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Structural and functional fatigue of NiTi shape memory alloys
Materials Science and Engineering A 378 (2004) 24–33
Structural and functional fatigue of NiTi shape memory alloys G. Eggeler∗ , E. Hornbogen, A. Yawny1 , A. Heckmann, M. Wagner Institut für Werkstoffe, Ruhr-Universität Bochum, Universitätsstrasse 150 44780 Bochum, Germany Received 18 June 2003; received in revised form 25 June 2003
Abstract Cyclic loading is one of the generic characteristic features of many of the present and potential future applications of NiTi shape memory alloys, no matter whether they exploit mechanical (pseudo-elasticity) or thermal shape memory (one and two way effect). Cyclic loading may well be associated with structural and functional fatigue, which both limit the service life of shape memory components. By “structural fatigue” we mean the microstructural damage that accumulates during cyclic loading and eventually leads to fatigue failure. There is a need to understand how microstructures can be optimized to provide good fatigue resistance. The term “functional fatigue” indicates that shape memory effects like the working displacement in a one way effect (1WE) actuator or the dissipated energy in a loading–unloading cycle of a pseudo-elastic (PE) damping application decrease with increasing cycle numbers. This is also due to a gradual change in microstructure. In both cases it is important to know how fatigue cycling affects shape memory properties. The present paper considers structural and functional fatigue of NiTi shape memory alloys. It discusses four cases of fatigue in NiTi shape memory alloys: (1) The evolution of the stress–strain hysteresis in low cycle pull–pull fatigue of pseudo-elastic NiTi wires. (2) Bending–rotation fatigue rupture of pseudo-elastic NiTi wires. (3) Strain localization during the stress induced formation of martensite. (4) Generic features of functional fatigue in NiTi shape memory actuator springs. The paper shows that fatigue of shape memory alloys is a fascinating research field and highlights the need for further work in this area. © 2004 Elsevier B.V. All rights reserved. Keywords: Fatigue; NiTi shape memory alloys; Structural fatigue; Functional fatigue
1. Introduction Fatigue of materials refers to the changes in properties resulting from an application of cyclic loads in strain or load control, and research into fatigue dates a long time back [1]. Fatigue research had reached a high level long before shape memory alloys were commercially successful. The technical importance of fatigue was realized in the middle of the nineteenth century, when the term fatigue was coined [2] and Wöhler [3] published his famous S-N concept. Materials science research into metal fatigue started with the work of Bauschinger [4] and Masing [5,6] who explained why fatigue is usually associated with tension–compression asymmetries. Further progress was made by Basquin [7], Manson [8] and Coffin [9], who related fatigue rupture to imposed elastic [7] (small total strains) and plastic strain ∗ Corresponding author. Tel.: +49-234-322-3022; fax: +49-234-321-4235. E-mail address: [email protected] (G. Eggeler). 1 on leave from Centro Atomico Bariloche, Argentina.
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.327
[8,9] (large total strains). The work of Paris [10] started the field of research into fatigue crack growth. Important contributions to the physical understanding of plastic deformation and crack growth were made by Lukas, Klesnil and Polak (detailed analysis of fatigue hysteresis) [11], Winter (dislocation substructures, hard and soft regions) [12], Mughrabi (dislocation substructures, persistent slip bands) [13], and Neumann (fatigue crack growth in single crystals) [14]. And it was also recognized that a stress induced phase transformation in front of a growing fatigue crack can be beneficial and can contribute to longer fatigue lives [15,16]. Many other researchers have contributed to the development of the fatigue field and today the basics of structural fatigue are well understood [1,17,18]. And it is well appreciated that the behaviour of different engineering materials under cyclic loading is generally complex and depends on the strength of the materials, their microstructures, their surface qualities, and the type of fatigue loading [19,20]. Engineers and scientists concerned with fatigue had to learn to accept that fatigue data are generally associated with some scatter related to testing, sampling and the nature of
G. Eggeler et al. / Materials Science and Engineering A 378 (2004) 24–33 Table 1 Some typical SM applications, underlying SM effects and expected fatigue lives Nf [52] Application
SM effect
Expected fatigue lives Nf
Thermal valve Positioning Robot gripper Orthodontic wire Stents Damping, internal friction
1WE 2WE 2WE PE PE PE
104 105 106 105 108 108
fatigue damage accumulation [20]. They therefore have to use safety factors in their design procedures against fatigue and they have to discuss fatigue data on a probabilistic basis [20]. Shape memory materials have unique properties and have been described in terms of basic materials science [21–23] and applications [24–26] on many occasions in the literature. The functional properties of shape memory alloys clearly represent the reason for their success; but there are also many applications where structural properties are very important. This particularly holds for cases where SMAs are cyclically loaded. In Table 1 we list some typical cycle numbers which typical SM components must withstand in service. We subdivide fatigue of shape memory alloys into structural fatigue and functional fatigue. By structural fatigue we mean that shape memory alloys subjected to high cyclic loads can fail like any other engineering material. But unlike normal engineering materials shape memory alloys show different properties in different temperature ranges and it has to be discussed how the characteristic temperature ranges [21–23] affect fatigue characteristics. It also has to be established how a stress induced martensitic transformation interacts with cyclic strain accumulation and fatigue damage accumulation. The term functional fatigue indicates that during cyclic loading, shape memory alloys generally suffer a decrease in functional properties (like the exploitable displacement in a 1WE application or the dissipated energy in a pseudo-elastic damping application). There is a need to understand the underlying microstructural processes for safe design of SMA components. An early study on structural fatigue in pseudo-elastic Ni–Ti appeared in 1979 [27] and a first review on extensive Japanese work in this area was published in 1990 [28]. But only within the last five years structural fatigue of NiTi shape memory alloys has become a popular research topic [25,29–36]. Tobushi et al. [32] and Miyazaki and co-workers [29,30] established bending–rotation fatigue (BRF) testing as a simple and powerful tool [31]; and Duerig et al. [25] showed that the BRF-data of Miyazaki’s group have a good predictive potential for other types of fatigue loading; they [25] moreover pointed out that fatigue loading is important for Ni–Ti components used in medical applications. Tobushi et al. [32] published low-cycle fatigue data on Ni–Ti wires in different environments and
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studied the influence of fatigue test temperature and alloy processing temperature. In addition, they proposed a simple phenomenological fatigue equation which accounts for imposed strain, temperature and martensite start temperature. Reinoehl et al. [33] reported that carbide inclusions do not significantly affect fatigue rupture behavior in BRF. Only recently it was qualitatively discussed [34] how stress induced formation of martensite in front of a growing crack can slow down crack growth rates [37]. And it was discussed [34–38] how strain localization can occur in stress controlled pull–pull fatigue tests and how the stress–strain hysteresis changes during cycling for different microstructures. So far we considered structural fatigue in NiTi, where a stress induced martensitic transformation needs to be considered. We now discuss fatigue effects in 1WE NiTi spring actuators. The design principles of such actuators have been described in the literature [39,40]. At ambient temperature, actuator springs are usually in their martensitic state. They deform when they are loaded with a work load W: this represents a pseudo plastic deformation of martensite, where the external stress favours certain martensite variants which grow and thus enforce an elongation of the spring. When the spring is heated above the austenite start temperature and towards the austenite finish temperature it contracts and lifts the load. During this process the stress due to the external load affects the transformation temperature and thus stabilizes the martensitic phase. Another important characteristic feature of the heating and cooling of a shape memory spring is the hysteresis which occurs [40]. Transformation temperatures and hysteresis widths are alloy dependent. They also depend on microstructure and can be altered by a change of chemical composition [40]. Tamura et al. [41] have discussed how microstructural evolution during thermal cycling can influence the performance of shape memory springs. Most importantly they conclude that the dislocation density increases during thermal cycling and that this affects functional properties. Recently, Morgan and Friend [42] published a review on fatigue of shape memory alloys and clearly demonstrated that both structural and functional fatigue need to be discussed in terms of changes of the microstructure during cycling. From what has been outlined so far it is clear that basic and applied research into fatigue of shape memory alloys must focus on many aspects which cannot all be covered in the present contribution. We therefore select four examples of fatigue phenomena which allow an appreciation of the questions and problems encountered when working on fatigue phenomena in shape memory alloys: (1) The evolution of the stress–strain hysteresis in low cycle pull–pull fatigue of pseudo-elastic NiTi wires. (2) Bending–rotation fatigue rupture of pseudo-elastic NiTi wires. (3) Strain localization during the stress induced formation of martensite. (4) Generic features of functional fatigue in NiTi shape memory actuator springs.
