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Pergamon Acra mater. Vol. 45, No. 11, pp. 44314439, 1997

0 1997 Acta Metallurgica Inc. Published bv Elsevier Science Ltd. All rights reserved

PPI: s1359-6454(97)00144-4 Printed in &eat Britain

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CRITERIA FOR PSEUDOELASTICITY IN NEAR-EQUIATOMIC NiTi SHAPE MEMORY ALLOYS

YINONG LIU and S. P. CALVIN Department of Mechanical and Materials Engineering, University of Western Australia, Nedlands,

WA 6097, Australia

(Receined 27 September 1996; accepted I5 April 1997)

Abstract-it was observed that the reverse transformation of stress-induced martensite occurred at a temperature some 20 K higher than that of thermal martensite. The increase in temperature for the reverse transformation was indicative of a stabilisation effect. This stabilisation effect was attributed to the change in the accommodation morphology of martensite variants from a self-accommodating state for the thermal martensite to an orientated state for the stress-induced martensite. This observation led to the reconsideration of the criteria for pseudoelasticity. Quantitative expressions of criteria on both testing temperature and austenite yield strength were derived, which showed satisfactory agreement with experimental observations. 0 1997 Acta Metallurgica Inc.

1. INTRODUCTION

NiTi shape memory alloys are known to exhibit pseudoelasticity under certain thermomechanical treatment and testing conditions. These conditions vary according to the chemical composition of an alloy. For binary NiTi alloys of < 50.4 at.% Ni (near-equiatomic alloys), pseudoelasticity is observed in specimens which have been cold worked and then annealed at temperatures below their critical tem- perature for recrystallisation [ 1, 21. The annealing temperature for optimum pseudoelasticity is typically in the range of 670-740 K. In specimens annealed in this temperature range a high density of dislocations resulting from the cold work remains. For alloys of > 50.6 at.% Ni (Ni-rich alloys), pseudoelasticity may be developed during ageing after a solution treatment [3]. The ageing treatment is usually carried out in a temperature range of 620-730 K. Ageing in this temperature range promotes the formation of coherent Ni-rich precipitates, such as TixN& or T&N&, in the matrix [4]. A common feature between these two pseudoelastic alloys is that they both exhibit an increased yield strength, owing to either dislocation hardening or precipitation hardening, as compared to fully annealed or solution treated specimens. It is, therefore, suggested that a high yield strength is a criterion for pseudoelasticity in shape memory alloys [ 1, 51.

Pseuoelasticity is the simultaneous reversal of the stress-induced martensite upon unloading, indicating that the stress-induced martensite is thermodynami- cally unstable relative to austenite at the testing temperature. It has, therefore, been suggested that a testing temperature exceeding the Ar temperature, the finish temperature of the reverse transformation, is

another criterion for achieving complete pseudoelas- ticity [6].

Both the yield strength criterion and testing temperature criterion are necessary for pseudoelastic- ity, i.e. pseudoelasticity is not to be observed if either of the two criteria is violated. Whereas the second criterion is well quantified as T > Af, there is a lack of reference in the literature to the critical value of yield strength necessary for complete pseudoelastic- ity. It has been observed that fully annealed near-equiatomic NiTi alloys deform via a stress-in- duced martensitic transformation at temperatures above Ar without apparent plastic yielding and yet exhibit no pseudoelasticity [l]. The absence of pseudoelasticity in this case, when both criteria are satisfied, needs to be explained.

2. EXPERIMENTAL PROCEDURE

The material used in this study was a Ti-50.2 at.% Ni alloy. The material was solution treated at 1173 K for 1.8 ks followed by quenching into water at room temperature. Following the solution treatment the material was cold rolled and then annealed at different temperatures between 600 and 1173 K in air. After annealing the material was quenched into water again and the surface was cleaned mechanically using fine abrasive papers. The recrystallisation temperature of the alloy is approxi- mately 860 K [7].

