Embed Size (px)
Citation preview
Fatigue life characterization of shape memory alloys undergoing thermomechanical cyclic loading
Olivier W. Bertacchini*a, Dimitris C. Lagoudasa, Etienne Patoorb
aAerospace Engineering Department, Texas A&M University, College Station, TX 77843-3141, Texas, USA
bLPMM UMR CNRS 7554/ENSAM Metz, 4 rue Augustin Fresnel, 57078 Metz, France
ABSTRACT This paper presents a study on the fatigue life of shape memory alloy (SMA) actuators undergoing thermally induced martensitic phase transformation under various stress levels. A microstructural study characterizing specific damage patterns is conducted. Formation of different types of microcracks has been observed, showing a superficial micro cracking, at the origin of the growth of circular cracks which are finally responsible for localizing the failure of the specimens. Interactions between the micro cracking pattern and the corrosion occurrence are also studied. A spallation oxidation occurring at the surface of the actuator, which damages its properties, is put to evidence. The failure pattern observed provides information necessary to introduce a correction to the classical Wohler curve for fatigue life of a SMA material undergoing cyclic loading. Keywords: shape memory alloys, actuator, fatigue life, microcracks, corrosion, spallation oxidation.
1. INTRODUCTION SMAs have seen growing use in the mechanical, medical and aerospace industries over the last decade [1]. The thermomechanical response of NiTi subject to various mechanical and thermal cycling has been widely investigated [2, 3, 4]. However, most of the results pertain to a limited number of cycles and mainly focus on the development and stability of two-way strain and the evolution of plastic strain. Melton et al. [5] gave the earliest report on fatigue properties of NiTi specimens. Their work included results on mechanical fatigue for isothermal fully reversed loading. Fatigue limits of 107 cycles were recorded for constant stress amplitude with no phase transformation. McNichols et al. [6] performed thermal transformation fatigue of NiTi SMA. Their results showed a fatigue life between 104 and 105 for constant strain amplitude levels between 4.4% and 8.3%. They also found that there was no failure even after 107 and 108 cycles for strain amplitudes below 3%. Lagoudas et al. [7] reported a thermal fatigue life of nearly 20,000 cycles for a TiCuNi alloy annealed at 550°C for 15 minutes and thermally cycled at a constant stress level of 150 MPa. This paper focuses on controlled thermomechanical fatigue study and the evolution of the damage pattern in the SMA specimens. The SMA material, in this setup, is actuated by resistive heating. The specimens are subject to constant stress and are thermally cycled to failure. In addition to the pure mechanical damage in the material during thermomechanical cycling, some corrosion [8, 9] and spallation oxidation [10] can also affect the fatigue properties of the SMA actuators [11]. With a rough or a slightly oxidized surface, an electric field can activate a local corrosion strongly reducing the fatigue life of the actuators. Considering the spallation oxidation, the combination of thermal and strain variations (the difference between the transformation strain and thermal expansion coefficient of the oxide particles) result in crack propagation and micro cracking.
*a O.B email : [email protected] a D.C.L email : [email protected] E.P email : [email protected]
This work reviews the methods that control the thermomechanical cycling fatigue. The microstructure of the material after failure is studied from the data acquired. The fracture surface morphologies are analyzed to identify the mechanisms and the damage patterns responsible for a macroscopic damaged state. First conclusions leading to a primary understanding of the behavior involved in the failure mechanism are presented.
2. EXPERIMENTAL SETUP AND METHODOLOGY The material used is a Ti.40Ni.10Cu (%wt) SMA drawn in 0.6-millimeter diameter wire partially recrystallized. The length of the specimens used in the fatigue experiments is between 9 and 10 inches (228 to 254 millimeters). The wires are thermally trained under a dead load applied until their failure. Miller [12] studied the effects of heat treatment on the fatigue life and the amplitude of the transformation strain in Ti.40Ni.10Cu (%wt) SMA. This work resulted in the optimized set up for the highest fatigue life with the best transformation strain. The principle of the experimental setup used at Texas A&M University to perform fatigue life testing on SMA is based on complete or partial thermomechanical cycles for different stress levels. The results of the comparison between the complete and the partial transformation with the study of the broken specimens lead to the characterization of the evolution of the microstructure until failure. For that purpose, the device shown in Figure 1 and Figure 2 has been designed to perform the fatigue life measurements. Figure 1. Illustration of the experimental device. Figure 2. Picture of the frame training 5 specimens.