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2. Materials and experiments 2.1. Pull–pull and bending–rotation fatigue of wires 50.9 at.% Ni–Ti wires with diameters of 1.0, 1.2 and 1.4 mm were purchased from Memory-Metalle, Weil am Rhein. The wire with a diameter of 1.4 mm was subjected to pull–pull fatigue testing (first set of fatigue tests; all details on pull–pull fatigue testing will be published elsewhere [43]). All three wire diameters were subjected to bending–rotation fatigue testing (second set of fatigue tests). The wires were produced by hot extrusion, wire drawing (final drawing ratio: 40%), final straightening (involving a 1 min anneal at 783 K) and chemical etching to clean the surface. The beginning of the R-phase transformation was below room temperature [44]. Transmission electron microscopy (TEM) showed [44] that the average grain size of the material is 50 nm, and that the matrix mainly consists of B2-phase. Ni-rich precipitates of type Ni4 Ti3 were not observed. Scanning electron microscopy (SEM) proved [44] that the wires contained TiC inclusions and that due to the wire drawing process fine scratches can be detected in the wire surfaces. Slow isothermal pull–pull fatigue tests were carried out on an Instron 5567 electro mechanical test machine. Pull–pull experiments were carried through to 30 loading/unloading cycles under displacement control (strain rate ≈ 10−4 s−1 ) in the temperature range between 301 and 323 K. Bending–rotation fatigue (BRF) testing was performed at an ambient temperature of 293 K, using a test rig where a wire (which was bent into a semi-circular shape) was forced into rotation by a motor running at a constant rotational speed; a schematic drawing of the BRF setup is shown in Fig. 1. Low friction bearings were used to keep torsion loading of the wire at a minimum; and an inductive proximity sensor was used to count the number of cycles to fatigue failure. Our BRF experiments are characterized by a strain amplitude εa of
Fig. 1. Schematic illustration of the bending–rotation fatigue test rig. The wire is bent into a semi-circular shape (radius of curvature: R) and forced to rotate along its axis by a motor attached to one end. In a simplified mechanical model, the strain in the cross section of the wire is a linear function of the distance from the neutral axis (y = 0).
εa =
d 2R
(1)
where “R” represents the radius of the semicircle and “d” the diameter of the wire [45]. 2.2. Pull–pull fatigue testing of flat specimens In a third set of experiments, flat electro polished tensile specimens from an alloy with 50.7 at.% NiTi (with an initial grain size of 34 m) were subjected to pull–pull fatigue testing on a ZWICK 1387. The material was investigated in three microstructural conditions: solution annealed (1123 K for 15 min followed by water quenching; this yields a single phase B2 microstructure), aged (solution annealed and subsequently aged at 623 K for 1 h; here metastable Ni4 Ti3 particles precipitate) and thermo mechanically treated (solution annealed, then cold rolled at 123 K in the martensitic state and finally aged at 623 K for 1 h; this yields a microstructure with precipitates and dislocations). In all three cases the martensite start temperatures are far below room temperature [46]. The tests were performed in strain control at a deformation rate vd of 0.5 mm/min at 294 K; however, the unloading cycles were only performed until a small rest load of 30 N remained (in order to avoid specimen disalignment). One objective of this third set of fatigue experiments was to demonstrate how microstructure affects the stress–strain characteristics during cyclic loading. Another objective was to study local transformation strain at high imposed total strains. For this purpose the gauge length of one specimen was marked with lines of micro hardness indents (spacing 500 m). Details of the experimental procedures have been published elsewhere [37,46]. 2.3. Functional fatigue of shape memory springs And finally, a fourth set of fatigue experiments was performed to study functional fatigue of shape memory springs which lift a load of 3 N. The shape memory actuator springs were produced from 49.5 at.% NiTi wires. The wires were cold worked to a final wire diameter of 0.80 mm (final drawing ratio 20.0%). They were then shaped into helical coil springs (outer spring diameter 6.5 mm, length 16 mm, number of active turns: 20) and subjected to a heat treatment of 600 s at 673 K. Our test rig for spring testing is schematically illustrated in Fig. 2. At 293 K the spring is in its martensitic state; the end load position is xM (low temperature position; index M for martensite). The spring is then heated (resistive direct current heating: 5 V, 4.8 A) to a temperature above the austenite finish temperature. The spring contracts and lifts the end load to the position xA (high temperature position; index A for austenite). When the spring has reached a stable high temperature position (austenitic state) the current is switched off and the spring cools back down to ambient temperature. On cooling the spring elongates and finally reaches another position xM . In our experiments we measure
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increasing cycle number. Fig. 3 shows that irreversible strain accumulates during strain controlled pull–pull loading. And it can be seen that plateau stresses depend very strongly on temperature. This reflects the stress dependence of the martensite start temperature as described by an equation of Clausius–Clapeyron type [34]. A detailed description of our pull–pull fatigue results will be given elsewhere [43]. 3.2. Bending–rotation fatigue of wires
Fig. 2. Schematic illustration of the actuator spring test rig. When the spring is heated to a temperature above Af , it contracts. Thus, it lifts the weight W from the low temperature position xM to the high temperature position xA .
how the positions xA and xM change with cycle number N and how this affects the working displacement of A which is defined by ∆(N) = xA (N) − xM (N)
(2)
In this paper we present results for N = 1000 thermal cycles.
3. Results 3.1. Pull–pull fatigue of wires Results from slow isothermal pull–pull wire testing obtained at test temperatures of 301 and 323 K are shown in Fig. 3a and b. Fig. 3a and b show the stress–strain curves for cycle numbers 1, 5 and 30. It is important to note that the total strain is a sum of elastic, plastic and pseudo-elastic contributions, and this also holds for all other pseudo-elastic loading/unloading scenarios discussed in this work. It can be seen that the stress–strain curves change throughout the first 30 load cycles: The plateau stresses and the areas between the loading and unloading stress–strain curves decrease with
BRF fatigue rupture results are presented in Fig. 4 [44]. Fig. 4a shows fatigue rupture data which were obtained for the three different wire diameters at a rotational speed of 200 rotations/min (rpm). In a good engineering approximation all data can be represented by one common master curve when plotting εa (as defined by Eq. (1)) versus N f (the number of cycles to failure). A close inspection of the individual data points, however, suggests that there is a small but systematic effect of wire diameter on rupture lives: data from wires with larger diameters (empty circles: d = 1.4 mm) systematically mark the left side of the narrow εa –N f scatter band while data associated with smaller wire diameters systematically show larger rupture lives (empty triangles: d = 1.0 mm). The εa –N f curve in Fig. 4a can be subdivided into three regimes. For εa > 1% (regime 1), rupture occurs early (low N f ) and fatigue rupture lives strongly depend on εa (steep slope of this linear part of the εa –N f curve). At 0.75% < εa < 1% (regime 2), fatigue lives strongly increase, the slope of the εa –N f curve in this second linear part decreases and there is significant scatter in fatigue rupture lives. For εa < 0.75% (regime 3), no fatigue rupture occurred up to cycle numbers of 106 . Fig. 4b shows BRF fatigue rupture data which were obtained for wires with diameters of 1.2 mm (Nf < 104 ) and 1.4 mm (Nf > 104 ) at different rotational speeds. It can be clearly seen that the deformation rate (which is directly proportional to the rotational speed) affects the BRF fatigue rupture data for high values of εa . For εa = 2.0%, the fastest roational speed (800 rpm) is associated with the
Fig. 3. Representative stress–strain data from slow loading–unloading tensile tests obtained for a wire with a diameter of 1.4 mm at 301 and 323 K (strain rate: 10−4 s−1 ).