The transformation behaviour of the specimens was determined by differential scanning calorimetry (DSC) using a Perkin-Elmer DSC-4. A cooling/heat- ing rate of 20 K/min was used. The deformation behaviour was studied in tension using wire specimens of 0.8 mm x 0.8 mm cross-section and

4431

LIU and GALVIN: PSEUDOELASTICITY

(a) 1025 K annealed

(c) 726 K annealed I

McR

- 180 200 220 240 260 280 300 320 340 360 380

Temperature (K)

Fig. 1. Transformation behaviour of NiTi after annealing.

25 mm gauge length. Tensile tests were performed on an Instron 4301 universal testing machine with the specimen immersed in a liquid bath capable of temperature control between 258 and 383 K with an accuracy of _t 0.2 K.

3. RESULTS

3.1. Transformation behaviour

The effect of annealing after cold working on the transformation behaviour of this alloy over the annealing temperature range of 600-I 173 K has been reported elsewhere [8]. Selected DSC spectra of specimens annealed at 1025 K, 776 K and 726 K for 3.6 ks are shown in Fig. 1. The transformation behaviour of the specimens annealed at temperatures above the recrystallisation temperature was found to be practically identical. Curve (a) in the figure is representative of all specimens annealed in this temperature range. In these specimens the transform- ation on cooling occurred in one step from austenite to martensite (A-M) and reverted from martensite to austenite on heating (M-+A). The critical temperatures of the transformations measured from the DSC curves are shown in Table 1 (denoted as thermal martensite). The thermal hysteresis, n, defined as the difference between Ar and M,, was 31 K. These measurements are consistent with those reported in previous studies [9, lo].

In the specimen annealed at 776 K, which was approximately 90 K below the recrystallisation

temperature, a two-stage transformation on cooling and a one-stage transformation on heating was observed, as shown in curve (b). The two stages on cooling correspond to the austenite-to-R phase (A+R) transition and the R phase-to-martensite (R-+M) transformations. The single step transform- ation upon heating corresponds an M-A transform- ation. The critical temperatures of the thermal transformations observed in this specimen are also shown in Table 1. The temperature difference between the Ar and M, temperatures was measured to be q = 53 K. It needs to be clarified that this temperature difference is not a thermodynamic hysteresis between the forward and reverse processes of a transformation. The M, temperature in this case is in fact associated with the R+M transformation and the Af temperature is associated with the M-+A transformation. With a reduction in the annealing temperature further from this temperature, both the DSC peak intensity and the critical temperature for the R-M transformation were observed to decrease. Consequently, the temperature difference between the R+M transformation on cooling and the M-A transformation on heating increased.

When the annealing temperature was further reduced to 726 K, a two-stage transformation was also observed on heating, corresponding to the reverse transformations of martensite to the R phase (M-R) and the R phase to austenite (R-+A), respectively. In this specimen, the cooling transform- ation was similar to that of the specimen annealed at 776 K but with the R+M transformation appearing as a broader peak at a lower temperature. Whereas the two transformations on cooling were well separated, the two reverse transformations on heating overlapped, making it impossible to measure the finish of the M+R transformation and the start of the R+A transformation. Measurements of the transformation temperatures for this specimen are also shown in Table 1. For specimens annealed at this temperature, the M, temperatures given in the table are not intended to be accurate measurements, because the transformation peaks were extremely broad. On lowering the annealing temperature further to below 673 K, the R-M transformation was no longer detected by the DSC.

The thermal transformation behaviour of these

Table 1. Transformation temperatures of NiTi

Annealing Martensite R, Rf Ms Mr A, A f v Thermal martensite 305 293 323 336 31

1025 K SIM-1st cycle 304 282 345 355 51 SIM-2nd cycle 304 282 318 334 32

Thermal martensite 304 296 274 261 314 327 53 II K SIM-1 st cycle 304 298 214 259 332 346 70

SIM-2nd cycle 314 324 49 Thermal martensite 317 307 256 297t 326f 70

126 K SIM-1st cycle 316 305 253 322 332 84 SIM-2nd cycle 315 304 256 302t 3271 75

tThe starting temperature of M-R transformation. $The finishing temperature of M+R transformation

