Strain rate dependence of a super-elastic NiTi alloy

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Experiments were performed on Nitinol SE 508 wire, obtained as rods of 10 mm diameter from. Euroflex GmbH [5]. The material has a composition of 55.8% Ni ...

DYMAT 2009 (2009) 1153–1159 Ó EDP Sciences, 2009 DOI: 10.1051/dymat/2009161

Strain rate dependence of a super-elastic NiTi alloy C.R. Siviour, J.E. Huber, T. Normanton and N. Petrinic Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK Abstract. The response of a super-elastic NiTi alloy to mechanical deformation has been investigated in tension and compression at strain rates of 10x3 and 103 sx1. The effect of loading direction has been understood through the nature of the phase transformation in the material, whilst comparison of quasi-static experiments at elevated temperatures to the response of the material at high strain rates provides better understanding of the importance of adiabatic heating in high strain rate loading.

1. INTRODUCTION Super-elastic materials such as NiTi alloys offer great potential in compliant, energy absorbing structures for the amelioration of impact damage. Key advantages in impact applications are: (1) a plateau in stress-strain response over several percent of strain enables the moderation of impact loads to a fixed level; (2) a substantial hysteresis that enables energy absorption or damping of oscillations; and (3) full return upon unloading to the initial state, allowing multiple reuse after moderate impact, without loss of component geometry or material performance. Despite these significant advantages, impact applications of NiTi are relatively few, perhaps because of the limited ductility (about 10%) of the alloys, which demands novel design approaches to avoid overstraining. There is also relatively little work on the high strain rate behaviour of NiTi alloys, and a need for improved understanding of the material behaviour. Chen et al. [1] conducted mechanical tests on super-elastic NiTi at a variety of strain rates, and demonstrated the strain-rate sensitivity of the plateau stress. NematNasser and Guo [2] used similar techniques with varying temperature, indicating that the temperature sensitivity was more significant than strain-rate sensitivity. Temperature rises of order 40 K have been observed [3] in super-elastic NiTi at modest strain rates. However, the extent to which adiabatic heating affects rate behaviour in these materials remains an open question. The origins of the super-elastic behaviour in NiTi alloys arise from a displacive cubic (austenite) to monoclinic (martensite) phase transformation [4]. Super-elastic response arises when the austenite finish temperature Af lies a little below the operating temperature, so that the austenite phase is stable, but stress induced martensite can be produced. Figure 1 shows schematically the range of resulting behaviour under tensile stress in a polycrystalline NiTi alloy. The elastic regime of behaviour leads to a plateau in stress strain response (point A) as austenite transforms to favourably oriented martensite. Eventually, the most favourably oriented austenite crystals have transformed and the transformation process saturates leading to a sharp rise in stress and a return to near-elastic behaviour at B. Upon unloading from this state a lower plateau stress is reached at C and the reverse phase transformation converts martensite to austenite until the elastic austenite state is reached. Loading far beyond the saturation strain results in yield and flow by conventional dislocation plasticity (D), and ductile failure at about 10% strain. Note that the proximity of the operating temperature to the phase transition temperature can be used to explain the observed temperature sensitivity [1]. Thus

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Figure 2. Tensile specimen geometry.

Figure 1. Schematic stress-strain curve of a NiTi alloy.

it is expected that raising the temperature (moving away from Af) increases the transformation stress str. In the present work, we investigate the stress-strain response of super-elastic NiTi alloy under tension and compression, in quasi static tests, and at strain rates up to 103 sx1. We also measure the influence of temperature on the plateau stress, and show that this can account for the observed hardening in the plateau stress at high rate.