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Fig. 4. BRF rupture data of wires tested in the test rig shown in Fig. 1(a). Fatigue rupture data which were obtained for three different wire diameters at a rotational speed of 200 rotations/min. The four data points at Nf = 106 represent experiments where no rupture occurred; this is indicated by the arrow which points in the direction of higher cyclic lives. (b) BRF rupture data which were obtained for wires with diameters of 1.2 mm (Nf < 104 ) and 1.4 mm (Nf > 104 ) at different rotational speeds ranging from 100 to 800 rotations/min.
shortest cyclic rupture life (Nf = 288) while at the slowest rotational speed (100 rpm) a cyclic rupture life of Nf = 1131 is observed. This difference in cycles to failure decreases as εa decreases and at εa = 0.88% no more influence of deformation rate on fatigue rupture behavior can be observed. The εa –N f curve in Fig. 4b shows the regimes 1 and 2. In regime 1 (for εa > 1.0%) rupture lives strongly depend on εa and this is most pronounced for slow rotational speeds. In regime 2, there is no more significant effect of rotational speed on fatigue rupture lives (εa < 1.0%). And below εa = 0.88% no fatigue rupture is observed for cycle numbers up to 106 . The apparent size effect and the effect of rotational speed on rupture lives are related to the production of heat during the stress induced formation of martensite. In order for the martensite to form martensite/austenite-interfaces must move and this process dissipates energy and produces heat; this leads to an increase in wire temperature during testing in regime 1, where a significant part of the outer wire cross section is subjected to the stress induced formation of martensite. For reasons of thermal conductivity, more heat is stored
in thicker wires than in thinner wires, because the thinner wire is more effectively cooled by the environment. And secondly, more heat is produced for higher rotational speeds than for lower rotational speeds, where more time is left for cooling. Therefore wire temperatures increase faster for thicker wires (small effect) and for higher rotational speeds (large effect). As can be seen from the uniaxial tensile data shown in Fig. 3, a small increase in temperature (from 301 to 323 K) results in a significant increase of plateau stress from 540 to 650 MPa. So when the wire temperature increases during testing, the surface stress associated with the strain controlled loading condition also increases and the strain controlled fatigue experiment corresponds to an ever increasing surface stress at constant εa . And under conditions where surface stresses increase faster, fatigue rupture occurs earlier. It has been recently demonstrated that these effects are no longer detected when the temperature of the wire specimen is kept constant [47]. Fig. 5 shows a wire specimen with a diameter of 1.4 mm with an imposed radius of curvature R = 40 mm which was subjected to a rotational speed of 200 rpm and failed after 1283 cycles. Fig. 5a shows a full view of the rupture surface in a low magnification SEM micrograph. Fig. 5b identifies the location where the fatigue crack started (CS) and indicates the directions of fatigue crack growth. And Fig. 5c provides a schematic three-dimensional picture of the direction of crack propagation in the tensile part of the BRF-cycle (note that our crack in Fig. 5c opens and closes as the wire rotates). In our recent study, [44] an effort was made to identify locations where fatigue cracks started to grow. For this purpose each ruptured specimen was carefully studied in the SEM. It turned out that fatigue cracks always nucleate at the specimen surface. Cracks were found to start at surface irregularities, scratches and TiC inclusions which act as stress raisers during cyclic loading [44]. 3.3. Pull–pull fatigue testing of flat specimens In our fatigue experiments with flat specimens [37,38,46] we demonstrate the importance of microstructure in total strain controlled fatigue. Fig. 6 shows the stress–strain responses of materials which were deformed at 294 K at a total deformation rate of 0.5 mm/min. Fig. 6a shows the stress–strain characteristics of a solution annealed material. The mechanical response of the thermo mechanically treated alloy, Fig. 6b, looks very different: Here stable stress–strain cycles are observed. The aged material shows a behaviour which is in between these two cases (not shown here). For all three microstructures strain localization is observed. This is shown in Fig. 7a and b for the solution annealed and thermo mechanically treated alloy, respectively. In the case of the solution annealed material extended localized shear/transformation-bands are observed, Fig. 8. Strain/transformation-localization is also observed in the aged and in the thermo mechanically treated alloys; but the degree of heterogeneity is much smaller and transformation
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Fig. 5. Rupture surface, location of crack initiation and direction of crack growth in a wire specimen (with a diameter of d = 1.4 mm and an imposed radius of curvature of R = 40 mm) which was subjected to a rotational speed of 200 rpm and failed after 1283 cycles: (a) low magnification overview SEM micrograph—full view of the rupture surface; (b) schematic drawing to identify the location where the fatigue crack started (“CS”) and to indicate the directions of crack growth (arrows starting at CS); (c) schematic three-dimensional picture of the direction of crack propagation in the tensile part of the BRF-cycle.
generally starts at more than one location [46]. Strain localization is a well known phenomenon in physical metallurgy. In iron carbon alloys Lüders bands nucleate and grow [48] and in low stacking fault and in precipitation hardened mate-
rials [49,50] strain localization occurs through the formation of slip and shear bands. A common feature for such localization phenomena is a scarcity of nucleation sites; and once nucleation (of a mechanical slip or shear band or of stress
Fig. 6. Stress–strain curves associated with 12 deformation cycles (first, second and 12th cycles shown) of materials which were deformed at 294 K at a total deformation rate of 0.5 mm/min: (a) solution annealed material; (b) thermo mechanically treated material.
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Fig. 7. Three-dimensional plot of the evolution of local strain with macroscopic strain in the first loading cycle. The three-dimensional plot indicates (i) the position of the gauge length, (ii) the local strain and (iii) the macroscopic strain. (a) Solution annealed material with strongly localized transformation strain. (b) Thermo mechanically treated material with a more homogeneous strain distribution.
induced martensite) has occurred, the strained/transformed regions grow by auto-catalytic processes. Here we have seen that microstructures are very important in affecting the stress–strain response of a NiTi alloy subjected to total strain controlled pull–pull loading; they also affect the degree of strain/transformation localization during cyclic loading. Microstructures can be optimized for good fatigue resistance. 3.4. Functional fatigue of shape memory springs Fig. 9a and b show results which are typical for the behaviour of NiTi spring actuators loaded in tension. Fig. 9a shows displacement–temperature curves after the first, second and thousandth actuator cycle. The evolution of the
high and low temperature positions xA and xM (as defined in Fig. 2) are shown as a function of the cycle number in Fig. 9b. During the first 100 cycles the actuator spring suffers irreversible plastic deformation in both phases: the spring elongates and xM and xA decrease. Finally the effect saturates and from then on xM and xA are more or less stable. The working displacement ∆, however, increases during the first 100 cycles, because the decrease of xM is stronger than that of xA . The results presented in Fig. 9 are representative for thermal cycling experiments with springs under various loads and heat treatment conditions and more results on the influence of microstructure and different spring geometries will be published elsewhere [51].
4. Discussion 4.1. Fatigue loading and temperature
Fig. 8. Extended localized shear/transformation band in solution annealed material which forms during the first load cycle. Optical micrograph of the microstructure associated with Figs. 6a and 7a (solution annealed and water quenched polycrystalline material state).
