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Effect of temperature on fatigue of superelastic NiTi wires
Journal Pre-proofs Effect of temperature on fatigue of superelastic NiTi wires Ondřej Tyc, Luděk Heller, Marek Vronka, Petr Šittner PII: DOI: Reference:
S0142-1123(20)30001-3 https://doi.org/10.1016/j.ijfatigue.2020.105470 JIJF 105470
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International Journal of Fatigue
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Please cite this article as: Tyc, O., Heller, L., Vronka, M., Šittner, P., Effect of temperature on fatigue of superelastic NiTi wires, International Journal of Fatigue (2020), doi: https://doi.org/10.1016/j.ijfatigue. 2020.105470
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Effect of temperature on fatigue of superelastic NiTi wires Ondřej Tyc a,c, Luděk Heller a,b, Marek Vronka a and Petr Šittner a,b a Institute of Physics of the CAS, Na Slovance 1992/2, 18221 Prague, CR b Nuclear Physics Institute of the CAS, Husinec - Řež 130, 250 68, Řež, CR c Faculty of Nuclear Sciences and Physical Engineering, CTU Prague, Prague 2, CR
Corresponding author: Ondřej Tyc, E-mail- [email protected] Postal address: Institute of Physics of the CAS, Na Slovance 1992/2, 18221 Prague, CR
Effect of temperature on fatigue of superelastic NiTi wires Abstract: The stress induced martensitic transformation in superelastic NiTi alloy can be accompanied by a plastic deformation. In this work, NiTi wires were subjected to tensile displacement-controlled tests in the temperature range -90 °C to 190 °C and lattice defects created by the deformation were analysed by TEM. The unrecovered strain significantly increased and fatigue life decreased with increasing test temperature. The rate of the accumulation of unrecovered strain in the stabilized stage of tensile cycling was taken as an indicator of the accumulation of material damage. Fatigue life ranged from 900 cycles at 80 °C to 4700 cycles at 15 °C.
Keywords: NiTi alloy; superelasticity; fatigue; unrecovered strain
1. Introduction NiTi based alloys have been utilized in a wide range of engineering applications in medicine, aerospace, transport, robotics and automotive industry owing to their unique superelastic and shape memory functional behaviour [1-3]. However, engineering applications utilizing cyclic martensitic transformation are seriously limited by the functional and structural fatigue of NiTi [4,5]. It is well known that the stress induced martensitic transformation in superelastic NiTi tends to be accompanied by unrecovered strain. Lattice defects are introduced upon thermomechanical cycling, microstructure evolves irreversibly, unrecovered strain accumulates and functional properties gradually change upon cycling [6-8]. In tension, the number of superelastic cycles to failure is limited to a few thousands only [9], while millions of cycles can be reached in compression [10]. Fatigue of superelastic NiTi wires in tension was extensively investigated from different perspectives and critical factors were identified as: transformation strain [11], transformation stress/temperature [12-14], inclusions (O-rich and C-rich phases) acting as nucleation sites of fatigue cracks mainly on a surface [15,16], strain localization [17], surface finishing [14] and Ni-rich precipitates [12]. What is not yet clear is how the functional fatigue is related to the structural fatigue. In this study, thin superelastic NiTi wires were subjected to tensile fatigue tests in displacementcontrolled regime (loading to the end of transformation plateau) at various temperatures. The aim was to investigate the effect of temperature on functional and structural fatigue in a view of our recent results concerning the transformation plasticity coupling in NiTi [6,18,19] and deformation twinning in martensite [20-23]. As the difference between the stress required for stress induced martensitic transformation and deformation twinning in martensite decreases with increasing temperature, the experimentally observed unrecovered strain increases. Deformation bands containing {114} austenite twins were observed in the microstructure of wires deformed in a single tensile cycle at elevated temperature for which the plateau stress equals to yield stress [21]. Similar deformation bands containing either martensite or {114} austenite twins were observed later after several cycles in [23], where the difference between plateau stress and yield stress is rather large. The deformation twinning in martensite has been called non-transformation pathway by Gao et al [24,25] from theoretical point of view and proposed to be an origin of functional fatigue of NiTi. To further explore the link between functional and structural fatigue of superelastic NiTi alongside the above ideas, functional and structural fatigue of superelastic NiTi wire was investigated at various temperatures. A new criterion for fatigue of superelastic NiTi alloys is
proposed assuming that the rate of unrecovered strain accumulation (functional fatigue) scales with number of cycles to failure (structural fatigue). 2. Material and Methods Cold-worked Ni-rich NiTi wire (Ti-50.9at. %Ni, 42.1 % CW, 0.1 mm in the diameter) was used in the experiments. The NiTi wire was heat treated by electric current pulse (25 Wmm-3/100 ms) to obtain superelastic samples with a nanograin structure (approx. 100-200 nm) and very low dislocation density within the grains (Fig. 1). Tensile tests were performed using miniature deformation rig MITTER (Fig. 2) allowing mechanical testing and pulse heat treatment by electric current. Peltier elements were controlling testing temperature in the range -30 °C to 200 °C. More detailed information on the testing rig can be found in [26,27]. Tests below the lower temperature limit of the Peltier elements were carried out by means of aluminium heat sink filled with liquid nitrogen placed on the top of the copper body of the chamber to reach temperatures down to -100 °C. Clamping ends of the wires into stainless steel capillaries (1.6 mm in the outer and 0.18 mm in the inner diameter) was needed for an easier manipulation and gripping. Length of the sample between the capillaries was 50 mm so the sample fits into the 80mm long copper chamber and can be kept at homogenous temperature.
Fig. 1. Stress-strain tensile curves to fracture of the NiTi wires in a cold worked (green) and the heat-treated (red) state at 20 °C. Bright field TEM micrograph shows the heat-treated microstructure used in the tensile and fatigue experiments.
Fig. 2. Miniature tensile tester MITTER (equipped with a load cell, stepper motor, position encoder, Peltier based environmental chamber, resistance measurement and closed-loop LabView-based control system) used to perform both the electro-pulse heat treatment and thermomechanical loading tests of the NiTi wires. Tensile tests were performed at various temperatures in the range –90 °C to 190 °C. The tests were run in a displacement-controlled regime according to the test program outlined in Fig. 3 with the aim to explore superelastic stress-strain response of NiTi wires and deformation until rupture simultaneously. The main evaluated quantities are: upper plateau stress pUP, upper plateau strain pUP and unrecovered strain US in the first superelastic cycle, yield stress Y (point above upper plateau of the first where stress-strain curve deviates from linear path) and tensile strength max. Strain rate of the test was 0.001 s-1.
Fig. 3. Testing of mechanical properties (upper plateau stress pUP, upper plateau strain pUP, unrecovered strain us, yield stress Y and tensile strength max) of the NiTi wire consisting of superelastic cycle to the end of stress plateau followed by tensile test to fracture at 80 °C and strain rate 0.001 s-1.
