Stress-induced transformation behavior of a ...brinson.mech.northwestern.edu/documents/... · 1988; Miyazaki et al., 1989a,b; Nishida et al., 1995; Madangopal, 1997) ... Due to the

Journal of the Mechanics and Physics of Solids52 (2004) 1549–1571

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Stress-induced transformation behavior of apolycrystalline NiTi shape memory alloy: microand macromechanical investigations via in situ

optical microscopy

L. Catherine Brinsona ;∗, Ina Schmidtb, Rolf LammeringbaMechanical Engineering Department, Northwestern University, Evanston, IL 60208, USA

bInstitute of Mechanics, University of the Federal Armed Forces, D-22043 Hamburg, Germany

Received 22 January 2003; received in revised form 7 January 2004; accepted 8 January 2004

Abstract

An experimental investigation of the micro and macromechanical transformation behavior ofpolycrystalline NiTi shape memory alloys was undertaken. Special attention was paid to macro-scopic banding, variant microstructure, e7ects of cyclic loading, strain rate and temperaturee7ects. Use of an interference 9lter on the microscope enabled observation of grain boundariesand martensitic plate formation and growth without recourse to etching or other chemical surfacepreparation. Key results of the experiments on the NiTi include observation of localized plasticdeformation after only a few cycles, excellent temperature and stress relaxation correlation, are9ned de9nition of “full transformation” for polycrystalline materials, and strain rate dependente7ects. Several of these 9ndings have critical implications for understanding and modeling ofshape memory alloy behavior.? 2004 Elsevier Ltd. All rights reserved.

Keywords: Phase transformations; Shape memory; NiTi; Microstructure; Optical microscopy

1. Introduction

Shape memory alloys have been studied intensively for the past two decades withexperimental and theoretical investigations spanning topics from thermally induced vari-ant formation (Saburi and Wayman, 1979; Saburi and Nenno, 1981; Adachi et al.,1988; Miyazaki et al., 1989a,b; Nishida et al., 1995; Madangopal, 1997) to multiaxial

∗ Corresponding author. Tel.: +1-847-467-2347; fax: +1-847-463-0540.E-mail address: [email protected] (L.C. Brinson).

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1550 L.C. Brinson et al. / J. Mech. Phys. Solids 52 (2004) 1549–1571

prediction of mechanical response (Boyd and Lagoudas, 1995; Lagoudas et al., 1996;Auricchio and Taylor, 1997; Goo and Lexcellent, 1997; Huang and Brinson, 1998;Raniecki and Lexcellent, 1998; Siredey et al., 1999; Gao et al., 2000; Huang et al.,2000). Much of the experimental work in the materials literature has focused on thetwinning structure of thermally induced martensite (e.g. Miyazaki et al., 1989a,b; Piaoet al., 1993; Nishida et al., 1995; Madangopal, 1997; Nishida et al., 1998), and onuniaxial thermomechanical response from the mechanics perspective (e.g. Liang andRogers, 1990; Ford and White, 1996; Miller and Lagoudas, 2000). Notable macroscaleexceptions in recent years include work by Gall et al. (1998) on triaxial loading statesand Lim and McDowell (1999) on nonproportional tension-torsion loading. Work within situ loading and microscopy is found less frequently, but these experiments o7era rich understanding of the SMA response as they address both microstructural andmacromechanical response simultaneously (Miyazaki et al., 1983, 1986; Abeyaratneet al., 1994; Vivet and Lexcellent, 1998; Fang et al., 1999; Jost, 1999; Liu et al.,1999; Zheng et al., 1999). Some examples of the latter are highlighted below.The early 1990s experiments by Abeyaratne et al. (1994) investigated biaxial re-

sponse of a CuAlNi single crystal. The specimen was martensitic and oriented suchthat one variant was preferred in each of the loading directions. Their work highlightsthe reorientation between these two martensitic variants when the loading is changedfrom one axis to another and focuses on the 9ne substruture of martensite at the in-terfaces between variants. Accompanying modeling of the Ginzburg–Landau type wasperformed to correlate with the experiments.More recently, Vivet and Lexcellent (1998) considered a similar biaxial loading

experiment on single crystal CuAlNi with the material starting in the austenite state. Inaddition to sequenced uniaxial tests (complete load–unload cycles in the x-direction,then in the y-direction), they performed unique nonproportional loading tests. Upon theaddition of the y-direction load to a constant x-direction stress, their results showedthe anticipated decrease of the variant preferred with uniaxial x-loading, followed byincrease of the variant preferred by uniaxial y-loading at a critical stress value in they-direction.Work by Miyazaki and co-workers (Miyazaki et al., 1981, 1983, 1986, 1989a,b) have