Engineers will normally focus on one specific type of component subjected to one specific type of fatigue loading exploiting mechanical or thermal shape memory. But nevertheless it is important to understand the effect of temperature T on deformation/transformation events which we expect when our shape memory alloy is subjected to isothermal cyclic loading. We expect that the fatigue behaviour will differ depending on whether the low temperature phase is stable, whether it is possible to transform the high temperature phase to martensite by applying a stress or whether the high temperature phase is stable. It was recently explained [52] why temperature effects on the response of shape memory alloys to cyclic loading have to be discussed with respect to the underlying phase transition temperatures Ms and Mf (temperatures where the formation of martensite starts and finishes on cooling) and As and Af (temperatures where the formation of austenite starts and finishes on heating). And these phase transition temperatures are known to depend on chemical composition, on microstructure and on applied
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Fig. 9. Change of spring geometry during thermal cycling with an end load of 3 N. (a) Displacement–temperature hysteresis in the first, second and thousandth cycle. (b) Positions xA and xM as a function of the numbers of cycles N.
stress. In the present study we have presented fatigue results for two characteristic cyclic loading conditions: mechanical cycling of a pseudo-elastic alloy (Af < T < Md , where Md represents the temperature above which a stress induced formation of martensite is no longer possible) and thermal cycling in a 1-WE application (low temperature: T < Mf ; high temperature: T > Af ). There also is a need to understand how NiTi behaves in other temperature ranges [52]. Thus, below the martensite finish temperature Mf , cyclic loading at constant temperature will result in the motion of twin boundaries. And above Md (and at temperatures where diffusion is not yet important) we observe normal fatigue of the high temperature phase. And at even higher temperatures where diffusion becomes significant, precipitation processes can occur and creep processes contribute to the microstructural evolution associated with cyclic loading. In BRF experiments, the apparent size effects and the apparent influence of loading rate on fatigue rupture are due to adiabatic heating of our pseudo-elastic wire specimens; these temperature effects also need to be considered when discussing fatigue of other pseudo-elastic NiTi components. 4.2. Cyclic loading and plasticity When investigating fatigue of shape memory alloys we need to consider how the microstructure of our material affects the stress–strain hysteresis. Here, we have seen that microstructure is very important. When suitable thermo mechanical treatments are applied it is possible to stabilize the stress–strain-behaviour during cycling and to influence the degree of strain/transformation–localization during cyclic loading. In order to achieve a high number of stable cycles during pseudo-elastic loading it is important to ensure that the pseudo-elastic plateau stress (where stress induced martensite forms) is smaller than the yield stress of the austenite; this guarantees that there is only a limited increase of dislocation density during cyclic loading and thus only little accumulation of residual strain (plastic and pseudo plas-
tic deformation). In this respect NiTi shape memory alloys outperform iron based SMAs where the high temperature phase is soft [52,53]. Our results suggest that marforming of NiTi followed by aging yields promising results. However, we also find that it is not possible to completely avoid that irreversible strains increase. This is due to an increase of dislocation density and the formation of stabilized martensite variants which do not transform back to austenite after unloading. In the case of our actuator spring we find that the positions xA and xM change; it seems reasonable to attribute the change of the position of xA to an increase of dislocation density. The more pronounced change of xM (as compared to xA ) is a consequence of the increase of dislocation density and additional formation of specific martensite variants. From an engineering point of view it seems reasonable to differentiate between dislocations which form during service of a shape memory alloy (or as a consequence of fatigue loading of a shape memory specimen) and other dislocations which are intentionally introduced into the material during training procedures for the two way effect (2WE); from a physical point of view training procedures may well be considered as one specific type of low cycle fatigue loading. Due to the high melting temperature of NiTi, diffusion processes are not important in the temperature range where shape memory effects are normally exploited [52,53]; this represents a disadvantage of the CuZn-based SMAs as compared to the more stable NiTi [52,53] (CuZn-based SMAs do not establish the equilibrium ordered phase during normal heat treatments; they therefore strive for higher degrees of order during mechanical cycling, and this is also associated with point defect mobility and a change of properties during cycling [52,53]). Deformation and transformation plasticity are associated with the two types of functional fatigue which we have described in the present study: the evolution of the stress–strain hysteresis during strain controlled mechanical cycling and the shape change of the 1WE spring during thermal cycling. Metal fatigue as well as high stress plastic deformation is often associated with strain localization. And
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in the present study we provide an example for transformation/deformation localization in pseudo-elastic NiTi. 4.3. Fatigue damage accumulation Fatigue damage accumulation is generally associated with the formation of surface cracks and subsequent crack growth. And it has been shown that crack growth in martensite is slower than in austenite and that stress induced formation of martensite reduces crack growth rates [54]. Bending–rotation fatigue is also characterized by crack initiation and crack growth. Engineering surfaces of shape memory wires provide stress raisers like scratches and inclusions where fatigue cracks eventually start; and while the formation of extrusions can also be considered as an alternative way to form fatigue cracks in an ideal surface it does not seem to be important in engineering SMAs. Fatigue striations in the early stages of fatigue crack growth have recently been identified [44]. Structural fatigue of pseudo-elastic shape memory alloys does not differ as far as crack initiation and crack growth are concerned. However, the capability of a shape memory material to form stress induced martensite near local stress raisers is beneficial, as it limits the stress intensity which loads small cracks and contributes to a good fatigue resistance of shape memory alloys [52]. Finally it should be noted that there is only an indirect correlation between stress and strain hysteresis (which is governed by bulk microstructure) and crack nucleation and growth; the latter represents structural fatigue of shape memory alloys and is mainly dependent on surface defects and local surface stress. Small cracks may long have nucleated and grown before their presence can be detected in the stress–strain hysteresis of a fatigue experiment [20]. A good surface finishing therefore can be expected to increase fatigue life.
5. Summary and conclusions The present paper provides a brief introduction into structural and functional fatigue of NiTi shape memory alloys. It then discusses four cases of fatigue in NiTi shape memory alloys: (1) The evolution of the stress–strain hysteresis in low cycle pull–pull fatigue of pseudo-elastic NiTi wires. (2) Bending–rotation fatigue rupture of pseudo-elastic NiTi wires. (3) Strain localization during the stress induced formation of martensite. (4) Generic features of functional fatigue in NiTi shape memory actuator springs. The paper discusses the influence of temperature on the fatigue performance of shape memory alloys. It shows that microstructure is important in governing (i) the stability of the stress– strain hysteresis during strain controlled fatigue loading and (ii) the localization of strain/transformation. Functional fatigue is associated with an increase of residual strain (with plastic and pseudo plastic components) which corresponds to an incomplete reverse transformation. Moreover, it is demonstrated that structural fatigue of pseudo-elastic shape memory alloys is governed by the initiation and growth of surface cracks. Pseudo-elastic shape memory alloys are damage tolerant because the stress induced transformation limits stresses and thus stress intensity factors which drive crack growth. Acknowledgements The authors would like to acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) and the Land Nordrhein-Westfalen (NRW) in the framework of SFB 459 Formgedächtnistechnik (a Research Centre on Shape Memory Technology at the Ruhr-Universität Bochum). References
4.4. Other factors affecting fatigue of shape memory alloys Fatigue is a multiple parameter phenomenon. The present paper has only presented some results on fatigue of NiTi shape memory alloys. It has been shown that temperature, microstructure and surface quality affect the fatigue behaviour. Many additional factors can affect SMA fatigue behaviour: the type of loading (stress or load control, tension/compression asymmetry), the strengths of austenite and martensite, the degree of order of the lattices, the volume fraction and size distributions of particles, the volume change during the transformation, how much PE plateau strain is imposed during strain controlled testing, structural incompatibilities and others. It should also be mentioned that cyclic loading can be accompanied by a change in phase transition temperatures; this also represents a form of functional fatigue. Further work is required to systematically study the importance of these factors.