Fatigue tests were performed at 0.01 s-1 strain rate in the displacement-controlled regime. Since the
higher
strain
rate
affects
the
stress-strain
response
[28]
owing
to
the
exothermic/endothermic character of the forward/reverse martensitic transformation, cycles at lower strain rate (0.001 s-1) were added to fatigue tests for monitoring of evolution of a stressstrain response. The lower loading limit was 10 MPa, which prevents buckling of the NiTi wires as unrecovered strain accumulates in the superelastic fatigue cycling above Af temperature. The upper loading limit was set to the end of stress plateau at a given temperature. The temperature range of fatigue experiments was 15 °C-80 °C. Fatigue tests on the superelastic samples were repeated 5 times, at each temperature level, to capture the scatter of the evaluated fatigue life. Samples for TEM studies of lattice defects in deformed wires were prepared by Focused Ion Beam (FIB) method using FEI Quanta 3D FIB-SEM electron microscope. TEM lamellas were extracted in such a way that the wire axis always lies in the plane of the TEM lamella. TEM observations were carried out using FEI Tecnai TF20 X-twin field emission gun microscope operated at 200 kV. 3. Experimental Results 3.1 Tensile tests Tensile tests were performed according to the test program introduced in Fig. 3. Selected results are presented in Fig. 4. After deformation to the end of stress plateau and unloading, the wires were stress-free heated up to 100 °C above test temperature to relieve residual martensite and determine the unrecovered strain [21] introduced during the first superelastic cycle. Finally, the wires were deformed to failure to determine the yield stress and strength. (For the tests above 100 °C, yield stress was determined from direct loading to failure as only one loading/unloading cycle significantly changes this variable.) The temperature dependence of the upper plateau stress pUP, upper plateau strain pUP, yield stress Y, and unrecovered strain us, are shown in Fig. 5.
Fig. 4. Stress-strain superelastic response of the NiTi wire in temperature range 0 °C-190 °C. One loading/unloading cycle to the end of upper plateau followed by heating of 100 °C to recover residual martensite and loading to fracture were performed to examine mechanical properties (pUP and Y) and stability (us) of superelastic loops.
With increasing test temperature, the superelastic loop shifts to higher stress, as common for all superelastic alloys, due to the characteristic temperature dependence of transformation stress [20]. However, the yield stress decreases and the unrecoverable strain and plateau strain increase with increasing temperature at the same time. It shall be pointed out that the tested NiTi wires deform in a localized manner by propagation of martensite band fronts at constant
plateau stress [17] at any test temperature. This does not necessarily mean that the stress induced cubic to monoclinic transformation is the only deformation mechanism activated within the propagating martensite band front. Stress plateau may involve deformation twinning in the martensite phase and dislocation slip to achieve strain compatibility in moving habit planes (see [21] for detailed discussion). The plateau strains are completely reversible upon unloading and heating (Fig. 5b) in tensile tests at low temperatures (T<20 °C). The unrecovered strain recorded after the first cycle in tensile test at 0 °C (pUP= 365 MPa and Y= 1140 MPa) was only 0.03 %. With increasing test temperature, the unrecovered strain gradually increases up to 1 % in the tensile test at 80 °C (pUP= 870 MPa and Y= 1090 MPa). In tensile tests at temperatures above 80 °C (Fig. 5b), the unrecovered strain starts to increase sharply. The forward plateau strain reaches 11 % out of which 8% remains unrecovered in the tensile test at 190 °C. This suggests an onset of the activity of different deformation mechanisms (transformation plasticity coupling and deformation twinning in martensite) in the tensile test [18, 21].
Fig. 5. Effect of temperature on mechanical and superelastic properties of the NiTi wire- a) evolution of upper plateau stress and yield stress, b) recoverable and unrecovered strain after loading cycle to the end of superelastic plateau in the range -20 °C to 190 °C (Af=-8°C). Recoverable strain is the sum of elastic and transformation strain in a loading cycle. The temperature range, in which the fatigue tests were performed, was set according to the experimental results in Figs. 4,5. Lower temperature limit was set to 15 °C since the lower plateau stress decreases upon cycling to 0 MPa, which makes the cyclic tensile test at constant temperature irrecoverable, although the plateau strains are recoverable on heating. Upper temperature limit was set to 80 °C, since the unrecovered strains become too large at higher temperatures and the lower plateau is not present even in the first loading cycle.
3.2 Accumulation of damage via cyclic martensitic transformation under stress It appears that the source of the problems created upon cycling at elevated temperature is the unrecovered strain generated by the martensitic transformation proceeding under very large stress. In this respect, we refer to our earlier work [19], where we concluded that unrecovered strain and lattice defects are introduced by the forward and/or reverse martensitic transformation only if it proceeds under external stress. The amount of unrecovered strain and lattice defects increases with increasing test temperature and stress, at which the forward and reverse martensitic transformation proceeds. This is demonstrated in the experiment shown in Fig. 6. Less than 0.05 % unrecovered strain was generated both in the tensile loading of martensite at -90 °C (Fig. 6a, g) and austenite at 150 °C (Fig. 6c, i) and very few dislocation defects were observed by TEM in the wires in these tests, since there was no martensitic transformation proceeding under stress. It shall be noted that this was the case in spite of the large stress (900 MPa) and large strain (9 %) applied in the shape memory tests (Fig. 6a, g). These evidences show that the austenite and martensite phases, if they do not transform under high stress, are highly resistant against dislocation slip or any other source of inelastic deformation. On the other hand, significant unrecovered strain of 1.3 % is generated by the forward and reverse martensitic transformation in the same wire at approx. 900 MPa and 500 MPa, respectively, even though the maximum stress and strain in the loading cycle are comparable to the previous tests performed at -90 °C and 150 °C. The unrecovered strain and lattice defects are generated during both forward and reverse transformation approximately equally [6] and the amount of unrecovered strain depends on the stress and temperature at which the transformation proceeds. The accumulated unrecovered strain exceeds 3% in just 10 cycles of superelastic tensile loading at 80 °C and the wire fails at ~900 cycles (Fig. 6h).
Fig. 6. Stress-strain response of the NiTi wire in tensile tests at various temperatures: a) -90 °C b) 80 °C, c) 150 °C. Lattice defect observed in the microstructure (bright field TEM micrographs) after deformation (d, e, f) and cyclic stress-strain response recorded in cyclic tensile tests (g, h, i). The wire is heated/cooled stress free to restore the austenite prior the next tensile loading in case of (g). Since no martensitic transformation under stress takes place in the tests (a, g) and (c,1), lattice defects and unrecovered strain are massively generated only in b) and h). 3.3 Fatigue tests of superelastic NiTi Superelastic stress-strain curves evolving upon tensile cycling in fatigue tests at various test temperatures are shown in Fig 7. The maximum strain applied in each test was set to the end of upper plateau strain at a given temperature, which means that it increased with increasing test temperature. This is because comparison of complete and partial superelastic tests is meaningless if the deformation is localized. Fatigue tests were repeated 5 times at temperatures 15 °C, 20 °C, 40 °C, 60 °C and 80 °C to capture probabilistic character of fatigue life. The upper plateau stress increases with increasing temperature from 450 MPa at 15 °C to 870 MPa at 80 °C. This is a decisive factor for functional fatigue as well as structural fatigue.