2. MATERIAL, SPECIMEN PREPARATION AND EXPERIMENTAL TECHNIQUES Experiments were performed on Nitinol SE 508 wire, obtained as rods of 10 mm diameter from Euroflex GmbH [5]. The material has a composition of 55.8% Ni and 44.2% Ti (by weight). The austenite finish temperature, Af, is highly dependent on processing, but is specified as being less than 15xC. Further relevant properties from the manufacturer’s data sheet and the literature are given in Table 1. A number of specimens were prepared from the rods, reflecting the competing requirements of high and low strain rate materials characterization. In order to reduce inertia and wave propagation effects in the high strain rate experiments, compressive specimens were cylinders of 2.5 mm length and 2.5 mm diameter. These specimens were also used in quasi-static experiments in order to provide a comparison between the strain rates; however, for such small specimens it was not possible make direct measurements of strain on the specimen surface. For this reason, further quasi-static experiments were performed with cylinders of 6 mm length and diameter – thus preserving the same aspect ratio but allowing measurements of specimen strain to be made directly. For tensile experiments, dog-bone specimens as shown in Figure 2 were used at all rates. Quasi-static experiments at room temperature were performed using a screw-driven Hounsfield testing machine. Force measurements were taken from the load cell, whilst displacement measurements were made using a laser extensometer (Fiedler Optoelektronik P-50); for the 2.5 mm compression specimens these measurements were of the displacement of the loading anvils, for the 6 mm specimens, measurements were made directly on the specimen surface. Measurements were made on the specimen surface for all of the tensile experiments.

DYMAT 2009 Literature Values Specific Heat Capacity / J gx1 xCx1

Table 1. Selected Properties of NiTi. From the Manufacturer [5] Density 6500 kg mx3 Af < 15xC Melting Point 1210xC

Latent Heat of Austenite to Martensite Phase Transition / J gx1

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Figure 3. (a) Stress-strain curves for NiTi in compression at a strain rate of 10x3 sx1, the two specimen sizes are indicated; (b) Comparison of stress-strain curves in tension and compression at a strain rate of 10x3 sx1.

Quasi-static experiments at elevated temperatures were performed using an Instron testing machine with an environmental chamber. These experiments were performed in compression on 6 mm specimens; in this case anvil displacements were again used and the room temperature experiments were repeated to ensure comparability with the data obtained from the Hounsfield machine. High strain rate experiments were performed using the split-Hopkinson bars described in [10]. In the compressive system, the Maraging Steel input and output bars are 500 mm long, 15 mm in diameter, and are instrumented with foil strain gauges. By using striker bars of different lengths, specimens were taken to a range of final strains. The specimens were allowed to unload ‘naturally’ after the loading pulse had finished – it will be seen later that this led to a different strain rate on loading and unloading. The tensile system has 500 mm long and 10 mm diameter bars, the input bar is Ti6Al4V and the output bar Phosphor Bronze. No unloading was undertaken in the high rate tensile experiments.

3. RESULTS 3.1 Quasi-static, 22°C Stress-strain curves for the compression experiments under quasi-static conditions are shown in Figure 3. Figure 3(a) compares the data obtained from the 2.5 mm and 6 mm specimens; as

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Figure 4. (a) Stress-strain curves for NiTi in compression at high strain rates, comparison with quasi-static data; (b) High rate stress-strain curves with unloading, the dashed specimen is explored further in Figure 5.

expected the strains are over-measured on the 2.5 mm specimens due to end effects and lubricant. Compression and tension data are compared in Figure 3(b). 3.2 High rate compression, 22°C Figure 4 shows stress-strain curves from the high strain rate compression experiments. The specimens in figure 4(a) were taken to failure, and a quasi-static result is shown for comparison. Figure 4(b) shows a number of specimens that were loaded with shorter input waves and then allowed to recover. By varying the length of the striker bar, (from 250 mm down to 100 mm) different final strains were achieved with only small changes in strain rate. Apart from those indicated, none of the specimens underwent irrecoverable deformation – this was confirmed by measurement of the final dimensions of the recovered specimens. The practice of allowing the specimens to recover naturally means that the strain rates on loading and unloading were not the same. This is demonstrated by the strain rate-time curve in Figure 5. The unloading strain rate can be increased through the use of a specimen with a larger area – although by increasing the strength of the specimen this also has the effect of making the loading strain rate more difficult to control. This loading rate could be made more constant through the use of pulse shapers. 3.3 High rate tension, 22°C Data obtained from the high rate tensile experiments were relatively poor; however, they are included as they illustrate an important point about the material behavior. Typical stress-strain curves are shown in Figure 6. The behaviour of the specimen around the plateau is masked by oscillations, the equivalent of which are not observed when performing experiments on materials such as steel or titanium with the same specimen geometry. This is possibly due to the variation in sound speed in the material under different amounts pffiffiffiffiffiffiffiffiffiffiffiffiffi of strain. During the initial phase of the stress-strain curve, the wavespeed, c ¼ r1=2 ds=de, is relatively high; however, once the plateau is reached c drops almost to zero. In addition, whilst on the plateau, the material is still elastic, and is therefore able to transmit any oscillations of the input stress wave to the transmitted