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G. Eggeler et al. / Materials Science and Engineering A 378 (2004) 24–33 [18] H.O. Fuchs, R.I. Stephens, Metal Fatigue in Engineering, Wiley, New York, 1980. [19] H. Mughrabi, in: J.B. Bilde Søerensen, N. Hansen, D. Juul Jensen, T. Leffers, H. Liholt, O.B. Pedersen (Eds.), Proceedings of the 10th Risø International Symposium on Metallurgy and Materials Science: Materials Architecture, Risø National Laboratory, Roskilde, Denmark, 1989. [20] G. Eggeler, in: J.B. Marriott (Ed.), Assessment of high temperature fatigue activities in the European research project COST 50 (Rounds I–III), Commission of the European Communities, Institute of Advanced Materials, Joint Research Centre Petten, P.O. Box 2, NL-1755 ZG Petten, EUCO/MCS/12/92, August 1992. [21] K. Otsuka, C.M. Wayman, Shape Memory Materials, Cambridge University Press, Cambridge, 1998, pp. 1–26. [22] L. Delaey, Diffusionless transformations, in: R.W. Cahn, P. Haasen, E.J. Kramer (Eds.), Phase Transformations in Materials, Materials Science and Technology—Comprehensive Treatment, vol. 5, VCH, Weinheim, 1991, pp. 339–404. [23] E. Hornbogen, in: W. G.J. Bunk (Ed.), Advanced Structural and Functional Materials, Springer, Heidelberg, 1991, pp. 133–163. [24] J. Van Humbeeck, Mater. Sci. Eng. A273–275 (1999) 134. [25] T. Duerig, A. Pelton, D. Stöckel, Mater. Sci. Eng. A273–275 (1999) 149. [26] K. Otsuka, T. Kakeshita, MRS Bull. 27 (2002) 91. [27] K.N. Melton, O. Mercier, Acta Met. 27 (1979) 137. [28] S. Miyazaki, Zairyo 39 (1990) 1329. [29] Y.S. Kim, S. Miyazaki, in: A. Pelton, D. Hodgson, R. Russel, T. Duerig (Eds.), SMST-97 Proceedings of the International Conference on Shape Memory and Superelastic Technologies, Pacific Grove, USA, 1997. [30] S. Miyazaki, K. Mizukoshi, T. Ueki, T. Sakuma, Y. Liu, Mater. Sci. Eng. A273–275 (1999) 658. [31] Y. Kim, Mater. Trans. 43 (2002) 1703. [32] H. Tobushi, T. Nakahara, Y. Shimeno, T. Hashimoto, Trans. ASME 122 (2000) 186. [33] M. Reinoehl, D. Bradley, R. Bouthot, J. Proft, in: S.M. Russel, A.R. Pelton (Eds.), SMST-2000 Proceedings of the International Confer-
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Structural and functional fatigue of NiTi shape memory alloys G. Eggeler∗ , E. Hornbogen, A. Yawny1 , A. Heckmann, M. Wagner Institut für Werkstoffe, Ruhr-Universität Bochum, Universitätsstrasse 150 44780 Bochum, Germany Received 18 June 2003; received in revised form 25 June 2003
Abstract Cyclic loading is one of the generic characteristic features of many of the present and potential future applications of NiTi shape memory alloys, no matter whether they exploit mechanical (pseudo-elasticity) or thermal shape memory (one and two way effect). Cyclic loading may well be associated with structural and functional fatigue, which both limit the service life of shape memory components. By “structural fatigue” we mean the microstructural damage that accumulates during cyclic loading and eventually leads to fatigue failure. There is a need to understand how microstructures can be optimized to provide good fatigue resistance. The term “functional fatigue” indicates that shape memory effects like the working displacement in a one way effect (1WE) actuator or the dissipated energy in a loading–unloading cycle of a pseudo-elastic (PE) damping application decrease with increasing cycle numbers. This is also due to a gradual change in microstructure. In both cases it is important to know how fatigue cycling affects shape memory properties. The present paper considers structural and functional fatigue of NiTi shape memory alloys. It discusses four cases of fatigue in NiTi shape memory alloys: (1) The evolution of the stress–strain hysteresis in low cycle pull–pull fatigue of pseudo-elastic NiTi wires. (2) Bending–rotation fatigue rupture of pseudo-elastic NiTi wires. (3) Strain localization during the stress induced formation of martensite. (4) Generic features of functional fatigue in NiTi shape memory actuator springs. The paper shows that fatigue of shape memory alloys is a fascinating research field and highlights the need for further work in this area. © 2004 Elsevier B.V. All rights reserved. Keywords: Fatigue; NiTi shape memory alloys; Structural fatigue; Functional fatigue
1. Introduction Fatigue of materials refers to the changes in properties resulting from an application of cyclic loads in strain or load control, and research into fatigue dates a long time back [1]. Fatigue research had reached a high level long before shape memory alloys were commercially successful. The technical importance of fatigue was realized in the middle of the nineteenth century, when the term fatigue was coined [2] and Wöhler [3] published his famous S-N concept. Materials science research into metal fatigue started with the work of Bauschinger [4] and Masing [5,6] who explained why fatigue is usually associated with tension–compression asymmetries. Further progress was made by Basquin [7], Manson [8] and Coffin [9], who related fatigue rupture to imposed elastic [7] (small total strains) and plastic strain ∗ Corresponding author. Tel.: +49-234-322-3022; fax: +49-234-321-4235. E-mail address: [email protected] (G. Eggeler). 1 on leave from Centro Atomico Bariloche, Argentina.
0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.10.327
[8,9] (large total strains). The work of Paris [10] started the field of research into fatigue crack growth. Important contributions to the physical understanding of plastic deformation and crack growth were made by Lukas, Klesnil and Polak (detailed analysis of fatigue hysteresis) [11], Winter (dislocation substructures, hard and soft regions) [12], Mughrabi (dislocation substructures, persistent slip bands) [13], and Neumann (fatigue crack growth in single crystals) [14]. And it was also recognized that a stress induced phase transformation in front of a growing fatigue crack can be beneficial and can contribute to longer fatigue lives [15,16]. Many other researchers have contributed to the development of the fatigue field and today the basics of structural fatigue are well understood [1,17,18]. And it is well appreciated that the behaviour of different engineering materials under cyclic loading is generally complex and depends on the strength of the materials, their microstructures, their surface qualities, and the type of fatigue loading [19,20]. Engineers and scientists concerned with fatigue had to learn to accept that fatigue data are generally associated with some scatter related to testing, sampling and the nature of
G. Eggeler et al. / Materials Science and Engineering A 378 (2004) 24–33 Table 1 Some typical SM applications, underlying SM effects and expected fatigue lives Nf [52] Application
SM effect
Expected fatigue lives Nf
Thermal valve Positioning Robot gripper Orthodontic wire Stents Damping, internal friction
1WE 2WE 2WE PE PE PE
104 105 106 105 108 108
fatigue damage accumulation [20]. They therefore have to use safety factors in their design procedures against fatigue and they have to discuss fatigue data on a probabilistic basis [20]. Shape memory materials have unique properties and have been described in terms of basic materials science [21–23] and applications [24–26] on many occasions in the literature. The functional properties of shape memory alloys clearly represent the reason for their success; but there are also many applications where structural properties are very important. This particularly holds for cases where SMAs are cyclically loaded. In Table 1 we list some typical cycle numbers which typical SM components must withstand in service. We subdivide fatigue of shape memory alloys into structural fatigue and functional fatigue. By structural fatigue we mean that shape memory alloys subjected to high cyclic loads can fail like any other engineering material. But unlike normal engineering materials shape memory alloys show different properties in different temperature ranges and it has to be discussed how the characteristic temperature ranges [21–23] affect fatigue characteristics. It also has to be established how a stress induced martensitic transformation interacts with cyclic strain accumulation and fatigue damage accumulation. The term functional fatigue indicates that during cyclic loading, shape memory alloys generally suffer a decrease in functional properties (like the exploitable displacement in a 1WE application or the dissipated energy in a pseudo-elastic damping application). There is a need to understand the underlying microstructural processes for safe design of SMA components. An early study on structural fatigue in pseudo-elastic Ni–Ti appeared in 1979 [27] and a first review on extensive Japanese work in this area was published in 1990 [28]. But only within the last five years structural fatigue of NiTi shape memory alloys has become a popular research topic [25,29–36]. Tobushi et al. [32] and Miyazaki and co-workers [29,30] established bending–rotation fatigue (BRF) testing as a simple and powerful tool [31]; and Duerig et al. [25] showed that the BRF-data of Miyazaki’s group have a good predictive potential for other types of fatigue loading; they [25] moreover pointed out that fatigue loading is important for Ni–Ti components used in medical applications. Tobushi et al. [32] published low-cycle fatigue data on Ni–Ti wires in different environments and
25
studied the influence of fatigue test temperature and alloy processing temperature. In addition, they proposed a simple phenomenological fatigue equation which accounts for imposed strain, temperature and martensite start temperature. Reinoehl et al. [33] reported that carbide inclusions do not significantly affect fatigue rupture behavior in BRF. Only recently it was qualitatively discussed [34] how stress induced formation of martensite in front of a growing crack can slow down crack growth rates [37]. And it was discussed [34–38] how strain localization can occur in stress controlled pull–pull fatigue tests and how the stress–strain hysteresis changes during cycling for different microstructures. So far we considered structural fatigue in NiTi, where a stress induced martensitic transformation needs to be considered. We now discuss fatigue effects in 1WE NiTi spring actuators. The design principles of such actuators have been described in the literature [39,40]. At ambient temperature, actuator springs are usually in their martensitic state. They deform when they are loaded with a work load W: this represents a pseudo plastic deformation of martensite, where the external stress favours certain martensite variants which grow and thus enforce an elongation of the spring. When the spring is heated above the austenite start temperature and towards the austenite finish temperature it contracts and lifts the load. During this process the stress due to the external load affects the transformation temperature and thus stabilizes the martensitic phase. Another important characteristic feature of the heating and cooling of a shape memory spring is the hysteresis which occurs [40]. Transformation temperatures and hysteresis widths are alloy dependent. They also depend on microstructure and can be altered by a change of chemical composition [40]. Tamura et al. [41] have discussed how microstructural evolution during thermal cycling can influence the performance of shape memory springs. Most importantly they conclude that the dislocation density increases during thermal cycling and that this affects functional properties. Recently, Morgan and Friend [42] published a review on fatigue of shape memory alloys and clearly demonstrated that both structural and functional fatigue need to be discussed in terms of changes of the microstructure during cycling. From what has been outlined so far it is clear that basic and applied research into fatigue of shape memory alloys must focus on many aspects which cannot all be covered in the present contribution. We therefore select four examples of fatigue phenomena which allow an appreciation of the questions and problems encountered when working on fatigue phenomena in shape memory alloys: (1) The evolution of the stress–strain hysteresis in low cycle pull–pull fatigue of pseudo-elastic NiTi wires. (2) Bending–rotation fatigue rupture of pseudo-elastic NiTi wires. (3) Strain localization during the stress induced formation of martensite. (4) Generic features of functional fatigue in NiTi shape memory actuator springs.
