Thermomechanical Characterization of Large ... - Texas A&M Smart Lab
Proceedings of 2003 ASME International Mechanical Engineering Congress and R&D Expo November 15-21, 2003, Washington, DC
IMECE2003-42933 THERMOMECHANICAL CHARACTERIZATION OF SMA ACTUATORS UNDER CYCLIC LOADING
Dimitris C. Lagoudas Department of Aerospace Engineering Texas A&M University College Station, TX 77843-3141, USA Email: [email protected]
Pavlin B. Entchev Department of Aerospace Engineering Texas A&M University College Station, TX 77843-3141, USA Email: [email protected]
ABSTRACT Shape memory alloy (SMA) wire actuators have been increasingly used in various devices and applications due to their high energy density and simple design. With the use of these actuators the questions of size effects on their behavior need to be addressed. This paper presents a study on the cyclic loading behavior of large diameter SMA wires subjected to different thermo-mechanical loading paths. Wires of two different diameters are investigated in the current study – 1.78 mm and 2.16 mm. The issues addressed in this work include the investigation and design of a gripping technique for the large diameter wires to avoid slippage and study of heat treatment conditions for optimized superelastic behavior. After the heat treatment, specimens are subjected to cyclic mechanical loading. Two different cyclic loading patterns have been investigated: loading up to a given value of stress or up to a given value of strain. Keywords: Shape memory alloys, actuators, mechanical loading paths, cyclic loading.
thermo-
1. INTRODUCTION Shape memory alloys (SMA) have gained popularity for use in large force actuators. There has been an increased use of SMAs for applications that are 1-D in nature, where rods, wires, and strips are employed as actuators, in active hydrofoil [1] and robotic systems [2]. Many researchers have investigated the effect of thermomechanical behavior on wires and strips of small cross sections. As the demand for SMA actuators grows,
Parikshith K. Kumar Department of Aerospace Engineering Texas A&M University College Station, TX 77843-3141, USA Email: [email protected]
it becomes essential to examine the effects of size and shape of the actuators on their performance. Chemical composition, cold work, heat treatment and thermomechanical cycling can widely influence the material properties of SMAs. The wire drawing process introduces large plastic deformations in the material. After the cold drawing, the material must be heat treated to reveal the pseudoelastic behavior. In addition, of great interest is the stability of the SMA pseudoelastic characteristics during cyclic mechanical loading. The residual strain, remaining after the load is relieved, and the energy dissipation measured from the hysteresis characterizes the stability of the pseudoelastic effect. Many investigations have been conducted on the effect of mechanical and thermal cyclic loading on the thermomechanical response of NiTi [3–10]. Earlier papers of thermomechanical testing of SMA wires and fatigue testing employed conventional techniques to characterize these materials [11]. Although similar testing techniques are adopted in this work, large diameter wires demand specific modifications. These wires are stronger and less flexible than the smaller diameter wires. Therefore, the gripping techniques must be modified to avoid effects of slipping and stress concentration. The remainder of the paper is organized as follows: Section 2 describes the equipment and the adopted experimental procedure; the experimental results are presented in Section 3; discussion of the results follows in Section 4; conclusions are given in Section 5.
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2. EXPERIMENTAL PROCEDURE The wires used for testing were Ni-44.62%Ti with diameters of 1.78 mm and 2.16 mm. The material was supplied by Special Metals. The received material was in the cold rolled condition without any heat treatment. Preliminary testing of the material in the as-received state revealed no superelastic effect. The Differential Scanning Calorimeter (DSC) analysis did not show any prominent peaks during the heating or the cooling cycle. However after heat treatment the DSC reveals the transformation temperatures. Figure 1 shows the DSC results for samples of both wire diameters after heat-treatment.
treatment for 5 minutes was chosen as optimal for the both wire diameters. The time is measured from the instance of placing the specimen into the furnace to the instance of taking it out of the furnace. A batch of 10 wires was annealed together in a furnace. The heat treatment of a batch of wires was performed due to the fact that individually annealed wires show varying results. Thus, the uniformity in a batch is maintained. DSC analysis after this heat treatment did not reveal any prominent peaks. However, earlier works reported in the literature have shown that there is not a drastic variation in the austenitic finish temperature (Af) for different temperatures of annealing. Thus, the Af temperature determined at 500°C was used at the reference temperature, based on which the test matrix was formulated [14].