Fig. 7. Evolution of stress-strain response of the NiTi wires in the superelastic fatigue test at constant temperature: a) 15 °C, b) 20 °C, c) 40 °C, d) 50 °C, e) 60 °C and f) 80 °C. The key characteristics of functional fatigue (accumulation of unrecovered strain, variation of plateau stresses, variation of stress hysteresis) are common for fatigue tests at all temperatures. The upper plateau stress decreases of around 200 MPa upon cycling. This is rather similar for all temperatures and hardly related to the significant change in fatigue life. However, important feature of fatigue tests below 50 °C is the persistence of plateau character of the stress-strain response up to failure. On the other hand, the upper and lower plateaus not only decrease but becomes gradually lost upon cycling above 50 °C. Because of that, the evolution of stress-strain response is clearly different below and above 50 °C.
The accumulated unrecovered strain increases with increasing temperature (Fig. 9) and there is no saturation upon cycling. However, the accumulation of unrecovered strain upon cycling can be divided into two stages. Large unrecovered strain u is rapidly accumulated in the stage I and much less in stage II. The two stages are clearly distinguished by different slopes in Fig. 9. The higher is the temperature the shorter is the stage I. The slopes in both stages increase with increasing test temperature. Fatigue life decreases with increasing temperature, but one cannot mutually separate the effects of test temperature, upper plateau stress, upper plateau strain and unrecovered strain (linked to the evolution of microstructure) on the number of cycles to failure Nf, since they are coupled. This is documented in 3D diagrams (Fig. 8a, b) showing how number of cycles to failure vary with the test temperature, upper plateau stress and unrecovered strain accumulated in the fatigue tests.
Fig. 8. Representation of the fatigue results in a 3D space: a) Temperaturetransformation stress-fatigue life and b) Temperature-unrecovered strain-fatigue life.
Fig. 9 Accumulation of the unrecovered strain during fatigue tests at various temperatures in a logarithmic scale. Majority of the unrecovered strain is accumulated in the stage I and after transition to the stage II follows approx. linear increase in the unrecovered strain.
Fig. 10. Fatigue life as a function of: a) unrecovered strain accumulated in 10 cycles (green) and the total unrecovered strain (red), b) unrecovered strain rate in stage II. Error bars shows standard deviation calculated out of 5 fatigue tests at the tested temperatures. Fig. 10 suggests how fatigue life correlates with: i) accumulated unrecovered strain in the 10th cycle, ii) accumulated unrecovered strain in the Nfth cycle and iii) unrecovered strain rate in the stage II. We assume that the accumulated unrecovered strain is linked to the accumulated damage upon cycling and that the accumulated damage includes slip dislocations, internal stress, microcracks on the surface or at inclusions etc., but we do not know which out of these have the decisive influence on the fatigue life.
Our preliminary TEM investigations of lattice defects in the microstructure of wires cycled to failure show one additional feature which appears in the microstructure after cycling deformation bands. Fig. 11 shows microstructure of NiTi wires cycled to failure at 20 °C (Nf≅ 3600 cycles) and 80 °C (Nf≅900 cycles). In addition to the high density of slip dislocations and bending contrast due to internal stress, there are deformation bands containing B19’ martensite or {114} austenite twins in the microstructure of fatigue cycled wires (especially at 80 °C).
Fig. 11. Microstructures observed in superelastically cycled NiTi wire at test temperature a) 20 °C (approx. 3600 cycles) and b) 80 °C (approx. 900 cycles).
Fig. 12. a) Evolution of stress-strain response of the NiTi wire in the superelastic fatigue test consisting of cycling at 50 °C for 100 cycles followed by cycling to failure (Nf≅3100 cycles) at 20 °C compared to b) fatigue test performed at 20 °C only. Fatigue test consisting of initial cycling/stabilisation for 100 cycles at 50 °C followed by decrease of temperature to 20 °C and cycling to failure were performed to investigate the effects of stabilisation at higher temperatures on functional and structural fatigue (see Fig. 12). (Stabilisation at temperatures above 50 °C was not used as superelastic plateau would be lost.) Fatigue life in this regime is much closer to tests carried out at 20 °C only than that of carried out at 50 °C only. Slightly lower fatigue life compared to 20 °C (3100 vs 3600 cycles) could be attributed to higher maximum strain (8 % instead of 7.5 %) and higher plateau stress in the initial 100-cycle phase. Unrecovered strain rate of the sample is also comparable to the samples tested at 20 °C only, however, slightly lower (10 × 10-6 %/cycle vs 17 × 10-6 %/cycle) suggesting that the initial microstructure is more stabilized/deteriorated by the initial 100 cycles at 50 °C than cycling at 20 °C only. 4. Discussion The central idea of the present work is that cyclic forward and reverse stress induced martensitic transformation leads to accumulation of lattice defects, internal strains and internal stresses in the bulk of NiTi wire which represents material damage leading to functional fatigue (change of stress-strain response) and structural fatigue (number of cycles to failure Nf). If that is the case, there shall be link between the functional and structural fatigue. This does not mean that there are no other sources of material damage as microcracks on the surface [29] or at the nonmetallic inclusions [15,16] which play significant role as well. They do but let us assume that the origin of the low cycle superelastic fatigue of NiTi consists in the above introduced accumulation of lattice defects, internal strains and stresses.
Since superelastic NiTi wires have been successfully employed in medical devices in the last decades, significant attention was paid to high cycle fatigue in elastic or near elastic regime. This is important from an application point of view. However, low cycle fatigue in which the wire is deformed up to the end of transformation plateau or beyond, is more interesting from the fundamental point of view, since it is directly related to the mechanism by which the cyclic stress-induced martensitic transformation brings about accumulation of the damage and failure. Since whole volume of the cycled NiTi wire nominally passes through the same cyclic deformation history, the lattice defects observed in the microstructure can be correlated with macroscopic variables and parameters determined from stress-strain tests. The occurrence of deformation bands with {114} austenite twins in the microstructure of wires deformed superelastically at elevated temperatures was ascribed to the activity of the stress induced B2=>B19’=>B2T martensitic transformation (involves deformation twinning in martensite) at elevated temperatures and stresses in [6, 19]. However, the unrecovered strain generated in a single cycle is relatively small in the present fatigue experiments and the difference between plateau stress and yield stress is rather large compared to the tensile tests above 100 °C (Fig. 4). The question is how high density of dislocations and a few deformation bands were introduced after 3600 tensile cycles at 20 °C and many deformation bands after 900 tensile cycles at 80 °C. Some information on the accumulation of slip dislocations and deformation bands upon superelastic cycling can be found in our related work [6]. For detailed information on the deformation bands generated by the cyclic superelastic deformation see [23]. Although we do not know the exact reason why deformation bands are created upon thousands of cycles at low temperature (Fig. 10a), it is closely related to the above-mentioned evolution of microstructure and damage upon cycling which is represented by the accumulation of unrecovered strain. Different approach to low-cycle superelastic fatigue of NiTi was applied in the literature [1,5,11-13,30-35] as concerns the role of the applied stress and strain amplitudes, mean stress and mean strain, strain rate, temperature or microstructure (grain size, precipitates etc.). We assume that the accumulation of unrecovered strain correlates better with changes in a microstructure and functional fatigue than the maximum applied stress or strain amplitude in a loading cycle commonly assumed in the NiTi fatigue research. We believe that this is mainly since the energy storage and damage accumulation is caused by plastic deformation accompanying the martensitic transformation under stress, which can be measured as the unrecovered strain of a superelastic stress-strain curve.
