The Effect of Texture on Stress-Induced Martensite Formation in Nickel-Titanium K Kim and S Daly Department of Mechanical Engineering, University of Michigan 2350 Hayward St. Ann Arbor, MI 48109
[email protected] Abstract An experimental study was performed to investigate the effect of texture on stress-induced martensitic phase transformation in the shape memory alloy Nickel-Titanium (Nitinol). Thin sheet specimens of Nitinol were examined under uniaxial tensile loading using three-dimensional digital image correlation in order to spatially and temporally track strain localization indicative of martensitic transformation. Tensile specimens were fabricated along directions oriented 0° (RD), 45°, and 90° (TD) to the rolling direction of the sheet and subjected to 50 cycles at prescribed strain rates of
ε g = 10-4 ,10-3 , and 10-2s-1 . It was found that upon loading, specimens unfavorably oriented for transformation (TD specimens) nucleated a greater number of deformation bands due to a smaller difference between nucleation and propagation stresses, and also accommodated less axial strain inside the band and more axial strain outside of the band. The unfavorable (TD) specimens also exhibited a stronger cycle-to-cycle similarity in the strain accommodated inside the deformation band, which has important implications for the design of SMA structures for fatigue applications. Finally, the (primarily martensite) region of the deformation band(s) consistently showed significantly stronger cycle-to-cycle similarity than the (primarily austenite) region outside of the band(s), regardless of specimen texture. 1. INTRODUCTION There is growing interest in the utilization of shape memory alloys (SMAs) for engineering applications due to their high work densities and other advantageous properties. SMAs exhibit unique behaviors, namely the shape memory effect and superelasticity (pseudoelasticity). The shape memory effect is a phenomenon in which the material reverts to its original shape after deformation upon unloading and heating above a critical transformation temperature. Superelasticity refers to the ability of these alloys to recover large amounts of strain when loaded above their critical transformation temperature. The superelastic properties of Nitinol are utilized in medical devices [1] amongst many other applications. Although the shape memory effect and superelasticity both manifest through a solid-to-solid phase transformation between a B2 cubic austenite (A) and a monoclinic martensite (M) phase, they do so by different paths. The path of the shape memory effect starts below the austenite finish temperature (Af) in a twinned martensite phase. As the material is deformed, the twinned martensite becomes detwinned. When the deformed material is then heated above Af, the detwinned martensite transforms to austenite, and the material reverts to its original shape. Though the austenite then transforms to twinned martensite as the material cools, there is no net shape change during this transformation. The entire path of superelasticity, however, occurs while the material is above its Af temperature. The initial phase of the material is To Appear in Smart Materials and Structures 1
austenite, which transforms to detwinned martensite under mechanical deformation. During unloading, the stress-induced martensite transforms back to austenite with relatively small permanent strain. In the stress-induced A → M phase transformation, one or more bands of primarily martensite appear as large localization(s) in the strain field and propagate through the specimen. During the superelastic A → M (M → A) transformation, latent heat is released (absorbed) in loading (unloading). The absorption and release of localized heat in the specimen affects the material behavior, including the stress required for the nucleation and propagation of the martensitic front, the recoverable strain, and the accumulated residual strain. The purpose of this study is to quantitatively examine how transformation parameters, such as the similarity in the strain incurred by martensitic transformation, evolve during superelastic deformation as a function of cycling, strain rate and texture. The processes used to produce SMA sheets and wires impart crystallographic textures that affect the shape memory and superelastic properties. Crystallographic effects are largely ignored in commercial computational tools for the design of Nitinol devices, which Mehta et al. demonstrated can lead to large deviations between the predicted and the actual response of the material [2]. Recent work by Barney et al. has demonstrated that local crystallographic effects, such as the path the martensitic transformation follows through the microstructure, can greatly impact the superelastic response [3]. In order to most efficiently and safely use Nitinol in superelastic applications, it is critical to understand the effect of microstructure and crystallographic texture on the stress-induced martensitic phase transformation that underlies superelasticity. Although the effect of crystallographic texture on certain macroscopic properties like nucleation stress and residual strain has been well characterized, the local dependencies of transformation are not well understood. This study examines crystallographic texture effects on the local distribution of strain (indicative of transformation extent), and additionally, its impact on cycle-to-cycle transformation similarity. The interplay between transformation characteristics, crystallographic texture, strain rates and cycling are investigated.
