THERMO-MECHANICAL CHARACTERIZATION OF NiTiCu AND NiTi

SMA ACTUATORS: INFLUENCE OF PLASTIC STRAINS

David A. Miller* and Dimitris C. Lagoudas§

Aerospace Engineering Department,

Texas A&M University

College Station, TX 77843-3141

ABSTRACT

The focus of this study is the thermomechanical characterization and comparison

between two different shape memory alloys (SMAs) quantifying the effect of plastic strain on the

transformation characteristics of SMA actuators. In this study, the thermomechanical response

and transformation characteristics of a NiTiCu and a NiTi SMA are studied as a function of the

induced plastic strain for four different loading paths: 1) an elastic-plastic loading of the

austenitic phase, 2) a stress-induced martensitic phase transformation, 3) an elastic-detwinning-

plastic loading of the martensitic phase and 4) thermally-induced phase transformation under a

constant applied stress. Each loading path is repeated multiple times, with an incremental change

of the total applied strain, to determine the effect of accumulated plastic strain on the phase

transformation characteristics of the two SMA material systems. The effects of plastic strain are

quantified by measurements of recoverable strain during a thermal cycle under zero applied

stress, measurements of heat of transformation from a differential scanning calorimeter and

microstructural evaluations.

* Graduate Research Assistant, E-mail: DAM2009@acs.tamu.edu

§ Professor, E-mail: dlagoudas@aero.tamu.edu

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1. INTRODUCTION

Over the last decade shape memory alloys have seen growing use in the mechanical,

medical, and aerospace industries (Birman 1997). Most of the applications have been 1-D in

nature where wires, strips, and rods were employed, i.e. as actuators in active wings (Garner et

al, 1999), robotic systems and self-extracting microstructures (Sachdeva and Miyazaki 1990).

Unfortunately, the inability to identify material properties and the inherent complex

thermomechanical behavior of SMAs has stifled widespread use. Material properties of SMAs

can undergo significant changes with differences in the chemical composition, cold work, heat

treatment and thermomechanical cycling. The addition of copper as a ternary element, for

example, has demonstrated favorable results for the development of SMA actuators due to a

reduction in the temperature hysteresis, while the yield stress is significantly lower than binary

NiTi (Funakubo 1987).

The austenite to martensite phase transformation characteristics of NiTi SMAs has been

shown in previous studies to be related to the presence of lattice defects introduced by cold

working (Hebda and White 1995, Liu and McCormick 1990, McNeese 1998, Matsumoto 1992,

Moraweic et al. 1995). The process of drawing NiTi wires imparts large plastic deformations, i.e.

cold work, on the material in the martensitic condition (Lin et al 1994, Jackson 1972). To reduce

the bulk material to typical wire diameters of 0.3 mm to 2 mm, multiple drawings are performed,

with each followed by an anneal at temperatures in the region of 800°C to 900°C for roughly 15-

30 minutes. Qualitatively, the effects of cold work on the transformation properties have been

shown to be independent of material composition for small percentage changes in binary

material. In general, the effects of cold work are a reduction in the transformation temperatures,

smaller reversible strains and increases in the yield stress for slip in martensite. Also, a high

3

dislocation density restricts phase boundary movement and the development of stress-induced

and reoriented martensite, which results in increased hardening in the stress-strain curve (Filip

and Mazanec 1995).

During the lifespan of the SMA actuator, loss of actuation can occur through repeated

cycling due to plastic strain development, and unlike common ductile metals, plastic deformation

in SMAs can be induced by the martensitic phase transformation and can occur at relatively low

stress levels. There are many experimental results on stress-induced martensite at temperatures

above the austenite finish temperature, Af, (pseudoelastic response) showing the effects of strain

level, stress level, cycle number, pre-straining and strain-rate on the transformation

characteristics (Lim and McDowell 1994, Shaw and Kyriakides 1994, McCormick et al. 1993,

Tobushi, et al. 1993, Eucken and Duerig 1989, Miyzaki et al. 1986, and Otsuka and Shimizu