LIU and GALVIN: PSEUDOELASTICITY 4433

- 1st cycle after deformation ...-.... 2nd cycle after deformation : : : 3L : : ,,: : ,: ., \ A, IsI _____...... o . . . . .,,; ... . .._..._. AP

v-n

240 260 280 300 320 340 360 380 400 Temperature (K)

Fig. 2. Effect of stress-induced martensitic transformation deformation on transformation behaviour of NiTi annealed

at 1025K.

specimens was found to be different after defor- mation via stress-induced martensitic transformation. Figure 2 shows the thermal transformation behaviour of a specimen annealed at 1025 K. The specimen had been deformed prior to the DSC measurement. The deformation was carried out in tension at 323 K, which was 18 K above the 1!4, temperature of the specimen. The deformation temperature was ap- proached by cooling the specimen from 373 K, which was above the Af temperature of the specimen, so that the deformation proceeded from an austenitic state via a stress-induced martensitic transformation. The specimen was deformed until the completion of the stress-induced martensitic transformation and then unloaded. No pseudoelastic recovery was observed upon unloading. Post-deformation handling of the specimen, including the cutting of DSC specimens and storage, was conducted at room temperature prior to DSC measurement. The room temperature was below the A, temperature and therefore no reverse transformation could have occurred before the DSC measurement was undertaken. The DSC measurement was performed with a heating cycle starting from room temperature. The two curves shown in Fig. 2 correspond to the transformation behaviour of the specimen in the first and second transformation cycles after the deformation, respect- ively. The transformation behaviour in subsequent cycles was found to be practically identical to that of the second cycle, with small variances similar to those observed when a specimen is subject to thermal cycling [ll]. It can be seen in the figure that the reverse transformation on heating during the first cycle occurred at a temperature higher than that in the second cycle, whereas little difference was observed between the two cooling transformations. Measurements of transformation temperatures for both the first and second transformation cycles are also shown in Table 1 (denoted as the SIM-first cycle and SIM-second cycle, respectively). The critical temperatures for the start and finish of the first reverse transformation after deformation, de-

noted as At and A,d, were measured to be 345 K and 355 K, respectively. Thermal hysteresis of the first transformation cycle was rlst = (At - ME) = 51 K whereas that of the second transformation cycle was qznd = (Ar - MS) = 32 K, respectively. Compared to the transformation behaviour of thermal martensite in the undeformed specimen, the reverse transform- ation of the stress-induced martensite appeared at a temperature approximately 20 K higher, whereas the transformation behaviour in subsequent cycles after the first reversion showed negligible differences to that of the thermal martensite.

The transformation behaviour after deformation of a specimen annealed at 776 K is shown in Fig. 3. The deformation was carried out at 323 K, which was 22 K above the R, temperature of the specimen. The experimental procedure was exactly the same as that stated above for the specimen annealed at 1025 K. Similar to the specimen annealed at 1025 K, little change was observed for the cooling transformation between the first and second cycles after deformation and therefore only the first cooling cycle is shown in the figure. The reverse transformation on initial heating was found to have shifted to approximately 20 K in temperature higher than in the second heating cycle. Measurements of transformation temperatures for this specimen are summarised in Table 1. For comparison, the transformation behaviour of the undeformed specimen is also shown in the figure. The transformation behaviour of the deformed specimen after the first reverse transform- ation was practically identical to that of the undeformed specimen.

Figure 4 shows the effect of deformation on the transformation behaviour of a specimen annealed at 726 K. This specimen was deformed at 318 K, just above the R, temperature, in the austenitic state. Unlike the previous two specimens annealed at 1025 K and 776 K, respectively, the transformation sequence in this specimen was found to have changed as a result of the deformation. The first reverse

- 1st cycle after deformation 776 K annealed .. --..--.. 2nd cycle after deformation - - without deformation

.!-!

240 mu 280 300 320 340 360 380 400 Temperature (K)

Fig. 3. Effect of stress-induced martensitic transformation deformation on transformation behaviour of NiTi annealed

at 776 K.

