General Introduction

Performing thermomechanical tests on small-sized specimens is a core activity in mechanics of materials. Indeed, these tests enable the experimentalist to study the response of engineering materials, to observe various phenomena occurring while loading is in progress, to propose suitable constitutive laws modeling the response, and to identify the parameters governing these laws. This is all the more important for shape memory alloys (SMAs) because such materials feature peculiar properties such as superelasticity, damping, or memory effect, which distinguish them from other metallic materials.

When testing materials, the classic route is to assume that the stress distribution is known a priori by using some simplifying assumptions and to measure the strain, the relationship between these two quantities providing the experimental stress–strain curve. For instance, with the most popular test, namely the tensile test, this stress distribution is assumed to be uniform and merely equal to the force divided by the cross section of the specimen. The strain is then measured at some points of the surface of the specimen with strain gages, or on average over a region with an extensometer. The stress–strain curves which are deduced are obviously of significant interest for SMAs since they enable the user to compare the response of different alloys and to observe and quantify specific features such as stress plateaus or hysteresis loops. These curves are, however, not sufficient to clearly understand the physical phenomena which directly cause these features, such as the appearance and growth of new phases or microstructures. The reason is that these phenomena are generally localized and spatially distributed, so classic measurement means such as strain gages or extensometers cannot really reveal them. This limitation has caused the recent lure of full-field measurement techniques in the SMA community, as illustrated by the increasing use of such techniques to characterize these materials (in fact, this is a general trend which concerns all engineering materials [1]). The benefit of using these tools for SMA characterization is that they provide, within certain limits, the amplitude and localization of strain or temperature heterogeneities which are the consequence of the physical phenomena of interest.

In this context, the objective of this paper is to give a comprehensive overview of the literature on SMAs where full-field measurement techniques are employed for thermomechanical characterization purposes. We first start by briefly describing the different techniques which are available to obtain these measurements, and specify their main metrological performance. Then we focus on nine typical papers from the SMA literature where full-field measurement techniques are used, and highlight the findings which could be made thanks to the use of such measuring techniques. A classification of the papers where full-field surface measurement techniques are used to characterize SMAs is finally offered. Different criteria are used such as the type of alloy under test, the nature of the technique used, or the type of test which is performed. We conclude by offering some suggestions for future studies in this research field.

Full-Field Methods Used to Characterize SMAs

Four surface and one 3D full-field measuring techniques have been identified in the papers of the literature dealing with SMA characterization. Concerning surface measurements, three of these fours techniques, namely digital image correlation (DIC), the grid method (GM), and moiré interferometry (MI), are dedicated to displacement and strain field measurement. infrared thermography (IRT) concerns thermal measurements, infrared cameras directly providing temperature fields after thorough calibration. The volume measurement technique is 3D X-ray diffraction (3D-XRD), which aims at measuring 3D stress distributions. All these techniques are briefly presented in turn in the following sections.

Digital Image Correlation

DIC is a versatile full-field measurement technique, which is now widespread in the experimental mechanics community. It consists first in depositing a random pattern onto the surface of the specimen under study in order to enhance the contrast in the corresponding images when the natural one is not sufficient. This is merely obtained by paint spraying these surfaces. The usual version of DIC consists then in considering small sub-images (called subsets) in the reference image, and in seeking their counterparts in the deformed one. This is made by iteratively minimizing, with respect to the sought displacement, the difference between the gray-level distribution in deformed and reference subsets. This minimization finally provides the displacements at the center of the subsets. Strain fields are deduced by smoothing and spatially differentiating these quantities. More sophisticate approaches are also available, such as the global version of DIC. In this latter case, a priori knowledge on the displacement field is used in the formulation of the companion minimization problem, which is resolved in order to determine the parameters governing this model. Even a finite element model for the displacement field can be used. In this case, the displacements at the nodes are returned by DIC, the displacement in between being described by shape functions supposed to precisely model the displacement within the elements [2,3,4]. Images processed with DIC are taken with cameras equipped with CCD or CMOS sensors. One camera is enough for in-plane displacement measurement, while two cameras at least are necessary to perform stereo-DIC. This version of DIC is used to estimate 3D displacement fields on the specimen surface. The surfaces over which measurements are made with DIC are typically several cm2 in size, but this technique can also be used at the microscale with SEM [5,6,7,8]. DIC is sometimes coupled with EBSD to correlate the results with crystal orientations, as illustrated later on in this paper.

It is difficult to summarize the metrological performance of DIC with some figures. The reason is that compared to other classic local measurement means such as strain gages, a new quantity appears here, namely the spatial resolution. This quantity is discussed in the literature (see Refs. [4, 9,10,11] for instance), but it is not clearly defined in any standard, to the best of the authors’ knowledge. In short, it reflects the ability of a measuring technique to reliably reveal close details in displacement or strain maps. The point is that this quantity changes as a function of some parameters arbitrarily set by the user such as the subset size. With commercially available DIC packages, it can be said that the strain resolution can typically reach 10−3 over small zones having some millimeters in size, with a field of view equal to some squared centimeters [10, 11]. More detail on DIC can be found in Ref. [12] for instance.

