Shape memory behavior and thermoelastic martensitic transformations

Materials Science and Engineering, 51 (1981) 181 - 192

181

Shape Memory Behavior and Thermoelastic Martensitic Transformations J E F F PERKINS

Materials Science Group, Department of Mechanical Engineering, Naval Postgraduate School, Monterey, CA 93940 (U.S.A.) (Received June 5, 1981)

SUMMARY

The current state of understanding o f shape memory behavior is reviewed. Microstructural, crystallographic and thermomechanical features, and their interrelationships, are considered. Practical limitations on shape memory behavior are discussed, including alloy selection and temperature limits. The phenomenon of "training" and two-way shape memory is outlined. Emphasis is placed on the stressstrain-temperature envelope as a tool for understanding and exploiting shape memory behavior.

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1. I N T R O D U C T I O N

Mortensite F'mish Range of 3 Mar fensite

When an ordinary metal is strained b e y o n d its yield point, permanent deformation is produced. For most metals the yield point corresponds to a fraction of a per cent strain; any strain b e y o n d this is defined as plastic deformation and is expected to remain. It would be very surprising, for example, if an extensively kinked metal wire were to straighten o u t spontaneously when heated. Yet this is exactly what certain alloys are able to do. If one of these "shape m e m o r y " alloys is deformed (while it is below a critical temperature and if the strain is limited to less than a b o u t 10%), it m a y recover its original shape when it is reheated, as illustrated schematically in Fig. 1. The reheating "reminds" the alloy that it should transform to a different crystal structure, and associated shape, at higher temperatures. This is just one example of shape m e m o r y behavior. In this presentation the term "shape m e m o r y " will be used in a general way and in a specific way. In its general usage, the term 0025-5416/81/0000-0000/$02.50

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Fig. 1. A schematic description of the shape memory effect: (a) a straight parent phase wire; (b) cooled through the athermal transformation range M s to Mr, producing a straight martensite wire; (c) a deformed martensite wire; (d) the deformed wire straightens out when heated through the reverse transformation range from Ps to Pf, reproducing the straight parent phase wire. It should be noted that there is typically a slight hysteresis between the forward and reverse transformation ranges, so that the transformation P -* M on cooling occurs over a slightly lower range (Ms to Mr) than that (Ps to Pf) for the transformation M ~ P on heating. M d is the temperature below which martensite can be stress induced from the parent phase.

"shape m e m o r y " refers to all the various thermoelastic behaviors in which there is a reversal of apparent plastic strain. This strain recovery may occur on heating, in which case © Elsevier Sequoia/Printed in The Netherlands

182 2. THERMOELASTIC MARTENSITIC TRANSFORMATION ¢/) w n,.. Ir~

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Fig. 2. Schematic stress-strain curves for a shape memory alloy at various deformation temperatures T d relative to the martensite transformation range, showing the complementary relationship of shape memory effect and pseudoelastic effect behavior (P, parent phase; M, martensite; M', martensite formed by or altered by stressing; , loading and unloadi n g ; - - - , heating): (a)Pf < T d = T 1 < M d (see Fig. 1 ); ( b ) P s < T d = T 2 < P f and Md (see Fig. 1); (c) Td = T 3 < Mf (see Fig. 1).

the behavior is traditionally called the "shape m e m o r y effect" p e r se, or may occur immediately on unloading, which is termed the "pseudoelastic effect". In general, there are components of both effects; the complementary relationship is shown in Fig. 2. At lower deformation temperatures a greater proportion of the initial strain is recovered by heating than by unloading, i.e. the shape m e m o r y effect behavior is more pronounced than the pseudoelastic effect. At higher temperatures, the reverse is true. There also is another shape m e m o r y behavior in which the alloy remembers both high and low temperature shapes, changing from one to the other on heating and cooling; this is called "two-way shape memory". At the Toronto meeting on shape m e m o r y effects in 1975 [ 1 ] , m u c h attention was given to the crystallography and microstructural features of shape m e m o r y martensites. Much less attention was given to mechanisms and mechanical behavior. Shape m e m o r y mechanisms are still u n k n o w n in m a n y cases and thermomechanical data are still very incomplete. In this paper we shall concentrate on the relationship of macroscopic thermomechanical behavior to crystallographic and microstructural features. In this respect it will be apparent that there are still m a n y aspects of shape m e m o r y behavior which remain unexplained.