1.1 Effect of Cycling Previous investigations have explored the influence of cycling on the stress-induced martensitic phase transformation that SMAs exhibit during superelasticity (for a detailed review of fatigue in Nitinol, please see [4] and the references contained therein). It is known that the stresses required for the nucleation and propagation of stress-induced martensite significantly decrease with cycling until stabilization (shakedown) is reached [5-10]. This decrease is likely caused by the retention of residual stresses associated with local microstructural-level deformations [11], and by the development of a dislocation structure and the retention of martensitic nuclei that act to assist martensite formation in subsequent cycles [12]. However, the stresses required for the start of the M → A transformation upon unloading remain relatively constant with cycling. It has also been observed that the rate of residual strain accumulation decreases and stabilizes as the cycle number increases [5, 6, 8-10]. Stress-induced martensitic phase transformation in Nitinol is thermally sensitive [10, 12-14]. One example of this is the increase in the accumulation of residual strain with cycling that occurs at higher temperatures, conjectured to be due to a decrease in the stress required for slip and an increase in the stress required for phase transformation at higher temperatures that results in slip taking an progressively
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more dominant role [5]. Because of this dependence on temperature, the phase transformation characteristics are sensitive to applied strain rate [8, 13, 15]. At slow strain rates on the order of
ε = 10-5 s-1 and smaller, the characteristics of phase transformation were observed to be independent of strain rate due to the inadequate accumulation of latent heat [16]. Temperature gradients in the material are small, and the macroscopic stress-strain curves exhibit a relatively flat stress plateau during which a single martensitic front nucleates and propagates through the specimen. At faster strain rates, like ε = 10-2 s-1 , a local temperature rise can occur at the martensitic front due to the ineffective escape of latent heat, causing the nucleation of numerous fronts and an inclination in the stress plateau of the macroscopic curve [13]. Prior strain rate sensitivity studies indicate that as the applied strain rate becomes faster than nominally 10-3 s-1, both the stress required to nucleate the martensitic front and the amount of energy dissipated significantly increase. In experiments performed on Nickel-Titanium at very fast strain rates (4200 s-1), transformation appeared to change from a diffusionless and shear-like mechanism to a dislocation-based slip mechanism, where the stress plateau disappeared and the stress-strain response resembled that of an ordinary austenitic metal [8].
1.2 Effect of Texture It is known that the microstructure resulting from rolling, extrusion, and drawing processes significantly impact the amount of transformation strain in stress-induced martensitic phase transformation [17-19]. Thin sheet shape memory alloy specimens oriented along the rolling direction (RD) tend to exhibit relatively large transformation strains [18-20], whereas in contrast, NiTi thin films with a random sputtering texture recover comparatively small strains [21]. Gao and Yi experimentally observed a maximum superelastic transformation strain at an angle of ~30° to the RD, and a minimum value at an angle of ~80° to the RD in thin sheets (thickness of 1 mm) of NiTi [22]. Additional dependencies on crystallographic texture were observed for the A → M transformation stress and the Young’s modulus of the austenite (EA), where both obtained a maximum value at an angle of ~70° to RD. In another study, constant load thermal cycling tests were conducted on a Ti-Ni-Cu alloy [23] to examine the role of texture in determining the amount of transformation strain. Progressing from the RD direction, the transformation strain was relatively constant until an angle of ~60° to the RD was reached, after which point it significantly decreased as the angle increased towards the transverse direction (TD). Bhattacharya and Kohn [24] postulate that in polycrystalline SMAs, these larger recoverable strains can arise from a greater change in crystallographic symmetry during transformation due to an increased number of martensite variants. Crystallographic texture also affects the residual strain accumulation in SMAs, where an unfavorably textured (TD) specimen will exhibit smaller residual strains. Mulder et al. [25] explained this smaller accumulation of residual strain in TD specimens (where the tensile axis is parallel to the TD) by calculating the angular dependence of the Schmid factor for slip for the four possible martensite textures corresponding with the same system in the austenite. They found that the Schmid factor for slip of the TD specimen was close to zero for all four of the textures, leading to less accumulated residual strain. Chang and Wu [26] measured the residual strains in NiTi flat plate specimens (thickness of 1mm) cut at various
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directions to the RD, and also found that the TD specimens exhibited the smallest residual strain; they also postulated that this is due to the small average Schmid factors of the grains in the TD specimen.
2. EXPERIMENTAL METHODOLOGY A cold-rolled thin (254 µm) sheet of polycrystalline Nickel-Titanium, 55 wt% Nickel and 45 wt% Titanium, was obtained from Nitinol Devices and Components (NDC). The austenite finish temperature (Af) was determined to be 1.3°C using differential scanning calorimetry (TA instruments, model Discovery) with the scan rate of 10 °C/min and a sample weight of 35mg (figure 1). Texture was characterized using a Rigaku Rotating Anode X-Ray Diffractometer and is described in detail in Section 3.1. Pole figures and inverse pole figures were obtained from the orientation density function (ODF) calculated using the commercially available MTEX program. Tensile specimens were fabricated using electric discharge machining at 0° (RD), 45°, and 90° (TD) to the rolling direction. Specimen dimensions followed ASTM standard E8 with a thickness of 0.254mm, width of 3.125mm and gage length of 12.5mm. Optical microscopy was conducted on an Olympus SC30 stereo-microscope with an MPlanFL N 20x lens in order to examine the surface of the as-received textured samples as shown in figure 3.