The Grid Method

DIC is user-friendly but also has some disadvantages. First, random speckles do not constitute the optimal pattern with respect to sensor noise propagation [13]. This is potentially an issue when the information only barely emerges from the noise floor. In the same way, employing a random pattern induces a pattern-induced bias (PIB) [14], especially in case of high-frequency strain distribution [15]. This is potentially the case when some microstructures like martensite needles appear in an austenitic specimen. Finally, DIC relies on a minimization problem, which is resolved iteratively. Thus, the computational cost may be significant if large images are considered, or if refined pixelwise calculations are needed, or if a large number of images are to be processed. This has led some authors to consider alternative approaches such as the GM, which consists in relying on periodic patterns instead of random ones. In this case, the periodic pattern is considered as a carrier and the displacement at any point as a modulation of the phase of this carrier. Fourier analysis is employed to extract this modulation and retrieve the displacement field from the images. The benefit is that the noise in final maps caused by sensor noise propagation is lower than with DIC [9], if not minimal when periodic patterns such as checkerboards are used [16]. In Ref. [17], it is shown that ceteris paribus, the compromise between spatial resolution and noise affecting displacement maps due to camera sensor noise propagation is about three times better with checkerboard images processed with a suitable spectral method than with speckle images processed with DIC. In addition, PIB is minimized (if not virtually eliminated) with periodic patterns [14, 16]. The strain maps deduced by differentiating displacement maps can even be enhanced by using deconvolution, all spatial frequencies involved in the strain maps being then provided without any bias up to a certain cutoff frequency [16]. Finally, the determination of the displacement is very fast, the calculation being performed in the Fourier domain [9, 16, 18]. Note that this technique can also be applied at microscale [19] but no use on SMA at small scale has been reported in the literature to the best of the authors’ knowledge. A first limitation of the GM is that only 2D measurements on flat specimens can be performed with the present version of this technique even though out-of-plane measurements are potentially measurable. The second one is that deposition of periodic patterns onto flat surfaces requires more time and effort than depositing a speckle for DIC [20]. Indeed, speckle patterns can be deposited with a mere airbrush for instance. It means that the use of periodic patterns is justified only in situations for which a good compromise between spatial resolution and measurement resolution is required to reliably observe displacement and strain maps on flat specimens, and/or if many images are to be processed, which is potentially the case with SMAs.

Moiré Interferometry

MI extends the range of conventional moiré to measure displacements with very high sensitivity. A diffraction grating is first deposited onto the surface of the specimen. Its frequency typically lies between some hundreds to some thousands of lines per millimeter, depending on the desired resolution for the measuring system. This grating is then illuminated by two beams of coherent light which are inclined with respect to the normal of the surface of the specimen. The angle of one beam is the opposite of the other, so these beams generate interferences in the zone of their intersection. The resulting virtual grating acts as the reference grating of classic moiré arrangement, the deformed grating being the one deposited onto the surface of the specimen. Both gratings interact and, thus, form moiré fringes, which are captured by a camera. The fringe images recorded during a test are then processed like those of classic moiré to deduce the displacement field. Among the three methods presented here (DIC, GM, and MI), the latter is certainly the one which provides the highest sensitivity. For instance, Ref. [21] reports that with a diffraction grating of 1300 lines per millimeter and a wavelength of 500 nm for the light, two consecutive fringes represent a difference of 350 nm for the displacement. It should, therefore, be employed in situations for which the displacement remains of low amplitude. Otherwise, the number of fringes may become too large to be processed to extract the sought displacement field. More details on this technique are available in Refs. [22,23,24,25] for instance.

Infrared Thermography (IRT)

Infrared (IR) thermography enables temperature measurement without any contact, directly from the electromagnetic waves emitted by an object in suitable ranges of wavelengths, namely between 1.7 and 14 µm [26]. There are two types of IR detectors: photon detectors (operating at cryogenic temperatures) and bolometer detectors (operating at room temperature). In general, “cooled” (quantum) cameras have better performance with reduced integration time, better sensitivity, and reduced noise compared to “uncooled” (microbolometer) cameras. Specific precautions must be taken for quantitative measurements. Some metrological considerations must also be taken into account [27]. As each IR detector of the focal plane array has its own response, a Non-Uniformity Correction procedure must be performed using a black body. The thermal emissivity of the surface of the material sample under study must also be known. For metals, it is advisable to use high emissivity paints, which are applied onto the specimen surface, but paint adherence issues may occur when the specimen deforms. When the surface of the specimen is curved (e.g., for wires or cylinders), the apparent emissivity changes as a function of the angle of view of the camera. However, it remains relatively constant up to a certain angle, which allows a simple processing of the raw output of the camera for a temperature measurement along a generatrix of a wire for example. Even for a thermal emissivity close to one, the temperature of the specimen environment must also be known to subtract remaining reflections. More generally, parasitic reflections must be minimized. A dummy specimen placed next to the mechanically tested one can be used for this purpose. An IR thermographic system is characterized by its so-called noise equivalent temperature difference (NETD) and by the spatial resolution of the thermal images. NETD corresponds to one standard deviation of the measurement noise, namely the temperature resolution. Cooled cameras can reach a NETD of about 20 mK in optimized conditions, with more than one million pixels for the latest generation of cameras.