systematically examined the crystallography and mechanical behavior of NiTi. In situobservation of single crystal NiTi is studied in (Miyazaki et al., 1983, 1989a,b). Opticalmicrographic observations were performed to investigate the self-accommodating mor-phology during transformation and subsequently, during loading, the martensite variantcoalescence to form the most favorable variant. E7ects of temperature and strain levelon macromechanical behavior of polycrystalline NiTi was investigated in (Miyazakiet al., 1981), while e7ects of cycling were examined in (Miyazaki et al., 1986). Cy-cling was shown to alter the mechanical behavior and optical microscopy revealedevidence of residual martensite near grain boundaries.Polycrystalline NiTi is observed under mechanical loading in several papers using

electron microscopy. For example, stress induced martensitic transformation and plasticdeformation in NiTi alloys are investigated in (Jiang et al., 1997) using transmissionelectron microscopy (TEM). The movement of the martensite–matrix interface andthe formation of dislocations during the reverse martensitic transformation induced by

L.C. Brinson et al. / J. Mech. Phys. Solids 52 (2004) 1549–1571 1551

stress have been studied at low strain rates. In Zheng et al. (2000) the microstructure ofcold-drawn NiTi alloys has been investigated using TEM and high-resolution electronmicroscopy. Of particular interest is the dominant twinning mode appearing in themartensite variants at di7erent loading stages. The anisotropy due to texture e7ects incold-drawn NiTi sheets have been examined in Liu et al., 1999. The di7erences instress–strain response for rolling and transverse directions are examined by post-testTEM and identi9ed to be due to di7ering dominant detwinning/reorientation modes anddislocation densities.A more macroscale approach with simultaneous imaging and stress–strain measure-

ment was performed by Shaw and Kyriakides (1995, 1997b). Here they used both astandard camera and a thermal camera to capture the macro-transformation state ofthe material and thermal signatures with loading at di7erent strain rates and underdi7ering isothermal/adiabatic heat transfer conditions. Their images of the specimensurface used the naturally forming oxide layer as an indicator of transformation andshowed striking macro-transformations bands forming and growing as the loading pro-gressed. The thermal camera supported the results with evidence of latent heat releaseduring transformation. More recent work (Shaw and Kyriakides, 1997a; Iadicola andShaw, 2002) has examined the e7ects of cycling on the macro transformation bandsand has looked more closely at the evolution of the macro-band transformation frontduring loading. The latter is shown to be heavily inLuenced by geometric features ofthe specimens.Inspired by the papers of Shaw and coworkers, the present study was undertaken

to address similar experiments at a di7erent scale level to investigate the correlationbetween the microstructure of grains and variants and the macromechanical responseof the material. Our loading is uniaxial like their previous work, with load measure-ment and overall strain measurement. Unlike Shaw and Kyriakides, we do not measurelocalized strains with mini-extensometers, but relate results to the strain of the entirespecimen length. For macroscopic photographs of the transformation surface a digi-tal camera is used, while an optical microscope is used for 9ne scale observations ofmicrostructural changes as a function of loading parameters. By using an optical micro-scope and a custom designed loading frame, we are able to observe microstructures atthe habit plane variant level while simultaneously obtaining macroscale transformationimages and stress–strain data. While similar to some of the earlier work by Miyazaki,the current work has yielded unique results on the relationship between variant forma-tion and macroscopic LMuders-like bands, localized permanent deformation and strainrate e7ects. In this paper, results for NiTi polycrystalline specimens are given; resultsfor copper based polycrystals and CuAlNi single crystal can be found in a separatepublication (Brinson et al., 2002).

2. Experimental techniques

2.1. Specimen preparation

For the experiments, NiTi specimens of two geometries were machined by wire-EDMfrom 1:57 mm thick plates obtained from the NDC Corporation (SE-508, Ni55.6Ti


Fig. 1. Geometry of two specimens used for experiments.

Fig. 2. Experimental set-up with loading stage shown in position with the optical microscope.

(wt%)). See Fig. 1. Specimen geometry 1 was used for all tests reported here ex-cept those to very large deformation (only results from Figs. 9 and 10 use specimengeometry 2). Individual specimens were then heat treated by annealing at 750◦C for 1 hunder low vacuum (approximately 0:01 mbar) followed by water quench; then heatedagain to 525◦C for 8 min and again water quenched. This heat treatment results in agrain size of approximately 60–70 �m and an Af temperature of −13◦C as measuredby DSC. The annealed specimens were then polished with the following procedure: asthe surface was rough, both sides of the specimens were sanded using papers of severaldi7erent roughnesses from 220 to 1000 grit (on the FEPA or P-scale; US CAMI scalefrom 220 to 500); the observation side of the specimen was then sequentially polishedwith 9ne powder solutions (to 0:25 �m) on a Struers Rotomat polishing machine.