Various fatigue criteria have been recently proposed in the literature to deal with the mechanism of damage accumulation. A fatigue criterion proposing that number of superelastic cycles to failure is related to the dissipated energy (area of hysteresis loop) was proposed in [30,31] for bulk samples with shorter plateau strain ~3 %. In [31] is stated that although the energy-based damage parameter based on the first cycle response is easier to obtain and provides reasonable predictions, the stable cycle response accounts for evolution of stress-strain curves, which is similar to our results based on accumulation of unrecovered strain (Fig. 10). The advantage of the energy-based criterion is that it takes properly into account the role of the energy dissipation due to the martensitic transformation (the more transformation in one cycle, the more damage accumulation and shorter fatigue life). The disadvantage is that only fraction of the dissipated energy is transferred to damage accumulation and the rest is dissipated as a latent heat. Another problem is that hysteresis area evolves upon cycling. Especially, hysteresis area quickly decreases to a fraction of the original value at higher temperatures (Fig. 7) and area of the hysteresis loop at 80 °C becomes smaller than at 20 °C suggesting higher fatigue life at 80 °C. In [32] is shown that cumulative energy-based damage parameter provides sufficient correlation of fatigue data from superelastic NiTi specimens with different cyclic deformation responses and transformation stresses are taken into account. The energy-based approach was further elaborated to stored energy-based criteria [33] that solved the problems with the neglected temperature/transformation stress and evolution of the hysteresis loop area upon cycling. It becomes clear that one needs to estimate only the fraction of the mechanical energy, which is stored into the lattice defects during the cycling. We have recently proposed an experimental method for evaluation of unrecovered strain generated separately by the forward and reverse transformation under stress [6]. We claim that the unrecovered strains are generated due to requirement for strain compatibility at the habit plane interfaces by the slip of dislocations generated in this process in austenite phase. The unrecovered strains generated in this way are proposed to be taken as a quantifier of the mechanical stored energy and damage during the superelastic cycling. This criterion predicts relatively well the effect of increasing temperature/stress on the fatigue life of superelastically cycled NiTi wire (Fig. 9,10). As the unrecovered strain is proportional to transformation strain, it works equally well as the dissipation energy criterion as concerns the effect of the extent of transformation. The fatigue life decreases with increasing accumulated unrecovered strain in the 10 cycles and that recorded at failure (Fig. 10a). That is mainly due to the unrecovered strain accumulated in stage I, which is, however, not the deciding parameter since the wire spends most of its lifetime
in the stage II. Moreover, fatigue life is not affected by conditions in the first cycles in the stage I as much as functional fatigue (see Fig. 12). Therefore, we evaluated the rate of accumulation of unrecovered strain in the stage II (the slope in Fig. 9) and plotted it in Fig. 10b instead of unrecovered strain. This dependence captures the effect of temperature, microstructure, stress amplitude etc. on the fatigue life even better than the unrecovered strain. Based on the results of superelastic experiments we performed so far, we propose that the rate of accumulation of unrecovered strain in the stage II best describes the accumulation of damage in the performed fatigue tests. In the frame of underlying theory of transformation-plasticity coupling [6,19], this means that the cumulative mechanism of transformation-plasticity coupling derived from the requirement for strain compatibility at the habit plane interfaces propagating during the reverse transition plays the key role in the damage accumulation. This implies that, if the coupling of martensitic transformation with plastic deformation at the habit plane interface can be completely avoided, millions of superelastic cycles shall be attainable (neglecting effects of inclusions, surface quality, corrosion etc.), similar to that observed in tensile cycling in the elastic range up to strain <1 %. Another important aim of these experiments is to estimate temperature range, at which the NiTi wire can be effectively used in the superelastic regime. As well known, there are restrictions in the temperature range both on the lower and upper end. The restriction comes mainly from the high unrecovered strain and rapid functional degradation upon cycling at high temperatures (Fig. 7). At low temperatures, the lower plateau must not decrease to 0 MPa upon cycling. It comes out that the tested superelastic wires with 100-200nm grain size can be used in the temperature range from 15 °C to 50 °C approximately. This range could be moderately increased by decreasing strain rate, which was 0.01 s-1 in these fatigue tests. Nonetheless, the temperature range is quite in a contrast to the temperature range given by Af=-8 °C and Md>200 °C temperatures. The underlying problem is a rather high
dσ dT
value in the
Clausius-Clapeyron relation for NiTi alloy (6.5 MPa/°C in the linear part of the σ-T diagram shown in Fig.5a). This high value restricts superelastic applications of NiTi alloy in a wider temperature range unlike Co49Ni21Ga30 alloy, where the
dσ dT
ratio is below 1 MPa/°C [36].
Therefore, upper plateau stress exceeds 1 GPa above 100 °C and reaches tensile strength at around 150 °C. As multiple processes are involved (B2=>B19’=>B2T transformation mechanism and plasticity) in the plateau at higher temperatures, Clausius–Clapeyron relation loses its conventional meaning as a way of characterizing a discontinuous phase transition between two phases only.
5. Conclusions Superelastic NiTi wires were deformed in tension until fracture in wide temperature range from -90 °C to 190 °C and fatigue tests in displacement-controlled regime (loading/unloading up to the end of transformation plateaus) were performed with following main results:
Unrecovered strain is generated only when forward or reverse martensitic transformations proceed under external stress in cyclic mechanical or thermomechanical loads, in particular unrecovered strain is generated neither upon tensile loading in the martensite state nor upon tensile loading at high temperatures in the austenite state, in spite of large strains up to 9 % and/or high stresses around 1 GPa applied in these tests.
The accumulation of unrecovered strain during the superelastic cycling correlates with accumulation of material damage, which controls fatigue performance of NiTi alloy (neglecting effects of inclusions, surface quality, etc.).
The unrecovered strains generated in fatigue tests increase with increasing test temperature and stresses at which forward and reverse martensitic transformations proceed.
Number of cycles to failure observed in tensile fatigue tests decreases with increasing test temperature and transformation stress.
Number of cycles to failure correlates with unrecovered strain in the first cycles as well as with unrecovered strain rate in the ‘stabilized stage’ of fatigue life.
It is proposed that fatigue life of superelastic NiTi cycled in tension at various temperatures can be estimated based on the 3D Nf-εus-T diagram characterising unrecovered strains generated by forward and reverse martensitic transformation at different temperatures and stresses. The temperature range, at which the tested NiTi wire with Af=-8°C can be effectively utilized with respect to recoverability of martensitic transformation and stability of superelastic cycles is approximately 15 °C to 50 °C. The rate of the accumulation of unrecovered strain in the stage II of tensile cycling increasing with increasing temperature was suggested as a predictor for accumulation of material damage upon cycling, which controls the superelastic fatigue performance of the wire.