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Figure 5. Strain-time and stress-time curves for the indicted specimen in figure 4b.

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Figure 6. Stress strain curves in high rate tension. The specimen at 1700 sx1 failed, the other did not.

bar, further complicated by the plateau stress being different on loading and unloading. Comparison of the stresses on the two ends of the specimens showed that they coincide after a strain of about 0.07, so the specimens were close to mechanical equilibrium after this point, notwithstanding the small wave oscillations that were clearly still present. Pulse shaping should help to improve equilibrium and remove some of these oscillations, this is the subject of further investigation. 1500

In order to further elucidate the mechanisms behind the observed strain rate dependence, further quasi-static experiments were performed at temperatures of 22, 39 and 60xC, Figure 7. The nature of the phase transformation in this material is that the plateau stress increases with increasing temperature, meaning that adiabatic high strain rate deformation is expected to lead to an increase in the plateau stress due to heating. The elevated temperature experiments allow us to quantify this effect.

4. DISCUSSION 4.1 Low strain rate tension and compression

Stress / MPa

3.4 Quasi-static compression, elevated temperatures

1000

500 22 °C 40 °C 60 °C 0 0

0.01 0.02 0.03 0.04 0.05 0.06 Strain

Figure 7. Quasi-static stress-strain curves at three different temperatures.

The general shape of the stress-strain curves is as expected; however, there are a number of differences between tension and compression that must be explained. The initiation of the austenite to martensite transition is observed to occur at approximately the same stress in both tension and compression; however, in tension the initiation is followed by a drop in stress and then a plateau, whilst in compression the stress continues to increase and the plateau is less distinct. In both cases, the first grain to transform will be the one that is most favourably orientated to the

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loading direction. In compression, less favourably orientated grains then follow, but require an increase in the critical resolved shear stress in order to do so. In tension, the initial formation of more favourably orientated martensite decreases the area of the crystal normal to the loading direction, increasing the local stress and leading to localisation of the transformation into a band of martensite which propagates through the specimen. Such bands have been observed by previous authors [3, 11]. The stress peak observed before the plateau in tension is not seen in some papers; it is observed here because the specimens used in the current study were dog-bone shaped, and therefore did not undergo initiation of the transformation where the specimen was gripped. It is also observed that the length of the plateau in tension is greater than in compression. This is due to the orientation of the stress induced martensite. Whilst the orientation of grains in the initial austenite material is random, the transformed martensite state has a long axis which will align with the direction of tensile strain in the deformed specimen. Because there are more ways for the axis to align to the plane containing the two transverse tensile strain components in compression experiments than there are to align to the single tensile direction in the tension experiments, the random initial state is closer to the compressed state, and therefore less transformation strain is possible in compressive loading than in tension.