LIU and GALVIN:

- 1st cycle after dcfomution 726 K annealed .......--. 2nd cycle after deformation -...- without dcfomtion

EJ ~_../I_

.__._.-..- ,...-..-..., ,c..--

A- ,.j ,,$ (XI --) _. ._ *:- i . __...._... ,_.,--s 180 200 220 240 260 280 300 320 340 360 380

Tempcnturc (K)

Fig. 4. Effect of stress-induced martensitic transformation deformation on transformation behaviour of NiTi annealed

at 726 K.

transformation occurred in one step from the stress-induced martensite to austenite. In subsequent cycles the transformation resumed the A+R-+M and M-+R-+A sequence. Comparing this to the unde- formed specimen, it is seen that the transformation behaviour of the deformed specimen after the first reversion was essentially the same. Measurements of transformation temperatures for this specimen are also summarised in Table 1. In the table the hysteresis for the undeformed specimen (thermal martensite) and the deformed specimen during the second cycle (SIM-2nd cycle) correspond to the temperature difference between the R-M transformation on cooling and the R+A transformation on heating.

3.2. Deformation behaviour

Upon loading, a fully annealed near-equiatomic NiTi shape memory alloy may experience an apparent yield via any one of three processes- martensite reorientation (MR), stress-induced martensitic transformation (SIM) and plastic yielding of austenite (AY), depending on the testing temperature [ 121. Several tensile stress-strain curves of specimens annealed at 1025 K are shown in Fig. 5. For each test a virgin specimen was used. Curve (a)

_

1 I

0 2 4 6 8 10 12 14 strain (Fb)

Fig. 5. Deformation behaviour of NiTi annealed at 1025 K.

PSEUDOELASTICITY

400 1025 K annealed

0 .I( : ,. . :, 260 280 300 320 340 360 380 0

Temperatan (K)

Fig. 6. Effect of temperature on the critical stress for inelastic deformation of NiTi.

was obtained at 309 K, 4 K above the M, temperature and 14 K below the A, temperature of the specimen. The testing temperature was approached by heating the specimen from below the IW~ temperature, thereby ensuring that the specimen was in a martensitic state before deformation and that the deformation process proceeded via martensite reorientation. Curve (b) as obtained at the same temperature as curve (a), but the specimen was first heated to above Ar before being cooled to the testing temperature. Therefore, the specimen was in an austenitic state and the deformation proceeded via a stress-induced marten- sitic transformation. Curve (c) was obtained at 338 K, 2 K above the Ar temperature of the specimen. The deformation proceeded via a stress-induced martensitic transformation. Unloading after the completion of the stress-induced martensitic trans- formation showed no pseudoelastic recovery. Curve (d) was tested at 346 K. At this temperature the critical stress required for stress-induced martensitic transformation exceeded the yield strength of the specimen and the deformation proceeded via plastic yielding of the austenite.

The critical stresses for inelastic deformation measured at the beginning of the apparent yielding on stress-strain curves are shown in Fig. 6. The transformation temperatures of the specimens are also marked in the figure for reference. The critical stress for martensite reorientation showed a linear dependence on testing temperature with a small negative slope of da/dT = - 0.4 MPa/K. A mini- mum stress of 117 MPa was measured for martensite reorientation at 319 K, 4 K below the A, temperature. The yield strength of austenite also showed a small negative dependence on testing temperature, as expected. The yield strength of austenite was measured to be 314 MPa at 349 K for the specimen. The critical stress for stress-induced martensitic transformation showed a linear dependence on testing temperature with a slope of da/ dT = 7.9 MPa/K. The critical stresses of c?IM and eAY intercept at a temperature of 344 K and a stress of

LIU and GALVIN: PSEUDOELASTICITY 4435

320 MPa (point A). The critical stress for stress-in- duced martensitic transformation at Ar is estimated from the curve to be 252 MPa, 68 MPa below point A. With decreasing temperature the critical stress extrapolates to 6, S*M = 16 MPa at T = M,. This stress corresponds to the minimum stress required for the stress-induced martensitic transformation.