Figure 1. DSC measurement of Nitinol sample. The austenite finish temperature (Af) is lower than the ambient temperature, ensuring that superelastic phase transformation occurred upon loading. Three-dimensional, quantitative full-field strain maps were obtained by digital image correlation (DIC). DIC is a non-contact, in-situ optical technique that measures surface strains by tracking markers on the surface of the specimen [27-29]. It is well suited towards characterizing the nucleation and propagation of martensitic phase fronts through observations of the large strain localizations that accompany these fronts
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[20, 30-32]. In this work, the Biot strain was calculated. Biot strain is defined by E B U I , where U is the right stretch tensor from the polar decomposition of the deformation gradient F R U , with rigid rotation R and identity tensor I . A pattern of randomly oriented, uniformly dispersed, and high contrast black speckles were applied to the surface using a spray gun (model Iwata Custom Micron B) with white titanium oxide paint as a base coat (Golden Airbrush Colors, Carbon Black and Titanium White by Golden Artist Colors, Inc.). Two 5-megapixel gray scale CCDs (model Point Grey GRAS-50S5M) were used to capture images of the specimens during testing. The CCDs each had a 2048 x 2448 pixel field of view and pixel size (on the sensor) of 3.45μm. Camera positioning resulted in a stereo angle between the cameras of approximately 32° and a spatial resolution of 9 μm/pixel. Two fluorescent lights and a light diffuser box were used to illuminate the specimen for fast shutter speeds at high strain rates. The range of exposure time was 23.2–50 ms and the aperture size (f-stop) was f/8. An infrared camera (model Inframetrics ThermaCam SC 1000) was placed between the CCDs to obtain full-field temperature maps. The emissivity of the infrared camera was 0.91 as calibrated by a K-type thermocouple. The experimental setup is shown in figure 2. A 45-kip Instron (model Instron 5585) uniaxial load frame with mechanical wedge grips (model 2736-004, 100kN capacity) was used to perform displacementcontrolled cycling tests up to N=50. Tests were performed under a ramp profile at three globally -4 -3 -2 -1 prescribed (measured by the distance between the grips) strain rates ( ε g = 10 ,10 , and 10 s ) for each
of the RD, 45°, and TD textures. Because these tests were performed under displacement control, the specimen did undergo a small amount of compression at the end of each cycle as residual strain accumulated. The 1st, 2nd, 5th, 10th, 25th, and 50th cycles were simultaneously recorded by the two CCDs and the infrared camera to measure the full-field maps of local strains and temperature. A diffuser light box provides uniform and diffuse light that enables a fast CCD frame rate and minimal blurring. A LabVIEW data acquisition system was used to collect the load (measured by a 1000 lb load cell), grip displacement and time data for cycles N=1, 2, 5, 10, 25, and 50. The LabVIEW data acquisition system and the cameras were connected with a trigger system in order to synchronize image capture. Full-field strain maps were generated using commercial DIC software [27-29] with a subset size of 17 and a step size of 1 using the default cross correlation function in the software. For strain calculations, a 15 pixel wide Gaussian filter was used.
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Figure 2. Experimental setup.
3. RESULTS 3.1 Characterization of Specimen Crystallographic Texture Optical micrographs of three specimens cut parallel, 45°, and perpendicular to the rolling direction of the sheet are shown in figure 3. It was determined by X-ray diffraction (XRD) that the RD specimens had a {110} texture, which is a favorable orientation for large recoverable transformation strains [33, 34] and which showed the largest recoverable strain under the uniaxial loading imposed in these tests. The 45° specimen had a texture that was favorably oriented for large recoverable transformation strains as well, though with a slightly smaller intensity than the RD. The TD specimens had a significantly less favorable texture for transformation strain (and correspondingly exhibited the shortest transformation plateau in the macroscopic stress-strain curves shown in figure 7).
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(a)
(b)
(c)
Figure 3. Optical micrographs of the textured surfaces at specimens cut at (a) RD, (b) 45°, and (c) TD to the rolling direction of the as-received sheet. X-ray diffraction of the as-received material revealed the presence of two dominant peaks shown in figure 4; a major peak intensity at 2θ=42.36° and a second peak intensity at 2θ=77.48°, which correspond to the (110) and (211) planes in the parent austenite phase, respectively. Strong texture in the (110) plane in cold-rolled NiTi has also been observed in previous research on NiTi plates [26, 34, 35]. Note that the minor third peak intensity at 2θ=43.36° was determined to be (200) of a TiO surface oxide. The {111} , {100} , and {110} pole figures of the test material were obtained by orientation density functions calculated by MTEX and are shown in figure 5a-5c respectively. The test specimens possessed a small average grain size on the order of tens to hundreds of nanometers (nominally 40nm as measured with the Scherrer equation). Note that there was some overlap between differently oriented grains in the pole figures because of the large diffraction spot size to grain size ratio. The pole figures and inverse pole figures indicate that the orientations of most grains were {111}[110] and {110}[110] , with the {h k l} plane parallel to the sample surface and the [u v w] direction parallel to RD.