The energy needed to achieve the austenitic transformation is provided by resistive heating, adjusted to account for the shift in transformation temperatures under increasing load level. A chiller is used to cool down the circulating coolant (glycol), which cools the specimens inducing the martensitic transformation. The parameters to induce a complete or a partial transformation during the cycles depends on the transformation velocity in the case of complete transformation and on a determined percentage of the transformation strain for the partial transformation. The type of transformation is characterized by the martensitic volume fraction (Figure 3). Figure 3 describes how the martensitic volume fraction is cycled in a complete and in a partial transformation. The characterization of the transformation and the proportions in which the two phases combine is realized through the martensitic volume fraction (ξ). Reaching the boundary where ξ = 0 in the stress-temperature diagram means the first crystal has started to transform. When ξ = 1, the last crystal has finished transformation and the material is fully transformed. The analysis of the fatigue life is based on cyclic loading under different stress conditions. In this case, the stress is constant and the temperature is the cyclic load. The two parameters needed to describe the cycles are ξ0 and ξa, the average martensitic volume fraction and the magnitude of the fluctuation around ξ0 respectively. For a complete transformation, 100% of initial phase has to be transformed into 100% of the other phase, so going from ξ=0 to ξ=1. Then, according to the Figure 4, ξ0 = 0.5 and ξa = 0.5. For the partial transformation, the two parameters ξ0 and ξa must both be adjusted to choose the transformation range. The partial transformation can be generalized knowing 0 ≤ ξ ≤ 1. (ξmin and ξmax form the upper and lower bounds for the cycling about ξ0)
ξ0 = (ξmin + ξmax)/2 ∈ for 0 ≤ ξ ≤ 1 (1) The choice was to work with 50% of the total transformation. (The mean volume fraction known as ξ0 will be set at 0.5 and the amplitude of the cycling martensitic volume fraction known as ξa will be 0.25) thus having the martensitic volume fraction cycled between ξ=0.25 and ξ=0.75. Strain measurements are performed for each transformation. The end of a transformation is characterized by the cancellation of its strain velocity and the change of its sign, which is the indication of the switch between a transformation and its reverse. Each cycle gives a strain value for each phase (εmartensite, εaustenite), and these measures allow calculating the transformation strain εtr. εtr = εmartensite - εaustenite (2)
Figure 3. Parameters ξ0 and ξa for complete and partial transformation. The initial conditions of the tests are stress free martensitic transformation in the cold bath. The load is then applied and the specimen is cycled. A cycle consists of two half cycles, the first half will be considered as the austenitic transformation cycle starting at a zero strain value for the plastic strain evolution. The constant stress transformation path resulting from the actuation of the SMA wires using only the variation of the temperature is called the “SATWME”. Thus a series of different tests can be performed under different load levels. However, when the specimens are under stress, the transformation temperatures become higher. A calibration using several thermocouples gives the range of the transformation temperatures. DSC measurement under stress free conditions allows calibration of the transformation temperatures and extrapolation of the range of the complete austenitic and martensitic domains as required with the increase of the stress level. The identified transformation temperatures of the DSC test are reported in the Table 1. The resistive heating increases the temperature of the wire from 9-10°C to 110-120°C in 1 second. A longer heating time will burn the specimens. During cooling, the chilled fluid is regulated at 9-10°C to allow heat exchanges between the SMA actuators and the liquid for 3 seconds. Temperatures of 15°C and 120°C were reached respectively after cooling and heating allowing a temperature range large enough to complete the required transformations.
Table 1. Description of the different transformation temperatures determined from DSC measurent.