The general basis of shape m e m o r y behavior is now accepted to be thermoelastic martensitic transformation. The shape changes that we observe on a macroscopic scale are associated on a microscopic scale with the reversion of stress-induced martensite and/or deformed thermal martensite. However, although we k n o w that shape m e m o r y behavior depends on the nearly perfect reversibility of thermoelastic martensites, we do not have universal models for the mechanistic details. A thermoelastic martensitic transformation is one in which the martensite plates form and grow continuously as the temperature is lowered and disappear by the exact reverse path as the temperature is raised, with a balance existing at all times between two opposing energy terms in the system. These terms are the chemical free-energy difference AGc between the two phases (which drives the transformation) and a non-chemical opposing energy ~Gnc. AGnc is essentially the elastic strain energy developed as the microstructural units of the new phase form in the original phase as a matrix. Therefore, either cooling or the application of an external stress tends to assist the transformation, while heating or unstressing will reverse it. Thus there are effectively similar roles for temperature and stress, in that a change in either of these parameters will adjust the balance of martensite and parent phases in the microstructure, and a generalized temperature-stress parameter m a y be used to represent the net transformation tendency. Since details of the analytical formulations for thermoelastic martensitic transformation are readily available in the literature [2 - 4], they will n o t be repeated here.

3. M I C R O S T R U C T U R A L MEMORY BEHAVIOR

ASPECTS

OF SHAPE

On a microstructural scale we have a reasonable understanding of what is happening when a shape m e m o r y alloy is deformed and then unloaded and/or heated to recover its original shape. First of all, the original (remembered) shape corresponds to the shape of the piece when the alloy was originally

183

annealed in the range of the high temperature parent phase. (In a great m a n y shape m e m o r y alloys this parent phase has a b.c.c, crystal structure with either B2- or D03-type ordering.) When the alloy is subsequently cooled to lower temperatures, it will tend to transform spontaneously to the martensite phase or, if not cooled sufficiently, the high temperature phase will persist but in a metastable condition that is ripe for transformation to martensite under stress. Thus straining a shape m e m o r y alloy corresponds either to deformation of athermal martensite which m a y already be present or to formation of stress-induced martensite from the retained high temperature phase, or to both of these mechanisms. In any case, the subsequent shape recovery is based on the fact that the strain introduced is in fact reversible, i.e. although it appears that there has been permanent plastic deformation (since recoverable strains of several per cent may be realized, far b e y o n d normal elastic limits) in fact there has been no permanent damage on a microstructural scale. The microstructure has deformed by mechanisms quite unlike the usual irreversible mechanisms of plastic deformation such as dislocation motion. Moreover, if the alloy is heated sufficiently that it prefers to transform back to the high temperature phase, it does so because the deformations retreat along the exact path by which they were introduced, so that the original shape is recovered. One of the main reasons for the reversibility of thermoe!astic martensite is that there are inherently low elastic strains associated with the crystal structure change, so that the elastic limit of the parent phase matrix is n o t exceeded and irreversible plastic deformation events do not occur. Furthermore, the strains which do build up as the martensite plates grow are effectively cancelled out by forming groups of mutually accommodating plates. In some cases these groups consist of simple alternating stacks of plates in which the strain vectors tend to be cancelled between neighboring plates; in other cases the plate groups are more complex. The typical martensitic microstructure of a Cu-Zn-A1 shape m e m o r y alloy is shown in Fig. 3. In addition, the individual plates themselves are internally twinned (as in Ti-Ni-based alloys, for example (Fig. 4)) or faulted (as in m a n y shape m e m o r y brasses (Fig. 5)) to accommodate the transformation

Fig. 3. A scanning electron microscopy photomicrograph of a typical martensitic microstructure of a 68.4at.%Cu-18.6at.%Zn-13.0at.%A1 shape memory alloy (Ms ~ 50 °C) at room temperature (20 °C).