In the context of thermomechanical characterization of materials, the analysis of temperature fields is difficult because of heat diffusion within the specimen. A heat exchange also takes place between specimen and its environment, for instance with the jaws of the testing machine and the ambient air. However, IR thermography can be employed to assess the fields of heat power density (simply called “heat source”) produced or absorbed by the material due to a change in its mechanical or crystalline state. The reconstruction of heat sources can be performed using suitable versions of the heat diffusion equation. Two main approaches are available in the literature to estimate heat sources in thermomechanics of materials: by minimizing the error between measured temperature fields and theoretical temperature fields provided by a model [28] or by directly calculating the terms of the heat equation from experimental thermal data [29]. A critical point in the latter approach is the estimation of the conduction term. Indeed, this term involves second partial derivatives and these quantities are strongly impacted by noise which unavoidably affects thermal images.

3D X-ray Diffraction

3D-XRD has emerged in the last 20 years [30, 31]. This is a microscopy technique for volume measurement performed by using X-ray energy between 30 and 100 keV. It enables the user to obtain the shapes and the crystal orientation of grains in polycrystalline specimens. For full-field measurements under mechanical loading, the strain tensor is measured on a grain-by-grain basis. The technique also enables the experimentalist to reconstruct strain and stress distributions within individual grains by using small beams and large grains [32,33,34]. The stress tensor can then be deduced assuming a linear elastic behavior of the crystal. 3D grain maps of deformed polycrystalline specimens are reconstructed from individual diffraction spots. Each diffraction spot is obtained from the diffraction pattern, which gives the crystallographic parameters of the material. The strain tensor of each grain is obtained from the comparison between the undeformed and deformed configurations of the lattice. In polycrystalline materials, the resolution can be as low as about 1 µm in position and, after [35], the measurement resolution is 1E-04 for strain and 20 MPa for stress.

The main advantage of 3D-XRD is that no specimen preparation is required. In addition, large and complex-shaped specimens can be studied. The rate of the data acquisition depends on the size of the beam and the region of interest, the instrumentation, and the speed of the detector. The acquisition can be fast enough to allow measurements in a few minutes. Full details on this technique can be found in Ref. [30].

Focus on Some Typical Examples of SMA Characterization with Full-Field Surface Measurement Techniques

There are many papers available in the literature, which report studies where full-field surface measurement techniques are used to characterize SMAs. A classification will be given later on in this paper. Providing a short review of all of them is out of the scope of the present contribution. It is, however, of interest to focus on a limited number of references, which typically reflect the benefit of using full-field measurement techniques for SMA characterization. Hence, the aim of this section is to briefly present some of these papers, by highlighting in each case the type of SMA which was studied, the type of specimen, test, and measuring technique which were employed, as well as the phenomena that could be observed and analyzed mainly thanks to the fact that full-field measurement techniques were employed instead of classic measuring tools.

Example 1: Performing DIC and IRT on NiTi Wires [36]

NiTi SMAs are mainly commercially available as wires, so many studies report results obtained with tensile tests performed on wire specimens. Ref. [36] provides various tips and tricks for the best characterization of such specimens with DIC and IRT. The authors present strain and temperature distributions during the mechanical stabilization of a superelastic wire over several cycles. Indeed, a repeatable behavior is crucial for successfully employing SMAs in engineering applications. Since as-received straight annealed NiTi wires are known to exhibit significant changes in their response during the first transformation cycles (mechanical training), the authors observed the evolution of the strain and temperature fields during the first load-unload cycles at constant macroscopic strain rate. In addition to discussing the experimental results, the authors give practical recommendations concerning specimen preparation, experimental setup, and data post-processing. Stereo-DIC was applied to measure the longitudinal strain. Figure 1a and b shows typical strain and temperature maps, respectively. They were obtained at the same time, during the loading phase of a superelastic NiTi wire. It can be seen in Fig. 1b that the strain distribution enables us to precisely locate a transformation front between austenite (A) and martensite (M+) thanks to the sudden strain increase. The 1D distribution of the longitudinal strain was then plotted over time during the first cycles of the test, which gives Fig. 1c. The spatiotemporal kinetics of the transformation can be evidenced in this figure thanks to the high difference between the strain level in austenite and martensite. Over the cycles, one or several transformation fronts are, thus, tracked in parallel to the evolution of the engineering stress, see the black curves superposed to the spatiotemporal strain distribution in Fig. 1c. The authors also show that it is possible to distinguish the actual material response and possible experimental problems such as slippage of the specimen in the jaws of the testing machine. This phenomenon sometimes appears with SMA wires, when phase transformation occurs in the clamped zones.

Fig. 1
figure 1

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Experimental Techniques, Tips and tricks for characterizing shape memory wire part 5: Full-field strain measurement by digital image correlation, B. Reedlunn, S. Daly, L. Hector, P. Zavattieri, and J. Shaw, copyright 2013 [36]

Analyzing with DIC and IRT the mechanical stabilization of a superelastic NiTi SMA wire.