4.2 Comparison of low and high strain rate data in compression It is observed that whilst the initial transformation stress is only slightly higher in high strain rate loading than at low rates, the gradient of the subsequent plateau is significantly steeper at high rate. It is well known, and can be shown from the thermal diffusivity in the material, that the high strain rate experiments are adiabatic, whilst the low rate experiments are isothermal. A calculation of the temperature rise expected in the high rate experiments was therefore performed in order to assess how this might affect the mechanical response. During deformation, there are two sources of thermal energy in the specimen: conversion of mechanical work into heat (which will be assumed to be 100%) and latent heat from the exothermic phase transition. The latent heat is approximately 20 J gx1 (Table 1), which will be available when all the austenite has transformed into martensite, i.e. at the end of the plateau. The mechanical work can be estimated by taking the area under the stress-strain curve in figure 3. Assuming an approximate triangular shape of the curve, and a stress of 1200 MPa at 0.05 strain, the work, W, is W ¼ 0:5r1200r106 r0:05 ¼ 30 MJ m3 ¼ 4:6 J g1 ;

ð1Þ

where a density of 6500 kg mx3 has been used. Thus, the total thermal energy available is approximately 25 J gx1 at a point where all the austenite has transformed into martensite; this corresponds to a temperature rise of between 30 and 50xC, depending on the heat capacity, at the end of the plateau. This is consistent with the measurement of 40xC obtained by Pieczyska et al. [3]. In order to ascertain whether this temperature rise would be enough to account for the difference between low and high strain rate response of the material, comparison can be made between the data in Figure 7 and Figure 4. Within the approximations of the calculations made, the dependence of stress on temperature is enough to increase the plateau stress from the quasi-static to the dynamic level. Since the heat is generated during the high rate experiment, and the temperature of the specimen therefore increases with strain, we would expect a steepening of the plateau in the high rate experiments, but no increase in initial transformation stress, compared to the quasi-static: this agrees with observation. It should also be noted that since the mechanical work has been calculated from the quasi-static data, the temperature rise expected in high rate loading would be towards the upper end of the values estimated above.

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5. CONCLUSIONS Compression and tension experiments have been performed on a super-elastic NiTi alloy at strain rates of 10x3 and 103 sx1. Differences between the two loading directions in quasi-static experiments can be understood by the details of the phase transition, which initiates at approximately the same stress in both directions but propagates more readily in tension than compression. The use of dog-bone specimens reduces stress concentrations which would otherwise initiate the formation of martensite at lower overall stresses, and leads to a small stress peak before the plateau. High strain rate tensile experiments were performed, however further work is required to improve the measurement of plateau stress in these experiments. High strain rate compression experiments showed a slight increase in the transformation stress, followed by a significant increase in the gradient of the subsequent plateau. Calculation of the potential temperature rise in these experiments, and comparison to quasi-static stress-strain curves at elevated temperatures, shows that the steeper plateau can be understood in terms of the adiabatic nature of high strain rate loading and the increase in transformation stress with increasing temperature. Acknowledgments The authors would like to thank P. Hardey for preparing the specimens used in this research. JEH gratefully acknowledges the support of the Nuffield Foundation.

References [1] Nemat-Nasser, S. and Guo, W.-G., Mech. Mat. 38 (2006), 463-474. [2] Chen, W.W. et al., Int. J. Solids Struct., 38 (2001), 8989-8998. [3] Pieczyska E.A. et al., Superelasticity and transformation-induced effects in TiNi SMA, in Proceedings of EMMC-10 Conference, Multi-phase and multi-component materials under dynamic loading. Kazimierz Dolny, Poland, 2007. [4] Otsuka, K. et al., Physica status solidi 5 (1971) 457-470. [5] Euroflex Datasheet for Nitinol SE 508 Tubing, http://www.nitinol-europe.com, accessed on 6 March 2009. [6] Johnson Matthey Medical, http://jmmedical.com/resources/221/Nitinol-Technical-Properties. html, accessed on 6 March 2009. [7] Brantley, W.A. et al., American Journal of Orthodontics and Dentofacial Orthopedics, 124 (2003), 387-394. [8] Da Silva, E.P., Materials Letters 38 (1999), 341-343. [9] Leo, P.H. et al., Acta metall. mater. 41 (1993), 2477-2485. [10] Gerlach, R. et al., Polymer 49 (2008) 2728-2737. [11] Daley, S. et al., Stress-induced Martensitic phase transformation in Nitinol, in Proceedings of XXII ICTAM, Adelaide, Australia, 2008.

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