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2. Materials and experiments 2.1. Pull–pull and bending–rotation fatigue of wires 50.9 at.% Ni–Ti wires with diameters of 1.0, 1.2 and 1.4 mm were purchased from Memory-Metalle, Weil am Rhein. The wire with a diameter of 1.4 mm was subjected to pull–pull fatigue testing (first set of fatigue tests; all details on pull–pull fatigue testing will be published elsewhere [43]). All three wire diameters were subjected to bending–rotation fatigue testing (second set of fatigue tests). The wires were produced by hot extrusion, wire drawing (final drawing ratio: 40%), final straightening (involving a 1 min anneal at 783 K) and chemical etching to clean the surface. The beginning of the R-phase transformation was below room temperature [44]. Transmission electron microscopy (TEM) showed [44] that the average grain size of the material is 50 nm, and that the matrix mainly consists of B2-phase. Ni-rich precipitates of type Ni4 Ti3 were not observed. Scanning electron microscopy (SEM) proved [44] that the wires contained TiC inclusions and that due to the wire drawing process fine scratches can be detected in the wire surfaces. Slow isothermal pull–pull fatigue tests were carried out on an Instron 5567 electro mechanical test machine. Pull–pull experiments were carried through to 30 loading/unloading cycles under displacement control (strain rate ≈ 10−4 s−1 ) in the temperature range between 301 and 323 K. Bending–rotation fatigue (BRF) testing was performed at an ambient temperature of 293 K, using a test rig where a wire (which was bent into a semi-circular shape) was forced into rotation by a motor running at a constant rotational speed; a schematic drawing of the BRF setup is shown in Fig. 1. Low friction bearings were used to keep torsion loading of the wire at a minimum; and an inductive proximity sensor was used to count the number of cycles to fatigue failure. Our BRF experiments are characterized by a strain amplitude εa of
Fig. 1. Schematic illustration of the bending–rotation fatigue test rig. The wire is bent into a semi-circular shape (radius of curvature: R) and forced to rotate along its axis by a motor attached to one end. In a simplified mechanical model, the strain in the cross section of the wire is a linear function of the distance from the neutral axis (y = 0).
εa =
d 2R
(1)
where “R” represents the radius of the semicircle and “d” the diameter of the wire [45]. 2.2. Pull–pull fatigue testing of flat specimens In a third set of experiments, flat electro polished tensile specimens from an alloy with 50.7 at.% NiTi (with an initial grain size of 34 m) were subjected to pull–pull fatigue testing on a ZWICK 1387. The material was investigated in three microstructural conditions: solution annealed (1123 K for 15 min followed by water quenching; this yields a single phase B2 microstructure), aged (solution annealed and subsequently aged at 623 K for 1 h; here metastable Ni4 Ti3 particles precipitate) and thermo mechanically treated (solution annealed, then cold rolled at 123 K in the martensitic state and finally aged at 623 K for 1 h; this yields a microstructure with precipitates and dislocations). In all three cases the martensite start temperatures are far below room temperature [46]. The tests were performed in strain control at a deformation rate vd of 0.5 mm/min at 294 K; however, the unloading cycles were only performed until a small rest load of 30 N remained (in order to avoid specimen disalignment). One objective of this third set of fatigue experiments was to demonstrate how microstructure affects the stress–strain characteristics during cyclic loading. Another objective was to study local transformation strain at high imposed total strains. For this purpose the gauge length of one specimen was marked with lines of micro hardness indents (spacing 500 m). Details of the experimental procedures have been published elsewhere [37,46]. 2.3. Functional fatigue of shape memory springs And finally, a fourth set of fatigue experiments was performed to study functional fatigue of shape memory springs which lift a load of 3 N. The shape memory actuator springs were produced from 49.5 at.% NiTi wires. The wires were cold worked to a final wire diameter of 0.80 mm (final drawing ratio 20.0%). They were then shaped into helical coil springs (outer spring diameter 6.5 mm, length 16 mm, number of active turns: 20) and subjected to a heat treatment of 600 s at 673 K. Our test rig for spring testing is schematically illustrated in Fig. 2. At 293 K the spring is in its martensitic state; the end load position is xM (low temperature position; index M for martensite). The spring is then heated (resistive direct current heating: 5 V, 4.8 A) to a temperature above the austenite finish temperature. The spring contracts and lifts the end load to the position xA (high temperature position; index A for austenite). When the spring has reached a stable high temperature position (austenitic state) the current is switched off and the spring cools back down to ambient temperature. On cooling the spring elongates and finally reaches another position xM . In our experiments we measure
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increasing cycle number. Fig. 3 shows that irreversible strain accumulates during strain controlled pull–pull loading. And it can be seen that plateau stresses depend very strongly on temperature. This reflects the stress dependence of the martensite start temperature as described by an equation of Clausius–Clapeyron type [34]. A detailed description of our pull–pull fatigue results will be given elsewhere [43]. 3.2. Bending–rotation fatigue of wires
Fig. 2. Schematic illustration of the actuator spring test rig. When the spring is heated to a temperature above Af , it contracts. Thus, it lifts the weight W from the low temperature position xM to the high temperature position xA .
how the positions xA and xM change with cycle number N and how this affects the working displacement of A which is defined by ∆(N) = xA (N) − xM (N)
(2)
In this paper we present results for N = 1000 thermal cycles.