Acknowledgements Support of the research from Czech Science Foundation projects 18-03834S (P. Šittner, O. Tyc), 17-00393J (L. Heller) is acknowledged. MEYS of the Czech Republic is acknowledged for the support of infrastructure projects FUNBIO-SAFMAT (LM2015088), LNSM (LM2015087), SOLID 21 (CZ.02.1.01/0.0/0.0/16_019/0000760) and ESS - participation of the Czech Republic – OP (CZ.02.1.01/0.0/0.0/16_013/0001794). References [1] ongoing
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Highlights:
Unrecovered strain is generated in martensitic transformation under external stress
The unrecovered strain is proposed to quantify accumulation of microstructure damage
Microstructure changes/damage significantly increases with increasing temperature
Superelastic fatigue life correlates with accumulation of unrecovered strain
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0142-1123(20)30001-3 https://doi.org/10.1016/j.ijfatigue.2020.105470 JIJF 105470
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
1 October 2019 27 December 2019 2 January 2020
Please cite this article as: Tyc, O., Heller, L., Vronka, M., Šittner, P., Effect of temperature on fatigue of superelastic NiTi wires, International Journal of Fatigue (2020), doi: https://doi.org/10.1016/j.ijfatigue. 2020.105470
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Effect of temperature on fatigue of superelastic NiTi wires Ondřej Tyc a,c, Luděk Heller a,b, Marek Vronka a and Petr Šittner a,b a Institute of Physics of the CAS, Na Slovance 1992/2, 18221 Prague, CR b Nuclear Physics Institute of the CAS, Husinec - Řež 130, 250 68, Řež, CR c Faculty of Nuclear Sciences and Physical Engineering, CTU Prague, Prague 2, CR
Corresponding author: Ondřej Tyc, E-mail- [email protected] Postal address: Institute of Physics of the CAS, Na Slovance 1992/2, 18221 Prague, CR
Effect of temperature on fatigue of superelastic NiTi wires Abstract: The stress induced martensitic transformation in superelastic NiTi alloy can be accompanied by a plastic deformation. In this work, NiTi wires were subjected to tensile displacement-controlled tests in the temperature range -90 °C to 190 °C and lattice defects created by the deformation were analysed by TEM. The unrecovered strain significantly increased and fatigue life decreased with increasing test temperature. The rate of the accumulation of unrecovered strain in the stabilized stage of tensile cycling was taken as an indicator of the accumulation of material damage. Fatigue life ranged from 900 cycles at 80 °C to 4700 cycles at 15 °C.
Keywords: NiTi alloy; superelasticity; fatigue; unrecovered strain
1. Introduction NiTi based alloys have been utilized in a wide range of engineering applications in medicine, aerospace, transport, robotics and automotive industry owing to their unique superelastic and shape memory functional behaviour [1-3]. However, engineering applications utilizing cyclic martensitic transformation are seriously limited by the functional and structural fatigue of NiTi [4,5]. It is well known that the stress induced martensitic transformation in superelastic NiTi tends to be accompanied by unrecovered strain. Lattice defects are introduced upon thermomechanical cycling, microstructure evolves irreversibly, unrecovered strain accumulates and functional properties gradually change upon cycling [6-8]. In tension, the number of superelastic cycles to failure is limited to a few thousands only [9], while millions of cycles can be reached in compression [10]. Fatigue of superelastic NiTi wires in tension was extensively investigated from different perspectives and critical factors were identified as: transformation strain [11], transformation stress/temperature [12-14], inclusions (O-rich and C-rich phases) acting as nucleation sites of fatigue cracks mainly on a surface [15,16], strain localization [17], surface finishing [14] and Ni-rich precipitates [12]. What is not yet clear is how the functional fatigue is related to the structural fatigue. In this study, thin superelastic NiTi wires were subjected to tensile fatigue tests in displacementcontrolled regime (loading to the end of transformation plateau) at various temperatures. The aim was to investigate the effect of temperature on functional and structural fatigue in a view of our recent results concerning the transformation plasticity coupling in NiTi [6,18,19] and deformation twinning in martensite [20-23]. As the difference between the stress required for stress induced martensitic transformation and deformation twinning in martensite decreases with increasing temperature, the experimentally observed unrecovered strain increases. Deformation bands containing {114} austenite twins were observed in the microstructure of wires deformed in a single tensile cycle at elevated temperature for which the plateau stress equals to yield stress [21]. Similar deformation bands containing either martensite or {114} austenite twins were observed later after several cycles in [23], where the difference between plateau stress and yield stress is rather large. The deformation twinning in martensite has been called non-transformation pathway by Gao et al [24,25] from theoretical point of view and proposed to be an origin of functional fatigue of NiTi. To further explore the link between functional and structural fatigue of superelastic NiTi alongside the above ideas, functional and structural fatigue of superelastic NiTi wire was investigated at various temperatures. A new criterion for fatigue of superelastic NiTi alloys is
proposed assuming that the rate of unrecovered strain accumulation (functional fatigue) scales with number of cycles to failure (structural fatigue). 2. Material and Methods Cold-worked Ni-rich NiTi wire (Ti-50.9at. %Ni, 42.1 % CW, 0.1 mm in the diameter) was used in the experiments. The NiTi wire was heat treated by electric current pulse (25 Wmm-3/100 ms) to obtain superelastic samples with a nanograin structure (approx. 100-200 nm) and very low dislocation density within the grains (Fig. 1). Tensile tests were performed using miniature deformation rig MITTER (Fig. 2) allowing mechanical testing and pulse heat treatment by electric current. Peltier elements were controlling testing temperature in the range -30 °C to 200 °C. More detailed information on the testing rig can be found in [26,27]. Tests below the lower temperature limit of the Peltier elements were carried out by means of aluminium heat sink filled with liquid nitrogen placed on the top of the copper body of the chamber to reach temperatures down to -100 °C. Clamping ends of the wires into stainless steel capillaries (1.6 mm in the outer and 0.18 mm in the inner diameter) was needed for an easier manipulation and gripping. Length of the sample between the capillaries was 50 mm so the sample fits into the 80mm long copper chamber and can be kept at homogenous temperature.
Fig. 1. Stress-strain tensile curves to fracture of the NiTi wires in a cold worked (green) and the heat-treated (red) state at 20 °C. Bright field TEM micrograph shows the heat-treated microstructure used in the tensile and fatigue experiments.
Fig. 2. Miniature tensile tester MITTER (equipped with a load cell, stepper motor, position encoder, Peltier based environmental chamber, resistance measurement and closed-loop LabView-based control system) used to perform both the electro-pulse heat treatment and thermomechanical loading tests of the NiTi wires. Tensile tests were performed at various temperatures in the range –90 °C to 190 °C. The tests were run in a displacement-controlled regime according to the test program outlined in Fig. 3 with the aim to explore superelastic stress-strain response of NiTi wires and deformation until rupture simultaneously. The main evaluated quantities are: upper plateau stress pUP, upper plateau strain pUP and unrecovered strain US in the first superelastic cycle, yield stress Y (point above upper plateau of the first where stress-strain curve deviates from linear path) and tensile strength max. Strain rate of the test was 0.001 s-1.
Fig. 3. Testing of mechanical properties (upper plateau stress pUP, upper plateau strain pUP, unrecovered strain us, yield stress Y and tensile strength max) of the NiTi wire consisting of superelastic cycle to the end of stress plateau followed by tensile test to fracture at 80 °C and strain rate 0.001 s-1.