Selected stress-strain curves of specimens annealed at 776 K are shown in Fig. 7. Specimen (a) was tested at 333 K, 1 K above the Ai temperature but 11 K below the A,d temperature. The critical stress for stress-induced martensitic transformation at this temperature was measured to be 346 MPa. Upon unloading, slight pseudoelastic recovery was evident. The maximum pseudoelastic recovery for this annealing temperature was obtained at a testing temperature of 353 K, 9 K above the At temperature, as shown in curve (b). At this temperature, approximately 70% of the total 10% pre-strain was recovered after unloading. A plateau stress of 516 MPa was measured for the stress-induced martensitic transformation at this temperature. Increasing the temperature further to 361 K led to a decrease in the pseudoelastic recovery and an increase in residual strain, as shown in curve (c). At this temperature some changes in the characteristics of the stress-strain curve are noticeable. The upper- lower yielding phenomenon and Liiders type deformation behaviour observed at lower tempera- tures are clearly replaced by a gradual yielding and hardening process during the early stages of deformation and a subsequent stress-induced marten- sitic transformation at higher strain levels. This indicates that at this temperature the critical stress for inducing martensite is very close to the yield strength of austenite.

For the specimens annealed at 726 K, full pseudoelasticity was observed in the testing tempera- ture range between 333 K and 373 K, as shown in Fig. 8. The upper limit of this temperature range was the maximum temperature for which pseudoelastic behaviour was tested in this work and does not indicate the temperature limit for pseudoelasticity in

700, 1 (c) 361 K

(b) 353 K

la1 333 K

0 2 4 6 8 10 12 strain (%)

Fig. 7. Deformation behaviour of NiTi annealed at 776 K.

_I

0 2 4 6 8 10 12 Strain(%)

Fig. 8. Deformation behaviour of NiTi annealed at 726 K.

this material. It is seen that with increasing temperature, residual strain increased at the expense of pseudoelastic recovery.

The stress hysteresis of pseudoelasticity of the specimens annealed at 726 K is shown in Fig. 9 as a function of testing temperature. The stress hysteresis was found to increase with increasing testing temperature, ranging from 350 MPa at 333 K to 397 MPa at 363 K. A stress hysteresis for the partial pseudoelasticity observed in a specimen annealed at 776 K, as shown in Fig. 7, was also measured. This value, 460 MPa, is shown in Fig. 9 for comparison.

3.3. Effect of annealing

The effect of annealing on the temperature dependence of the critical stresses for stress-induced martensitic transformation is shown in Fig. 10. As mentioned earlier, specimens annealed at tempera- tures above the critical temperature for recrystallisa- tion were found to have practically identical transformation behaviour. In these specimens the M, temperature was measured to be 305 K. Extrapolat- ing rrSiM to A4, = 305 K, different values of aFM were obtained for different annealing temperatures. This is demonstrated by the two specimens shown in the figure, which were annealed at 1025 K and 1131 K,

480

460 - 0 776 K annealed

B j=400 X

i 380

330 340 350 360 370 Tempenhve (K)

Fig. 9. Effect of testing temperature on stress hysteresis of pseudoelasticity.

LIU and GALVIN: PSEUDOELASTICITY

Temperaturn (K)

Fig. 10. Effect of annealing on temperature dependence of critical stress for pseudoelasticity.

respectively. Measurement of Q,S? impossible for specimens annealed at temperatures below the recrystallisation temperature because a thermal A-M transformation was not observed (Fig. 1). Extrapolating eSrM to rr = 0 for specimens annealed at 776 K, a temperature of T = 290 K is obtained. This temperature is 6 K below the Rf temperature and 16 K above the iV, temperature (Table 1). For the annealing temperature of 726 K, aSiM extends to T = 279 K at Q = 0, this being 28 K below Rr and 23 K above IV?,.