Austenitic transformation temperatures Martensitic transformation temperatures As = 54.4 C Ms = 46.7 C
Af = 60.6 C Mf = 39.5 C
3. STUDY OF STRAIN-NUMBER OF CYCLES CURVE The Strain(ε)-Number of cycles (N) curve shows that following the saturation phenomenon of the martensitic and austenitic strains, while the transformation strain is stabilizing during the first hundred cycles, a plateau is observed. While a slight increase of the martensitic and austenitic strains is noticed, the transformation strain stabilizes and remains constant until the failure. Interpretation of the ε-N curves characterizes the behavior of the SMA in accordance
with the number of cycles, different load levels, and with the nature of the transformation. Thus plastic strain in the austenitic phase seems to play a major role and a Wohler curve description of the fatigue life versus the load. It is noticed that during the first hundred cycles (for the complete transformation) and during the first thousands cycles (for the partial transformation) a transitional phase was observed, showing a quick increase in austenitic and martensitic phase. This results in an increase of the total strain (martensitic strain), leading to a saturation phenomenon, which is considered as a stabilization of the transformation strain. The plastic strain (austenitic strain) characterizes an irreversible phenomenon leading to the failure of the specimens. In the case of complete transformations (Figure 4), the transformation strain is close to 3%, but the fatigue life is reduced in comparison to the specimens trained under partial transformations (Figure 5). During the partial transformation, the evolution is similar, but the fatigue life is increased. The specimens were trained using only 50% of the transformation range. The periodic notches seen every thousand cycles are to adjust the values of ξ0 and ξa to stay in the expected transformation range as the original length was constantly increasing.
Figure 4. Complete transformation: ε-N curve for a constant
load of 192 MPa. Characterization of the evolution of martensitic and austenitic strain.
Figure 5. Partial transformation: ε-N curve for a constant load of 192 MPa. Characterization of the evolution of martensitic and austenitic strain.
4. MICROSTRUCTURE AND FATIGUE LIFE EFFECTS In this section, the failure mechanism and the damage pattern will be emphasized. The study is based on analysis performed with a Scanning Electron Microscope (SEM). The focus is on the influence of thermomechanical cycling on the failure mechanism. The influence of chemical phenomenon occurring at the surface of the specimens is also analyzed. The specimens are subjected to five different stress levels from 54 MPa to 247 MPa and tested for both complete and partial transformations. The Table 2 describes the sampling of the experiments where (ai
j, bij, ci
j) represents the stress level with the type of transformation (i = “c” or “p” respectively for the complete or the partial transformation and j = 1 to 5 for the constant load level such as 54 MPa: level 1, 106 MPa: level 2, 154 MPa: level 3, 192 MPa: level 4, 247 MPa: level 5).
Table 2. Testing matrix for both transformations.
Load applied 54 MPa 106 MPa 154 MPa 192 MPa 247 MPa Complete transformation ac
1, bc1, cc
1 ac2, bc
2, cc2 ac
3, bc3, cc
3 ac4, bc
4, cc4 ac
5, bc5, cc
5Partial transformation ap
1, bp1, cp
1 ap2, bp
2, cp2 ap
3, bp3, cp
3 ap4, bp
4, cp4 ap
5, bp5, cp
5
4.1 Microstructural observations Observation of the fracture surfaces after thermomechanical cyclic loading gives additional information on the damage mechanism. In previous work performed at Texas A&M University [12], the wires from Table 2 suffered from more severe conditions giving rise to higher level of cracks. A calibration is performed on the energy supplied to the specimens to reach the point just before the beginning of dynamic response of the actuators. Beyond this point, the
weights wouldn’t operate as a constant load under quasi-static conditions. Independent of the type of transformation, two different kinds of fracture surfaces are observed. The first one will be called “classic” and the second one will be referred to as “high stress” fracture surfaces. For complete transformation between 54 MPa and 154 MPa, the fracture surfaces are in accordance with the previous fracture surfaces observed by David Miller. The stress range is reduced in partial transformations for a “classic” fracture surface from [54MPa - 154 MPa] to [54 MPa - 106 MPa](see Figures 6b and 6d). Over these levels (154 MPa for the complete transformation and 106 MPa for the partial transformation), the fracture surfaces start to show some circular and radial cracks as