(a)
_______ 5 min at 400°C ___ ___ 10 min at 400°C _ _ _ _ _ 15 min at 400°C
(b)
Figure 1. (a) DSC curve for NiTi wire with diameter of 2.16 mm annealed at 500ºC for 5 minutes. Two peaks are observed during cooling, which is an evidence of an R-phase; (b) DSC curve for NiTi wire with diameter of 1.78 mm annealed at 500ºC for 5 minutes. It was concluded that heat treatment must be performed in order to obtain superelastic behavior. A parametric study on these wires was conducted by heat treating them at different temperatures and testing them to determine the ideal temperature and time for optimizing the superelastic behavior [12, 13]. The samples were heat treated at temperatures ranging from 375°C to 500°C for time periods from 5 to 15 minutes. The results of the parametric study at 400°C for the wires with diameter of 2.16 mm are shown in Figure 2. It can be seen that the material heat treated for 5 minutes shows best pseudoelastic response. It undergoes complete reverse phase transformation, characterized by the elastic portion of the stress-strain curve during the late stages of unloading. The results for the other two specimens, heat treated at 10 and 15 minutes at 400°C, as well as the results for heat treatment at 500°C, which are not shown in this work, do not exhibit clear elastic unloading portion. Thus, based on this parametric study, 400°C heat
Figure 2. Parametric study of the effect of heat treatment time at 400°C on the pseudoelastic behavior of wires with diameter of 2.16 mm. After the optimal heat treatment parameters were established, the wires were mechanically tested to obtain their stress-strain response. The tests were performed on an MTS servo-hydraulic loading frame fitted with a custom made heating chamber. The chamber is equipped with heating elements and a temperature controller, which maintains an accuracy of 0.5°C. The temperature of the specimens was continuously monitored using a thermocouple attached to each specimen’s surface. The strain during the experiments was measured using both the crosshead displacement of the MTS frame and an Epsilon extensometer attached to the wire. The load was measured using a Transducer Techniques load cell. The experimental setup is shown in Figure 3. As a part of the research effort, different gripping techniques for the large diameter wires were investigated. Jaw grips with perforated jaws create regions of stress concentrations on the surface of contact. These regions become points where the specimen fractures. Grips with flat gripping surfaces lead to slipping of the specimen at high load levels. Thus, custom grips were designed and fabricated. The grips
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were designed to prevent slip while at the same time provide capabilities of gripping wires of various diameters without any stress concentrations. The grips are shown in Figure 4.
close to saturation after 20 cycles. Another effect of the cycling is the decrease of the area enclosed by the hysteresis loop. Table 1. Test matrix for cyclic mechanical loading of large diameter NiTi wires.
Load cell
Heating Chamber Custom Grips Extensometer
Thermocouple Temperature controller
Figure 3. Experimental setup for mechanical testing of the wires.
Test # Number of Loading tested type specimens Maximum 1 2 strain Maximum 2 2 strain Maximum 3 2 stress Maximum 4 2 stress Maximum 5 2 strain Maximum 6 2 strain Maximum 7 2 stress Maximum 8 2 stress
Wire Limit diameter
Temperature
Number of cycles
1.78mm 6%
70°C
20
2.16mm 6%
70°C
20
1.78mm 750 MPa
70°C
20
2.16mm 650 MPa
70°C
20
1.78mm 6%
80°C
20
2.16mm 6%
80°C
20
1.78mm 800 MPa
80°C
20
2.16mm 800 MPa
80°C
20
Figure 4. Manufactured grips. Also shown is a gripped wire. 3. EXPERIMENTAL RESULTS The wires of both diameters were tested under isothermal conditions above the austenitic finish temperature. Tests at different temperatures and loading patterns were performed. The first temperature for both wires was chosen to be 70°C. The second temperature was 80°C for the 2.16 mm wire and the 1.78 mm wire. Two loading patterns were chosen: cyclic loading up to a constant maximum strain level and cyclic loading up to a constant maximum stress level. A study was performed to examine the effect of loading rate on the test results. It was noticed that strain rate of 10-4 s-1 results in quasistatic response. Thus, this loading rate was chosen to ensure constant temperature of the wire during forward and reverse transformation. The test matrix for both wire diameters is summarized in Table 1. Figure 5 shows the results of two wires of 1.78 mm diameter, tested at 70°C for 20 cycles to a constant maximum strain of 6%. The results indicate a good correlation between the test results of the two wires. The initial curve shows a sharp transition in the slope, which indicates transformation from austenite to martensite. However, as the number of cycles increases, the transformation becomes more gradual. The residual strain that accumulates in this case is approximately 0.7% to 0.8%. The accumulation of this permanent strain slows down with the increasing number of cycles and the strain is
Figure 5. Test results from cyclic mechanical loading at 70°C for 1.78 mm diameter NiTi wires: loading up to maximum strain of 6%. Figure 6 shows the results of two wires of 2.16 mm diameter, tested at 70°C for 20 cycles to a constant strain of 6%. The test results shown indicate a gradual accumulation of residual strain as the number of cycles increase. However the accumulated permanent strain is 0.23%, which is less than what is observed in the 1.78 mm diameter wire. Similar to the previous case the strain is close to saturation after 20 cycles.