2.2. Testing stage

The testing stage was a custom designed horizontal loading device that holds thespecimen for viewing under a standard optical microscope (Fig. 2). A stepper motordrives a linear rail unit with two joined ballscrews with opposite rotation direction.This unit controls the displacement for both grips for the specimen. The maximumspeed obtainable with the gear ratios chosen is 30 mm=s. An LVDT (HBM W10TK)measures grip displacement on one of the grips. Both grips are driven by the sameballscrew, mounted similarly and therefore assumed to move identically. Control testswere performed to quantify the uncertainty in the average strain measurement using asingle LVDT. In the control tests both grip displacements were measured simultane-ously and the error was shown to be less than 1% over the full working range of the


LVDT, which is adequate for our results. The asymmetric design with a ballscrew ononly one side of the specimen leads to an initial backlash at low stress levels. Theset up was carefully calibrated and results for displacements corrected with a linearapproximation of the calibration curve, however the values at very low stress levels(far below the transformation stress of the specimens) remain imprecise.Special attention was required in design of several features of the loading device.

Due to the horizontal layout, the grips were supported with brass plates where thefrictional resistance was minimized. The grips were allowed to rotate freely in onlyone direction to allow for more precise alignment of all the device elements. A movablestage was designed for the microscope to enable movement of the objectives over anypart of the specimen. The entire loading stage is supported on four columns and ismovable in the vertical direction in very 9ne degrees enabling focus of the microscopeeven at 1000×magni9cation. When the microscope was moved or the stage was movedduring tests, very slight imperfections were observed in the load and/or displacementsensor measurements. However, the magnitude was small enough (less than 10 N inload) not to inLuence the experimental results. Although care was taken to design thedevice to be as sti7 as possible, several sources of small inaccuracies exist, in particularthe frictional surfaces between grips and brass supporting plates, and tolerances of thedriving screws and all connections.

2.3. Optical microscopy

Microscopy was carried out with a Leica DMRM microscope 9tted with a digitalvideo camera (Canon XLS-1) with output received by a computer with specializedvideo card. In most cases movies were taken of the specimen either at a single locationduring loading/unloading sequences to observe variant formation in grains or imageswere taken at a particular strain level moving the objective along the length of thespecimen to provide a picture of the transformation state in di7erent regions of thespecimen.An interference 9lter (IC objective prism B2 with polarized light) was used on

the Leica microscope which enhances surface relief contours. Even pristinely polishedspecimens, prior to 9rst loading, revealed most of the grain boundaries under this 9lter(see Fig. 3), eliminating the need for more elaborate etching treatments of specimens. Inaddition, as specimens were cycled through several loading sequences grain boundariesbecame more distinct. Martensitic variants due to the surface angle changes were highlyvisible at all stages with use of the 9lter.

2.4. Loading sequences

Any given specimen was typically subjected to numerous loading cycles to viewthe evolving microstructure with cycling. For all the experiments shown, displacementcontrol was used and tests were performed at room temperature (25◦C). Given the lowAf temperature of the material, all specimens were fully austenitic in the original un-loaded state and stress-induced phase transformation to martensite occurred during load-ing. In order to better observe the microstructure at di7erent states of transformation,


Fig. 3. Same location on NiTi specimen viewed prior to initial load sequence with (right) and without (left)9lter. Without the 9lter, only an oil mark is visible.

Fig. 4. Typical loading and unloading sequence for specimen allowing microstructural observation at di7er-ent states of transformation. Typical location of 9rst observation of martensite notated. Specimen is NiTipolycrystal loaded at �̇ = 4 × 10−3 s−1.

in some loading cycles the loading was temporarily stopped and the specimen heldat constant displacement for several minutes while photos/videos were taken of thespecimen surface, after which loading continued. A representative stress–strain dia-gram of this type is shown in Fig. 4. Note that the strain (and strain rates) in thispaper are specimen average values, calculated by total grip displacement divided byspecimen gage length. There are large inhomogeneities in the strain 9elds along thespecimen length, as demonstrated by Shaw and Kyriakides (1995) and also apparenthere by the localization of variant formation revealed in the microscopy. In Fig. 4,the stress relaxation at the displacement holds during loading (and the “anti stress re-laxation” at the holds during unloading) are due to temperature e7ects, as discussedlater. Some specimens were also tested in typical ramp load–unload histories, with no


pauses for microstructural viewing. Strain rates ranging from 10−4 to 100 s−1 wereused in the investigations. For some specimens, temperature at one or more locationswas measured simultaneously with a thermocouple and correlated to transformation andstress pro9les.

3. Results

Although experimental observations of SMA transformation can be found in the ref-erences cited earlier, the simultaneous micro–macro scale observations here are uniqueand provide both new results and are able to clarify or con9rm hypotheses from ear-lier research. The relation between macroscopic deformation bands and microstructuralmartensite will be introduced 9rst. Then we will discuss formation of “residual marten-site”—areas of localized permanent deformation and their growth with increasing cycles—and consistency of variants with cycles. Finally, we will address other observations,including stress relaxation and e7ect of strain rate.