seen in Figures 7b and 7d. The classical fracture surface exhibits a ductile morphology combined with the propagation of fatigue lines, having higher intensity near the crack initiation. As the specimens were not polished, their surfaces exhibit excrescences favoring crack initiation. As seen in Figure 8, the core of the wire seems relatively unaltered while these fatigue lines converged to the crack initiation (Figure 9). As pinpointed in Figure 10, the fatigue lines try to reach the surface of the specimen while they are connected to predominant cracks. However, there remains a domain exhibiting a contrasting area where the material shows a smoother surface morphology. Figures 11 and 12 describe not only the fatigue lines but also the smoother section while Figure 13 gives an overall view of the external de-bonded ring and the fatigue lines from the core to the predominant crack. On exceeding the highly stressed state limit, the region in Figure 13 is subjected to fail at a de-bonded ring, meaning the creation of an interface. In high stress surface, the first step in the crack development is characterized by the formation of outer brittle layer inducing the circular cracks as in Figure 12. The second step is a radial stress release occurring first in the outer circular layer, and sometimes starting in the interior of the specimen (Figure 13). Beyond a specific stress limit, cracking occurs in the core of the specimens. Figure 14 shows the formation of two kinds of internal cracks. Finally, the outer hardened and brittle layer exhibits its circular crack very close to the region, identified as the interface between the core and the superficial layer (Figure 15). 4.2 Damage pattern evolution Observation of the longitudinal surface also yields valuable information about all specimens showing a microcrack pattern around the failure location. This phenomenon, observed around the failure locations is also noticed along the whole length of the specimens. The dimensions of these microcracks are typically 5 to 10 microns, which is of the same order as the grain size. Therefore the crack opening and the density of these cracks are related to the applied load (Figures 16 and 17). The crack initiation may be occurring at irregularities of the surface creating local stress concentration and also favoring a corrosion phenomenon. Moreover, the morphology of the specimens from the outer layer to a few microns deeper (≈20-30 µm) has the pattern of cells or needles radially oriented corresponding to the microcracking pattern. The microcracks are potentially subjected to create random sites for the propagation of stress release during training. Figure 18 shows the needle configuration of the de-bonded cells and a macrocracks crossing through. Figure 19 describes a random serrated path through the cells. An almost periodic distance between each crack characterizes the phenomenon of circular cracks along the length. With more than one circular crack, the material can nearly fail in each of these crack nodes and thus this could be a great weakness for the actuator. For a fixed load level, the distance between two cracks is wider in the partial transformations. In addition, the complete transformation requires a higher stress level to generate these cracks but as soon as they appear, the distance between them is nearly half as in the partial transformation (Figures 20, 21). The Figures 22a and 22b show a comparison between the distances of cracks for full and partial transformation subjected to similar stress levels. The Figure 22a also exhibits a macrocrack indicating a very high stress level that required releasing although there is no evidence of such a stress level in the figure 22b for the partial transformation.
6a (test ac2) 6b (test cp
2)
6c (test bc4) 6d (test bp
4) Figures 6a, 6b, 6c, 6d: Comparison between the complete and the partial transformations of the fracture surfaces. Over a specific stress level, two different domains appear where the second indicates a “high stress” level.
7a (test cc
3) 7b (test bc4)
7c (test cp
2) 7d (test ap3)
Figures 7a, 7b, 7c, 7d: Characterization of the transitions between a classic fracture surface and a “high stress” state damaging the specimens for both complete and partial transformations. Transition between classic and “high stress” state is one level below in the partial transformation.
Figure 9. Fatigue lines oriented to the surface around a main crack. Test cp
2.
Figure 8. Main crack of test ac2. Orientation of fatigue
lines converging to the crack.
Hardened superficial layer with a smooth morphology
Figure 11. Characterization of the different morphology between the unaffected and the smooth region. Test cc
2.