1986). In these works, plastic deformation is developed during the loading as a result of the

phase transformation process and the amount of plastic strain remains small compared to the

overall applied strain. Miyazaki, et al. (1981) investigates large plastic deformations for

isothermal mechanical loading, however, no quantitative results are given for changes in the

transformation characteristics. Bo and Lagoudas (1999) and Liu and McCormick (1990) have

studied the development of transformation induced plastic strain and two-way strain during

thermally induced cyclic phase transformations under a constant applied stress. Two-way strain

is the term used to describe the strain that develops during the austenitic to martensitic phase

transformation under zero load. This strain is the result of dislocation arrangements that guide

the formation of martensite variants to a preferred orientation, thus resulting in an overall change

in length. These works have shown that two-way strain and plastic deformation are developed

through multiple cycles of these loading paths. While in Bo and Lagoudas (1999) large plastic

4

strains have been observed for fully annealed NiTi SMA, much smaller strains have been

measured in Liu and McCormick (1990) for NiTi with a cold worked microstructure.

Even though the transformation induced plastic strain development has been studied

extensively, the influence of plastic strains on transformation characteristics has not been fully

addressed. The main focus of this study is to quantify the effects of plastic strains developed

during a thermomechanical loading on the transformation characteristics of binary NiTi and

NiTiCu specimens. In addition to plastic strain induced during the phase transformation, the

influence of plastic strain induced in the austenitic phase and the detwinned martensitic phase on

the transformation characteristics will be studied in this work.

The paper is divided in the following manner. The experimental procedures employed in

this study are detailed in section two describing the material selection, equipment and

mechanical tests performed. Section three presents the experimental results and is divided into

four sub-sections detailing the four loading paths performed. The fourth section discusses the

results and the conclusions are given in the fifth and final section of the paper.

5

2. EXPERIMENTAL PROCEDURE

To investigate the influence of plastic strains on the transformation characteristics of

SMAs, a thorough experimental investigation was performed. Motivated by the multiple phases

that occur during the application of SMAs, tests were performed for each material phase

independently, i.e., pure austenitic and pure martensitic loading, and for loading paths which

involve a phase change, i.e. stress-induced martensite and thermally-induced martensite. These

loading paths are depicted in Figure 1. In this section the specimens, experimental procedures

and equipment used to perform this investigation are fully described.

The geometry of SMA specimens has largely been driven by the desired applications into

which the SMAs are envisioned. Numerous SMA test specimens utilizing different cross sections

have been experimentally investigated including rectangular specimens (Gall et al 1999), bar

specimens (Howard 1995), wire specimens (Shaw and Kyriakides 1995), square specimens (Liu

and McCormick 1990), thin film specimens (Miyazaki and Ishida 1992) and tubular specimens

(Lim and McDowell 1999). However, over the last decade, SMAs have been primarily employed

in 1-D applications where small strips and wires are required. Due to this fact and the knowledge

that SMA response is strongly a function of the prior processing, it becomes necessary to test the

response of SMAs in the geometry in which it will be applied. Therefore, the specimens chosen

for this experimental study are in the form of wires.

The specimens utilized in this study were provided by Memry Corporation and are a Ni-

45at%Ti - 10at%Cu wire with a diameter of 0.6 mm and a Ni- 50at%Ti wire with a diameter of

0.91 mm, both in the as-drawn condition. Before testing, a 600°C/ 30-minute heat treatment was

performed on the NiTiCu specimen. A Perkin-Elmer Pyris 1 Differential Scanning Calorimeter

(DSC) was utilized to determine the phase transformation temperatures and heat of

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transformation, ∆H, (Jardine 1989) measured as the total area under the curve during the heating

and cooling cycle, for each specimen prior to testing and after the testing is completed. DSC

results for the specimens prior to testing are shown in Figure 2, with the hatched potion of the

NiTi curve delineating the area used for the calculation of ∆H.

SMA specimens were loaded under three different isothermal mechanical loading paths,

labeled as loading path 1, 2 and 3 in Figure 1. As seen in the figure, these paths each represent a

significantly different test; loading path one represents an elastic-plastic loading of the austenitic

phase, loading path two represents a stress-induced martensitic phase transformation, and

loading path three represents an elastic-detwinning-plastic loading of the martensitic phase. Each

of these loading paths are repeated multiple times, incrementing the total applied strain by 1.0%

to 2.0% for each loading, to determine the effect of plastic strain on the phase transformation

characteristics of the SMA. To quantify the effect of the plastic strain, each mechanical loading

cycle is followed by a thermal cycle under a constant stress of 5 MPa from which the

transformation temperatures and two-way strain are measured. The final thermo-mechanical

loading performed were multiple thermal cycles under a constant applied stress, shown as

loading path 4 in Figure 1, a loading path commonly used to induce a two-way shape memory

effect in the SMA.