Effects of annealing temperature on the yield strength of austenite (oAY), the critical stress for martensite reorientation (g) and azlM are shown in Fig. 11. The value of o MR shown in the figure for each annealing temperature is the average value of the critical stress over a temperature range 45 K below the A, temperature. It is seen that oAY showed a rapid increase with decreasing annealing temperature in the range below the recrystallisation temperature. For annealing temperatures above T,,, all three stresses, aAY ,a MR and a,SI, increased gradually with increasing temperature.

4. DISCUSSION

The effects of annealing after cold working on the transformation behaviour and mechanical behaviour of near-equiatomic NiTi shape memory alloys have been extensively studied and well characterised. The present results are consistent with those studies previously reported [l, 9, lo].

4.1. Martensite stabilisation

The phenomenon wherein NiTi specimens behave differently in the first thermal transformation cycle after deformation than in subsequent transformation cycles has been observed previously. Lin and Wu [ 131 reported that the critical temperature for the reverse transformation in a specimen deformed by 5% in rolling was increased by 26 K during the first heating cycle as compared to that in subsequent cycles. This increment in the critical temperature became larger

0 . 4 I ::,=.=, . I 600 700 800 900 1000 1100 1:

Annealing Temperamre (K)

K)

Fig. 11. Effect of annealing temperature on strength of NiTi.

when the amount of cold deformation increased and reached 68 K for a deformation of 20%. The present results are consistent with these studies. A similar observation has also been made in NiTi alloys after martensite reorientation deformation, in which the reverse transformation occurred at a temperature approximately 20 K higher during the first transform- ation cycle as compared to the transformation in subsequent cycles. The increase in the critical temperature for the reverse transformation is indicative of a stabilisation effect acting on the deformed martensite. Two possible mechanisms exist which explain this stabilisation effect. Firstly, in a heavily deformed specimen, a certain number of structural defects, in particular dislocations, have been introduced in the martensitic matrix by the deformation. These dislocations are expected to be evolved and arranged in such a way that they match the orientation of the oriented martensite variants. Therefore upon heating, extra resistance has to be overcome for the reverse transformation to proceed, resulting in an increase in the critical temperature for the reverse transformation. Once the oriented martensite has been forced to revert back to austenite (in other words liberated from the traps of the dislocations) the stabilisation effect vanishes in subsequent thermal cycles in which a different, self-accommodating martensite is formed. However, the dislocations created by the deformation remain in the matrix and this is expected to cause some relatively minor changes in the transformation behaviour. Secondly, at low levels of deformation (e.g. within the strain limit of stress-induced martensitic transform- ation or martensite reorientation), the changes in the dislocation structure caused by the deformation are negligible. In this case, the stabilisation effect can only relate to changes in variant accommodation mor- phologies, i.e. the change in morphology from the self-accommodating thermal martensite to the stress- induced single-variant martensite. Once the orien- tated martensite reverts back to austenite, self- accommodating martensite is formed in subsequent

LIU and GALVIN: PSEUDOELASTICITY 4437

cycles and, therefore, the stabilisation effect disap- pears. To illustrate this, the different structures of the specimens are indicated in Figs 24 with 0 representing the austenite phase, l??~ representing the self-accommodating multi-variant martensite and 0 representing the oriented martensite which could have been produced by either a stress-induced martensitic transformation or a martensite reorienta- tion deformation.

The stabilisation effect observed in this study is mainly due to the change in the structure of martensite variants. This is evident by comparing the transformation behaviour of the deformed specimens in subsequent cycles after the first reversion of the oriented martensite to the transformation behaviour of the undeformed specimens. The near-identical transformation behaviour indicates that permanent changes to the matrix are negligible. The stabilisation effect in this case is attributed to the change in internal elastic energy [14] associated with the change in the structure of martensite. It is known that during a thermoelastic martensitic transformation, an internal elastic energy (stress state) is created. This is due to the restriction of the matrix to the lattice distortion of the martensite. This internal elastic energy opposes the existence of the martensite, in other words destabilises the martensite [15]. This corresponds to self-accommodating thermal marten- site. In the case of stress-induced martensite, the deformation effectively removes the restrictions of the matrix. Under this condition, an internal elastic stress in the direction of the oriented martensite is created. This elastic energy imposes extra resistance to the reverse transformation of the martensite during heating, causing the stabilisation effect. Therefore, the magnitude of the temperature difference between the reverse transformation of the oriented martensite and that of the thermal martensite is determined by the sum of the resisting elastic energy in the thermal martensite and the assisting elastic energy in the oriented martensite.