3.1. Macroscopic bands and relation to microstructural martensite

With reference to the earlier work of Shaw and Kyriakides (1995, 1997b), we 9rstinvestigate the formation of macroscopic transformation bands of martensite at relativelyslow strain rates (here 4×10−3 and 10−4 s−1 are used) and relate this superstructure tothe variants forming in the grains. Both of these strain rates are slow enough to avoidthe dramatic self-heating e7ects that can lead to more homogeneous transformationbehavior. Consistent with (Shaw and Kyriakides, 1995, 1997b), the results here atthese strain rates exhibit macroscopically localized transformation bands that propagatefrom the gripped ends across the specimen. Although these bands macroscopicallyhave similarities to LMuders type bands, the deformation mode is quite di7erent andis microscopically far from homogeneous both inside and outside of the deformationbands as will be seen.While Shaw and Kyriakides used the oxide layer on the specimen surface as a

convenient indication of large scale transformation, our specimens are highly polishedand therefore have no oxide layer. Using careful lighting, macroscopic images wereobtained and adjusting the contrast between light and dark regions enabled the macro-scopic transformation bands to be seen. Fig. 5 shows macrophotos taken at 1% and2.5% strain and the transformation band forming initially at the left end of the specimenis distinctly visible. By 2.5% strain, a second band has begun on the right end of thespecimen and the left band has broadened considerably.Microscopy on the same specimen during transformation reveals several very inter-

esting results. First, for nearly all specimens tested, the 9rst martensite plates appear inthe specimen at approximately 0.7% strain. These plates are isolated from one anotherand most likely appear in grains that are optimally oriented for transformation given theloading direction. In a scan of the specimen length (covering approximately 104 grains)at 0.7% strain, approximately 10 grains will be observed with 1–2 variants each. Notefrom Fig. 4 that the formation of these initial variants is just before the knee in the


Fig. 5. Macrophotos of NiTi specimen tested at 4×10−3 s−1. Top image is at 1% strain while lower imageis at 2.5% strain. Width of specimen 3 mm. Boxes indicate location of enlarged images shown in Fig. 6,while the arrows indicate the extent of the macroscopic transformation band.

Fig. 6. Micrographs in the transformation band (left) and toward the center of the specimen (not in mac-roband) at 1% strain.

Fig. 7. Micrographs at 2.5% strain in the heavily transformed band at left end of specimen (left) and towardthe center of specimen (right) where macrophotos indicate beginnings of transformation.

stress–strain curve. This direct observation correlating microscopic appearance of the9rst variants in grains to the macroscopic stress–strain curve con9rms earlier results(Liu et al., 1998; Sun et al., 2001) that were based on macroscopic evidence.


Fig. 8. Martensite formation, 3% strain, at medium resolution revealing origin of stripes seen macroscopicallyin transformation band.

At 1% strain, the macrophoto in Fig. 5 shows a visible transformation band to-ward the left end of the specimen and micrographs of this region (Fig. 6, left) alsoshow strong transformation. More notable, however, the regions in the specimen centerindicated to be pure austenite in Fig. 5, in fact contain signi9cant martensitic vari-ants throughout the grains (Fig. 6, right). As the strain is increased, the martensiticvariants continue to form throughout the specimen, although at a higher rate in themacroscopically observable transformation bands (see Fig. 7). Thus the macroscopictransformation bands seen via disturbance of the oxide layer on most specimens in-deed do denote regions of high transformation; nevertheless, these results indicate thattransformation occurs outside of these bands to a signi9cant degree.Returning to the macroscopic images in Fig. 5, in the photos and to the eye, the

macroscopic bands appear on this highly polished surface almost striped, with an-gled lines closely spaced together. The striped nature of the surface of the specimenbegins even at the 9rst formation of a macroband (1% strain) and remains throughouttransformation of the entire specimen. Beyond strain levels of approximately 3% thedistinct striped nature begins to degrade and be replaced by a more uniform mottledappearance. Microscopy of a transformation band region at 3% strain reveals a sim-ilar striped microstructure (Fig. 8). Here it is seen that the grains have transformedmore strongly in small bands approximately 100 �m wide, separated from one an-other by similarly sized bands where grains have transformed less and many grainsremain untransformed. This striped morphology may be due to geometric inLuences ofthe specimens, as explained on a macroscale for NiTi strips in Shaw and Kyriakides(1997a).A 9nal feature of these micro–macro observations is a rede9ned meaning of 100%

or “full” transformation in a polycrystalline specimen. Here, tests on two separate spec-


Fig. 9. Stress–strain curves: loading to failure and loading in a sequenced fashion to observe microstructuralevolution from zero to “full” transformation. Strain rate 10−4 s−1.