As A → M+ and M+→ A transformations are accompanied by latent heat release and absorption, coupling strain and temperature measurements coupling provides additional information where the spatiotemporal distribution of the temperature along the specimen is shown, see Fig. 1d. In their paper, the authors discuss the changes observed in Fig. 1c and d as well as their coupling. It can be seen that deducing the location of the transformation fronts from the temperature distribution is more difficult because of heat diffusion within the specimen (see next section). Heat diffusion tends to smooth out the temperature fields over time. Thus, by nature, the temperature change distribution is often smoother than the strain distribution. However, this paper illustrates the fact that the spatiotemporal thermal signature is complementary to the mechanical response.

Example 2: Performing Deformation Calorimetry in a Superelastic NiTi SMA Wire by IRT and Heat Source Reconstruction [37]

As temperatures are impacted by heat diffusion within the specimen and heat exchange with the environment, another option for the analysis of thermal maps is to retrieve the heat source distribution from the temperature distribution by using the heat diffusion equation. It is worth remembering that a heat source is defined here as the power density of heat produced or absorbed by the material itself (in W m−3 or in K s−1 when multiplied by the volumetric heat capacity as in Fig. 2). Ref. [37] is a typical example of this type of deformation calorimetry. In this study, the authors performed a superelastic cycle on a wire specimen made of stabilized NiTi SMA. The response of this specimen was studied with IR thermography. In addition to considering the heat source distribution instead of the temperature distribution, a difference with the preceding example is that the test is performed here at constant force rate instead of constant displacement rate. A consequence is that the plateau of the stress/strain curve is crossed at a much higher rate, enforcing the specimen to transform quickly. Figure 2a shows the spatiotemporal distribution of the temperature change in this specimen during the test. Rapid increase and decrease in temperature logically follow the rapid changes in engineering strain (black curve): see the four thermal waves in Fig. 2b and c, respectively (two waves upon loading and two waves upon unloading). The main point here is that the spatiotemporal transformation kinetics is much better revealed by considering the heat source distribution depicted in Fig. 2d and e than the temperature change distribution depicted in Fig. 2b and c. Associating these heat sources with thermomechanical couplings enabled then the authors to identify martensite nucleation events (1 to 10) and martensite merging events (11 to 20) upon loading, as well as austenite nucleation events (21 to 30) and austenite merging events (31 to 41) upon unloading. Based on the heat source data, the authors found that the mechanical dissipation heat associated with the nucleation and melting events corresponds to about 25% of the released/absorbed latent heat.

Fig. 2
figure 2

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Experimental Mechanics, Reconstruction of Heat Sources Induced in Superelastically Loaded Ni–Ti Wire By Localized Deformation Processes, A. Jury, X. Balandraud, L. Heller, P. Šittner, and M. Karlik, copyright 2020 [37]

Analyzing with IRT and heat source reconstruction the calorific response of a stabilized NiTi SMA wire subjected to a force-controlled superelastic cycle.

Example 3: Examining with Stereo-DIC the Response of a NiTi Tube Subjected to Tensile, Compression, and Bending Tests [38]

Although NiTi SMAs are mainly available in the form of a wire, other shapes such as tubes can also be found. Consequently, other tests than the classic tensile test such as compression or bending can be performed in this case, and full-field measurements reveal other phenomena. In this spirit, stereo-DIC was used in Ref. [38] to obtain the axial strain fields on the outer surface of a superelastic NiTi tube. Uniaxial compression and four-point bending were applied on a tube specimen in addition to uniaxial tension. Figure 3 shows typical strain maps obtained during these tests. In tension, propagation fronts are classically observed upon loading (maps 2 to 7 in Fig. 3a) and unloading (8 to 12). Finger-shaped strain patterns inclined with respect to the loading direction are clearly visible at the interface between the austenite and martensite zones. In compression, no such localization was observed, neither upon loading (maps 2 to 7 in Fig. 3b) nor upon unloading (8 to 12), although a transient buckling was evidenced in map 10. Consistently with the tension–compression asymmetry, the bending test revealed strain localization in the part of the specimen subjected to tension, and no localization in the other part subjected to compression. A shift of the neutral axis toward the compression side can also be observed, see Fig. 3c. DIC strain measurements provide details enabling the authors to discuss the classic assumptions of elementary beam theory in the case of SMAs.

Fig. 3
figure 3

Reprinted from Journal of the Mechanics and Physics of Solids, Vol 63, B. Reedlunn, C.B. Churchill, E.E. Nelson, J.A. Shaw, and S.H. Daly, Tension, compression, and bending of superelastic shape memory alloy tubes, pages 506–537, copyright 2014, with permission from Elsevier [38]

Analyzing with stereo-DIC the strain distribution at the outer surface of a superelastic NiTi tube subjected to a uniaxial tension, b uniaxial compression, and c four-point bending.