4.2. Minimum stress jar stress-induced martensite

A minimum stress, a,SI, is recognised to exist for the stress-induced martensitic transformation at M,. This stress is attributed to the mechanical resistance to phase boundary movement during the stress-in- duced martensitic transformation, since the thermo- dynamic resistance to the A-rM transformation at this temperature is expected to be practically nil. This stress is believed to originate from the same source as the resistance to twin boundary movement during martensite reorientation and to be dependent on the history of thermomechanical treatment of a speci- men. This expectation agrees with the experimental observation that rrz?ncreased with increasing an- nealing temperatures in a similar manner to frMR, a measure of the resistance to twin boundary movement. The reason for the increase in .iIM with annealing temperature in the range above T,, is not

understood. The rrFM is also expected to increase with decreasing annealing temperature in the range below the recrystallisation temperature. However, due to the absence of the A+M transformation in specimens annealed in this temperature range, crziM is practically impossible to measure.

4.3. Criteria for pseudoelasticity

Taking 6, IM into account, the critical stress for a stress-induced martensitic transformation, denoted as of for the notation of forward transformation, at T > MS can be expressed as:

0, = .s,, + (T - &)$T. (1)

Assuming that 0 zM is also effective in resisting phase boundary movement during the reverse transform- ation, the critical stress for the reverse transform- ation, g,, can be expressed as

,J~ = - .z, + (T - Ad)* dT (2)

Then the stress hysteresis of pseudoelasticity is

An = CT~ - or = 2a,SlM + (Ai - MJFT

= 2a,SM + 9*gT.

Therefore, the yield strength criterion for pseudoelas- ticity is

uY > Aa = 20;~ + q,jgT. (4)

The temperature criterion for complete pseudoelas- ticity is determined as ur > 0:

This temperature is clearly higher than the Af temperature measured using DSC for the reverse transformation of thermally induced self-accommo- dating martensite. It may be even higher than the A,d temperature measured with DSC for the reverse transformation of stress-induced martensite, depend- ing on c$~. This criterion is schematically illustrated in Fig. 12, where reference is made to a specimen exhibiting a thermal transformation sequence of A-R-M-A. In the figure the shaded areas represent the conditions for pseudoelasticity. M,(R) and M,(A) indicate the starting temperatures of the R-+M and A+M transformations, respectively; c?(A) is the critical stress for stress-induced martensitic transformation from austenite and aStM(R) is the critical stress for stress-induced martensitic transformation from the R phase; P is the critical stress for stress-induced R phase transition from austenite; aR(SIM) is the critical stress for the reverse transformation of stress-induced martensite; and ~9~ is the yield strength of (orientated) martensite. The relative value of aMY to

4438 LIU and GALVIN: PSEUDOELASTICITY

M,(R) M,(A) R, As 4 AsdAP Md Temperahut +

Fig. 12. Schematic illustration of criteria for pseudoelastic- ity.

cAY is arbitrary. The maximum temperature at which martensite can be stress-induced is denoted as Md. The upper and lower boundaries of the shaded areas represent the upper and lower critical stresses for pseudoelasticity. The temperature window for com- plete pseudoelasticity is A,d < T < Md when u21M = 0. This illustration is in fact a modification of the scheme suggested by Miyazaki et al. [l].

