as those for SMA wires, Eqs. (7) and (8). A similar conclusion, that the nonreversing heat flow is quite small, is thus also applicable for SMA composites. Previous work on similar TiNiCu composites has confirmed that, for a composite pre-strained by a small amount (1% for example), the interface is well-bonded and the

recovery stress generated is a linear function of temperature [19]. From the analysis above, we expect that the non-reversing heat flow of a 1% pre-strained TiNiCu composite should be quite small. One can see from Fig. 6a that the nonreversing heat flow is quite small, just as expected. Also according to previous investigations, composites with a larger pre-strain level (higher than 3% for similar TiNiCu composites), the interface is more susceptible to interfacial debonding [6,19]. Once the interface begins to debond, further increase of temperature will enlarge the interfacial cracks, and the recovery stress will therefore decrease with increasing temperature [6,19]. As a result, the (ds / dT) value is not a constant anymore. Thus, the term (∂H / ∂s)T,x ds / dt cannot be simplified into K⬘(∂H / ∂T)s,x dT / dt, and Eq. (10) cannot be simplified into Eq. (11) either. In fact, during a temperature-modulating period, the stress will decrease monotonously no matter how the temperature is modulated, indicating that the change of s with the change of T loses its reversibility once the interface is debonded. The third term in Eq. (10) turns into the non-reversing heat flow value, no matter what the enthalpy, thermodynamically reversible chemical enthalpy, elastic strain energy or friction dissipated energy is. The non-reversing heat flow is thus increased significantly. A higher stress level and more POM are expected for a larger pre-strain level; therefore the ratio of NHF to THF increases with increasing prestrain level, which is consistent with the experimental results observed in this research.

5. Conclusions Temperature, modulated differential scanning calorimetry (MDSC) was used in this research to study the constrained thermoelastic martensitic transformation behaviour of TiNiCu wires embedded in an epoxy matrix. For comparison, the transformation behaviour of TiNiCu wires in free condition was also studied by MDSC. Results showed that for TiNiCu wires in free condition, the reversing heat flow (RHF) almost equals the total heat flow, leaving the non-reversing heat flow (NHF) quite small. Results also showed that the pre-strain

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does not change the ratio of RHF to THF significantly. This is quite reasonable, because a small NHF is an intrinsic characteristic of thermoelastic martensitic transformation. For TiNiCu wires embedded in an epoxy matrix, the reverse martensitic transformation is influenced by the presence of recovery stresses, and therefore only shows a small endothermic peak on the DSC curve. The area of the endothermic peak (the transformation enthalpy) decreases with increasing prestrain level, meaning that more martensite is retained at a higher pre-strain level. In practice, the interface of the composite always debonds at a certain elevated temperature. As a result, the retained martensite always shows an endothermic peak on the DSC curve at an elevated temperature. For this postponed thermal peak, the RHF signal contributes only a limited amount to the THF, while the NHF increases significantly. For pre-strains larger than 3%, the NHF value is even larger than RHF. Analysis showed that this significant increase of the NHF quantity is related to the decrease of the recovery stress generated when the interface is debonded. For TiNiCu wires embedded in an epoxy matrix, a new term, as a function of the stress rate (ds / dT), is added to the heat flow equation. If the interface is perfectly bonded, this new term contributes to the RHF signal, while if the interface is debonded, this term will contribute to the NHF signal. A higher stress level and more POM are expected for a larger pre-strain level; therefore the ratio of NHF to THF increases with increasing pre-strain level, which is consistent with the experimental results observed in this research. Acknowledgements This work has been done in the framework of the ADAPT project funded by the European Com-

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mission, in the Industrial and Materials Technologies research and technology programme.

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