Example 4: Comparing at Different Temperatures the Strain Fields Measured with DIC in a Superelastic NiTi Thin Sheet [39]

In experimental mechanics, DIC is mainly used to observe 2D displacement and strain fields on the outer surface of flat specimens, so there are many such examples in the SMA literature. Ref. [39] discusses for instance the transformation kinetics in a flat superelastic NiTi thin specimen. The authors mainly focus on the difference in the mechanical response observed for different ambient temperatures. In particular, the stress plateau upon unloading tends to disappear and the residual strain to increase as the temperature increases. Figure 4 shows 2D maps of the longitudinal strain in uniaxial tension. They were obtained at 25 °C and 100 °C. Strain localization is observed upon loading at 25 °C and 100 °C. The sharp transitions between low-strain and high-strain regions can be observed in Fig. 4a and b. They correspond to austenite and martensite, respectively. The same phenomenon occurs upon unloading at 25 °C, whereas the reverse phase transformation appears to be homogeneous at 100 °C. Coupling DIC measurements obtained during a set of various experiments with a suitable model enabled the authors to discuss the impact of local strain rate on the residual strain obtained at the end of the unloading stage.

Fig. 4
figure 4

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Shape Memory and Superelasticity, Local Mechanical Response of Superelastic NiTi Shape-Memory Alloy Under Uniaxial Loading, Y. Xiao, P. Zeng, L. Lei, and H. Du, copyright 2015 [39]

Comparing with DIC the strain fields in a superelastic NiTi thin sheet at two ambient temperatures.

Example 5: Revealing with GM the Microstructures Appearing in a Superelastic CuAlBe Flat Single Crystal [40]

As mentioned in Sect. 2 above, DIC is the most popular full-field measurement technique, but it suffers from some limitations. In particular, recent papers [9, 17] clearly show that using regular patterns instead of random ones and processing the corresponding images with a spectral technique instead of DIC lead to displacement and strain maps with a better compromise between spatial resolution and measurement resolution. This favors the observation of localized phenomena like those occurring during phase transformation in SMA specimens. This is the reason why GM has been used in Ref. [40] to study the microstructures which appear in a superelastic CuAlBe flat single crystal subjected to a tensile test. Figure 5 shows typical longitudinal strain maps obtained at different stages of the test. Martensite needles, habit planes, and martensite twins were identified, see also the video attached to the online version of Ref. [40]. Despite the absence of macroscopic residual strain at the end of the mechanical cycle observed in Fig. 5a, significant differences were observed in terms of microstructures between the loading and unloading phases. While loading was simply accompanied by the nucleation and merging of parallel martensite needles, see Fig. 5b, a much more complex microstructure evolution is revealed upon unloading in Fig. 5c, which may explain a part of the mechanical hysteresis.

Fig. 5
figure 5

Reprinted from Mechanics of Materials, Vol 45, D. Delpueyo, M. Grédiac, X. Balandraud, and C. Badulescu, Investigation of martensitic microstructures in a monocrystalline Cu–Al–Be shape memory alloy with the grid method and infrared thermography, pages 34–51, copyright 2012, with permission from Elsevier [40]

Employing GM to measure the strain distribution in a superelastic CuAlBe single crystal (see also the video available online).

With full-field measurement techniques, experimentalists have easy access to other strain components than the longitudinal one during uniaxial mechanical loading, which gives valuable information to analyze phenomena occurring in the specimen under test. For instance, the transverse strain map depicted in Fig. 5d shows that a different martensite variant is involved at the bottom part of the specimen. It is separated from the already transformed zone by a thin austenite band, which accommodates the two martensite variants and, thus, prevents the specimen from full transformation to martensite.

Example 6: Applying DIC to Reveal Microstructures at the Grain Scale [41]

While single- and multi-crystals can be used to have large martensitic microstructures in copper-based SMAs, a need for measurements at microscale is required in order to better understand the thermomechanical response of NiTi. Small-scale full-field measurement techniques can again help the experimentalist get valuable information to reach this goal. As an example of such measurements, Fig. 6 shows longitudinal strain fields extracted from SEM images and high-definition DIC applied on several grains with a mean size of 35 µm [41]. Strain fields for the maximum value of the uniaxial loading (Fig. 6a) and after unloading (Fig. 6c) show that a part of the strain was recovered (Fig. 6b). Interesting conclusions were drawn by the authors by correlating strain maps with EBSD maps. By analyzing the orientation of the interfaces and considering Schmid factors, the authors showed that recoverable strain is due to the martensitic transformation, for which more than one variant per grain can be activated. They also showed that the selection of martensite variant can be influenced by shear transmission across grain boundaries. The strain levels that were locally measured are in good agreement with their theoretical counterparts for single crystals. Besides, non-recoverable strains are shown to be due to deformation slip in austenite, twinning in martensite and residual martensite. The benefit of using a full-field measurement technique at small scale to explain phenomena observed at a greater scale, especially when coupled with other analysis means (here EBSD), is illustrated here since these conclusions could not be drawn from classic global stress–strain curves.

Fig. 6
figure 6

Reprinted from Materials & Design, Vol 191, E. Polatidis, M. Šmíd, I. Kuběna, W.-N. Hsu, G. Laplanche, and H. Van Swygenhoven, Deformation mechanisms in a superelastic NiTi alloy: An in-situ high resolution digital image correlation study, page 108622, copyright 2020, with permission from Elsevier [41]

Studying at the grain scale with high-definition DIC a superelastic NiTi specimen subjected to uniaxial loading.