imens are described, but the results are consistent with observations on all specimenstested. One specimen was pulled to failure in a standard testing machine (to avoidpotential damage to the microscope objectives) while the second specimen was testedwith microstructural observation in the load-hold–load-hold pattern (as in Fig. 4) toa high strain level, both at strain rate 10−4 s−1. The stress–strain diagram of bothtests is shown in Fig. 9. Exact data overlap is not possible due to the di7erent speci-mens used and small, but di7erent, inaccuracies in each of the di7erent machines used.In particular, the specimen tested with microscopy was polished, while the specimentested to failure was not; the thin oxide layer remaining on the specimen surface forthe latter sample likely carried little load, although contributed to the cross-sectionalarea. Hence the stress magnitude for the test to failure is potentially under-calculated.Note that at approximately 6% strain in both cases, the stress begins to sharply riseas the macroscopic indication of the end of transformation in the specimen. Obser-vation of the surface also revealed that the macroscopic band traversed the entirespecimen at that point. At this slowest strain rate only one macroband formed andpropagated.Micrographs were taken along the specimen surface at each strain level yielding

similar results to those already presented (i.e., transformation was dominant in macrotransformation band, but some martensitic plates formed continuously in grains out-side of the macro-band). In this specimen however, loading continued to much higherstrain levels. Fig. 10 shows the same location at several strain magnitudes. Note thatthe last picture is at a strain of 10%, well beyond the “full transformation” point ofthis material. Similar images were compared at various locations along the sample andtaken together demonstrate that the “complete” transformation state of this polycrys-talline material is not 100% martensite, and likely lies around 60–70% transformed.The approximate volume fraction is determined based on surface metallography onlyand is therefore a qualitative value due to possible di7erences in surface versus bulkmartensitic transformation.


Fig. 10. Microscope images at strain levels 0%, 2%, 4%, 10% showing “full transformation”. Note that inlast image, beyond full transformation point, microstructure indicates that the specimen contains at most 60%martensite due to “locking” of variant structure as sequential grain transformation occurs.

Miyazaki and co-workers (Miyazaki et al., 1983) mention remaining parent phaseafter the main transformation plateau (stage I) in single and polycrystalline NiTi basedon macroscopic evidence. Here, we provide microstructural evidence for polycrystallinespecimens that indeed the “full transformation” corresponds to less than 100% marten-site. Grains that are unfavorably oriented never transform and even grains that are fa-vorably oriented only transform partially, rarely attaining 100% martensite in a grain.This latter result can be explained as follows: as transformation begins in one particulargrain, martensitic plates begin to appear in increasing numbers as the stress is slowlyincreased; however, as the stress increases, neighboring grains begin also to transformchanging the local stress state from one favorable to continued transformation in theoriginal grain, to one unfavorable. Due to this sequenced transformation behavior, vari-ants become “locked” in each grain in turn and unable to transform fully, in contrastto what is seen typically in single crystal samples. Fig. 10 also demonstrates that theprocesses of stress-induced martensite formation and plastic Low are largely sequential,with very few additional martensite plates forming after the macroband has swept thespecimen and large scale plastic Low begins.


Fig. 11. E7ect of cycling on the stress–strain diagram, showing decreasing transformation stress, increasingstrain hardening, decreasing hysteresis. Symbols indicate approximate location of macroscopic transformationstress; consistent 0.02% o7set of linear portion of loading curve used for de9nition.

3.2. Formation of residual martensite with cycling

With each load–unload cycle, a small amount of residual deformation remains in thematerial, accumulating with increasing cycles. In our experiments, specimens strainedfrom zero to 4% strain each cycle (as in Fig. 4) accumulated residual strain signi9cantlyfaster, and thus for the remaining results, specimens were cycled to a maximum of 2%strain to prolong sample life. The macroscopic e7ects of cycling manifest in the stress–strain diagrams similar to other well-documented cases (Funakubo, 1987; Otsuka andWayman, 1998; Xie et al., 1998): the transformation-start stress decreases, the “strainhardening” slope of the transformation plateau increases and the hysteresis decreases.These e7ects can be seen in Fig. 11, where several select cycles without the interruptionof displacement holds at di7erent displacement levels are shown. Note that althoughthe hysteresis loops for the three cycles shown appear substantially di7erent, onlya 0.1% residual strain remains in the specimen after cycle 9. It is also noted thatdue to the somewhat large size of the grains in the samples tested, there may bean increased propensity for slip at the grain boundaries. Results by Saburi (1998)show a correlation between plastic deformation and grain size on initial pseudoelasticstress cycles. Although samples with grain size similar to ours (50 �m) are shown toexhibit normal pseudoelasticity without slip in an initial cycle, these results explain thesomewhat faster accumulation of plastic deformation with cycling in our samples.Comparisons of the micrographs taken at identical locations during di7erent cycles

are striking. Fig. 12 shows a compilation of micrographs of the same grains at the endof several loading cycles. Fig. 13 shows the same location at the 2% strain level withthe martensitic variants active in several cycles. Fig. 14 shows a sequence of images inthe same area at di7erent strain levels on two di7erent cycles. Note that in all cycles,the 9nal strain achieved was identical, although the initial strain varied due to small


Fig. 12. Accumulation of localized plastic deformation within the grains upon load cycling. Identical locationsimaged on virgin specimen and after four di7erent cycles, specimen fully unloaded.