3. Results 3.1. Pull–pull fatigue of wires Results from slow isothermal pull–pull wire testing obtained at test temperatures of 301 and 323 K are shown in Fig. 3a and b. Fig. 3a and b show the stress–strain curves for cycle numbers 1, 5 and 30. It is important to note that the total strain is a sum of elastic, plastic and pseudo-elastic contributions, and this also holds for all other pseudo-elastic loading/unloading scenarios discussed in this work. It can be seen that the stress–strain curves change throughout the first 30 load cycles: The plateau stresses and the areas between the loading and unloading stress–strain curves decrease with
BRF fatigue rupture results are presented in Fig. 4 [44]. Fig. 4a shows fatigue rupture data which were obtained for the three different wire diameters at a rotational speed of 200 rotations/min (rpm). In a good engineering approximation all data can be represented by one common master curve when plotting εa (as defined by Eq. (1)) versus N f (the number of cycles to failure). A close inspection of the individual data points, however, suggests that there is a small but systematic effect of wire diameter on rupture lives: data from wires with larger diameters (empty circles: d = 1.4 mm) systematically mark the left side of the narrow εa –N f scatter band while data associated with smaller wire diameters systematically show larger rupture lives (empty triangles: d = 1.0 mm). The εa –N f curve in Fig. 4a can be subdivided into three regimes. For εa > 1% (regime 1), rupture occurs early (low N f ) and fatigue rupture lives strongly depend on εa (steep slope of this linear part of the εa –N f curve). At 0.75% < εa < 1% (regime 2), fatigue lives strongly increase, the slope of the εa –N f curve in this second linear part decreases and there is significant scatter in fatigue rupture lives. For εa < 0.75% (regime 3), no fatigue rupture occurred up to cycle numbers of 106 . Fig. 4b shows BRF fatigue rupture data which were obtained for wires with diameters of 1.2 mm (Nf < 104 ) and 1.4 mm (Nf > 104 ) at different rotational speeds. It can be clearly seen that the deformation rate (which is directly proportional to the rotational speed) affects the BRF fatigue rupture data for high values of εa . For εa = 2.0%, the fastest roational speed (800 rpm) is associated with the
Fig. 3. Representative stress–strain data from slow loading–unloading tensile tests obtained for a wire with a diameter of 1.4 mm at 301 and 323 K (strain rate: 10−4 s−1 ).
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Fig. 4. BRF rupture data of wires tested in the test rig shown in Fig. 1(a). Fatigue rupture data which were obtained for three different wire diameters at a rotational speed of 200 rotations/min. The four data points at Nf = 106 represent experiments where no rupture occurred; this is indicated by the arrow which points in the direction of higher cyclic lives. (b) BRF rupture data which were obtained for wires with diameters of 1.2 mm (Nf < 104 ) and 1.4 mm (Nf > 104 ) at different rotational speeds ranging from 100 to 800 rotations/min.
shortest cyclic rupture life (Nf = 288) while at the slowest rotational speed (100 rpm) a cyclic rupture life of Nf = 1131 is observed. This difference in cycles to failure decreases as εa decreases and at εa = 0.88% no more influence of deformation rate on fatigue rupture behavior can be observed. The εa –N f curve in Fig. 4b shows the regimes 1 and 2. In regime 1 (for εa > 1.0%) rupture lives strongly depend on εa and this is most pronounced for slow rotational speeds. In regime 2, there is no more significant effect of rotational speed on fatigue rupture lives (εa < 1.0%). And below εa = 0.88% no fatigue rupture is observed for cycle numbers up to 106 . The apparent size effect and the effect of rotational speed on rupture lives are related to the production of heat during the stress induced formation of martensite. In order for the martensite to form martensite/austenite-interfaces must move and this process dissipates energy and produces heat; this leads to an increase in wire temperature during testing in regime 1, where a significant part of the outer wire cross section is subjected to the stress induced formation of martensite. For reasons of thermal conductivity, more heat is stored
in thicker wires than in thinner wires, because the thinner wire is more effectively cooled by the environment. And secondly, more heat is produced for higher rotational speeds than for lower rotational speeds, where more time is left for cooling. Therefore wire temperatures increase faster for thicker wires (small effect) and for higher rotational speeds (large effect). As can be seen from the uniaxial tensile data shown in Fig. 3, a small increase in temperature (from 301 to 323 K) results in a significant increase of plateau stress from 540 to 650 MPa. So when the wire temperature increases during testing, the surface stress associated with the strain controlled loading condition also increases and the strain controlled fatigue experiment corresponds to an ever increasing surface stress at constant εa . And under conditions where surface stresses increase faster, fatigue rupture occurs earlier. It has been recently demonstrated that these effects are no longer detected when the temperature of the wire specimen is kept constant [47]. Fig. 5 shows a wire specimen with a diameter of 1.4 mm with an imposed radius of curvature R = 40 mm which was subjected to a rotational speed of 200 rpm and failed after 1283 cycles. Fig. 5a shows a full view of the rupture surface in a low magnification SEM micrograph. Fig. 5b identifies the location where the fatigue crack started (CS) and indicates the directions of fatigue crack growth. And Fig. 5c provides a schematic three-dimensional picture of the direction of crack propagation in the tensile part of the BRF-cycle (note that our crack in Fig. 5c opens and closes as the wire rotates). In our recent study, [44] an effort was made to identify locations where fatigue cracks started to grow. For this purpose each ruptured specimen was carefully studied in the SEM. It turned out that fatigue cracks always nucleate at the specimen surface. Cracks were found to start at surface irregularities, scratches and TiC inclusions which act as stress raisers during cyclic loading [44]. 3.3. Pull–pull fatigue testing of flat specimens In our fatigue experiments with flat specimens [37,38,46] we demonstrate the importance of microstructure in total strain controlled fatigue. Fig. 6 shows the stress–strain responses of materials which were deformed at 294 K at a total deformation rate of 0.5 mm/min. Fig. 6a shows the stress–strain characteristics of a solution annealed material. The mechanical response of the thermo mechanically treated alloy, Fig. 6b, looks very different: Here stable stress–strain cycles are observed. The aged material shows a behaviour which is in between these two cases (not shown here). For all three microstructures strain localization is observed. This is shown in Fig. 7a and b for the solution annealed and thermo mechanically treated alloy, respectively. In the case of the solution annealed material extended localized shear/transformation-bands are observed, Fig. 8. Strain/transformation-localization is also observed in the aged and in the thermo mechanically treated alloys; but the degree of heterogeneity is much smaller and transformation
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Fig. 5. Rupture surface, location of crack initiation and direction of crack growth in a wire specimen (with a diameter of d = 1.4 mm and an imposed radius of curvature of R = 40 mm) which was subjected to a rotational speed of 200 rpm and failed after 1283 cycles: (a) low magnification overview SEM micrograph—full view of the rupture surface; (b) schematic drawing to identify the location where the fatigue crack started (“CS”) and to indicate the directions of crack growth (arrows starting at CS); (c) schematic three-dimensional picture of the direction of crack propagation in the tensile part of the BRF-cycle.
generally starts at more than one location [46]. Strain localization is a well known phenomenon in physical metallurgy. In iron carbon alloys Lüders bands nucleate and grow [48] and in low stacking fault and in precipitation hardened mate-
rials [49,50] strain localization occurs through the formation of slip and shear bands. A common feature for such localization phenomena is a scarcity of nucleation sites; and once nucleation (of a mechanical slip or shear band or of stress
Fig. 6. Stress–strain curves associated with 12 deformation cycles (first, second and 12th cycles shown) of materials which were deformed at 294 K at a total deformation rate of 0.5 mm/min: (a) solution annealed material; (b) thermo mechanically treated material.
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Fig. 7. Three-dimensional plot of the evolution of local strain with macroscopic strain in the first loading cycle. The three-dimensional plot indicates (i) the position of the gauge length, (ii) the local strain and (iii) the macroscopic strain. (a) Solution annealed material with strongly localized transformation strain. (b) Thermo mechanically treated material with a more homogeneous strain distribution.
induced martensite) has occurred, the strained/transformed regions grow by auto-catalytic processes. Here we have seen that microstructures are very important in affecting the stress–strain response of a NiTi alloy subjected to total strain controlled pull–pull loading; they also affect the degree of strain/transformation localization during cyclic loading. Microstructures can be optimized for good fatigue resistance. 3.4. Functional fatigue of shape memory springs Fig. 9a and b show results which are typical for the behaviour of NiTi spring actuators loaded in tension. Fig. 9a shows displacement–temperature curves after the first, second and thousandth actuator cycle. The evolution of the
high and low temperature positions xA and xM (as defined in Fig. 2) are shown as a function of the cycle number in Fig. 9b. During the first 100 cycles the actuator spring suffers irreversible plastic deformation in both phases: the spring elongates and xM and xA decrease. Finally the effect saturates and from then on xM and xA are more or less stable. The working displacement ∆, however, increases during the first 100 cycles, because the decrease of xM is stronger than that of xA . The results presented in Fig. 9 are representative for thermal cycling experiments with springs under various loads and heat treatment conditions and more results on the influence of microstructure and different spring geometries will be published elsewhere [51].