Fig. 4. A transmission electron microscopy photomicrograph of internally twinned martensite plates in 50at.%Ti-50at.%Ni (Ms ~ 55 °C) at 20 °C.

strains. The reason that steels and many other martensitic alloys cannot exhibit shape memory behavior is simply that the transformation strains are too great to be accommodated in this way, so that irreversible events occur during transformation and thermoelastic behavior is ruled out. When shape m e m o r y alloys are deformed, they change their shape by shearing parent phase regions to martensite, by detwinning within individual martensite plates (for internally twinned martensites) and by complementary growth and/or shrinkage of

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Fig. 5. A transmission electron microscopy photomicrograph of internally faulted martensite plates in 66.7at.%Cu-24.3at.%Zn-9.0at.%A1 (Ms ~ 80 °C) at 20 °C.

neighboring martensite plates in groups. This means that most of the boundaries seen in Figs. 3 - 5 must be able to move freely under stress. For example, if a single crystal of the high temperature phase is transformed completely to martensite by cooling and then stressed, in the limit this will lead to a single crystal of martensite corresponding to the plate variant in the original microstructure that gives the largest extension in the direction of the applied stress.

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4. THERMOMECHANICAL CHARACTERISTICS OF SHAPE MEMORY ALLOYS

A number of unique thermomechanical parameters must be introduced to describe shape memory behavior: most importantly the flow stress ap-. M required to stress induce martensite; the amount cR of strain reversion; the strain limit eL for complete strain recovery; the internal stress which develops on heating a deformed but constrained sample, known as the "reversion stress" aR. Some of these parameters are defined schematically in Fig. 6, and in Figs. 7 and 8 which exemplify the experimental data obtained for Ti-Ni-based alloys [ 5]. Clearly each of these parameters can be measured experimentally, and probably each has a certain fundamental relationship to structural parameters. However, these relationships are in most cases not yet very well established. In order to develop shape memory alloys for technological applications, parameters such as these must be predictable, reproducible

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and of appropriate magnitude. In order to develop data such as those in Figs. 7 and 8 experimentally, an experimental arrangement such as that in Fig. 9 is employed. The shape m e m o r y alloy sample in this case is a rod of diameter 2.5 mm and of gauge length 25 mm held in special coUet-type grips in a cage below the movable cross-head of the tension-testing machine. The strain in the sample is monitored in three ways: (a) by the relative a m o u n t of cross-head movement; (b) b y strain gauges attached to the specimen and cage; (c) by proximator devices on the cage. The sample cage is immersed in a temperature-controlled bath that can be varied continuously in temperature from a b o u t - - 1 7 6 °C (liquid nitrogen temperature) to a b o u t +200 °C. The apparatus has been refined so that we can vary both strain and temperature very smoothly with time and so that we can control and measure the actual transformation strain in the sample at any time, taking into account thermal expansions or contractions in the sample and

Fig. 9. T h e e x p e r i m e n t a l a p p a r a t u s used in t h e d e t e r m i n a t i o n o f Op-. M vs. c i a n d a R vs. T data.

apparatus during the various temperature excursions. 4.1. The stress ap-. M to induce martensite

Figure 10 illustrates the typical temperature dependence of oe -. M between Ms and Md. Because of the effective equivalence of temperature and stress with respect to thermoelastic martensitic transformations, O'p--~M decreases from a maximum near M d to a minimum near Ms. This relationship can be expressed by a modified form of the ClausiusClapeyron equation: do dT

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where eL is the maximum macroscopic strain which is crystallographically realizable due to the stress-induced martensitic transformation, AGe is the chemical free energy of transformation, To is the characteristic transformation temperature (usually defined as To = 1 (Ms + At)) and p is the density of the alloy. The t y p e of temperature dependence of av-. M illustrated in Fig. 10 has been demonstrated for many shape m e m o r y alloys, including Ti-Ni-based alloys [5, 6 ] , C u - Z n - X alloys [ 7 - 9], Cu-A1-Ni [10, 11], A u - C d [12] and Ag-Cd [ 1 3 ] . The parameter a v - . M decreases with decreasing temperature because of decreasing stability of the parent phase as Ms is approached (see Fig. 10). Similarly, the parameter OM--+ p, defined in Fig. 6 as the level to which the stress must drop to allow the stress-induced martensite to revert to the parent phase, increases with increasing temperature from a minimum near As. This is because, the lower the temperature, the more stable is the martensite, so that the stress must be reduced to a greater extent to allow reversion to the parent phase. In fact, if the temperature is t o o low, no reversion at all will occur on unstressing the sample, i.e. no pseudoelastic behavior will occur, and reversion to the parent phase will occur only on heating, i.e. only the shape m e m o r y effect will occur. It should be n o t e d that, although av _. M is greatly affected by temperature, it is n o t a strong function of strain, as seen in the schematic figures, Figs. 2, 6 and 10, and as