Figure 10. Identification of fatigue lines reaching and converging to the predominant crack. Test cc
2.
Figure 14. Magnification of the core of the specimen. Under high stress level, the material develops internal cracks. Test cc
5.
Figure 15. Crack observation at the core-superficial layer interface: circular cracks almost stopped at the edge of the fatigue zone. Test cc
5.
Figure 12. Observation of a circular crack added to an internal rough surface converging to the predominant crack. Test cc
5.
Figure 13. Strongly damaged specimen: circular cracks combined with internal cracks crossing through the specimen. Test bc
5.
Figure 16. Stress level: 106 MPa. Figure 16a. Complete transformation, test cc
2. Figure 16b. Partial transformation, test cp2.
Figure 17. Stress level: 154 MPa. Figure 17a Complete transformation, test bc
3. Figure 17b Partial transformation, test ap3.
Figure 18. SEM picture of a macrocrack crossing microcracks made from needle cells. Complete transformation under 247 MPa, test ac
5.
Figure 19. Macrocrack crossing microcracks. Observation of the serrated aspect of the macrocrack’s path. Complete transformation under 247 MPa, test ac
5.
Figure 20. SEM pictures of the periodical circular cracks in the specimens. 20a. Complete transformation 154 MPa. Test ac
3. 20b. Partial transformation 154 MPa. Test bp3.
Figure 21. SEM pictures of the periodical circular cracks in the specimens. 21a. Complete transformation 192 MPa. Test bc
4. 21b. Partial transformation 192 MPa. Test bp4.
Figure 22. SEM pictures of the periodical circular cracks in the specimens.
22a. Complete transformation 192 MPa. Test bc4. 22b. Partial transformation 192 MPa. Test bp
4.
5. CORROSION AND SPALLATION OXIDATION PHENOMENON Even though chemical analysis has not yet been performed on the specimens, microstructural observations give enough information to suspect the occurrence of fatigue –corrosion mechanism to explain the difference between classical and high stress morphology. As the specimens are cooled down with a chilled liquid (glycol) and heated by resistive heating, some residual current activates corrosion. Consequently, the residual current spreads while the specimens are at a high temperature level. The power required to fully transform the wires is around 400 W, which is important for 0.6 mm diameter specimens actuated on a length of nearly 10 inches but not aberrant regarding the efficiency of such material. In addition, the failure always occurs at the ground-connected side of the specimens. 5.1 Corrosion As mentioned previously, the existence of two different concentric zones in the material is supposed to be linked to the hypothesis of the formation of stabilized twinned martensite. However, such a pattern would not be the sole reason for these observations. The accumulation of defects at the interfaces inducing the incapacity for the austenitic grains to recover their original structure is rational, thus creating a hardened and yielded material in the outer layer. However this cannot be the only reason. The Ni-40Ti-10Cu wires may have suffered from chemical change on the surface. A proposed mechanism of hardening is described in the Figure 23. The SMA wire is cycled from the austenitic to the martensitic phase. At the surface of the specimen, the material is changing its microstructure from a homogeneous austenite to a detwinned martensite with the formation of plates, reaching the surface to create irregularities. A large part of the oxidized layer formed on the rough surface is put inside the sample when the martensite reverts into austenite. These are taken from the outer layer and reach deeper when the martensite goes back into austenite and constant cycling is responsible for an accumulation of oxidized particles in a large outer zone of the wire turning this zone brittle. Focusing on the slightly corroded part of the specimen, the brittle area is limited by a circular crack (Figure 24a). This pattern can be responsible for weakening the outer layer and for the development of microcracks. The brittle part of the material is supposed to be the initiation of localized failure, providing information about the thickness of the hardened layer and the effect of the cycling time. The thickness of the layer seems to correlate to the time spent in the bath, and in turn to the number of cycles. Figures 24a and 24b exhibit the thickness of the hardened layer and the number of cycles until failure.
Superelastic zone Brittle zone
Figure 23. Principle of hardening and depth increase of the superficial layer.