All mechanical tests were performed on an MTS servo-hydraulic load frame equipped

with a custom built environmental chamber, see Figure 3. The environmental chamber uses a

resistive heating coil to heat the specimen and liquid CO2 for cooling. The temperature of the

specimen is measured in three locations on the specimen using K-type thermocouples held in

contact with the specimen and mounted with a thermally conductive paste to ensure good heat

transfer qualities between the specimen and thermocouple. The thermocouples are .005” in

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diameter to ensure a fast response and small disruption of the temperature field on the specimen.

A control program utilizing LabWindows was used to control the crosshead displacement,

heater and CO2 operations and collect the temperature of the specimen, force and displacement.

The mechanical loading was performed in displacement control with a constant strain rate of

1x10-4 in/in/sec and the thermal cycles were performed at approximately 2 °C/min. The reported

strain levels were calculated using ε=∆L/L0 where the length, L0, represents the original

specimen length and ∆L is measured from the crosshead displacement. Due to the small loads

that were applied to the wire as compared to the overall stiffness of the test frame, a machine

compliance correction was not computed into the results. The thermal strain induced in the grips

due to the heating and cooling cycles was measured and determined to be a negligible quantity in

the strain calculations.

It has been shown that phase fronts occur in annealed SMAs and that diffused phase

fronts occur in cold worked SMAs due to multiple nucleation sites (Shaw and Kyriakides 1995,

and Howard, 1995). Since hardening and multiple phase fronts exist during the mechanical

loading, and extensometers and strain gauges are not suitable for measuring the strain in the

specimen unless specially designed for this application. Since plastic strain development cannot

be confined to a specific gauge section, a global strain measurement is the obvious choice for

strain measurement. Thus, the crosshead displacement is used for the strain calculation in the

SMA specimen. The effect of the grips on the overall stress field is minimized by the length of

the specimen contrasted to the diameter of the wire. Slipping of the specimen in the grip was

closely monitored and did not occur in the any of the tests.

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3. EXPERIMENTAL RESULTS

3.1. Loading Path 1: Austenitic Plastic Loading

Loading path 1 entails a mechanical loading of the austenitic microstructure into the

plastic region of deformation, see Figure 1. The temperature for loading path 1 was chosen such

that the specimen would plastically deform before the formation of stress induced martensite. It

was calculated using estimated values of the martensitic stress-temperature slope, Cm in Figure

1, the initial DSC result for the martensitic start temperature and an estimate of the yield stress of

austenite. Using this criterion, tests were performed at 155°C for the NiTiCu specimen, and

120°C for the NiTi specimen. The mechanical response of the austenitic phase is similar to that

of typical engineering materials for both material systems, showing initial yielding followed by

linear hardening, as seen in the stress-strain curves in Figure 4a for the NiTiCu specimen and

Figure 5a for the NiTi specimen. Measurements from the initial loading cycle result in an

austenitic elastic Young’s Modulus, EA, of 67.9 GPa and 64.5 GPa, and a 0.2% offset yield stress

of 290 MPa and 370 MPa for the NiTiCu specimen the NiTi specimen, respectively. Following

each mechanical unloading, a thermal cycle under a constant stress of 5 MPa is applied to

evaluate the effect of the plastic strain on the transformation characteristics. A summary graph of

the strain-temperature results is seen Figure 4b and Figure 5b for each specimen, where each

thermal cycle shown starts at the strain level from which the previous mechanical loading ended.