Figure 4. X-ray diffraction analysis of the as-received NiTi sample. There is a major peak intensity at 2θ=42.36° and a second peak intensity at 2θ=77.48°, which correspond to the (110) and (211) planes in the parent austenite phase, respectively.
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(a)
(b)
(c)
Figure 5. The pole figures obtained by orientation density functions of (a) {111} , (b) {100} , and (c) {110} are shown with a legend of intensity. Specimen coordinates of the pole figures are shown at upper right. Strong intensities appear at RD and 45° in the {110} pole figure.
The orientation of the crystallite axis in the specimen is known to significantly affect transformation strain in thin rolled plates and sheets [33, 34]. Miyazaki et al. theoretically calculated this dependence of transformation strain during martensitic transformation, projected on a [001] [011] [111] standard stereographic triangle. The recoverable strain was found to depend on whether the crystallite axes were preferentially located around the [011] [111] line of this orientation dependent transformation strain map [33]. Similarly, the transformation strain became small if the crystallite axes were preferentially located around the [001] direction. This map [33] was calculated by using the lattice parameters of the austenite and martensite phases to compute lattice distortion due to martensitic transformation, where it was assumed that the most favorable martensite variant grows to induce the maximum transformation strain in each grain. A similar map was constructed in [34], where higher transformation strains were again calculated along the [011] [111] line and inhibited transformation strain calculated along the [001] direction. Larger recoverable strains observed in some of the calculated versus experimentally measured results in [34] were attributed to the introduction of permanent strain via slip; also, differences in the recoverable strain versus orientation curves were attributed to constraints becoming more pronounced as the quantity of grain boundaries increased near TD. Note that this orientation dependence of the transformation strain was only found for thin rolled plates and sheets; in sputter-deposited thin films, transformation strain was found to be nearly irrespective of in-plane direction.
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(a)
(b)
(c)
(d)
Figure 6. The inverse pole figures of the (a) normal direction to the surface (ND); (b) rolling direction (RD); (c) 45° direction; and (d) transverse direction (TD). In plane, the density of {0 11} is the highest at RD and decreases as the angle approaches TD; the density of {001} is the lowest at RD and increases as the angle approaches TD.
Following these calculations, diffraction studies of the RD and 45° test specimens indicated that they had crystallographic textures favorably oriented for large transformation strains, and that the TD specimen had a crystallographic texture that was relatively unfavorably oriented for transformation. Inverse pole figures of the test specimens were experimentally obtained to examine the crystallite axis density distributions along specific directions, and are shown in figure 6. The RD inverse pole figure in figure 6b showed a high density around {0 11} and {1 11} . The highest density of {0 11} was observed for RD and decreased as the in-plane angle approached 90° (TD). Conversely, the intensity of {001} was lowest at RD and increased as the in-plane angle approached 90° (TD). This finding is in agreement with the macroscopic stress-strain responses shown in figure 7, where the TD orientation shows a markedly lower transformation strain.
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3.2 Effect of Crystallographic Texture and Applied Strain Rate on Stress-Strain Response and Localization The macroscopic stress-strain response of a TD specimen was markedly different from the RD and 45° responses at all strain rates studied here, requiring a higher load to nucleate and propagate martensite, and exhibiting a transformation plateau with a shorter length and a smaller strain at completion. Details of these phenomena are well explained in Shaw and Kyriakides [36]. Macroscopic stress-strain responses are -4 -3 -2 -1 shown in figure 7 for globally applied strain rates of ε g = 10 ,10 , and 10 s . Each strain value on the
x-axis ( ε AVG ) is an average of the DIC-measured full-field strains (εyy) in the gage section at a given YY global stress (y-axis), where P is the applied load measured by the load cell and A0 is the reference crosssectional area of the specimen. At a set strain rate, the macroscopic stress-strain curves of the RD and 45° specimens were nominally similar. These characteristics are consistent with the crystallographic textures of the RD and 45° specimens, which were found to be favorably oriented for large transformation strains (long transformation plateaus), and with the assertion that crystallographic texture is an important factor in determining the propensity of a SMA to transform [20]. It was determined through IR measurements that crystallographic texture did not significantly affect the amount of released/absorbed latent heat during phase transformation.