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Figure 6. Test results from cyclic mechanical loading at 70°C for 2.16 mm diameter NiTi wires: loading up to maximum strain of 6%. Figure 7 shows the results of two wires of 2.16 mm diameter, tested at 80°C for 20 cycles to a constant strain of 6%. The results indicate that the material is not completely transformed to martensite at that temperature and strain level. In the former result the 2.16 mm wire tested at 70°C under the exact same conditions showed clear sign of complete transformation with the end of the plateau region and start of the second elastic region. The residual strain in this case is much higher compared to the test at 70°C. Similar to the earlier cases, the onset of transformation is initially sharp and smoothens as the number of cycles increase. The results shown in Figure 7 indicate that there is significant discrepancy between the two identical specimens, tested under the same conditions. Similar discrepancies are also observed for other test case, as discussed below. Test results shown if Figure 8 and 9 correspond to 1.78 mm and 2.16 mm wires tested to constant stress levels of 750 MPa and 650 MPa respectively at a temperature of 70°C. As in the previous cases there is permanent strain accumulation (1.0% to 1.2% for the 1.78 mm diameter wire and 1.0% to 1.5% for the 2.16 mm diameter wire) and saturation of this strain is observed towards the end of 20 cycles. While the residual strain in the wires with diameter of 1.78 mm is attributed to the development of plastic strains due to the phase transformation, in the case of the wire with diameter of 2.16 mm some of the residual strain may be due to incomplete reverse phase transformation. This conclusion is based on the observation on the stress-strain curve upon unloading for the wire which response is presented on Figure 9 with the dashed line.
Figure 7. Test results from cyclic mechanical loading at 80°C for 2.16 mm diameter NiTi wires: loading up to maximum strain of 6%.
Figure 8. Test results from cyclic mechanical loading at 70°C for 1.78 mm diameter NiTi wires: loading up to maximum stress of 750 MPa. It should be noted from the results in Figures 8 and 9 that there is a pronounced deviation in the response of the wires, which were heat treated and tested under the same conditions. As seen from Figure 8, after 20 cycles one of the wires exhibits larger transformation strain (the results indicated by the dashed line) than the second one (the results plotted in solid line). In addition, the value of the accumulated residual strain after 20 cycles differs for the two wires. Even if the accumulated residual strain is not completely due to plasticity, still the response of the two wires suggests that the material behaves
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differently even after identical heat treatment and testing under the same conditions.
Figure 10. Test results from cyclic mechanical loading at 80°C for 1.78 mm diameter NiTi wires: loading up to maximum stress of 800 MPa. Figure 9. Test results from cyclic mechanical loading at 70°C for 2.16 mm diameter NiTi wires: loading up to maximum stress of 650 MPa. Figure 10 shows the results for 2 wires of 1.78mm diameter tested to constant stress level of 800MPa at 80°C. The residual strain reached approximately 1.5% in both wires. The results obtained indicate that the residual strain in the wires in this case is much higher than for the same wires tested at 70°C (Figure 8). Unlike in the 2.16mm wires the plateau is not flat and sharp. Comparing it to the results in Figure 8, the inconsistency in the results clearly shows up. The deviation at 80°C is less pronounced compared to the former case. To examine the effect of the incomplete reverse phase transformation, the wires with diameter of 2.16 mm are tested at higher temperature of 80°C, which is well above the austenitic finish temperature. Thus, complete reverse phase transformation is ensured. The results of these tests are shown in Figure 11 for two wires for 20 cycles up to a constant stress level of 800 MPa. The results are compatible with the results obtained at 70°C and shown in Figure 9. However, the residual strains for this case are slightly higher, compared with the strains in the previous test. The residual strain for one of the wires is 1.4% while the second wire exhibits residual strain of 2%. Based on these observations, it can be concluded that the incomplete reverse phase transformation does not play major role in the results for 70°C, shown in Figure 9. It is again noted that the results for two identical specimens show significant discrepancies. Both the initial and final responses (after 20 cycles) are different.