Fatigue tests were performed at 0.01 s-1 strain rate in the displacement-controlled regime. Since the
higher
strain
rate
affects
the
stress-strain
response
[28]
owing
to
the
exothermic/endothermic character of the forward/reverse martensitic transformation, cycles at lower strain rate (0.001 s-1) were added to fatigue tests for monitoring of evolution of a stressstrain response. The lower loading limit was 10 MPa, which prevents buckling of the NiTi wires as unrecovered strain accumulates in the superelastic fatigue cycling above Af temperature. The upper loading limit was set to the end of stress plateau at a given temperature. The temperature range of fatigue experiments was 15 °C-80 °C. Fatigue tests on the superelastic samples were repeated 5 times, at each temperature level, to capture the scatter of the evaluated fatigue life. Samples for TEM studies of lattice defects in deformed wires were prepared by Focused Ion Beam (FIB) method using FEI Quanta 3D FIB-SEM electron microscope. TEM lamellas were extracted in such a way that the wire axis always lies in the plane of the TEM lamella. TEM observations were carried out using FEI Tecnai TF20 X-twin field emission gun microscope operated at 200 kV. 3. Experimental Results 3.1 Tensile tests Tensile tests were performed according to the test program introduced in Fig. 3. Selected results are presented in Fig. 4. After deformation to the end of stress plateau and unloading, the wires were stress-free heated up to 100 °C above test temperature to relieve residual martensite and determine the unrecovered strain [21] introduced during the first superelastic cycle. Finally, the wires were deformed to failure to determine the yield stress and strength. (For the tests above 100 °C, yield stress was determined from direct loading to failure as only one loading/unloading cycle significantly changes this variable.) The temperature dependence of the upper plateau stress pUP, upper plateau strain pUP, yield stress Y, and unrecovered strain us, are shown in Fig. 5.
Fig. 4. Stress-strain superelastic response of the NiTi wire in temperature range 0 °C-190 °C. One loading/unloading cycle to the end of upper plateau followed by heating of 100 °C to recover residual martensite and loading to fracture were performed to examine mechanical properties (pUP and Y) and stability (us) of superelastic loops.
With increasing test temperature, the superelastic loop shifts to higher stress, as common for all superelastic alloys, due to the characteristic temperature dependence of transformation stress [20]. However, the yield stress decreases and the unrecoverable strain and plateau strain increase with increasing temperature at the same time. It shall be pointed out that the tested NiTi wires deform in a localized manner by propagation of martensite band fronts at constant
plateau stress [17] at any test temperature. This does not necessarily mean that the stress induced cubic to monoclinic transformation is the only deformation mechanism activated within the propagating martensite band front. Stress plateau may involve deformation twinning in the martensite phase and dislocation slip to achieve strain compatibility in moving habit planes (see [21] for detailed discussion). The plateau strains are completely reversible upon unloading and heating (Fig. 5b) in tensile tests at low temperatures (T<20 °C). The unrecovered strain recorded after the first cycle in tensile test at 0 °C (pUP= 365 MPa and Y= 1140 MPa) was only 0.03 %. With increasing test temperature, the unrecovered strain gradually increases up to 1 % in the tensile test at 80 °C (pUP= 870 MPa and Y= 1090 MPa). In tensile tests at temperatures above 80 °C (Fig. 5b), the unrecovered strain starts to increase sharply. The forward plateau strain reaches 11 % out of which 8% remains unrecovered in the tensile test at 190 °C. This suggests an onset of the activity of different deformation mechanisms (transformation plasticity coupling and deformation twinning in martensite) in the tensile test [18, 21].
Fig. 5. Effect of temperature on mechanical and superelastic properties of the NiTi wire- a) evolution of upper plateau stress and yield stress, b) recoverable and unrecovered strain after loading cycle to the end of superelastic plateau in the range -20 °C to 190 °C (Af=-8°C). Recoverable strain is the sum of elastic and transformation strain in a loading cycle. The temperature range, in which the fatigue tests were performed, was set according to the experimental results in Figs. 4,5. Lower temperature limit was set to 15 °C since the lower plateau stress decreases upon cycling to 0 MPa, which makes the cyclic tensile test at constant temperature irrecoverable, although the plateau strains are recoverable on heating. Upper temperature limit was set to 80 °C, since the unrecovered strains become too large at higher temperatures and the lower plateau is not present even in the first loading cycle.
3.2 Accumulation of damage via cyclic martensitic transformation under stress It appears that the source of the problems created upon cycling at elevated temperature is the unrecovered strain generated by the martensitic transformation proceeding under very large stress. In this respect, we refer to our earlier work [19], where we concluded that unrecovered strain and lattice defects are introduced by the forward and/or reverse martensitic transformation only if it proceeds under external stress. The amount of unrecovered strain and lattice defects increases with increasing test temperature and stress, at which the forward and reverse martensitic transformation proceeds. This is demonstrated in the experiment shown in Fig. 6. Less than 0.05 % unrecovered strain was generated both in the tensile loading of martensite at -90 °C (Fig. 6a, g) and austenite at 150 °C (Fig. 6c, i) and very few dislocation defects were observed by TEM in the wires in these tests, since there was no martensitic transformation proceeding under stress. It shall be noted that this was the case in spite of the large stress (900 MPa) and large strain (9 %) applied in the shape memory tests (Fig. 6a, g). These evidences show that the austenite and martensite phases, if they do not transform under high stress, are highly resistant against dislocation slip or any other source of inelastic deformation. On the other hand, significant unrecovered strain of 1.3 % is generated by the forward and reverse martensitic transformation in the same wire at approx. 900 MPa and 500 MPa, respectively, even though the maximum stress and strain in the loading cycle are comparable to the previous tests performed at -90 °C and 150 °C. The unrecovered strain and lattice defects are generated during both forward and reverse transformation approximately equally [6] and the amount of unrecovered strain depends on the stress and temperature at which the transformation proceeds. The accumulated unrecovered strain exceeds 3% in just 10 cycles of superelastic tensile loading at 80 °C and the wire fails at ~900 cycles (Fig. 6h).
Fig. 6. Stress-strain response of the NiTi wire in tensile tests at various temperatures: a) -90 °C b) 80 °C, c) 150 °C. Lattice defect observed in the microstructure (bright field TEM micrographs) after deformation (d, e, f) and cyclic stress-strain response recorded in cyclic tensile tests (g, h, i). The wire is heated/cooled stress free to restore the austenite prior the next tensile loading in case of (g). Since no martensitic transformation under stress takes place in the tests (a, g) and (c,1), lattice defects and unrecovered strain are massively generated only in b) and h). 3.3 Fatigue tests of superelastic NiTi Superelastic stress-strain curves evolving upon tensile cycling in fatigue tests at various test temperatures are shown in Fig 7. The maximum strain applied in each test was set to the end of upper plateau strain at a given temperature, which means that it increased with increasing test temperature. This is because comparison of complete and partial superelastic tests is meaningless if the deformation is localized. Fatigue tests were repeated 5 times at temperatures 15 °C, 20 °C, 40 °C, 60 °C and 80 °C to capture probabilistic character of fatigue life. The upper plateau stress increases with increasing temperature from 450 MPa at 15 °C to 870 MPa at 80 °C. This is a decisive factor for functional fatigue as well as structural fatigue.
Fig. 7. Evolution of stress-strain response of the NiTi wires in the superelastic fatigue test at constant temperature: a) 15 °C, b) 20 °C, c) 40 °C, d) 50 °C, e) 60 °C and f) 80 °C. The key characteristics of functional fatigue (accumulation of unrecovered strain, variation of plateau stresses, variation of stress hysteresis) are common for fatigue tests at all temperatures. The upper plateau stress decreases of around 200 MPa upon cycling. This is rather similar for all temperatures and hardly related to the significant change in fatigue life. However, important feature of fatigue tests below 50 °C is the persistence of plateau character of the stress-strain response up to failure. On the other hand, the upper and lower plateaus not only decrease but becomes gradually lost upon cycling above 50 °C. Because of that, the evolution of stress-strain response is clearly different below and above 50 °C.