Example 7: Characterizing Sharp Austenite/Martensite Interfaces with Moiré Interferometry [42]

A mention to the use of MI can be made here concerning small-scale measurements. Since applications of this technique to SMAs are quite rare in the literature, comparison cannot be made here with other techniques in terms of quality of the obtained results. However, the potential of MI to provide information at the scale of the martensitic microstructures has been successfully demonstrated in some examples. For instance, Fig. 7 shows the displacement fringe patterns in a shape-memory CuAlNi specimen after stress-induced transformation [42]. Several sharp interfaces between austenite and martensite are visible in a zone smaller than 1 mm2. Martensitic domains feature dense fringes (because of high-strain level) compared to austenitic domains, where only elastic strains can be observed. Austenite wedges inside martensite are also evidenced. Various properties were extracted by the authors from the fringe distributions, such as the phase distribution, the strain jump over the interfaces, and the orientation of the habit planes. Only MI reveals such sharp interfaces and allows such refined full-field measurements at the scale of microstructures.

Fig. 7
figure 7

Reprinted from On the Full-Field Deformation of Single Crystal CuAlNi Shape Memory Alloys-Stress-Induced β1 → γ′1 Martensitic Transformation, J. Phys. IV France, 1997, Vol 7, No. C5 [42]

Employing moiré interferometry to observe microstructures in a shape-memory CuAlNi specimen after stress-induced transformation: a horizontal displacement fringes, b vertical-displacement fringes.

Example 8: Coupling DIC and IRT to Perform Deformation Calorimetry [43]

A logical approach when studying SMAs is to couple full-field strain and temperature measurement techniques. The reason is that both the large strain levels (several percents) and the intense heat release/absorption (several kJ kg−1) which are observed are the consequence of phase transformation. Ref. [43] is a typical example of such a coupling on a superelastic NiTi sheet subjected to a load–unload cycle in uniaxial tension. It also describes some practical aspects related to temporal and spatial synchronization. In particular, the authors discuss the difference in spatial resolution of the two systems used to obtain their measurements, namely DIC and IRT. Figure 8a and b shows the variation in time of the 1D distribution of the longitudinal strain and the temperature change, respectively. Both distributions are displayed in the underformed/Lagrangian configuration. Indeed, the synchronization allowed temperature tracking at every material point during the deformation of the specimen. Heat sources could, therefore, be precisely reconstructed, see Fig. 8c. Finally, the temporal integration of the heat sources at every material points provided the value of the local heat produced along the test, see Fig. 8d. Beyond the precise analysis of the spatiotemporal transformation kinetics in NiTi SMAs, various technical aspects were studied in this paper such as the impact of the difference in thermal conductivity of austenite and martensite, which impacts heat source calculation. As a conclusion, such a coupled approach provides a truly comprehensive thermo-mechanical analysis once the practical implementation and processing difficulties are overcome.

Fig. 8
figure 8

Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Experimental Mechanics, Heat Source Processing for Localized Deformation with Non-Constant Thermal Conductivity. Application to Superelastic Tensile Tests of NiTi Shape Memory Alloys, H. Louche, P. Schlosser, D. Favier, and L. Orgéas, copyright 2012 [43]

Coupling DIC and IR thermography for the thermomechanical analysis of a superelastic NiTi sheet specimen subjected to a uniaxial loading–unloading cycle: a variation in time of the longitudinal strain distribution, b same for the temperature changes, c same for the heat sources, d same for the heat.

Example 9: Using 3D X-ray Diffraction to Reveal Heterogeneous Stress Fields in a NiTi Wire During a Uniaxial Tensile Test [35]

The preceding examples deal with 2D measurements only. The reason is that except one paper which is discussed in this section, all the papers found in the literature concern surface measurements. As discussed in Sect. 2.5, XRD allows strain tensor measurements in the bulk with the so-called 3D-X-ray technique. The stress tensor is then deduced grain by grain assuming that the constitutive equations are known a priori. To the best of the authors’ knowledge, this technique has been applied only once for SMAs, namely in Ref. [35]. The objective was to observe the heterogeneity of the stress distribution in austenite in the vicinity of a martensitic band front (MBF), see Fig. 9. The stress could not be evaluated in martensite because of the high number of refraction angles and the fact that the measurement resolution of the technique was not sufficient to detect all of them. Upstream of the MBF (z > 125 µm), a heterogeneity of the stress distribution is visible. Looking at the surface of the wire, the MBF classically appears to be large and perpendicular to the longitudinal axis. Thanks to 3D-XRD, it was possible to observe the shape of the MBF, which is a cone. The angle of this cone is about 55°, which is consistent with the results obtained in NiTi sheets and tubes with other techniques. This angle allows the minimization of the deformation incompatibilities at the macroscopic interface between the elastically deformed austenitic grains on the one hand (about 1%), and the grains already transformed into martensite on the other hand (about 10%). Beyond the axial stress component, the complete stress tensor was measured in the austenite grains to go further in the analysis. For example, it is shown that the principal direction attached to the maximum principal strain is aligned with the wire axis in all the grains except those located on the conical interface between austenite and martensite, see additional figures attached to Ref. [35]. The main results of the study are that the local stress in austenite grains is modified ahead of the nose of the cone-shaped buried interface where the martensitic transformation begins, and that elevated shear stresses at the conical interface explain why the transformation is localized.