Fig. 13. Micrographs of activated variants at 2% strain in one set of grains at di7erent cycle numbers (cycle1, 6 and 10 from left to right). Note that although the same habit plane variants are activated each loadingcycle, the spatial position of the variants within the grains varies from cycle to cycle.

accumulating residual deformation. Several features are notable from these images andare described in the following paragraphs.First, after the 9rst cycle, no di7erence is visible between the images in Fig. 12.

However, by cycle 5, localized deformation is clear to see in the lower right grain and


Fig. 14. Micrographs of activated variants at several strain levels in two di7erent cycles. Location of residualmartensite noted with arrows in the outlined grain at 0% strain level. At higher strain levels, arrows indicateformation of the initial martensite plates. Note that the 9rst martensite plates do not appear in a grain withresidual martensite plates visible.

several other locations in the image. This localized deformation increases in magni-tude with each cycle, producing a signi9cant residual martensite image by cycle 15.In contrast to earlier work by Miyazaki et al. (1986) where residual martensite was


con9ned to the area around the grain boundary, these images clearly show residualmartensite e7ects spanning across entire grains. These long regions may be small re-tained martensite plates, also accompanied by localized slip as suggested by Miyazakiet al. (1986).Note in comparison between Figs. 12 and 13 that the localized deformation occurs in

the same direction and locations as the martensite plates visible at the 2% strain level.Upon unloading, the plates largely disappear, but in certain grains each cycle resultsin additional localized permanent deformation near the variants (e.g. the lower rightgrain in Fig. 12). In Fig. 12, the grain at the center-left shows no residual martensiteeven after many cycles. These results are typical of image sequences captured at otherlocations on the specimens with respect to the e7ects of cycling: the plastic deformationis localized along locations of active variants and occurs in some grains while not inothers.In addition to the accumulating deformation with cycles, the consistency of variants

with cycles was also examined. It is clear from images in Fig. 13 that the activevariants in each grain are the same in each cycle (i.e., the same habit plane variant isactivated each time), however the exact spatial position of the variants changes fromcycle to cycle. This result has important implications for modeling. It is also seen thatin general there is a slight increase in the number of martensitic plates from cycle 1to cycle 15.Fig. 14 also demonstrates that the spatial locations of active variants change from

cycle to cycle. However, here we also see that the 9rst martensite plates to formdo not necessarily form at the site of a visible residual martensite plate, nor evennecessarily in a grain with residual martensite. In both cycles, the 9rst martensiteplates to appear are marked with arrows in frame 2 (0.97% strain). Of these, severaldo occur at the location of residual martensite, while others occur in grains free ofresidual martensite. In frame 3, the 9rst martensite plates appear in the outlined grainwith signi9cant residual martensite, also marked with arrows. Note that the locationof the 9rst martensite in frame three does not coincide with location of an existingresidual martensite plate. In both cycles, the location of the active martensite plates inthe outlined grain vary signi9cantly and are uncorrelated with the location of residualmartensite plates.Linking the microstructural observations to the macroscopic response, the decrease

of the threshold stress to begin transformation (seen in Fig. 11) is likely due to residualstresses associated with the localized deformations: the defect sites perturb the localstress 9eld, enabling variants to form at lower macroscopic loads due to the addedresidual stress 9eld. Note that due to the evidence in Fig. 14, the local stress stateswill be altered in a complex fashion such that variant formation is not necessarilyfacilitated at a residual martensite plate. In addition, we believe that the slight increasein variants with cycling may also be linked to the permanent deformation that is visiblein the grains: as cycle number increases, the number of variants needed to achieve theprescribed strain level increases due to the inability of the variants in the damaged areasto achieve as high a strain as in the 9rst cycle. This hypothesis may also explain theincreasing strain hardening with cycles (Fig. 11), as higher stress levels are requiredto activate additional variants.


Fig. 15. A transformed region of the specimen with scratches (marked by arrows) and other surface defectsdue to polishing. Note that transformation is not a7ected by the surface defects: activated variants passthrough scratches and scratches can run through grains that never transform.

A 9nal feature of transformation that was noted during the microscopy was thenegligible impact of scratches and other defects on transformation. The NiTi specimenswere challenging to polish, often resulting in some scratching and/or pitting of thesamples. We carefully observed such defect regions during the testing and consistentlyresults proved that these defects had no impact on transformation behavior. An exampleis shown in Fig. 15, where both scratches and other surface defects are visible. Notethat in some grains, the variants formed pass directly through the scratch; and in othergrains, no transformation occurs in spite of the scratch or surface defects near the grainboundaries. These results turned out to be bene9cial to the experiments in that surfacedefects could be e7ectively used to easily locate the same grains on the surface duringdi7erent cycles.