4. Discussion 4.1. Fatigue loading and temperature
Fig. 8. Extended localized shear/transformation band in solution annealed material which forms during the first load cycle. Optical micrograph of the microstructure associated with Figs. 6a and 7a (solution annealed and water quenched polycrystalline material state).
Engineers will normally focus on one specific type of component subjected to one specific type of fatigue loading exploiting mechanical or thermal shape memory. But nevertheless it is important to understand the effect of temperature T on deformation/transformation events which we expect when our shape memory alloy is subjected to isothermal cyclic loading. We expect that the fatigue behaviour will differ depending on whether the low temperature phase is stable, whether it is possible to transform the high temperature phase to martensite by applying a stress or whether the high temperature phase is stable. It was recently explained [52] why temperature effects on the response of shape memory alloys to cyclic loading have to be discussed with respect to the underlying phase transition temperatures Ms and Mf (temperatures where the formation of martensite starts and finishes on cooling) and As and Af (temperatures where the formation of austenite starts and finishes on heating). And these phase transition temperatures are known to depend on chemical composition, on microstructure and on applied
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Fig. 9. Change of spring geometry during thermal cycling with an end load of 3 N. (a) Displacement–temperature hysteresis in the first, second and thousandth cycle. (b) Positions xA and xM as a function of the numbers of cycles N.
stress. In the present study we have presented fatigue results for two characteristic cyclic loading conditions: mechanical cycling of a pseudo-elastic alloy (Af < T < Md , where Md represents the temperature above which a stress induced formation of martensite is no longer possible) and thermal cycling in a 1-WE application (low temperature: T < Mf ; high temperature: T > Af ). There also is a need to understand how NiTi behaves in other temperature ranges [52]. Thus, below the martensite finish temperature Mf , cyclic loading at constant temperature will result in the motion of twin boundaries. And above Md (and at temperatures where diffusion is not yet important) we observe normal fatigue of the high temperature phase. And at even higher temperatures where diffusion becomes significant, precipitation processes can occur and creep processes contribute to the microstructural evolution associated with cyclic loading. In BRF experiments, the apparent size effects and the apparent influence of loading rate on fatigue rupture are due to adiabatic heating of our pseudo-elastic wire specimens; these temperature effects also need to be considered when discussing fatigue of other pseudo-elastic NiTi components. 4.2. Cyclic loading and plasticity When investigating fatigue of shape memory alloys we need to consider how the microstructure of our material affects the stress–strain hysteresis. Here, we have seen that microstructure is very important. When suitable thermo mechanical treatments are applied it is possible to stabilize the stress–strain-behaviour during cycling and to influence the degree of strain/transformation–localization during cyclic loading. In order to achieve a high number of stable cycles during pseudo-elastic loading it is important to ensure that the pseudo-elastic plateau stress (where stress induced martensite forms) is smaller than the yield stress of the austenite; this guarantees that there is only a limited increase of dislocation density during cyclic loading and thus only little accumulation of residual strain (plastic and pseudo plas-
tic deformation). In this respect NiTi shape memory alloys outperform iron based SMAs where the high temperature phase is soft [52,53]. Our results suggest that marforming of NiTi followed by aging yields promising results. However, we also find that it is not possible to completely avoid that irreversible strains increase. This is due to an increase of dislocation density and the formation of stabilized martensite variants which do not transform back to austenite after unloading. In the case of our actuator spring we find that the positions xA and xM change; it seems reasonable to attribute the change of the position of xA to an increase of dislocation density. The more pronounced change of xM (as compared to xA ) is a consequence of the increase of dislocation density and additional formation of specific martensite variants. From an engineering point of view it seems reasonable to differentiate between dislocations which form during service of a shape memory alloy (or as a consequence of fatigue loading of a shape memory specimen) and other dislocations which are intentionally introduced into the material during training procedures for the two way effect (2WE); from a physical point of view training procedures may well be considered as one specific type of low cycle fatigue loading. Due to the high melting temperature of NiTi, diffusion processes are not important in the temperature range where shape memory effects are normally exploited [52,53]; this represents a disadvantage of the CuZn-based SMAs as compared to the more stable NiTi [52,53] (CuZn-based SMAs do not establish the equilibrium ordered phase during normal heat treatments; they therefore strive for higher degrees of order during mechanical cycling, and this is also associated with point defect mobility and a change of properties during cycling [52,53]). Deformation and transformation plasticity are associated with the two types of functional fatigue which we have described in the present study: the evolution of the stress–strain hysteresis during strain controlled mechanical cycling and the shape change of the 1WE spring during thermal cycling. Metal fatigue as well as high stress plastic deformation is often associated with strain localization. And
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in the present study we provide an example for transformation/deformation localization in pseudo-elastic NiTi. 4.3. Fatigue damage accumulation Fatigue damage accumulation is generally associated with the formation of surface cracks and subsequent crack growth. And it has been shown that crack growth in martensite is slower than in austenite and that stress induced formation of martensite reduces crack growth rates [54]. Bending–rotation fatigue is also characterized by crack initiation and crack growth. Engineering surfaces of shape memory wires provide stress raisers like scratches and inclusions where fatigue cracks eventually start; and while the formation of extrusions can also be considered as an alternative way to form fatigue cracks in an ideal surface it does not seem to be important in engineering SMAs. Fatigue striations in the early stages of fatigue crack growth have recently been identified [44]. Structural fatigue of pseudo-elastic shape memory alloys does not differ as far as crack initiation and crack growth are concerned. However, the capability of a shape memory material to form stress induced martensite near local stress raisers is beneficial, as it limits the stress intensity which loads small cracks and contributes to a good fatigue resistance of shape memory alloys [52]. Finally it should be noted that there is only an indirect correlation between stress and strain hysteresis (which is governed by bulk microstructure) and crack nucleation and growth; the latter represents structural fatigue of shape memory alloys and is mainly dependent on surface defects and local surface stress. Small cracks may long have nucleated and grown before their presence can be detected in the stress–strain hysteresis of a fatigue experiment [20]. A good surface finishing therefore can be expected to increase fatigue life.
5. Summary and conclusions The present paper provides a brief introduction into structural and functional fatigue of NiTi shape memory alloys. It then discusses four cases of fatigue in NiTi shape memory alloys: (1) The evolution of the stress–strain hysteresis in low cycle pull–pull fatigue of pseudo-elastic NiTi wires. (2) Bending–rotation fatigue rupture of pseudo-elastic NiTi wires. (3) Strain localization during the stress induced formation of martensite. (4) Generic features of functional fatigue in NiTi shape memory actuator springs. The paper discusses the influence of temperature on the fatigue performance of shape memory alloys. It shows that microstructure is important in governing (i) the stability of the stress– strain hysteresis during strain controlled fatigue loading and (ii) the localization of strain/transformation. Functional fatigue is associated with an increase of residual strain (with plastic and pseudo plastic components) which corresponds to an incomplete reverse transformation. Moreover, it is demonstrated that structural fatigue of pseudo-elastic shape memory alloys is governed by the initiation and growth of surface cracks. Pseudo-elastic shape memory alloys are damage tolerant because the stress induced transformation limits stresses and thus stress intensity factors which drive crack growth. Acknowledgements The authors would like to acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) and the Land Nordrhein-Westfalen (NRW) in the framework of SFB 459 Formgedächtnistechnik (a Research Centre on Shape Memory Technology at the Ruhr-Universität Bochum). References
4.4. Other factors affecting fatigue of shape memory alloys Fatigue is a multiple parameter phenomenon. The present paper has only presented some results on fatigue of NiTi shape memory alloys. It has been shown that temperature, microstructure and surface quality affect the fatigue behaviour. Many additional factors can affect SMA fatigue behaviour: the type of loading (stress or load control, tension/compression asymmetry), the strengths of austenite and martensite, the degree of order of the lattices, the volume fraction and size distributions of particles, the volume change during the transformation, how much PE plateau strain is imposed during strain controlled testing, structural incompatibilities and others. It should also be mentioned that cyclic loading can be accompanied by a change in phase transition temperatures; this also represents a form of functional fatigue. Further work is required to systematically study the importance of these factors.
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