confirmed by experimental data such as that in Figs. 7 and 8. It is important to note that the martensitic transformation temperatures in general are affected by stress [14]. For most shape m e m o r y martensitic transformations, where the transformation volume change is quite small, the stability of the martensitic phase is enhanced by applied stress, so that the transformation temperatures Me, Ms, As and Af shift to higher values with increased stress. The stress-strain-temperature dependences of phase stabilities in shape m e m o r y alloys may be represented graphically as in Fig. 8. Also, Shimizu and coworkers [15, 16] have introduced the use of stress-temperature phase diagrams such as Fig. 11. It should be n o t e d that these diagrams are able to account for the occurrence of various martensite-tomartensite transformations under stress and the occurrence of series of stress-induced martensite plateaux in o - e curves depending on the test temperature.

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Cu-14.0wt.%A1-4.2wt.%Ni alloy. (After Shimizu [15].) 4.2. The reversion strain eR and the recoverable strain limit eL

The most obvious feature of shape m e m o r y behavior is the removal of large amounts of induced strain on heating and/or unstressing, designated the reversion strain eR. However, there is for each shape m e m o r y alloy a strain limit eL. This is a critical value of induced strain, typically of the order of 5% - 10%, which if exceeded leads to true plastic deformation and a decrease in eR, OR and useful work output. Thus, if a strain greater than eL is induced, the shape m e m o r y behavior deteri-

187

orates. In general, deformation mechanisms associated with shape memory behavior involve stress-induced transformation of the parent phase to martensite and/or pseudoelastic deformation of the existing martensite. In either case the basic prerequisite for shape memory behavior is that no true plastic deformation occurs, in either the martensite or the parent phases. Thus the strengths of the phases, and the temperature dependences of these strengths, are important. The strengths of many of the parent phases in shape memory alloys are enhanced by the fact that they are ordered. The strain limit e L is dependent on the crystallography of the martensitic transformation in the particular alloy of interest, and particularly on the magnitude of the macroscopic shape change, which can be measured experimentally using a single crystal and rationalized with the phenomenological models of martensite crystallography. The martensitic microstructure also has an effect on the strain limit. Many thermoelastic martensites organize themselves into microstructures in which neighboring microstructural units are arranged to accommodate transformation strains mutually, thus obtaining a low net shape change [17, 18] (Fig. 12). When self-accommodating martensitic microstructures are subjected to stress or are stress induced from the parent phase, the arrangement of units is modified so as to produce the appropriate sense of strain [19, 20]. This may occur by means of various reorientation and retransformation mechanisms, including martensite-martensite boundary movement, internal twin boundary adjustments and martensite-to-martensite transformations. This requires mobile boundaries between the microstructural units. It is found that the full theoretical value of e L can more readily be obtained for single crystals than for polycrystalline material; this is because of the constraint of grain boundaries on the reorientation processes noted above. 4.3. The reversion stress OR

If the induced strain is held in the sample as it is heated through the reversion temperature rangeAs to A~ (by constraining the sample against the tendency to shape memory), an internal (reversion) stress will develop. This stress increases in sigmoidal fashion over the

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As to A~ range. It should be noted that the Af temperature is shifted upward by the internal stress so developed, while As is not (since there is no stress yet developed at As), so that the normal reversion temperature range is widened. The maximum level of reversion stress obtained on heating, which is obtained near A~, is a direct function of the initial induced strain. It has been shown that a R (max) can be increased by increasing the induced