From each thermal cycle, the transformation temperatures and two-way strain are measured and

plotted as a function of the plastic strain and included in Figure 6. For both material systems, the

strain-temperature response shows the growth of a negative two-way strain, and an enlarging of

the hysteresis loop. The data shows that similar levels of two-way strain are created for each

9

material system, however, the NiTi specimen peaks before attaining this value and begins to lose

the two-way shape memory effect at plastic strains larger than 8.5%. The negative two-way

strain is contrary to the positive two-way strain typically seen in SMAs, however, it does provide

insight into the training and transformation process. From these results, it is seen that

dislocations developed in the austenitic microstructure are inherited into the martensitic

microstructure. As temperature-induced martensite is formed, the internal stresses created by the

plastic deformation influence the martensitic variant formation and a global negative strain

results. Fremond and Miyazaki (1996) have experimentally observed that plastic deformation in

the austenitic state results in zero two-way strain, however, it is seen in both material systems

presented in this work. Post-test DSC results are shown in Figure 7 and Figure 8, along with a

comparison of the original DSC result and the final strain-temperature curve for the NiTiCu and

NiTi specimens respectively. As seen in the figures, the latent heat of transformation is reduced

and shifted down in temperature for both material systems. Also, the austenite to martensite peak

for the NiTi specimen is broadened such that a discernable peak is not obvious, a fact not seen

for the NiTiCu specimen and attributed to initial cold-drawn condition of the NiTi wire. The

values for the latent heat of transformation, ∆H, are given in Table 1. Using the average ∆H

value of A⇒M and M⇒A, a reduction in latent heat to 49.6% and 56.7% of the pre-tested value

is shown for the NiTiCu and NiTi specimen. The large drop in the ∆H values is attributed to the

dislocations inhibiting the amount of material allowed to undergo the phase transformation (Lim

and McDowell, 1994).

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3.2. Loading Path 2: Stress-Induced Martensitic Loading

The second mechanical loading path, see Figure 1, was conducted at temperatures such

that stress-induced martensite was created and the pseudoelastic response would be seen upon

unloading. Using initial DSC results, isothermal mechanical loadings were performed at 85°C

for the NiTiCu and 40°C for the NiTi specimen, temperatures above austenitic finish. Figure 9a

and Figure 10a show the stress-strain results for the stress-induced martensitic loading path for

the NiTiCu and NiTi specimens respectively. It is of interest to note that the pseudoelastic

response is not seen in the stress-strain results, a fact explained by Otsuka and Shimizu (1986)

and Miyazaki et al (1982) as a result of having a low critical stress for slip. To fully recover the

detwinned strain imparted into the specimen during the mechanical loading, the specimens are

heated upon unloading under a constant load of 5 MPa to a temperature 50°C above the

austenitic finish temperature. The oscillations seen in the stress-strain response in Figure 9 are

attributed to ± 1.5°C oscillations of the specimen temperature induced by to the inability of the

temperature controller to adequately respond to the release of latent heat. The increase of the

specimen temperature requires a higher stress for the creation of stress-induced martensite, as

seen in Figure 1 and described in Shaw and Kyriakides (1995), and the material response is an

increase of the slope in the stress-strain response. As the specimen temperature decreased, the

stress required for transformation also decreased and the slope of the stress-strain response was

also decreased. After the specimens were heated to recover the remaining detwinned martensite,

a thermal cycle under 5 MPa was performed to evaluate the effect of the plastic strain on the

transformation characteristics. A summary graph of the strain-temperature results is seen in

Figure 9b and Figure 10b for each specimen, where each thermal cycle shown starts at the strain

level from which the previous mechanical loading ended As seen in the figures, plastic strain

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was applied into the specimen in each cycle, which in turn, altered the stress-strain response for

the following cycle and imparted a two-way strain as evidenced in the strain-temperature

response. Figure 11 shows the development of two-way strain for both specimens as a function

of the induced plastic strain. The data points elucidate the trend of two-way strain development

as the plastic strain level increases, and shows that similar two-way strain levels are achieved for

both specimens. As the level of plastic strain increased, Figure 9a and Figure 10a show that the

stress level at the initiation of stress-induced martensite was lowered. Also, increased hardening

was exhibited during the phase transformation in the stress-strain response as the level of plastic

strain increased. These two observations are both related to the broadening of the transformation

temperature region as seen in the DSC and two-way strain graphs shown in Figure 12 and Figure

13. The final DSC for both specimens shows essentially no phase transformation peak in the

austenitic to martensitic transformation due to the extreme broadening of the transformation over

the entire temperature range, a fact which is echoed in the strain-temperature curves in Figure 9

and Figure 10. Using the average ∆H value of A⇒M and M⇒A, a reduction in latent heat to

29.1% and 33.0% of the pre-tested value is shown for the NiTiCu and NiTi specimen,

respectively.