3.3. Temperature and strain rate e<ects

All tests reported here were performed at room temperature, however the self-heatingand self-cooling of the specimens due to latent heat at various strain rates was exam-ined. During the loading sequences containing constant displacement holds, a stress-relaxation was observed as seen earlier in Fig. 4 for all tests. The magnitude ofthe stress relaxation decreased with decreasing strain rate. The stress relaxation (andanti-relaxation for unloading) stems from the non-isothermal nature of the experimentsdue to the latent heat released in the specimen. Correlation between stress level andlatent heat has been reported widely for SMA materials (Leo et al., 1993; Shaw andKyriakides, 1995; Lin et al., 1996; Brinson et al., 2002), and has focused mainly onthe increasing strain hardening seen for higher strain rates which can be explained bythe increase of specimen temperature with transformation due to latent heat.


Fig. 16. Section of a schematic transformation stress–temperature phase diagram for the loading case. Thenonisothermal loading path due to release of latent heat is shown. Midway through transformation, theloading is stopped and the specimen held at constant displacement. The temperature and stress decay asindicated.

In our experiments, we have taken a di7erent approach and have measured thestress and temperature changes during constant displacement holds during loading. Mi-crostructural observations are made simultaneously. A schematic macroscopic stress–strain diagram commonly found to describe SMA behavior is shown in Fig. 16 (Tanakaet al., 1986; Ivshin and Pence, 1994; Bekker and Brinson, 1998; Auricchio and Sacco,1999; Govindjee and Kasper, 1999) note that such a diagram does not reLect localnon-monotonic stress–strain behavior, nor does it capture the often higher initial nu-cleation stress. A transformation path for the loading case is depicted on Fig. 16: as thespecimen heats due to the latent heat of transformation, the loading path diverts fromthe isothermal line as indicated. At a constant displacement hold point, the temperaturein the specimen will slowly return to room temperature and simultaneously a decayof the stress is also seen, as less load is required to maintain a given transformationlevel at a lower temperature (assuming iso-martensite fraction lines are parallel to thetransformation zone boundaries).For several specimens, the temperature decay and stress decay was measured simul-

taneously. Fig. 17 shows the results of one typical test, performed at a strain rate of3× 10−2 s−1. Strain rate is chosen to be higher for these tests in order to increase thee7ects of latent heat. Temperature measurement is from a thermocouple located at themacroband location in this test. Since the stress and temperature decay in tandem andapproach equilibrium values at identical times, it is believed that the temperature decayafter latent heat release is primarily responsible for the stress relaxation observed inthese specimens. The Clausius–Clayperon slope was measured for one specimen witha value of 7 MPa=K. This value coincides well with other published values for NiTi(Leo et al., 1993; Lin et al., 1996). More detailed results of this nature are presentedelsewhere (Brinson et al., 2002).

From the simultaneous microscopic observations, it was found that the martensitevolume fraction and the variant structure in the grains remained constant during thetime of the stress and temperature decay for the constant displacement holds during


Fig. 17. Temperature and stress decay during a constant displacement hold at 2% strain after loading at3× 10−2 s−1. Note that the time to equilibrium for temperature and stress are identical, indicating that thetemperature decay after latent heat release is the primary cause of the stress relaxation seen.

Fig. 18. Micrographs of the specimen during a constant displacement hold during unloading, taken at di7erenttimes during the hold (identical location): left image at start of hold, right image 60 s later. While the stressslowly increases and the temperature rises back to room temperature during the hold, additional martensitealso converts back to austensite. These results are in contrast with the constant martensite state of thespecimen during loading pauses.

loading. Quite the opposite was observed in holds during the unloading portions ofthe curve. Note that during unloading, latent heat is absorbed by the material causinga decrease in temperature; consequently, during an unloading pause, the temperatureof the specimen is seen to rise toward ambient temperature. In these cases, althoughagain the temperature and stress data are in excellent agreement during their rise, thenumber of variants within the grains is observed to decrease simultaneously (Fig. 18).The additional conversion of martensitic variants to austenite can also be seen from


more macroscopic views, where it is observed that a macroscopic transformation bandsigni9cantly narrows or even disappears during the unloading pause.This asymmetry between loading and unloading pauses indicates that although the

loading pauses for these specimens appear to be iso-martensite fraction, the unloadingpauses follow a non-iso-martensite fraction path. A rationale for constant volume frac-tion results can be made since the experiments are kinematically driven: upon loadingto a given displacement level, a constant martensite fraction is required to sustain thatstrain magnitude and is not a7ected by a relatively small temperature change. However,the results from unloading pauses cannot be explained in this fashion. One possiblemechanism for results in Fig. 18 is that upon unloading as the temperature drops somevariants undergo a twin recon9guration to decrease the strain magnitude; upon heat-ing in the unloading pause, these twin related variants convert to austenite with nochange in strain. With optical microscopy it is not possible to obtain microstructuralevidence to support such a hypothesis, however. Thus, the reason for the asymmetry isas yet unclear and warrants further study, underscoring the complex thermomechanicalbehavior of shape memory alloy materials.During the testing of specimens at di7erent strain rates, typical macroscopic stress–