The accumulated unrecovered strain increases with increasing temperature (Fig. 9) and there is no saturation upon cycling. However, the accumulation of unrecovered strain upon cycling can be divided into two stages. Large unrecovered strain u is rapidly accumulated in the stage I and much less in stage II. The two stages are clearly distinguished by different slopes in Fig. 9. The higher is the temperature the shorter is the stage I. The slopes in both stages increase with increasing test temperature. Fatigue life decreases with increasing temperature, but one cannot mutually separate the effects of test temperature, upper plateau stress, upper plateau strain and unrecovered strain (linked to the evolution of microstructure) on the number of cycles to failure Nf, since they are coupled. This is documented in 3D diagrams (Fig. 8a, b) showing how number of cycles to failure vary with the test temperature, upper plateau stress and unrecovered strain accumulated in the fatigue tests.
Fig. 8. Representation of the fatigue results in a 3D space: a) Temperaturetransformation stress-fatigue life and b) Temperature-unrecovered strain-fatigue life.
Fig. 9 Accumulation of the unrecovered strain during fatigue tests at various temperatures in a logarithmic scale. Majority of the unrecovered strain is accumulated in the stage I and after transition to the stage II follows approx. linear increase in the unrecovered strain.
Fig. 10. Fatigue life as a function of: a) unrecovered strain accumulated in 10 cycles (green) and the total unrecovered strain (red), b) unrecovered strain rate in stage II. Error bars shows standard deviation calculated out of 5 fatigue tests at the tested temperatures. Fig. 10 suggests how fatigue life correlates with: i) accumulated unrecovered strain in the 10th cycle, ii) accumulated unrecovered strain in the Nfth cycle and iii) unrecovered strain rate in the stage II. We assume that the accumulated unrecovered strain is linked to the accumulated damage upon cycling and that the accumulated damage includes slip dislocations, internal stress, microcracks on the surface or at inclusions etc., but we do not know which out of these have the decisive influence on the fatigue life.
Our preliminary TEM investigations of lattice defects in the microstructure of wires cycled to failure show one additional feature which appears in the microstructure after cycling deformation bands. Fig. 11 shows microstructure of NiTi wires cycled to failure at 20 °C (Nf≅ 3600 cycles) and 80 °C (Nf≅900 cycles). In addition to the high density of slip dislocations and bending contrast due to internal stress, there are deformation bands containing B19’ martensite or {114} austenite twins in the microstructure of fatigue cycled wires (especially at 80 °C).
Fig. 11. Microstructures observed in superelastically cycled NiTi wire at test temperature a) 20 °C (approx. 3600 cycles) and b) 80 °C (approx. 900 cycles).
Fig. 12. a) Evolution of stress-strain response of the NiTi wire in the superelastic fatigue test consisting of cycling at 50 °C for 100 cycles followed by cycling to failure (Nf≅3100 cycles) at 20 °C compared to b) fatigue test performed at 20 °C only. Fatigue test consisting of initial cycling/stabilisation for 100 cycles at 50 °C followed by decrease of temperature to 20 °C and cycling to failure were performed to investigate the effects of stabilisation at higher temperatures on functional and structural fatigue (see Fig. 12). (Stabilisation at temperatures above 50 °C was not used as superelastic plateau would be lost.) Fatigue life in this regime is much closer to tests carried out at 20 °C only than that of carried out at 50 °C only. Slightly lower fatigue life compared to 20 °C (3100 vs 3600 cycles) could be attributed to higher maximum strain (8 % instead of 7.5 %) and higher plateau stress in the initial 100-cycle phase. Unrecovered strain rate of the sample is also comparable to the samples tested at 20 °C only, however, slightly lower (10 × 10-6 %/cycle vs 17 × 10-6 %/cycle) suggesting that the initial microstructure is more stabilized/deteriorated by the initial 100 cycles at 50 °C than cycling at 20 °C only. 4. Discussion The central idea of the present work is that cyclic forward and reverse stress induced martensitic transformation leads to accumulation of lattice defects, internal strains and internal stresses in the bulk of NiTi wire which represents material damage leading to functional fatigue (change of stress-strain response) and structural fatigue (number of cycles to failure Nf). If that is the case, there shall be link between the functional and structural fatigue. This does not mean that there are no other sources of material damage as microcracks on the surface [29] or at the nonmetallic inclusions [15,16] which play significant role as well. They do but let us assume that the origin of the low cycle superelastic fatigue of NiTi consists in the above introduced accumulation of lattice defects, internal strains and stresses.
Since superelastic NiTi wires have been successfully employed in medical devices in the last decades, significant attention was paid to high cycle fatigue in elastic or near elastic regime. This is important from an application point of view. However, low cycle fatigue in which the wire is deformed up to the end of transformation plateau or beyond, is more interesting from the fundamental point of view, since it is directly related to the mechanism by which the cyclic stress-induced martensitic transformation brings about accumulation of the damage and failure. Since whole volume of the cycled NiTi wire nominally passes through the same cyclic deformation history, the lattice defects observed in the microstructure can be correlated with macroscopic variables and parameters determined from stress-strain tests. The occurrence of deformation bands with {114} austenite twins in the microstructure of wires deformed superelastically at elevated temperatures was ascribed to the activity of the stress induced B2=>B19’=>B2T martensitic transformation (involves deformation twinning in martensite) at elevated temperatures and stresses in [6, 19]. However, the unrecovered strain generated in a single cycle is relatively small in the present fatigue experiments and the difference between plateau stress and yield stress is rather large compared to the tensile tests above 100 °C (Fig. 4). The question is how high density of dislocations and a few deformation bands were introduced after 3600 tensile cycles at 20 °C and many deformation bands after 900 tensile cycles at 80 °C. Some information on the accumulation of slip dislocations and deformation bands upon superelastic cycling can be found in our related work [6]. For detailed information on the deformation bands generated by the cyclic superelastic deformation see [23]. Although we do not know the exact reason why deformation bands are created upon thousands of cycles at low temperature (Fig. 10a), it is closely related to the above-mentioned evolution of microstructure and damage upon cycling which is represented by the accumulation of unrecovered strain. Different approach to low-cycle superelastic fatigue of NiTi was applied in the literature [1,5,11-13,30-35] as concerns the role of the applied stress and strain amplitudes, mean stress and mean strain, strain rate, temperature or microstructure (grain size, precipitates etc.). We assume that the accumulation of unrecovered strain correlates better with changes in a microstructure and functional fatigue than the maximum applied stress or strain amplitude in a loading cycle commonly assumed in the NiTi fatigue research. We believe that this is mainly since the energy storage and damage accumulation is caused by plastic deformation accompanying the martensitic transformation under stress, which can be measured as the unrecovered strain of a superelastic stress-strain curve.