Figure 11. Test results from cyclic mechanical loading at 80°C for 2.16 mm diameter NiTi wires: loading up to maximum stress of 800 MPa. 4. DISCUSSION The results of the cyclic testing of wires with two different diameters are presented in this work. Some of the differences in the behavior of the specimens with two different diameters can be observed from the test results. Most notably, there is a sharp transformation point in the case of wires with larger diameter (2.16 mm), while the transformation is more gradual in the case of wires with smaller diameter of 1.78 mm. In addition, the width of the hysteresis loop is larger for the wires with diameter
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800
Experiment Model
Stress (MPa)
600
400
200
0 0.00
0.02
0.04
0.06
0.08
Strain
Figure 12. Model simulations and experimental data for cyclic loading up to a maximum stress of 650 MPa at 70°C for 2.16 mm diameter NiTi wires: the experimental results are used to calibrate the model. 800
Experiment Model
600
Stress (MPa)
of 2.16 mm. These differences have been consistently observed for all of the reported tests. In general, the results presented in this work are consistent with the results presented in the literature for tensile SMA specimens [15,16]. However, some of the specifics of the current results must be pointed out. The main difference between the current results and the results previously reported in the literature is the observation that the results for identical specimens tested under the same conditions exhibit discrepancies, which in some cases are significant (see Figures 9 and 11). This observation has strong implications on the modeling of the response of these alloys. It is clear that if one test is used for calibration of the material parameters of a deterministic SMA constitutive model, discrepancies will be observed in the predictions of other testing results. These discrepancies may be significant, since in the case of SMAs small variations in the input material parameters may lead to large variations in the output results, such as stress-strain response. To briefly show this, consider that the critical stress for phase transformation at given (constant) temperature varies between two identically treated and tested specimens. This small variation will lead to significantly different output results. This difference is due to the nonlinearity of the material response during the martensitic phase transformation, where small changes in the stress lead to large changes in the strain. Thus, a situation is possible where at given stress level one of the specimens is still in the austenite phase, while the second specimen is already in advanced stages of the martensite transformation (see, for example, the first loading cycle in Figure 11 for an illustration of the above discussion). To further illustrate the implications of the material uncertainties in the modeling approach, the stress-strain response presented in Figure 9 with solid line is used to calibrate the material parameters for an SMA model, which can take into account the evolution of plastic strains [16]. The results from the model simulation are shown in Figure 12 with the corresponding experimental results, used in the calibration of the material parameters. It can be seen that the model can capture the material behavior very well. Next, the model simulation results are compared with the second set of experimental results for the same wire diameter and identical heat treatment and loading conditions (see the stress-strain curve shown with dashed line in Figure 9). The comparison is shown in Figure 13, where it can be seen that the discrepancies between the model simulations and the experimental results are substantial. It must be mentioned that the discrepancies observed in Figure 13 are not due to the model used. The different response of seemingly identical specimens is due to the differences in their microstructure. Since the microstructure is not taken into account by the existing phenomenological models, the variation of the stress-strain response for different specimens could not be reproduced.
400
200
0 0.00
0.02
0.04
0.06
0.08
Strain
Figure 13. Model simulations and experimental data for cyclic loading up to a maximum stress of 650 MPa at 70°C for 2.16 mm diameter NiTi wires: the experimental results are obtained for a specimen with identical heat treatment and loading conditions as in Figure 12. Based on the results presented in this work, an argument can be made that a new approach to modeling may be required. Future model development should focus on the description of the statistical distribution of the material parameters and its effect on the constitutive modeling of the SMAs. The SMA model predictions must also be interpreted with the understanding of the limitations of current models, which
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cannot take into account the observed uncertainties of the material response. 5. 5. SUMMARY AND CONCLUSIONS Large diameter SMA actuators were tested under cyclic loading in this work. Before testing the actuators were heat treated to reveal the pseudoelastic effect. The wires were tested under two different loading patterns: cyclic loading up to a maximum value of strain and cyclic loading up to a maximum value of stress. In both cases twenty loading/unloading cycles were performed. It was observed that during testing relatively large unrecoverable plastic strain accumulated. During the initial cycles the strain accumulates with a higher rate, while at later stages the rate of accumulation slowed down and the plastic strain was close to saturation. Other effects of the cyclic loading also include decrease of the critical stress for onset of the stress-induced martensitic transformation, increase of the transformation hardening and decrease of the area enclosed by the hysteresis loop. In addition, after approximately 10 cycles the pseudoelastic response of the material stabilizes and the stress-strain response during subsequent cycles is repeatable. These observations are compatible with results observed by other researchers and presented in the literature. Another important observation is the difference in the stress-strain response and in the accumulation of plastic strain of identical specimens, tested under identical conditions. These uncertainties in the material response need further investigation and must be taken into account in the modeling efforts, since small variations in material parameters may lead to large variations of the resulting modeling predictions. It is observed that the 2.16 mm wires have a much more even plateau of transformation in comparison with the 1.78 mm wires. In most cases the residual strains are larger in the 2.16 mm wires than the 1.78 mm wires. Observing earlier trends and test results in small diameter wires subject to cyclic loading and relating it with current test results, it is observed in small diameter wires that there is a rapid degradation in the hysteresis with the same number of cycles compared to the large diameter wires. The 2.16 mm wires have a significantly stable hysteresis compared to the 1.78 mm. Further microstructural investigation of the specimens is being carried out.