4.4. Thermal hysteresis of stress-induced martensite in NiTi

The thermal hysteresis of stress-induced marten- site, i.e. the temperature difference between the reverse transformation of stress-induced martensite and the forward transformation of thermal marten- site, can be directly measured for specimens annealed at T > T,,. For the specimens annealed at 1025 K, the hysteresis was measured to be 51 K. For specimens annealed at T < T, when the R phase transition is present, the hysteresis cannot be measured directly from thermal measurement. It can, however, be estimated by extrapolating the linear relationship between 0 and T to 0 = 0, which defines the critical temperature for the A+M transformation if ozIM is assumed to be zero. For the specimens annealed at 776 K and 726 K, this temperature is determined to be 290 K and 279 K, respectively (Fig. lo), giving a thermal hysteresis of 56 K and 53 K for the two annealing temperatures. It is interesting to notice that the thermal hysteresis of stress-induced martensite for these three annealing temperatures show little variation, although the dislocation structures are expected to be drastically different among the specimens.

4.5. Pseudoelasticity of NiTi

Assuming a constant thermal hysteresis of stress- induced martensite in specimens annealed at T > T, and taking da/dT = 7.9 MPa/K for the entire annealing temperature range, the stress hysteresis of pseudoelasticity can be estimated using equation (3). This stress hysteresis corresponds to the requirement

of minimum yield strength of austenite for pseudoe- lasticity, up. The calculated values of ep are shown in Fig. 11 as a function of annealing temperature. For the two annealing temperatures below T,,, 776 K and 726 K, actual values of stress hysteresis measured from pseudoelastic curves are shown. It can be sen that for annealing temperatures greater than T,,, the strength requirement for pseudoelasticity exceeds that of the yield strength measured for austenite. This explains the absence of the pseudoelasticity in this annealing temperature range. Under this condition, complete pseudoelasticity is predicted in near-equi- atomic NiTi alloys to occur when the annealing temperature is below 800 K. This prediction is indicated in Fig. 11 by the shaded area, with the Y-axis representing the stress widow for the upper stress (critical stress for inducing martensitic trans- formation) of pseudoelasticity. The low temperature boundary of the pseudoelastic region is undecided in this work. In principle, there has to exist a minimum annealing temperature below which no pseudoelastic- ity is to be observed. This minimum temperature is required to revert the stress-induced martensite formed during cold working back to austenite.

The actually measured stress hysteresis of pseudoe- lasticity of specimens annealed at 726 K was found to increase with increasing testing temperature. It is believed to be due to an increase in the degree of matrix damage caused by simultaneous plastic deformation during the pseudoelastic transformation as a result of the increase in the critical stress for stress-induced martensitic transformation at higher temperatures. The stress hysteresis of the partial pseudoelasticity of the specimen annealed at 776 K is remarkably higher than that of the specimens annealed at 726 K. This is also attributed to the damage to the matrix caused by excessive plastic deformation during the stress-induced martensitic transformation. The yield strength of the matrix of this specimen is lower than that of the specimens annealed at 723 K and thus more plastic deformation is expected. Plastic deformation imposes extra frictional resistance to phase boundary movement, causing an increase in the stress hysteresis.

5. CONCLUSIONS

1. The stress-induced martensite is observed to be thermally more stable relative to the thermal martensite. This stabilisation effect is believed to be associated with the change in variant accommodation morphology from self-accommodation for thermal martensite to the oriented state of the stress-induced martensite. The same stabilisation effect is also expected for martensite deformed by a reorientation process.

2. As a result of this martensite stabilisation effect, the oriented martensite will revert back to the parent phase either at a higher temperature during thermal measurement or at a lower stress level in pseudoelas-

LIU and GALVIN: PSEUDOELASTICITY 4439

ticity. Therefore, care must be taken when numerical expression relating the stress-hysteresis of pseudoe- lasticity and the temperature hysteresis of a thermal transformation are to be formulated.

3. A minimum stress is required to induce martensitic transformation at M,. This stress is attributed to the mechanical resistance to phase boundary movement during the transformation and is believed to be related to the critical stress for martensite reorientation. This stress is dependent on the metallurgical conditions of an alloy.

4. The criteria for pseudoelasticity in near-equi- atomic NiTi shape memory alloys are derived, as expressed in equations (4) and (5). The expressions show satisfactory quantitative agreement with exper- iment results.

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