(a)
(b)
(c)
Figure 7. Macroscopic stress vs. DIC-averaged strain curves of textured specimens (cycle1) at the -4 -3 -2 -1 -1 -1 applied strain rate of (a) ε g =10 s , (b) ε g =10 s , and (c) ε g =10 s . The TD specimen requires higher stress to nucleate and propagate martensitic bands. Martensite band nucleation and propagation in the TD specimen starts at a higher averaged strain value and completes at a lower averaged strain value than in the RD and 45° specimens.
As seen in table 1, the macroscopic (averaged) strain at the start of phase transformation in the TD specimen was higher than in the RD and 45° specimens at all strain rates. Because it was not possible to assess the exact strain at which the first band nucleated due to the discrete nature of the imaging, and it is likely that the amount of microscale martensite that accumulated prior to band nucleation depended on specimen texture, the initiation strain of the A → M transformation was obtained using a 0.1% offset from linearity of the elastically loaded austenite. A schematic of this method is shown in figure 8. The larger macroscopic strain at the start of transformation in TD specimens is reasonable given its
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unfavorable crystallographic texture. The globally applied stress at the start of transformation (σMS), and its dependence on cycling, is shown in figure 9. In addition to these characteristics, the accumulated residual strain was smallest for the TD specimen. The effect of cycling on the accumulation of residual strain (εP) is shown in figure 10. Note that a small amount of bending was apparent in the unloaded specimen due to accumulated plasticity, which created a slight nonlinearity in the stress-strain curve at the tail end of unloading; thus, residual strain was calculated using the intersection between the linearly extended stress-strain line and the x-axis. Even though transformation is inhibited for the TD specimen, there is a small residual strain accumulation likely due to low Schmid factors for slip. For a similar cold-rolled Nickel-Titanium TD sheet specimen, Mulder et al. found that the possible slip Schmid factors were close to zero [25]. Similarly, Chang and Wu [26] also measured a low accumulation of residual strain in unfavorably textured specimens.
Table 1. Averaged strain values at the start of phase transformation, calculated by 0.1% offset from the linear austenite region in the stress-strain curve at cycle 1. Phase transformation in the TD (unfavorable) specimen begins at higher (averaged) strain values than in the RD and 45° specimens, for all applied strain rates. Strain Rate
ε g =10-4 s -1 ε g =10-3 s-1
ε g =10-2 s -1
Texture RD 45° TD RD 45° TD RD 45° TD
at beginning of phase transformation [%] ε AVG YY 0.76 0.84 0.94 0.81 0.86 0.97 0.81 0.82 0.95
Figure 8. Schematic of the 0.1% offset from linearity used to calculate the average strain values ( ε AVG ) at YY the start of martensitic transformation, tabulated in table 1.
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(a)
(b)
(c)
Figure 9. Stress required for the onset of stress-induced martensitic phase transformation at globally -4 -3 -2 -1 -1 -1 applied strain rates of (a) ε g =10 s , (b) ε g =10 s , and (c) ε g =10 s . The transformation stress is calculated by a 0.1% offset from linearity.
(a)
(b)
(c)
-4 -3 -1 -1 Figure 10. Residual strain at the applied strain rate of (a) ε g =10 s , (b) ε g =10 s , and (c)
ε g =10-2 s-1 .
The unfavorably oriented (TD) specimens also tended to nucleate a greater number of deformation bands than the RD and 45° specimens at a given strain rate, and this behavior became more pronounced at faster strain rates. This is evident in the full-field strain maps of the sample gage section shown in figure 11. The strain fields were obtained when the specimen was in the middle of the phase transformation plateau during loading on the first cycle. High strain regions indicate primarily stress-induced martensite, and low strain regions indicate regions of primarily austenite. Note that each pixel contains hundreds of grains (the pixel resolution was 9 μm), and individual grains can and usually do contain both austenite and martensite [11, 37]. Thus, each point value in these strain fields represents an averaged contribution from both the austenite and martensite phases. As the applied stress level initially increased from zero, small sub-grain
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and grain-level pockets of austenite began to transform to martensite prior to the nucleation of a large macroscopic band, as first observed by Brinson et al. [11]. When the applied stress reached a critical level, large localized bands of strain nucleated and propagated; these martensitic fronts are clearly visible in figure 11.
(a)
(b)
(c)
Figure 11. Full-field local strain maps of the gage section at cycle 1 at the middle of the phase -4 -3 -2 -1 -1 -1 transformation plateau at the applied strain rate of (a) ε g =10 s , (b) ε g =10 s , and (c) ε g =10 s . Though the number of deformation bands increases with faster strain rates, the TD specimen shows greater number of deformation bands at a given strain rate.