Fig. 9
figure 9

From P. Sedmák, J. Pilch, L. Heller, J. Kopecek, J. Wright, P. Sedlák, M. Frost, and P. Šittner, Grain-resolved analysis of localized deformation in nickel-titanium wire under tensile load, Science, 2016, 353, p 559–562 [35]. Reprinted with permission from AAAS

Grain-resolved stresses in austenite, evaluated by the 3D-XRD method.

Since many other examples than those discussed above are available in the literature, the idea is now to provide the reader with a comprehensive classification of papers on SMAs where full-field measurement techniques are involved. This is the aim of the following section.

Classification of the Papers Found in the Literature

We propose in this section a classification of the papers found in the literature, in which the full-field measurement techniques described above are used to characterize SMAs. The Web of Science databaseFootnote 1 was used to identify the papers. Note that the papers which mention the use of a full-field measurement technique without displaying thermomechanical fields (displacements, strains, temperatures,…) are not accounted for in the following tables.

The reader will first find in Table 1 these references classified according to the type of measurement technique used, alone or in combinations with others. As expected by the two main properties associated with phase transformation in SMAs, namely large deformations and intense heat release/absorption, the two most widely used techniques are DIC and IRT. They are often used in a complementary manner. The studies reporting the use of DIC are more numerous than those reporting the use of IRT, but it is worth noting that the first publication involving DIC was published after the first publication involving IRT: 2002 and 1997 respectively, see Fig. 10a and b. The number of studies using DIC increases almost continuously over the years, reaching 26 in 2020. As a general remark, there is a strong diffusion of DIC in the experimental mechanics community, thus, explaining this increasing trend for SMA characterization. For IRT, the number of publications has stagnated since the 2010s, with about 10 per year. However, this number can be considered as significant compared to the applications to other types of materials than SMAs. This is certainly due to the strong and localized thermal signature of phase transformations in SMAs, which means that SMAs are “good candidates” for IRT applications. The stagnation of the number of publications using IRT can be explained by a number of pixels that struggles to increase in cooled IR cameras compared to their counterparts designed for the visible domain. It is worth noting that cooled IR cameras exceeding one million of pixels are now available. This should, therefore, bring a new impetus to the study of SMAs with such tools in the future. It can also be noted that few IRT studies (less than 10%) involve heat source reconstruction (HSR). This approach for processing thermal data should be used more frequently to complement strain measurements, in particular because the use of both types of measurements enables the calculation of energy balances. Figure 10c shows that MI, GM, and 3D-XRD were rarely used. After a few studies in the late 1990s and again in the late 2000s, MI no longer appears in the literature. GM has only been used three times, between 2012 and 2020. These two techniques certainly deserve to be more frequently used because they would bring additional information compared to DIC and IRT, especially thanks to their good compromise between measurement resolution and spatial resolution. To the best of the authors’ knowledge, strain field distributions in the bulk obtained with 3D-XRD are displayed in only two publications. The limited access to this type of measuring device probably explains this small number. Finally, it is worth noting that Refs. [44, 45] mention the use of photoelasticimetry in complement to IRT and DIC + IRT, respectively, for the characterization of a composite containing one SMA fiber.

Table 1 Classification by type of measurement technique
Fig. 10
figure 10

Number of papers on SMAs over the years involving a DIC, b IRT, and c MI, GM, and 3D-XRD

Table 2 gives the list of references according to the chemical elements of the tested SMA. The monocrystalline or polycrystalline character is also reported. Multi-crystals (containing a few grains) are gathered with single crystals. As expected, most of the studies described in the literature concern polycrystalline NiTi specimens, so this table provides the references only for the other types. Polycrystalline NiTi SMAs being the most widely used in engineering applications because of their biocompatibility, their stability, and the possibility of tuning their properties by cold working and heat treatment, they are the most widely studied with full-field measurement techniques. It is, however, quite surprising to note that copper-based SMAs are not so much studied despite their use in a variety of existing or promising applications such as damping devices or elastocaloric systems. For NiTi alloys, only two references concern single crystals, which are to be compared to the about 200 references found for their polycrystalline counterparts. The trend is opposite for NiTiHf: five references among eight deal with single crystals for this type of alloy. Single-crystal copper-based alloys are also more studied than polycrystalline ones but the total number of studies for these alloys is small. Studies (in small numbers) on single crystals exist for other types of alloys, as also shown in the table. Single crystals should, however, be more widely studied in the future because they potentially give more insight into the understanding of martensitic microstructures than polycrystals. Besides, small-scale measurements (allowing access to microstructures within grains) are also promising to build relevant macroscopic behavior models for polycrystals. It can be noted that there is only a few studies on areas smaller than 1 mm2, see Table 3 which gives the classification of the publications with respect to the size of the region of interest. In this table, it can also be noted that most of the references correspond to an observation of areas smaller than 100 mm2, which can be considered as small compared to full-field measurement studies dealing with other types of materials such as non-active ones. This is due to the fact that many studies on SMAs are carried out on NiTi wires of which diameter seldom exceeds a few millimeters, which penalizes measurements on long specimens. The use of new cooled IR cameras with sensors featuring more than one million pixels should allow to increase the length of the wires or cables under study, which should be beneficial for engineering applications.