188

strain, to a limit near eL, the strain limit (Fig. 13). If an initial strain greater than e L is introduced, the potential to develop reversion stress decreases, as can be seen in Fig. 8. Also, if a proportion of the initial strain is allowed to reverse freely prior to constraint of the remaining strain, the sample will have a correspondingly lower value of reversion stress at A~. In all, the value of aR (max) depends on the a m o u n t of reversible strain constrained in the sample as it is heated to A~. Work in our laboratories has shown that for design purposes the value of OR at a given temperature and strain can be approximated b y the value of ap ~ M at that same temperature and strain, which is useful in that the latter data are much more easily obtained in the laboratory. The correlation is shown in Fig. 14. In fact it is more reasonable to associate aR with O M -~ p ( a s defined in Fig. 6), since these both relate the reverse transformation to the parent phase. However, since all these parameters m a y be regarded as measures of the relative stability of the martensite phase, ap _. M at a given temperature and strain may be used as an approximate upper limit on aR : Fig. 14 shows that aR will be a b o u t 20% lower than ap _. M at that temperature and strain. This allows Up-~M(T,e), obtainable from a simple tensile test, to be used as a design guide. The fact that the stress az(max)/T2 developed during constrained reversion of martensite to the parent phase m a y be substantially greater than the stress Op ~ M / T 1 required to induce the martensite from the

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parent phase at some lower temperature has led to the utilization of shape m e m o r y alloys in energy conversion devices. These so-called "shape m e m o r y heat engines" are able to employ a relatively small temperature differential (AT = T2 -- T1) to realize a work o u t p u t due to the stress differential noted above. To illustrate this, we m a y consider Fig. 7 where we see that, for a sample deformed at a relatively low stress below Ms and then heated while holding the induced strain in the sample, the internal stress developed on reverting to the mar~ensite is substantially higher than the stress required to deform the martensite in the first place. Recently, several excellent reviews of the thermodynamic aspects of shape m e m o r y heat engines have been published [ 2 2 - 25], so that the subject will n o t be developed here.

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5. P R A C T I C A L L I M I T A T I O N S ON S H A P E MEMORY BEHAVIOR

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Perhaps the main practical requirement for shape m e m o r y behavior is an appropriate alloy, since only certain martensitic alloys exhibit the effects described. Ti-Ni alloys near the equiatomic composition are of course the prototypical shape m e m o r y alloys. Although shape m e m o r y behavior was first observed in other alloys, it was first recognized for its practical value and first applied commercially in Ti-Ni alloys. In recent years,

189 development of copper-based shape memory alloys, particularly Cu-Zn-A1 and Cu-A1-Ni, has caught up with that of Ti-Ni-based alloys, and at present these systems are being developed with similar enthusiasm for new apphcations. There are, of course, numerous other shape memory alloy systems that may be exploited in the future. Because of the close links with the crystallography of the transformation in a given alloy, there are inherent limits on eR in a particular alloy system. Also, because of the connection with the transformation, there are narrow restrictions on the temperature range in which the effects will occur. Fortunately in most alloy systems the martensitic transformation range can be manipulated by slight variations in alloy composition. For most shape memory alloys the transformation range is in the vicinity of room temperature (+150 °C) and 20- 100 °C wide.

5.2. Temperature stability The operating temperature for shape memory devices is somewhat restricted in that certain shape memory characteristics may deteriorate significantly as the temperature is changed. The most revealing data in this regard are the strong temperature dependence of several shape memory parameters, particularly oe -. M and oR, as seen in Figs. 7, 8 and 10. For example, if an application is dependent on the maintenance of a certain level of oR, it can be seen that the temperature must be held in a rather narrow temperature range near As. If the temperature is decreased, oR will fall off sigmoidally as martensite forms from austenite (see Fig. 7). If the temperature is increased, oR will also fall, although less strongly (see Figs. 7, 8 and 10), because of the decreasing strength of the high temperature phase with increasing temperature. As noted earlier, the reversion stress obtainable is inherently limited by the strength of the high temperature phase. If, during heating, OR attains the parent phase yield strength, the parent phase will yield and relax the reversion stress. This stress relaxation process can be expected to continue with further elevation of the temperature. Also, by this process, the initial strain may be partially converted to true plastic strain, thus eliminating the possibility of repeating the shape memory behavior.

Another situation in which true plastic deformation may be introduced is if the temperature is decreased toward Ms while maintaining a constant stress on the sample (as for a dead load). Because the flow stress for stress-induced martensite is very low near Ms, this may lead to true plastic deformation of the stress-induced martensite.