Figure 24. Characterization of the thickness of the hardened layer versus the number of cycles. 24a. Complete transformation, 247 MPa, Test ac
5. 24b. Partial transformation, 247 MPa, test bp5.
5.2 Spallation oxidation Another phenomenon observed at the surface of the specimens is the spallation oxidation. In common materials, the spallation oxidation is due to a combination of oxidation and thermal cycling. The thermal cycling creates large internal stresses due to the different thermal expansion coefficients of the material and its oxide layer. As a brittle and non-ductile material, the oxide layer will crack along its interface with the unaffected part resulting in a local crumbling. The part of the specimen exposed is the surface already weakened by hardening and corrosion, thus creating a less deformable layer, while the core of the material is unaffected. The difference between the core and the outer layer of the SMA actuators can also be identified as a composite with a ductile and a brittle layer. Moreover, the strains due to the temperature variations are the transformation strain for the SMA and a reduced SME in the composite of the outer layer. During training, the specimens tested were heated up to 120°C. This temperature is not enough to initiate oxidation but in some areas where cracks appear, the gradient of temperature is very high and can locally affect the material. As shown in Figures 25 and 26, the localization of the spallation is all around the circular cracks. Looking closely at the phenomenon, it is seen that there is cohesion between the oxide deposit and the surface of the specimen. The Figure 27 shows the surface of the wire with its microcracked structure and a deposit covering it. The particularity of that phenomenon is the effect of the cycles, causing the specimen to crumble.
Local Spallation Microcracking
Figure 27. Magnification on the microcracked structure and its cohesion to the spallation layer. Complete transformation under 247 MPa, test bc
4.
Figure 25. SEM picture of circular cracks with formation of spallation oxidation. Complete transformation under 247 MPa, test bc
4.
Figure 26. Zoom on the circular crack. Complete transformation under 247 MPa, test bc
4.
6. DISCUSSION The main focus of this work is the cause of the general damaged state of the specimens, which are almost all affected in the same way. The hypothesis of mechanical stabilization of detwinned martensite in the matrix could be an explanation, but not the only one. The beginning of such a form of corrosion and oxidation brings about an accelerated worsening in the behavior with regard to the classical fatigue life without any damaging interactions with the outside environment.
One can merely think that the identified fatigue life versus its stress level applied is reduced compared to the theoretically expected fatigue life for the same material. Thus a quick modeling describes how the theoretical lifetime can be reduced with regard to the evolution of the stress level in the specimens tested. The true stress level in the wires increases with the reduction of the active section. As a first step, the Wohler curve characterizing the stress applied and the fatigue life can be used to deduce the life of the material. The internal stress level during the complete transformation is higher than in the partial transformation, since the SMA requires more energy to transform entirely. The addition of a large strain results in a higher density of circular cracks for each stress level and a constant relation between the crack distances. d complete transf. < d partial transf. (3) This correction considers the impact of the evolution of the stress level in the “working” section, the stress level rising with the increase of the circular cracks and also their depth. This stress limit is closely connected to the region where the periodic circular cracks appear. A major point is the interaction between the time spent in the cooling bath (training time until failure) and the corrosion/spallation oxidation strongly affecting the properties of the material. The partial transformation exhibits an average fatigue life 10 times superior to the one of the complete transformation. But, the corrosion/oxidation is an important factor, especially under partial transformation conditions. The effect of the phenomenon is a superficial layer, which exhibits brittleness during the cooling cycle and ductile behavior during the heating cycle. During cooling the wires get longer due to the martensitic transformation and the surface layer is stressed under tension, resulting in increased risk of cracks appearing in the oxidized layer and, ultimately, failure. During the high temperature phase, the material shrinks and gets warmer, and the oxidized layer exhibits a more ductile behavior, which is less favorable to crack growing.
ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support of Air Force Office of Scientific Research, Grant No. F49620-01-1-0196. They would also like to express their appreciation to Parikshith K Kumar & Rajagopal S. Pachalla for technical editing.