Various fatigue criteria have been recently proposed in the literature to deal with the mechanism of damage accumulation. A fatigue criterion proposing that number of superelastic cycles to failure is related to the dissipated energy (area of hysteresis loop) was proposed in [30,31] for bulk samples with shorter plateau strain ~3 %. In [31] is stated that although the energy-based damage parameter based on the first cycle response is easier to obtain and provides reasonable predictions, the stable cycle response accounts for evolution of stress-strain curves, which is similar to our results based on accumulation of unrecovered strain (Fig. 10). The advantage of the energy-based criterion is that it takes properly into account the role of the energy dissipation due to the martensitic transformation (the more transformation in one cycle, the more damage accumulation and shorter fatigue life). The disadvantage is that only fraction of the dissipated energy is transferred to damage accumulation and the rest is dissipated as a latent heat. Another problem is that hysteresis area evolves upon cycling. Especially, hysteresis area quickly decreases to a fraction of the original value at higher temperatures (Fig. 7) and area of the hysteresis loop at 80 °C becomes smaller than at 20 °C suggesting higher fatigue life at 80 °C. In [32] is shown that cumulative energy-based damage parameter provides sufficient correlation of fatigue data from superelastic NiTi specimens with different cyclic deformation responses and transformation stresses are taken into account. The energy-based approach was further elaborated to stored energy-based criteria [33] that solved the problems with the neglected temperature/transformation stress and evolution of the hysteresis loop area upon cycling. It becomes clear that one needs to estimate only the fraction of the mechanical energy, which is stored into the lattice defects during the cycling. We have recently proposed an experimental method for evaluation of unrecovered strain generated separately by the forward and reverse transformation under stress [6]. We claim that the unrecovered strains are generated due to requirement for strain compatibility at the habit plane interfaces by the slip of dislocations generated in this process in austenite phase. The unrecovered strains generated in this way are proposed to be taken as a quantifier of the mechanical stored energy and damage during the superelastic cycling. This criterion predicts relatively well the effect of increasing temperature/stress on the fatigue life of superelastically cycled NiTi wire (Fig. 9,10). As the unrecovered strain is proportional to transformation strain, it works equally well as the dissipation energy criterion as concerns the effect of the extent of transformation. The fatigue life decreases with increasing accumulated unrecovered strain in the 10 cycles and that recorded at failure (Fig. 10a). That is mainly due to the unrecovered strain accumulated in stage I, which is, however, not the deciding parameter since the wire spends most of its lifetime
in the stage II. Moreover, fatigue life is not affected by conditions in the first cycles in the stage I as much as functional fatigue (see Fig. 12). Therefore, we evaluated the rate of accumulation of unrecovered strain in the stage II (the slope in Fig. 9) and plotted it in Fig. 10b instead of unrecovered strain. This dependence captures the effect of temperature, microstructure, stress amplitude etc. on the fatigue life even better than the unrecovered strain. Based on the results of superelastic experiments we performed so far, we propose that the rate of accumulation of unrecovered strain in the stage II best describes the accumulation of damage in the performed fatigue tests. In the frame of underlying theory of transformation-plasticity coupling [6,19], this means that the cumulative mechanism of transformation-plasticity coupling derived from the requirement for strain compatibility at the habit plane interfaces propagating during the reverse transition plays the key role in the damage accumulation. This implies that, if the coupling of martensitic transformation with plastic deformation at the habit plane interface can be completely avoided, millions of superelastic cycles shall be attainable (neglecting effects of inclusions, surface quality, corrosion etc.), similar to that observed in tensile cycling in the elastic range up to strain <1 %. Another important aim of these experiments is to estimate temperature range, at which the NiTi wire can be effectively used in the superelastic regime. As well known, there are restrictions in the temperature range both on the lower and upper end. The restriction comes mainly from the high unrecovered strain and rapid functional degradation upon cycling at high temperatures (Fig. 7). At low temperatures, the lower plateau must not decrease to 0 MPa upon cycling. It comes out that the tested superelastic wires with 100-200nm grain size can be used in the temperature range from 15 °C to 50 °C approximately. This range could be moderately increased by decreasing strain rate, which was 0.01 s-1 in these fatigue tests. Nonetheless, the temperature range is quite in a contrast to the temperature range given by Af=-8 °C and Md>200 °C temperatures. The underlying problem is a rather high
dσ dT
value in the
Clausius-Clapeyron relation for NiTi alloy (6.5 MPa/°C in the linear part of the σ-T diagram shown in Fig.5a). This high value restricts superelastic applications of NiTi alloy in a wider temperature range unlike Co49Ni21Ga30 alloy, where the
dσ dT
ratio is below 1 MPa/°C [36].
Therefore, upper plateau stress exceeds 1 GPa above 100 °C and reaches tensile strength at around 150 °C. As multiple processes are involved (B2=>B19’=>B2T transformation mechanism and plasticity) in the plateau at higher temperatures, Clausius–Clapeyron relation loses its conventional meaning as a way of characterizing a discontinuous phase transition between two phases only.
5. Conclusions Superelastic NiTi wires were deformed in tension until fracture in wide temperature range from -90 °C to 190 °C and fatigue tests in displacement-controlled regime (loading/unloading up to the end of transformation plateaus) were performed with following main results:
Unrecovered strain is generated only when forward or reverse martensitic transformations proceed under external stress in cyclic mechanical or thermomechanical loads, in particular unrecovered strain is generated neither upon tensile loading in the martensite state nor upon tensile loading at high temperatures in the austenite state, in spite of large strains up to 9 % and/or high stresses around 1 GPa applied in these tests.
The accumulation of unrecovered strain during the superelastic cycling correlates with accumulation of material damage, which controls fatigue performance of NiTi alloy (neglecting effects of inclusions, surface quality, etc.).
The unrecovered strains generated in fatigue tests increase with increasing test temperature and stresses at which forward and reverse martensitic transformations proceed.
Number of cycles to failure observed in tensile fatigue tests decreases with increasing test temperature and transformation stress.
Number of cycles to failure correlates with unrecovered strain in the first cycles as well as with unrecovered strain rate in the ‘stabilized stage’ of fatigue life.
It is proposed that fatigue life of superelastic NiTi cycled in tension at various temperatures can be estimated based on the 3D Nf-εus-T diagram characterising unrecovered strains generated by forward and reverse martensitic transformation at different temperatures and stresses. The temperature range, at which the tested NiTi wire with Af=-8°C can be effectively utilized with respect to recoverability of martensitic transformation and stability of superelastic cycles is approximately 15 °C to 50 °C. The rate of the accumulation of unrecovered strain in the stage II of tensile cycling increasing with increasing temperature was suggested as a predictor for accumulation of material damage upon cycling, which controls the superelastic fatigue performance of the wire.
Acknowledgements Support of the research from Czech Science Foundation projects 18-03834S (P. Šittner, O. Tyc), 17-00393J (L. Heller) is acknowledged. MEYS of the Czech Republic is acknowledged for the support of infrastructure projects FUNBIO-SAFMAT (LM2015088), LNSM (LM2015087), SOLID 21 (CZ.02.1.01/0.0/0.0/16_019/0000760) and ESS - participation of the Czech Republic – OP (CZ.02.1.01/0.0/0.0/16_013/0001794). References [1] ongoing
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Highlights:
Unrecovered strain is generated in martensitic transformation under external stress
The unrecovered strain is proposed to quantify accumulation of microstructure damage
Microstructure changes/damage significantly increases with increasing temperature
Superelastic fatigue life correlates with accumulation of unrecovered strain
Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: