# Virtual Extensometer Analysis of Martensite Band Nucleation, Growth, and Strain Softening in Pseudoelastic NiTi Subjected to Different Load Cases

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{4}Ti

_{3}precipitates [25] and resulted in a higher critical stress level for irreversible plastic deformation by a dislocation slip, thus improving pseudoelastic behavior of the NiTi material. During this heat treatment, the average grain size remained constant (~45 µm) and the material showed excellent pseudoelastic recovery [7,8]. Further details on microstructural characterization of the as-received and heat-treated materials are presented in [7].

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^{−1}), which is important to a reduce the heat effect caused by the latent heat of the stress-induced martensitic transformation on the thermomechanical response of pseudoelastic NiTi [8,26]. The uniaxial tensile tests were performed on a conventional tensile/compressive testing machine (Zwick Allround-Line 20 kN, Ulm, Germany) under displacement-controlled loading conditions. Dog-bone-shaped specimens with a free gauge length of 10.5 mm and a diameter of 3.56 mm were tested (Figure 1a). The uniaxial compressive and combined compression-shear tests were performed in a universal testing machine (Zwick UPM1475-100 kN, Ulm, Germany). For simple compression testing, cylindrical specimens with a diameter of 9 mm and a length of 9 mm (the short aspect ratio prevents bending and buckling that can easily occur in NiTi because of the large strains associated with the SIMT) were used, and for combined compression-shear tests, cylindrical samples (6 mm diameter × 6 mm length) with an inclination angle of 6° with respect to the loading direction, were used (see Figure 1b,c).

#### 2.1. Optical Strain Measurements Using DIC

#### 2.2. Determination of Nominal Uniaxial Stresses and Strains

## 3. Results and Discussion

## 4. Summary and Conclusions

- Under uniaxial tension, characteristics of the stress–strain curves in terms of the absolute length of the pseudoelastic plateau, and especially in terms of the shape of the nucleation peak, can be considerably affected by the position of a (virtual) extensometer with respect to the nucleation site of distinct martensite bands. In the case of a localized deformation, which primarily occurs in tension in NiTi, the positioning of the extensometer used for the strain analysis is highly important when analyzing subtle features of the resulting stress–strain curves. We show, for the first time, that the specific softening behavior of NiTi SMAs under uniaxial tensile loading can, to some extent, be directly analyzed experimentally by locating an extensometer in post-experimental DIC data analysis directly onto the region where a martensite band is nucleated. The amount of strain softening (slope of the resulting stress–strain curve: 16 MPa/%) may form an experimental basis for advanced mechanical modeling studies.
- The mechanical response of pseudoelastic NiTi associated with the stress-induced martensitic transformation exhibits a strong difference in tension and compression. This can be attributed to the different macroscopic modes of deformation. Under tension, the stress-induced martensitic transformation proceeds in a localized manner (via formation and growth of martensite bands). Under simple compression, the deformation proceeds homogeneously (without distinct martensite bands/strain localization. Therefore, the position and total gauge length of a (virtual) extensometer has no influence on the stress–strain curves in compression.
- In the multi-axial load case created by the special geometry of compression-shear specimens, the material exhibits a strong inhomogeneity of the transformation. However, no lateral growth of distinct martensite bands (as observed under uniaxial tension) occurs, and therefore the macroscopic stress–strain behavior closely resembles the behavior under simple compression. However, there is a small but systematic effect of the virtual extensometer’s gauge length on the resulting stress–strain curves in this special load case. While it is less pronounced when compared to tensile loading, it clearly highlights the inhomogeneous deformation mode of NiTi when subjected to compression-shear loading.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Geometries of the samples used for the mechanical testing and artificially-produced speckle patterns on the samples required for the measurement of the surface strain fields using digital image correlation (DIC): (

**a**) cylindrical dog-bone-shaped tensile test sample; (

**b**) cylindrical compression test sample; (

**c**) cylindrical compression-shear test sample with an inclination angle of 6° that results in superimposed shear stresses during compressive loading. The conventional clip-on extensometer for tensile testing (indicated in (

**a**)) and virtual extensometers used for the deformation measurements in all our mechanical tests are shown schematically on the specimen surfaces. In tensile, compression, and also in compression-shear tests, the uniaxial strain was determined from the DIC images by considering two surface points (black dots) and their relative displacements in the axial direction, dy; positioning of these points was varied in post-experimental analysis.