The propensity of a TD specimen to nucleate more martensitic bands than RD or 45° specimens at a given strain rate arises from a dependence on crystallographic texture of the difference between the nucleation -4 -1 -3 -1 and propagation stress. For ε g =10 s and 10 s , the nucleation stress (σN) was defined as the maximum
stress prior to the onset of the first deformation bands (all bands nucleated in the gage section and not at the fillets), and the propagation stress (σP) was defined as the reduced value observed after nucleation of -2 -1 the first band. However, at ε g =10 s it became difficult to define the nucleation and propagation stresses
-2 -1 because of the nearly simultaneous nucleation of multiple fronts; thus, the nucleation stress for ε g =10 s
is defined as the stress where the multiple fronts (near simultaneously) nucleated, and the propagation stress is defined as the stress where the multiple fronts (near simultaneously) began to propagate. Note -2 -1 that at the applied strain rate of ε g =10 s , five and four fronts nucleate simultaneously in the RD and the
45° specimens respectively – thus, in this case, a larger stress drop is observed in the 45° specimen than in -2 -1 the RD specimen. Finally, note that (σN - σP) for the TD specimen at ε g =10 s was unable to be
determined due to the continuous nucleation of numerous new fronts that resulted in no clear delineation between the two values. The stresses required for nucleation (σN) and propagation (σP) of the martensite are calculated in table 2. At a set strain rate, the TD specimen exhibited both higher nucleation (σN) and propagation (σP) stresses than the RD and 45° specimens. However, the difference between these stresses (σN - σP) was substantially smaller, as shown in table 2. The smaller (σN - σP) difference resulted in the 13
TD specimen being more inclined to nucleate a new deformation band in a cooler location, rather than propagate an existing deformation band in a location that had accumulated latent heat. Although accumulated latent heat will trigger the nucleation of multiple bands as the strain rate increases regardless of texture [36] (for example, see figure 11), the number of deformation bands is greatest in the TD specimen.
Table 2. The stress required to nucleate (σN) and propagate (σP) deformation bands of primarily martensite during loading at cycle 1. At a given strain rate, the TD specimen requires higher stresses for band nucleation and propagation than the RD and 45° specimens, but exhibits a smaller difference between stresses (σN - σP). This smaller (σN - σP) leads to a greater number of deformation bands, as the TD specimen is more willing to nucleate a new front in a cooler location rather than try to propagate an existing front in a location that has accumulated latent heat. Strain Rate
ε g =10-4 s -1 ε g =10-3 s-1 ε g =10-2 s -1
Texture RD 45° TD RD 45° TD RD 45° TD
σN [MPa] 445 443 492 467 473 513 475 490 520
σP [MPa] 411 412 480 450 460 511 472 479 N/A
σN - σP [MPa] 34 31 12 17 13 2 3 11 N/A
During stress-induced martensitic transformation, the TD specimen exhibited more axial (εyy) strain outside the localized (primarily martensite) deformation band, and less axial strain inside the band, compared to the more favorably orientated RD and 45° specimens. Otherwise stated, in the TD specimen, a ‘less strained’ band propagated through a ‘more strained’ matrix during loading. This was true at all three globally applied strain rates. One possible cause for this is the low Schmid factors for both slip and transformation in the TD specimen. An increased number of non-transforming grains and grain clusters in the TD specimen would result in a more constrained transformation landscape, where individual pockets of martensite could still nucleate in the austenite region, but saturation of martensitic transformation in the deformation band would occur at lower strains. This would also have coherence with the viewpoint that well-oriented grains drive the onset of transformation, and the constraints imposed by poorly oriented grains drive saturation. Additionally, the low Schmid factors for both transformation and slip may limit any synergistic interactions between the two mechanisms. However, there are hypotheses that need to be explored with studies on the length scale of the microstructure, currently under investigation. The range of all pixel strain values taken inside and outside of the deformation band(s), where each pixel encompassed hundreds of grains, are shown in table 3 at globally applied strain rates of
ε g =10-4s-1 , 10-3s-1 , and 10-2s-1 . Pixel strain ranges were determined when the specimen was in the middle of the phase transformation plateau during the first loading cycle, where the averaged ε AVG = 3.77%, YY 3.67%, and 3.25% for RD, 45° and TD specimens, respectively. The macroscopically austenite region in
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the TD specimen accommodated an average strain of 1.1%, versus an average strain of 0.9% in the RD and 45° specimens. Conversely, the macroscopically martensite region in the TD specimen accommodated an average strain of 5.1%, versus an average of 6.2% in the RD and 45° specimens. In all cases, the strains were spatially heterogeneous, with the minimum and maximum pixel strain values varying by as much as a factor of 18.
Table 3. The range of strain values observed in individual pixels (each pixel encompassing hundreds of grains), as well as averaged across the region, outside and inside of the localized deformation band during loading at cycle 1. Strains are spatially heterogeneous, exhibiting a large range of pixel strain values. When the specimen had an unfavorable crystallographic texture for martensitic transformation (TD), smaller average strains were observed inside the (primarily martensitic) deformation band and larger average strains were observed outside the deformation band.