3.3. Loading Path 3: Martensitic Plastic Loading

Mechanical loading path 3, see Figure 1, was performed at temperatures such that

martensitic detwinning and plastic deformation were the primary deformation mechanisms. The

isothermal mechanical loading was performed at 22°C for the NiTiCu specimen and -30°C for

the NiTi specimen and the stress-strain and strain temperature results are included in Figure 14

and Figure 15. Upon unloading to zero stress in each cycle, the specimen was held at a constant

12

stress of 5 MPa and heated to a temperature 50 °C above Af to recover the detwinned strain and

measure the permanent strain in the specimen. The strain-temperature results show the

development of two-way strain, which is quantified in Figure 16. Measurements from the initial

loading cycle result in an martensitic elastic Young’s Modulus, EM, of 16.0 GPa and 23.5 GPa,

for the NiTiCu specimen the NiTi specimen, respectively. Both specimens show similar stress-

strain behavior with respect to the development of plastic strain.

The initial cycles, where the plastic strain level is small, show a Lüders type of

deformation (Miyazaki et al 1981), i.e. the strain level increases without an increase in the stress

level. However, as the plastic strain level is increased, the Lüders type of deformation begins to

disappear, the stress level for the initiation of detwinning decreases and a dramatic hardening

effect is seen resulting in large stress levels. This deformation mode is utilized for the cold

working and drawing procedures (Lin, Wu, and Lin 1994), and these results are evidence to the

lack of Lüders deformation in heavily cold worked materials. However, is has not been shown

that cold worked materials display the two-way strain observed in the plastically deformed

specimens of this study, but it could be concluded from these results that for small amounts of

cold work a two-way strain could be developed. Figure 16 shows the history of two-way strain

development as a function of the plastic strain. As seen in the stress-induced martensitic case, the

final two-way strain values are similar, however, the plastic strain level for the NiTi specimen is

only half of the NiTiCu specimen, and might in fact decrease at higher levels of plastic strain.

The final DSC curves are shown in Figure 17 for the NiTiCu and Figure 18 for the NiTi

specimens. The figures show the extreme broadening of the phase transformation temperature

range and the reduction of the latent heat of transformation. Using the average ∆H value of

13

A⇒M and M⇒A, a reduction in latent heat to 25.7% and 17.5% of the pre-tested value is shown

for the NiTiCu and NiTi.

3.4. Loading Path 4: Thermal Cycles under Constant Applied Stress

The fourth loading path applied to the specimens consisted of multiple thermal cycles

through the transformation temperatures, i.e. from T< MF to T>AF, under a constant applied

stress of 200 MPa, see Figure 1. The strain-temperature results of the first fifty thermal cycles are

included in Figure 19 and Figure 20 for the NiTiCu and NiTi specimens, respectively. These

results show the development of plastic strain with each thermal cycle and the saturation of the

plastic strain as the number of cycles increased. The transformation strain in the final cycle was

similar for each material system, 5.25% for the NiTiCu and 5.30% for the NiTi specimen,

however, the NiTiCu specimen had nearly twice the plastic strain accumulation at 8.65%

compared to 4.02% for the NiTi specimen. Figure 21 and Figure 22 show the initial and final

DSC results along with the final two-way strain as a function of temperature for the NiTiCu and

NiTi specimens. In these graphs, the shifting and broadening effect on the DSC curves induced

by the loading is shown, as well as a final two-way strain of 2.1% for the NiTiCu specimen and

3.2% for the NiTi specimen. The latent heat of transformation for each specimen is shown in

Table 1. Using the average ∆H value of A⇒M and M⇒A, a reduction in latent heat to 44.6%

and 42.0% of the pre-tested value is shown for the NiTiCu and NiTi specimens respectively.