5.3. Repeatability "training" and transformation strengthening As long as the restrictions on strain and temperature are not exceeded, shape memory behavior can be produced repeatedly in the same sample. The initial induced strain is limited by the parameter eL; the upper temperature limit is in a range near As. If a shape memory alloy is cycled many times, the sample may develop a partial "twoway shape memory", i.e. may bend in one direction when heated and in the opposite direction when cooled, in effect remembering both high and low temperature shapes. This effect may often be used to advantage. The two-way effect is considered to be related to a microstructural training effect in which transformation-induced debris of some sort leads to the nucleation of certain martensite variants in the microstructure on each cooling cycle. "Training" for two-way shape memory behavior can be accomplished by several routines [26] (Fig. 15). (a) The sample may be strained in the martensitic condition, then heated above As (thus exhibiting the normal shape memory effect) and subsequently cooled below Ms; if the initial deformation is great enough and/or if the routine is repeated several times, the two-way shape memory will be exhibited on cooling, i.e. the sample will spontaneously move toward the initial low-temperaturedeformed shape on cooling. This is termed "shape memory effect training". (b) The sample may be repeatedly strained above As, thus creating and reverting from stress-induced martensite via the pseudoelastic effect; the two-way shape memory may then be exhibited on cooling below M~. This is termed "stress-induced martensite training". (c) In a combination of the two above routines ("combined training"), which produces the best results, the sample may be strained pseudoelasticaUy above As and then cooled below Ms while maintaining the strain

190

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Fig. 15. (a) A schematic illustration of the variation in the a - e curve with test temperature; (b) a schematic illustration of training routines used to obtain two-way shape memory (TWSM) behavior;stress-induced martensite (SIM) training for two-way shape memory involves repeating the pattern ABCDA (~); shape memory effect (SME) training for two-way shape memory involves repeating the pattern AEFGHIJA ([>); combined training for two-way shape memory involves repeating the pattern ABCGHIJA (,). After training, the alloy will spontaneously follow the two-way shape memory behavior pattern 1 -~ 2 -* 3 -* 4 (~) on cooling and heating.

191

in the sample; the sample is then unloaded and heated above A f; if this routine is repeated several times, the two-way shape memory behavior is exhibited. In all cases, the two-way shape memory is considered to result from the preferential formation of a "trained" variant of martensite on cooling, apparently due to the production of a certain pattern of local stresses or defects in the training process [ 27]. This leads to the formation, on cooling, of a microstructure that would normally correspond to a strained condition, and as the sample adopts this "strained" martensitic microstructure it naturally exhibits the associated external shape change. The two-way shape memory has been shown to be repeatable many times without loss of strain magnitude. Another feature of transformation cycling is the development of transformation strengthening of the parent phase due to the deposition of dislocation debris by the martensitic transformation. This occurs both for martensite formed on cooling and for stress-induced martensite. Some examples of this are presented in Fig. 16. Whether these features represent the sort of defects associated with two-way shape memory is not clear. What is clear [ 5] is that transformation cycling leads to an improvement in the reproducibility of the normal shape memory effect (as exhibited by the e-T profile) as well as to an improvement in the OR-T profile and a slight increase in oR(max), effects which are consistent with transformation strengthening of the parent phase.

(a)

(b)

6. APPLICATIONS OF SHAPE MEMORY BEHAVIOR

Applications have taken clever advantage of two main parameters: the shape change (reversion strain eR) on heating through a certain temperature range and the internal stress (reversion stress OR ) developed if this reverse transformation is opposed (such as by physically blocking the movement or adding an external load). These two parameters, the reversion strain and reversion stress respectively, have already been combined to invent a wide variety of heat-activated fasteners, switches, couplings, controls, deployment devices, force-applyingmembers and even heat

(c) Fig. 16. Microstructural evidence of transformation strengthening by cycling through the martensitic transformation: (a) 1 cycle; (b) 3 cycles; (c) 5 cycles (49.5at.%Ti-49.5at.%Ni-l.0at.%Fe; Ms ~ --40 °C). The transmission electron microscopy photomicrographs were obtained at room temperature (20 °C) after cycling in the bulk form.

engines (by combining the strain and stress parameters to do work). There have been some interesting medical and dental applica-