strain curve di7erences were seen: increase of transformation stress, increase of strainhardening and decrease of hysteresis. These results are all tightly linked to the latentheat released by the specimen upon transformation, as indicated by the stress relaxationexperiments (Brinson et al., 2002). The microstructural observations showed little dif-ferences for the various strain rates—the same habit plane variants were formed in thegrains at di7erent strain rates, with spatial location di7erences similar to repeat tests atthe same strain rate. At the highest strain rate achievable in our set-up, we consistentlycaptured a small amount of variant redistribution within the 9rst 60 s after the 9naldisplacement is achieved. The di7erences were small and usually consisted of a givenmartensitic plate within a grain splitting into two thinner plates. In testing of CuAlNisingle crystals (Brinson et al., 2002) we observed dramatic variant redistribution at thehigh strain rates. Additional testing of the polycrystalline NiTi at higher strain rates tofurther investigate the phenomenon is warranted and will be pursued.

4. Conclusions

In this paper we examined the microstructural and macroscopic transformation behav-ior of polycrystalline NiTi shape memory alloys. The experiments were accomplishedwith a custom-built loading stage designed to allow simultaneous loading and viewingof transformation behavior with an optical microscope. The results of the experimentsclarify several important issues regarding the transformation behavior of shape memoryalloys under loading at di7erent strain rates and changes due to cycling.In contrast to perception that transformation occurs only in the macroscopically vis-

ible transformation bands, the results here show clearly that martensitic transformationoccurs throughout the material at all strain levels. Macroscopic bands are regions ofmore intense transformation, but areas outside the bands are not martensite-free. Thebands themselves are shown to contain striations of higher and lower transformation,


especially in the earlier transformation stages. Even at full transformation of the spec-imen, our results show that the polycrystalline NiTi material is approximately 70%martensitic: the sequenced transformation of grains within the specimen inLuence thelocal stress states such that variants become locked-in and grains unable to transformfurther.Low level cyclic loading of the NiTi specimens was also pursued which revealed

signi9cant microstructural changes in the material after as few as 10 cycles. Local-ized plastic deformation occurs in the vicinity of the martensitic plates that form, withslightly increasing permanent deformation each cycle. Although the macroscopic “per-manent” strain is only 0.1% after 15 cycles, the amount of localized damage is highlyvisible at the grain level via the microscopy. The variants activated in each grain werevery consistent with cycles, varying only in exact spatial location from one cycle tothe next. However, due to the increased localized deformation, additional variants areformed at each cycle, providing an explanation of the strain hardening seen macroscop-ically. It was also demonstrated that although residual martensite plates likely alter thelocal stress 9elds facilitating transformation, the 9rst martensitic plates do not typicallyappear at the exact location of the residual martensite.Strain rate e7ects were also examined and it was shown that the self-heating of

the specimen due to release of latent heat is the primary cause of stress relaxationduring constant displacement holds during testing. Microstructurally, it was observedthat the stress relaxation during a loading pause was iso-martensitic, while an anti-stressrelaxation during an unloading pause involved additional martensite conversion. It wasalso observed that the variants activated remained the same at the various strain ratestested, however at the highest strain rate possible in our set-up, small redistributionsof martensitic plates within grains were seen after loading. This latter point requiresfurther investigation at higher strain rates to elucidate the mechanism.The results of these experiments are important for understanding shape memory alloy

transformation behavior and some points will be of particular interest in modeling phasetransformations. Models that account for distributions of grains in a material, such assome micromechanics models or 9nite element based approaches, should pay specialattention to the martensite distribution within the specimen, with respect to macroscopicbanding and actual grain transformation. The result that “full transformation” of thepolycrystal is not 100% transformed to martensite due to variant locking as the macrotransformation band sweeps the specimen is also critical to consider in validation ofmicromechanics models. The almost immediate presence of residual martensite in somegrains will be potentially useful for understanding and modeling damage accumulationin SMAs. And the con9rmation that strain rate e7ects are largely due to the latent heatin the specimen is encouraging and implies that accurate predictions on strain rate ef-fects can be obtained by relatively simple thermo-mechanical coupling with appropriateheat transfer equations.

Acknowledgements

The authors would like to thank the USA National Science Foundation and theAlexander von Humboldt Foundation (LCB), and the Bundesamt fMur Wehrtechnik und


Bescha7ung (RL, IS) for partial support of this research. All authors express gratitudeto Prof. Kreye and co-workers for generous use of their equipment and technical adviceduring the course of the work.

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Stress-induced transformation behavior of a ...brinson.mech.northwestern.edu/documents/... · 1988; Miyazaki et al., 1989a,b; Nishida et al., 1995; Madangopal, 1997) ... Due to the