Strain Rate
ε g =10-4 s -1 ε g =10-3 s-1 ε g =10-2 s -1
Texture RD 45° TD RD 45° TD RD 45° TD
Axial Strain Outside Deformation Band (Macroscopically Austenite) Min. – Max. (Avg.) [%] 0.4 – 1.5 (0.9) -0.3 – 2.1 (0.9) 0.4 – 1.8 (1.1) 0.3 – 1.5 (0.9) 0.2 – 1.5 (0.9) 0.6 – 1.9 (1.3) 0.1 – 1.7 (1.0) 0.1 – 1.8 (1.0) 0.7 – 2.5 (1.4)
Axial Strain Inside Deformation Band (Macroscopically Martensite) Min. – Max. (Avg.) [%] 4.9 – 7.3 (6.2) 4.7 – 7.6 (6.2) 3.5 – 6.2 (5.1) 5.5 – 7.2 (6.3) 5.4 – 7.3 (6.3) 3.7 – 6.3 (5.1) 4.3 – 10.1 (6.4) 5.3 – 7.4 (6.3) 3.3 – 6.8 (5.0)
3.3 Effect of Texture and Strain Rate on Cyclic Strain Similarity A strong similarity in the strains incurred by stress-induced (primarily martensite) regions of localized deformation was observed from cycle to cycle in previous work by the authors [30], indicating that the manner in which the localized deformation accommodates strain in the first loading cycle strongly dictates how it will accommodate strain in future cycles. In this paper, the dependence of this cyclic strain memory on texture and strain rate is examined in both the (primarily martensite) region inside the deformation band and the (primarily austenite) region outside of the band. Recall that although the stressinduced deformation band(s) are largely martensite, they do contain a significant amount of untransformed austenite. Similarly, although the regions outside of the deformation band are largely austenite, they contain a significant amount of transformed martensite [11, 37]. Thus, we will refer to the regions as “(primarily) martensite” and “(primarily) austenite” in the analysis below and we urge the reader to remember that we are referring to regions that are mixed in their composition. It was found that the strain accommodated by the (primarily) martensite region exhibited a greater cycle-to-cycle similarity in the unfavorably oriented (TD) specimen than in the RD and 45° specimens. Additionally, the (primarily) martensite region consistently showed much stronger cycle-to-cycle similarity than the
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(primarily) austenite region, regardless of specimen crystallographic texture. Finally, the strain similarity in the (primarily) martensite region evolved with cycling for all specimens and strain rates. For example, the similarity between cycles 25 and 50 was larger than the similarity between cycles 1 and 50, indicating that dislocation networks and the retention of martensitic nuclei continued to evolve, although at a reduced rate, as cycling progressed. DIC-calculated strains on a vertical line down the center of the specimen at the 1st and 50th cycles were examined when: the specimen was fully (primarily) austenite before band nucleation; during stressinduced deformation band propagation; and after the specimen was fully (primarily) martensite. The phases are denoted here as (primarily) austenite and (primarily) martensite as a reminder that there exist microscopic pockets of martensite in the macroscopically austenite region prior to band nucleation, and there also exist microscopic pockets of austenite in the transformed deformation band, as observed in [11, 37]. Strains down the centerline of the specimen at cycle 1 and 50, after the deformation band(s) had fully propagated through the specimen, are shown in figure 12 for the three textures. The strains are taken down the dotted line shown in the sample schematic to the right bottom of figure 12. The cycles are overlaid for clear comparison of their strain profiles, since only the trend of the accommodated strain, and not the magnitude, is under consideration here. The left vertical axis shows the axial strain values for the first cycle and the right vertical axis shows the axial strain values for the 50 th cycle. Note that each point on these profiles represents the averaged strain of hundreds of grains, and thus contains an averaged contribution from both martensite and austenite phases. In order to compare the effect of texture on the amount of strain similarity between cycle 1 and 50, correlation coefficients of the centerline strain profiles from cycle 1 and 50 were calculated and are shown in table 4. The correlation coefficient captures the amount of periodic similarity between the strains of two cycles, and is defined as the following, where r value approaching 1 indicates a greater degree of similarity, here Amn and Bmn are the data sets of cycle 1 and 50 respectively, and A and B are mean of the data sets:
r
( A
mn
m
A)( Bmn B)
n
2 2 ( Amn A) ( Bmn B) m n m n
As evidenced by the calculated correlation coefficients, the strain accommodated by the stress-induced (primarily) martensite exhibited significantly greater cycle-to-cycle similarity in the unfavorably oriented (TD) specimen than in the RD and 45° specimens. Additionally, the (primarily) martensite consistently showed a significantly stronger cycle-to-cycle similarity than the (primarily) austenite, regardless of specimen texture. Recall that the local strain values (encompassing numerous grains) inside the martensite band of the TD specimen were found to be significantly less than in the RD and 45° specimens. The strong cycle-to-cycle strain similarity and the smaller strains contained within the (primarily) martensite bands of the TD specimen could be due to preferentially oriented microscale pockets of austenite transforming to martensite prior to band nucleation. These microscale pockets of transformed martensite, in a sea of heavily constrained grains, could then lead to a stronger cycle-to-cycle similarity in the strain
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accommodated by the martensitic transformation. This hypothesis and its relation to the variation in Schmid factors will be scrutinized in our current efforts to characterize martensitic transformation at the length scale of the microstructure.