REFERENCES 1. V.Birman, Review of Mechanics of Shape Memory Alloy Structures, Applied Mechanics Reviews, 50(11), pp 629- 645 (1997). 2. D. Hebda and S. R. White, 1995 Effect of Training Conditions and Extended Thermal Cycling on Nitinol Two-way Shape Memory Behavior Smart Materials and Structures 4 pp 298-304. 3. Z. Bo, and D. C. Lagoudas, 1999 Thermomechanical Modeling of Polycrystalline SMAs under Cyclic Loading, Part III: Evolution of Plastic Strains and Two-Way Memory Effect Int JEng Sci., at press. 4. T. J. Lim and D.L. McDowell, 1994 Degradation of a Ni-Ti alloy During Cyclic Loading, Proceedings of the 1994 North American Conference on Smart Structures and Materials, SPIE, Orlando, Florida pp 153-165. 5. K.N. Melton and O. Mercier, Fatigue of NiTi thermoelastic martensites, Acta Metallurgica, V-27, 137-144 (1979) 6. J.L. McNichols and P.C. Brooks, NiTi fatigue behavior, Journal of Applied Physics, V-52, 7442-7444 (1981) 7. D. C. Lagoudas, C. Li, D. A. Miller, L. Rong, Thermomechanical transformation fatigue of SMA actuators, Proceedings of SPIE, vol. 3992, pp 420-429 (2000) 8. G. Rondelli, Corrosion resistance tests on TiNi shape memory alloy, Biomaterials, 17, 1996, pp 2003-2008. 9. G. Rondelli, B. Vincentini, Effect of copper on the localized corrosion resistance of Ti-Ni shape memory alloys, Biomaterials, 23, 2002, pp 639-644. 10. S. Baleix, G. Bernhart, P. Lours, Oxidation and oxide spallation of heat resistant cast steels for superelastic forming dies, Materials Science and Engineering, A327, 2002, pp 155-166. 11.C. Vernault, J. Mendez, Influence des couches d’oxyde sur l’endommagement par fatigue d’un acier inoxydable de type 316L, Ann. Chim. Mat., vol. 24, 1999, pp 351-362. 12. D. A. Miller, Thermomechanical characterization of plastic deformation and transformation fatigue in Shape Memory alloys, PhD thesis, Texas A&M University, 2000. 13. D. A. Miller, D. C. Lagoudas, Thermomechanical characterization of NiTiCu and NiTi SMA actuators: Influence of plastic strains, Smart Mater. Struct. 9 (2000) 640-652.
14. H. Tobushi, Y. Onashi, H. Saidi, T. Hori and S. Shirai, 1993 Pseudoelasticity of NiTi Shape Memory Alloy (Dependence on Maximum Strain and Temperature) JSME Int.J., 36 (3), pp314-318. 15. H. Morawiec, D. Stroz and D. Chrobak, 1995 Effect of Deformation and Thermal Treatment of NiTi Alloy on Transition Sequence J. de Physique, Suppl 5 pp C2-205-209. 16. H. Matsumoto, 1993 Transformation behavior of NiTi in relation to thermal cycling and deformation Physica B 190 pp 115-120. 17. P.G. McCormick, Y. Liu and S. Miyazaki, 1993 Intrinsic thermal-Mechanical Behavior Associated with the stress- induced martensitic transformation in NiTi Material Science and Engineering A167 pp51-56. 18. T. J. Lim and D.L. McDowell, 1994 Degradation of a Ni-Ti alloy During Cyclic Loading, Proceedings of the 1994 North American Conference on Smart Structures and Materials, SPIE, Orlando, Florida pp 153-165. 19. S. Miyazaki, T. Imai, Y. Igo and K. Otsuka, 1986 Effect of Cyclic Deformation on the Pseudoelasticity Characteristics of Ni-Ti Alloys Metal. Trans.A 17A pp 115-120. 20. S. Miyazaki, K. Otsuka and Y. Suzuki, 1981 Transformation Pseudoelasticity and Deformation Behavior in a Ti 50.6at%Ni Alloy Scr. Metall. 15 pp 287-292.