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ACKNOWLEDGMENTS The authors acknowledge the financial support of the Boeing Company by Contract No. Z10560 monitored by Edward White.
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REFERENCES 1. Lagoudas, D.C., Garner, L.J., Rediniotis, O.K., and Wilson, N. (2000). Development of shape memory alloy actuated biomimetic vehicle. Smart Materials and Structures 9(5), 673-683. 2. Reynaerts, D. and Brussel, H. V., Design aspects of shape memory actuators. Mechatronics 8(6), 635-656 3. Wayman, C. M. (1983). Phase Transformations, Nondiffusive. BV: Elsevier. 4. Hebda, D. and White, S. R. (1995). Effect of Training Conditions and Extended Thermal Cycling on
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Nitinol Two-way Shape Memory Behavior. Smart Materials and Structures 4, 298-304. Lim, T. J. and McDowell, D. L. (1994). Degradation of a Ni-Ti alloy During Cyclic Loading, Smart Materials and Structures 2189(47), 153-165. Miyazaki, S., Imai, T., Igo, Y. and Otsuka, K. (1986). Effect of Cyclic Deformation on the Pseudoelasticity Characteristics of Ni-Ti Alloys. Metal. Trans.A 17A, 115-120. Tanaka, K., Nishimura, F., Hayashi, T., Tobushi, H., and Lexcellent, C. (1995). Phenomenological analysis on subloops and cyclic behavior in Shape-Memory Alloys under mechanical and or thermal loads, Mechanics of Materials 19, 281-292. Lagoudas, D.C. and Bo, Z. (1999). Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part II: Material characterization and experimental results for a stable transformation cycle. International Journal of Engineering Science 37 (9), 1141-1173. McCormick, P. G. and Liu, Y. (1994). Thermomechanical modeling of the martensitictransformation in NiTi. 1. Effect of heat-treatment on transformation behavior. Acta Metallurgica et Materialia 42 (7), 2401-2406. Miller, D. A., and Lagoudas, D. C. (2000). ThermoMechanical Characterization of NiTiCu and NiTi SMA Actuators: Influence of Plastic Strains. Smart Materials and Structures 9(5), 640-652. Miller, D. A. (2000). Thermo-mechanical characterization of plastic deformation and transformation fatigue in Shape Memory alloys. PhD thesis, Texas A&M University. Saburi, T. (1999). Ti-Ni Shape Memory Alloys. In: Otsuka, K., Wayman, C. M. (Eds.), Shape Memory Materials. Cambridge University Press, Cambridge. Ch. 3, 49-96. Huang, X. and Liu, Y. (2001). Effect of annealing on the transformation behavior and super elasticity of NiTi shape memory alloy. Scripta Materialia 45, 153160. Wurzel, D. (1999). Marforming and tempering of binary Ni-Ti alloys including precipitation effects. Materials Science and Engineering A273-275, 634638 Strnadel, B., Ohashi, S., Ohtsuka, H., Ishihara, T. and Miyazaki, S. (1995). Effect of mechanical cycling on the pseudoelasticity characteristics of Ti- Ni and TiNi-Cu alloys. Materials Science and Engineering A203, 187-196 Strnadel, B., Ohashi, S., Ohtsuka, H., Ishihara, T. and Miyazaki, S. (1995). Cyclic stress-strain characteristics of Ti-Ni and Ti-Ni-Cu shape memory alloys. Materials Science and Engineering A202, 148156.