14

4. DISCUSSION

The method in which plastic strain is induced into the specimen is shown in the

experimental results to strongly influence the amount of two-way strain developed. Plastic

deformation of the austenitic microstructure showed the development of a negative two-way

strain. This unique result was seen in two separate material systems and shows the effect

dislocations have on the deformation characteristics of SMAs. A negative two-way strain

indicates that dislocations in the austenitic microstructure influence the preferred orientation of

the variants formed during thermally induced martensite.

Of the three loading paths that introduced positive two-way strains, the single-phase

martensitic loading path developed the highest two-way strain for both material systems.

Additionally, the rate of two-way strain development with plastic strain accumulation was

highest for the martensitic loading path, resulting in higher two-way strains at lower plastic

strains. This observation implies that dislocation development through the detwinning process

and plastic slip of the martensitic microstructure generates a higher preferential ordering of the

martensitic variants, and thus a higher two-way strain, than does dislocation development

through stress-induced martensite or thermally induced martensite. This result may be explained

by examining the deformation mechanisms involved with the stress-induced martensitic loading

path and the temperature-induced martensitic loading path. Lim and McDowell (1994) describe

that plastic strain in SMAs cycled in the pseudoelastic regime is a combination of the existence

of martensite which is “locked in” by the dislocations generated at the austenitic-martensitic

phase boundaries during the transformation and plastic deformation of the induced martensitic

phase itself.

15

McCormick and Lui (1994) make a similar argument that for thermal cycles under a

constant load an increasing fraction of martensite is retained at the end of each cycle, and

comprises a portion of the permanent strain. Plastic slip of the thermally induced martensitic

phase will not be present unless the cycles are applied at a stress level above the yield limit of the

martensitic phase. Therefore, the existence of plastic strain induced by these loading paths,

loading paths 2 and 4 in this study, may be a combination of the retention of the martensitic

phase and plastic deformation of the martensitic phase resulting in higher plastic strains with

lower two-way strains. Experimental verification of this fact is seen in post-test microstructural

evaluation of the specimens, and shows that retained martensite is present in the austenitic phase

for loading path 2 and 4, as well as loading path 3.

A representative microstructure is shown in Figure 23 for the martensitic plastic

deformation NiTi specimen after being heated above the austenitic finish temperature and

photographed at room temperature, above the martensitic start temperature. This micrograph

shows the existence of martensitic plates, marked by the arrows, throughout the grains

confirming the existence of retained martensite. Additionally, Figure 24 shows the evolution of

the martensitic strain recovered upon heating as a function of the plastic strain in loading path 2

and 3. The reduction of detwinned strain for both specimens is further evidence that martensite is

retained in the austenitic microstructure for both material systems. Micrographs of the NiTiCu

austenitic microstructure are not currently available due to the elevated temperature of the

austenitic finish temperature. However, using the results of the recoverable strain, it can be

concluded that retained martensite is present for the NiTiCu specimen as well.

For each loading path a broadening and downward shift in temperature of the

transformation peaks is seen in the DSC results, showing that the influence on the transformation

16

temperatures is independent of the method in which plastic strain is induced. The shift in the

transformation temperatures is created by the existence of dislocations, which introduces

obstacles for the moving interfaces (Moraweic et al 1995). The method of applied plastic strain

does show a consistent influence on the heat of transformation, ∆H, for both material systems

studied. For all loading paths a significant reduction in the heat of transformation was observed,

which can be attributed to retention of the martensitic phase at temperatures above austenite

finish (Moraweic et al 1995). In both material systems, the martensitic detwinning loading path

had the lowest heat of transformation, followed by the stress-induced martensitic loading path

and thermally-induced loading path. The austenitic loaded material retained the highest heat of

transformation for both material systems. From these results is apparent that the martensitic

detwinning loading path creates the highest amount of retained martensite. Qualitative

microstructural evaluation of the specimens supports this result.

17

5. CONCLUSIONS

In this study dislocations have been introduced, quantified by a measurable permanent

strain, and the effect of the plastic deformation on the transformation characteristics of two-way

strain, transformation temperature and heat of transformation has been reported.