Table 2 Classification by type of alloy
Table 3 Classification by size of the zone observed by full-field measurement technique

Before concluding, the reader can find in Tables 4 and 5 a classification of the publications according to the sample geometry and the type of loading. It can be seen in the first table that most of the publications concerns stress-induced transformation, i.e., under mechanical loading. This can be explained by the fact that managing a thermal loading while performing a measurement by camera is more complex to achieve than applying a mechanical loading at constant room temperature. Besides, a temperature-induced transformation leads to a “modification” of the thermal loading due to the production/absorption of latent heat (heat production during cooling and heat absorption during heating), this makes the analysis of the results as complex. It can also be seen that only two references concern the use of a magnetic excitation. It was for a magnetic NiMnGa single crystal. In practice, the authors performed DIC under magneto-thermo-mechanical loading, namely cyclic magnetic field, constant compression load and variable heat exchange conditions. Table 5 focuses on some specific types of mechanical loadings. It shows that there is a wide range of specimen geometries and types of tests discussed in the literature for which full-field measurement systems have been used.

Table 4 Classification by type of specimen, with a distinction between thermal, mechanical, and magnetic loadings
Table 5 Classification by type of specimen and type of test (apart from the classical tensile test)

Conclusion and Suggestions for Future Work

This review on the use of full-field surface measurement techniques for SMA characterization clearly shows that these techniques have gained popularity in the recent years. Their ability to reveal rich microstructures which appear in SMA specimens during thermomechanical tests, and the fact that various commercial codes are available for some of these techniques, certainly explain this success.

The classification proposed in this paper indicates that a wide range of materials, techniques, tests, and specimen geometries are concerned by these techniques. An important point which should be underlined is that full-field measurement techniques are not yet stabilized, in the sense that their development should be seen as an evolutionary process. This is illustrated by the fact that no standard is currently available to calibrate these systems and assess their metrological performance in a common and unified way. In the same way, the number of pixels of camera sensors, both in the visible and infrared range, is steadily increasing. The same remark holds for the performance of computers in terms of speed and memory size. Future results will certainly involve larger image sizes and image processing techniques leading to a better compromise between measurement and spatiotemporal resolutions. We can also expect that artificial intelligence will bring new post-processing tools. In conclusion, we would like to highlight the following topics, which certainly deserve dedicated studies in the near future:

  • Techniques such as those suitable for strain and temperature measurements have already been coupled in some studies. This approach should certainly be rolled out in a more systematic way, in particular because such techniques offer complementary information, thus, enabling the experimentalists to carry out energy balance for instance;

  • Displacement and strain fields are generally obtained with DIC, which relies on a random marking of the surfaces of interest. However, it has been shown that using periodic patterns processed with a spectral method gives a better compromise between spatial and measurement resolutions, which is crucial for a better characterization of sharp details in strain maps. Such techniques, therefore, deserve to be used more frequently when complex microstructures are to be characterized;

  • Displacement and strain measurements are often performed along one direction only, for instance the longitudinal direction for a uniaxial tensile test, while full-field measurement systems generally provide the three in-plane components at the surface of the specimen. These three components should be more often taken into account in the analysis of the results obtained;

  • Despite the richness of the information provided by 3D-XRD, very few papers involving this technique for measurements in the bulk have been found in this review. 3D-XRD can be used to obtain various quantities such as crystallographic orientation fields, but the measurement of strain fields has only been seldom performed for the analysis of phase transformation in SMAs;

  • Temperature changes are often used as primary quantities to analyze phase changes in SMAs. It is, however, now well established that such quantities are prone to parasitic effects, while heat sources provide reliable information about the heat signature of various mechanical phenomena. Experimentalists using IR thermography should, therefore, bear in mind this possibility, the price to pay being to extract heat source maps from temperature change distributions by using a suitable image processing technique relying on the heat equation;

  • Single-crystal specimens are more difficult to get from suppliers than polycrystal ones. However, they give access to the “elementary” microstructures which are at the basis of many SMA properties. They should, therefore, be considered with more attention when using full-field measurement techniques;

  • MI seems to have nearly disappeared in the most recent papers reported in this study. This is probably a consequence of the popularity and improved ease of use of DIC. Yet, MI still remains incomparable to reveal sharp details in microstructures at the microscale;

  • Most of the publications concern the use of full-field measurement techniques to investigate the stress-induced transformation at ambient temperature. It would also be of interest to further study the temperature-induced transformation as well as the magnetic field-induced transformation (for magnetic SMAs) with full-field measurement techniques;

  • Finally, too few studies deal with strain measurements at the microscale. SMA researchers should be aware of that some full-field measurement techniques are adaptable to the microscale with some caution. They provide in this case valuable information to understand mechanisms occurring at the grain level of polycrystals.