**Figure 2.**(

**a**) Schematic representation of the dog-bone-shaped tensile test specimen with four virtual extensometers used for investigation of the effect of the extensometer position, with respect to the nucleation side of the martensite band; (

**b**) axial surface strain field image measured at a macroscopic strain of about 2.1%. The analyzed extensometers are shifted sideways from the center line (where they were located in the actual analysis of DIC data) to provide a better overview.

**Figure 3.**Engineering stress–strain curves determined using various virtual extensometers (see Figure 2) under uniaxial quasi-static tensile loading. The different extensometer positions with respect to the nucleation site of the martensite band lead to a systematic and significant effect on the resulting stress–strain curves, especially on the shape of the nucleation peak.

**Figure 4.**(

**a**) Placement of several virtual extensometers in the region where martensite band nucleation first occurs. The strain map clearly shows that (in contrast to the grown band during latter stages of deformation), lower strains occur because the band’s nucleus effectively consists of two meso-scale interfaces that have not yet moved apart; (

**b**) Effect of positioning the virtual extensometers in direct proximity to the martensite band on the resulting engineering stress–strain curves during tensile loading. For all virtual extensometers located in the region of the nucleating martensite band, broad nucleation peaks that exhibit pronounced softening are observed.

**Figure 5.**(

**a**) Schematic representation of the cylindrical compressive test specimen; (

**b**) axial surface strain field recorded at a macroscopic strain of about 3%. Three virtual extensometers (again located next to each other for a better overview) were used under simple compression, where the martensitic transformation proceeds homogeneously on a macroscopic scale without distinct strain localization.

**Figure 6.**Engineering stress–strain curves determined using various virtual extensometers under simple compression. The different positions and gauge lengths of the virtual extensometers (see Figure 5) have no effect on the resulting stress–strain curves due to the very homogeneous deformation of pseudoelastic NiTi in compression.

**Figure 7.**(

**a**) Schematic representation of the cylindrical specimen with an inclination angle for compression-shear testing; (

**b**) axial surface strain field image measured at the end of compression-shear loading (prior to unloading). Four virtual extensometers that are located here next to each other for a better overview were investigated under compression-shear loading, where the strain fields are inhomogeneous (localization of deformation) due to the more complex stress-state created by the superimposed shear stresses and the special specimen geometry.

**Figure 8.**Nominal/axial engineering stress–strain curves determined under compression-shear loading. Various positions of virtual extensometers (shown in Figure 7a) result in a small but systematic effect on the resulting stress–strain curves. Larger gauge lengths are associated with larger total strain values, because they put more relative weight on the regions that exhibit the largest strains.

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**MDPI and ACS Style**

Elibol, C.; Wagner, M.F.-X.
Virtual Extensometer Analysis of Martensite Band Nucleation, Growth, and Strain Softening in Pseudoelastic NiTi Subjected to Different Load Cases. *Materials* **2018**, *11*, 1458.
https://doi.org/10.3390/ma11081458

**AMA Style**

Elibol C, Wagner MF-X.
Virtual Extensometer Analysis of Martensite Band Nucleation, Growth, and Strain Softening in Pseudoelastic NiTi Subjected to Different Load Cases. *Materials*. 2018; 11(8):1458.
https://doi.org/10.3390/ma11081458

**Chicago/Turabian Style**

Elibol, Cagatay, and Martin F.-X. Wagner.
2018. "Virtual Extensometer Analysis of Martensite Band Nucleation, Growth, and Strain Softening in Pseudoelastic NiTi Subjected to Different Load Cases" *Materials* 11, no. 8: 1458.
https://doi.org/10.3390/ma11081458