Pure austenitic plastic deformation for both NiTiCu and NiTi has been shown to induce a

negative two-way strain, a contrasting result to published literature. Positive two-way strains

have been produced for loading paths involving stress-induced martensite, temperature-induced

martensite and martensitic detwinning. For both the NiTiCu specimen and the binary NiTi

specimen the martensitic detwinning loading path resulted in the highest two-way strain. Also,

this two-way strain was developed at the lowest level of plastic strain. Therefore, the martensitic

detwinning loading path is established as the best method of two-way strain development.

Post-test DSC results show a significant reduction in the heat of transformation, ∆H. The

influence of the plastic strain on ∆H is due to the retention of martensite in the austenitic

microstructure. The generation of dislocations associated with the plastic strain “locks in” the

martensitic microstructure, thus removing a portion of the microstructure from the

transformation and reducing the heat of transformation. The reduction of available

microstructure for transformation is also observable through the reduction of recoverable strain

and microstructural evaluation.

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ACKNOWLEDGEMENTS

The authors acknowledge the financial support of Air Force Office of Scientific Research under

grant No. F49620-98-1-0041.

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2407-2413.

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21

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314-318.

22

TM os AosM of Aof

MartensiteAustenite

σPlastic Deformation

LoadingPath 1

LoadingPath 4

LoadingPath 3

LoadingPath 2

Cm

Figure 1 Loading Paths In Stress/Temperature Space

0.45

0.55

0.65

0.75

0.85

0.95

1.05

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110

Temperature, °C

Hea

t F

low

, W/g

(en

do u

p)

NiTiCuNiTi

∆H

Figure 2 Initial DSC results for NiTiCu and NiTi specimens showing heat of

transformation, ∆∆H

23

LoadCell

Grip

ThermocouplesSMASpecimen

LVDT Servo-HydraulicActuator

Furnace

Figure 3 Experimental Set-up

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Temperature, °C

Austenitic Plastic Deformation

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16

Strain

Figure 4 Stress-Strain and Strain-Temperature Results for Austenitic deformation on aNiTiCu SMA

24

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120

Temperature, °C

memaust :120°C

0

100

200

300

400

500

600

700

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain

Figure 5 Stress-Strain and Strain-Temperature Results for Austenitic

deformation on a NiTi SMA

-0.008

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Plastic Strain

Tw

o-W

ay S

trai

n

NiTiCu Specimen

NiTi Specimen-

Figure 6 Two-way Strain vs. Plastic Strain for Austenitic

Deformation on NiTiCu and NiTi specimens

25

0.13

0.131

0.132

0.133

0.134

0.135

0.136

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Temperature, °C

Stra

in

0.5

0.6

0.7

0.8

0.9

1

1.1

Hea

t F

low

, W/g

(en

do u

p)

strain

DSC-Austenitic Series

DSC- Pre-Test

Figure 7 Initial and Final DSC and Two-Way Strain for NiTiCu Specimen deformed in

Austenitic Condition

0.15

0.152

0.154

0.156

0.158

0.16

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100

Temperature, °C

Stra

in

0.35

0.45

0.55

0.65

0.75

0.85

0.95

Hea

t F

low

, W/m

g (e

ndo

up)

strainPost Test DSCPre-Test DSC

Figure 8 Two-Way strain and Initial and Final DSC for NiTi Specimen Deformed in

Austenitic Condition

26

Table 1 Heat of Transformation values for each loading history, ∆∆H (J/g)

Pre-Test

Condition

Austenitic

Plastic

Loading

Thermal

Cycling

under stress

Stress-Induced

Martensitic

Loading

Martensitic

Plastic Loading

M⇒⇒A A⇒⇒M M⇒⇒A A⇒⇒M M⇒⇒A A⇒⇒M M⇒⇒A A⇒⇒M M⇒⇒A A⇒⇒M

NiTiCu 12.41 -12.60 5.94 -6.45 5.79 -5.36 3.69 -3.61 3.23 -3.20

NiTi 15.56 -15.38 9.18 -8.36 8.62 -4.39 6.29 -2.07 3.63 -1.77

ActTrans- SeriesT=85 °C

0

100

200

300

400

500

600

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain

Summary-Acta Tranformation

00.010.020.030.040.050.060.070.080.090.1

0.110.120.130.140.150.160.17

-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temperature, °C

Figure 9 Stress-Strain and Strain-Temperature Results for Stress-Induced MartensiticDeformation on a NiTiCu SMA