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tions, including teeth braces, orthopedic bonestraightening and fracture-aligning devices, blood clot filters, intracranial aneurism clips, prosthetic muscles for an artificial heart and intrauterine contraceptive devices. Also under development are applications such as thermostatic radiator valves and cooling fan clutches for automobiles, automatic window openers for greenhouses and many other ingenious inventions based on the unique behavior. The current status of applications in the U.S.A. has recently been surveyed by Wayman [28]. ACKNOWLEDGMENT

This work was supported by the U.S. National Science Foundation through Grant DMR-81-08407. REFERENCES 1 J. Perkins (ed.), Shape Memory Effects in Alloys, Plenum, New York, 1975. 2 H. C. Tong and C. M. Wayman, Acta MetaU., 22 (1974) 887. 3 R . J . Salzbrenner and M. Cohen, Acta Metall., 27 (1979) 739. 4 H. Warlimont, L. Delaey, R. V. Krishnan and H. Tas, J. Mater. Sci., 9 (1974) 1545. 5 J. Perkins, G. R. Edwards, C. R. Such, J. M. Johnson and R. R. Allen, in J. Perkins (ed.), Shape Memory Effects in Alloys, Plenum, New _York, 1975, pp. 273 - 303. 6 K. N. Melton and O. Mercier, Acta Metall., 29 (1981) 393. 7 H. Pops, Metall. Trans., 1 (1970) 251. 8 L. C. Brown, Metall. Trans. A, 12 (1981) 1491. 9 J. D. Eisenwasser and L. C. Brown, Metall. Trans., 3 (1972) 1359. 10 C. Rodriguez and L. C. Brown, Metall. Trans. A, 11 (1980) 147.

11 K. Otsuka, C. M. Wayman, K. Nakai, H. Sakamoto and K. Shimizu, Acta Metall., 24 (1976) 207. 12 N. Nakanishi, T. Mori, S. Miura, Y. Murakami and S. Kachi, Philos. Mag., 28 (1973) 277. 13 R. V. Krishnan and L. C. Brown, Metall. Trans., 4 (1973) 423. 14 J. R. Patel and M. Cohen, Acta Metall., 1 (1953) 531. 15 K. Shimizu, Trans. Jpn. Inst. Met., Suppl., 17 (1976) 171. 16 K. Otsuka and K. Shimizu, in Proc. Int. Conf. on Martensitic Transformations, 1979, Massachusetts Institute of Technology Press, Cambridge, MA, 1979, pp. 607 - 618. 17 H. Tas, L. Delaey and A. Deruyttere, Metall. Trans., 4 (1973) 2833. 18 T. Saburi and C. M. Wayman, Acta Metall., 27 (1979) 979. 19 L. Delaey, F. Vande Voorde and R. V. Krishnan, in J. Perkins (ed.), Shape Memory Effects in Alloys, Plenum, New York, 1975, pp. 3 5 1 364. 20 T. Saburi, C. M. Wayman, K. Takata and S. Nenno, Acta Metall., 28 (1980) 15. 21 W. B. Cross, A. H. Kariotis and F. J. Stimler, N A S A Contract. Rep. 1433, September 1969. 22 H. C. Tong and C. M. Wayman, Metall. Trans., 6 (1975) 29. 23 L. Delaey and G. Delepeleire, Scr. Metali., 10 (1976) 959. 24 P. Wollants, M. DeBonte, L. Delaey and J. R. Roos, in Proc. Int. Conf. on Martensitic Transformations, ~1979, Massachusetts Institute of Technology Press, Cambridge, MA, 1979, pp. 283 - 288. 25 K. Mukherjee, Scr. Metall., 14 (1980) 405. 26 L. Delaey, Film E2251, 1976 (Institut fiir Wissenschaft Film, Gottingen). L. Delaey, G. Hummel and J. Thienel, Publ. Wissenschaft Fiim, Set. 3, 12/E2551, 12 pp., 1977 (Sektion Technische Wissenschaft und Naturwissenschaft, Institut ftir Wissenschaft Film, Gottingen). 27 T. A. Schroeder and C. M. Wayman, Scr. Metall., 11 (1977) 225. 28 C.M. Wayman, J. Met., 32 (9) (1980) 129 - 137.