(a)
(b)
(c) Figure 12. Axial strains for cycle 1 and 50 of (a) RD, (b) 45°, and (c) TD specimens at a globally -4 -1 applied strain rate of ε g =10 s , taken when the specimen is fully (macroscopically) martensite. The strain is taken on a vertical line down the center of the sample as shown by the dotted line in the sample schematic. The strain profiles for cycle 1 and 50 are shifted and overlaid, since only the profile and not magnitude is under consideration. The strain accommodated by the (macroscopically) martensite phase shows significant similarity from cycle to cycle for all textures, and particularly for the TD specimen. Correlation coefficients between the cycle 1 and 50 profiles are calculated in table 4.
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Table 4. Correlation coefficients of the strain similarity between cycles 1 and 50, at each texture, and globally applied strain rate ε g , indicating greater periodical similarity as it approaches 1. Cycle-to-cycle strain similarity is greater for martensite than austenite at all textures and applied strain rates, and appears to increase with unfavorable texture. Strain Rate
ε g =10-4 s -1 ε g =10-3 s-1 ε g =10-2 s -1
Texture RD 45° TD RD 45° TD RD 45° TD
Austenite Correlation coefficient 0.59 0.66 0.54 0.55 0.58 0.63 0.38 0.20 0.65
Martensite Correlation coefficient 0.82 0.79 0.91 0.83 0.83 0.85 0.80 0.86 0.95
4. CONCLUSIONS Full-field methods were used to explore the effects of crystallographic texture on the formation of stressinduced martensite during the cyclic loading of Nitinol. Three texture orientations from a cold-rolled 254 µm thick sheet (RD, 45°, TD) were examined under displacement-controlled cycling at globally applied -4 -3 -2 -1 strain rates of ε g = 10 ,10 , and 10 s .
The RD and 45° test specimens were found to have crystallographic textures that were favorably oriented for large transformation strains, and the TD specimen had a crystallographic texture that was relatively unfavorably oriented for transformation.
The observed propensity of the TD specimen to nucleate more deformation bands than the RD or 45° specimens arises from the difference between the nucleation and propagation stresses. At a set strain rate, the TD specimen exhibited significantly higher nucleation (σN) and propagation (σP) stresses than the RD and 45° specimens. However, the difference between these stresses (σ N - σP) was substantially smaller. Thus, the TD specimen was more inclined to nucleate a new deformation band in a cooler location, rather than propagate an existing deformation band in a location that had accumulated latent heat.
During stress-induced martensitic transformation, the TD specimen accommodated more average axial strain outside the (primarily martensite) deformation band, and less axial strain inside the band, compared to the more favorably orientated RD and 45° specimens. Otherwise stated, in the TD specimen, a ‘less strained’ deformation band propagated through a ‘more strained’ matrix during loading.
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The pixel strain distribution (each pixel encompassing hundreds of grains and containing contributions from both martensite and austenite), once the deformation band has fully propagated through the specimen, is remarkably similar from cycle to cycle. The (primarily) martensite region consistently showed a stronger cycle-to-cycle strain similarity than the (primarily) austenite region for all three globally applied strain rates and textures.
Additionally, the strain similarity in the (primarily) martensite region evolved with cycling for all specimens and applied strain rates. For example, the similarity between cycles 25 and 50 was larger than the similarity between cycles 1 and 50. This indicates that the dislocation networks and retention of martensitic nuclei continued to evolve, although to a reduced extent, as cycling progressed.
The cycle-to-cycle strain similarity is stronger in the TD specimen than in the RD and 45° specimens. The strong cycle-to-cycle strain similarity and the relatively smaller strains contained within the (primarily martensite) deformation bands of the TD specimen could be due to preferentially oriented microscale pockets of austenite transforming to martensite prior to band nucleation. These microscale pockets of transformed martensite, in a sea of heavily constrained grains, could then lead to a stronger cycle-to-cycle similarity in the strain accommodated by the martensitic transformation. This hypothesis and its relation to the variation in Schmid factors will be scrutinized in our current efforts to characterize martensitic transformation at the length scale of the microstructure.
ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support of the US Department of Energy, Office of Basic Energy Sciences (contract No. DE-SC0003996 monitored by Dr. John Vetrano), who funded the experiments and analysis detailed in this paper. The authors would also like to thank Dr. Benjamin Reedlunn for his experimental assistance and helpful discussions.
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