27

memtrans- :40°C

0

50

100

150

200

250

300

350

400

450

500

550

600

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

Strain

Stre

ss, M

Pa

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110Temperature, °C

Stra

inFigure 10 Stress-Strain and Strain-Temperature Results for Stress-Induced Martensitic

Deformation on a NiTi SMA

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15

Plastic Strain

2-w

ay S

trai

n

NiTiCu Specimen

NiTi Specimen

Figure 11 Two-way strain development for Stress-Induced Martensitic Loading as a

function of Plastic Strain

28

0.12

0.125

0.13

0.135

0.14

0.145

0.15

0.155

0.16

-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temperature, °C

Stra

in

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Hea

t F

low

, W/m

g (e

ndo

up)

strainPost-Test DSCPre-test DSC

Figure 12 Initial and Final DSC and Two-Way Strain for NiTiCu Specimen through the

Stress-Induced Martenitic Loading

0.13

0.135

0.14

0.145

0.15

0.155

0.16

0.165

0.17

0.175

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110

Temperature, °C

Stra

in

0.5

0.6

0.7

0.8

0.9

1

1.1

Hea

t F

low

, W/g

(en

do u

p)

Strain

Post-Test DSC

Pre-Test DSC

Figure 13 Initial and Final DSC and Two-Way Strain for NiTi Specimen through the

Stress-Induced Martenitic Loading

29

Martensitic-plastic strainT=22°C

-100

0

100

200

300

400

500

600

700

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28

Strain

Stre

ss, M

Pa

Acta-Martensite

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temperature, °C

Stra

in

Figure 14 Stress-Strain and Strain-Temperature Results for Martensitic Deformation on aNiTiCu SMA

-0.002

0.018

0.038

0.058

0.078

0.098

0.118

0.138

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120

Temperature, °C

Stra

in

0

100

200

300

400

500

600

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain

Stre

ss, M

Pa

Figure 15 Stress-Strain and Strain-Temperature Results for Martensitic Deformation on aNiTi SMA

30

Martensitic 2way strain

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Plastic Strain

Tw

o-w

ay s

trai

n NiTiCu Specimen

NiTi Specimen-

Figure 16 Two-way strain development for the Martensitic Loading as a function of Plastic

Strain

31

0.14

0.145

0.15

0.155

0.16

0.165

0.17

0.175

0.18

0.185

-40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temperature, °C

Stra

in

0.5

0.6

0.7

0.8

0.9

1

1.1

Hea

t F

low

, W/m

g (e

ndo

up)

Strain

Post-Test DSC

Pre-Test DSC

Figure 17 Initial and Final DSC and Two-Way Strain for NiTiCu Specimen through a

Martensitic Loading

32

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100

Temperature, °C

Stra

in

0.5

0.6

0.7

0.8

0.9

1

1.1

Hea

t F

low

, W/m

g (e

ndo

up)

Strain

Post-Test DSC

Pre-Test DSC

Figure 18 Initial and Final DSC and Two-Way Strain for NiTi Specimen through a

Martensitic Loading

33

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

Temperature, °C

Stra

in

Figure 19 Thermal Cycles under Constant 200 MPa for NiTiCu

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

-30 -20 -10 0 10 20 30 40 50 60 70 80

Temperature, °C

Stra

in

Figure 20 Thermal Cycles under Constant Stress for NiTi

34

0

0.005

0.01

0.015

0.02

0.025

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Temperature, °C

Stra

in

0.5

0.6

0.7

0.8

0.9

1

1.1

Hea

t F

low

, W/m

g (e

ndo

up)

6 Mpa

Post-Train DSC

Pre-Test DSC

Figure 21 Two-way strain and Initial and Final DSCs for thermally cycled NiTiCu

Specimen

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110

Temperature, °C

Stra

in

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Hea

t F

low

, W/m

g (e

ndo

up)

Strain

Pre-Test DSCPost-Test DSC

Figure 22 Two-way strain and initial and final DSC results for thermally cycled NiTi

Specimen

35

Figure 23 Microstructure showing residual martensite after heating above austenite finish

Figure 24 Recoverable strain as a function of the plastic strain for the NiTi Specimen