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IMECE2003-42933 THERMOMECHANICAL CHARACTERIZATION OF SMA ACTUATORS UNDER CYCLIC LOADING
Dimitris C. Lagoudas Department of Aerospace Engineering Texas A&M University College Station, TX 77843-3141, USA Email: [email protected]
Pavlin B. Entchev Department of Aerospace Engineering Texas A&M University College Station, TX 77843-3141, USA Email: [email protected]
ABSTRACT Shape memory alloy (SMA) wire actuators have been increasingly used in various devices and applications due to their high energy density and simple design. With the use of these actuators the questions of size effects on their behavior need to be addressed. This paper presents a study on the cyclic loading behavior of large diameter SMA wires subjected to different thermo-mechanical loading paths. Wires of two different diameters are investigated in the current study – 1.78 mm and 2.16 mm. The issues addressed in this work include the investigation and design of a gripping technique for the large diameter wires to avoid slippage and study of heat treatment conditions for optimized superelastic behavior. After the heat treatment, specimens are subjected to cyclic mechanical loading. Two different cyclic loading patterns have been investigated: loading up to a given value of stress or up to a given value of strain. Keywords: Shape memory alloys, actuators, mechanical loading paths, cyclic loading.
thermo-
1. INTRODUCTION Shape memory alloys (SMA) have gained popularity for use in large force actuators. There has been an increased use of SMAs for applications that are 1-D in nature, where rods, wires, and strips are employed as actuators, in active hydrofoil [1] and robotic systems [2]. Many researchers have investigated the effect of thermomechanical behavior on wires and strips of small cross sections. As the demand for SMA actuators grows,
Parikshith K. Kumar Department of Aerospace Engineering Texas A&M University College Station, TX 77843-3141, USA Email: [email protected]
it becomes essential to examine the effects of size and shape of the actuators on their performance. Chemical composition, cold work, heat treatment and thermomechanical cycling can widely influence the material properties of SMAs. The wire drawing process introduces large plastic deformations in the material. After the cold drawing, the material must be heat treated to reveal the pseudoelastic behavior. In addition, of great interest is the stability of the SMA pseudoelastic characteristics during cyclic mechanical loading. The residual strain, remaining after the load is relieved, and the energy dissipation measured from the hysteresis characterizes the stability of the pseudoelastic effect. Many investigations have been conducted on the effect of mechanical and thermal cyclic loading on the thermomechanical response of NiTi [3–10]. Earlier papers of thermomechanical testing of SMA wires and fatigue testing employed conventional techniques to characterize these materials [11]. Although similar testing techniques are adopted in this work, large diameter wires demand specific modifications. These wires are stronger and less flexible than the smaller diameter wires. Therefore, the gripping techniques must be modified to avoid effects of slipping and stress concentration. The remainder of the paper is organized as follows: Section 2 describes the equipment and the adopted experimental procedure; the experimental results are presented in Section 3; discussion of the results follows in Section 4; conclusions are given in Section 5.
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2. EXPERIMENTAL PROCEDURE The wires used for testing were Ni-44.62%Ti with diameters of 1.78 mm and 2.16 mm. The material was supplied by Special Metals. The received material was in the cold rolled condition without any heat treatment. Preliminary testing of the material in the as-received state revealed no superelastic effect. The Differential Scanning Calorimeter (DSC) analysis did not show any prominent peaks during the heating or the cooling cycle. However after heat treatment the DSC reveals the transformation temperatures. Figure 1 shows the DSC results for samples of both wire diameters after heat-treatment.
treatment for 5 minutes was chosen as optimal for the both wire diameters. The time is measured from the instance of placing the specimen into the furnace to the instance of taking it out of the furnace. A batch of 10 wires was annealed together in a furnace. The heat treatment of a batch of wires was performed due to the fact that individually annealed wires show varying results. Thus, the uniformity in a batch is maintained. DSC analysis after this heat treatment did not reveal any prominent peaks. However, earlier works reported in the literature have shown that there is not a drastic variation in the austenitic finish temperature (Af) for different temperatures of annealing. Thus, the Af temperature determined at 500°C was used at the reference temperature, based on which the test matrix was formulated [14].
(a)
_______ 5 min at 400°C ___ ___ 10 min at 400°C _ _ _ _ _ 15 min at 400°C
(b)
Figure 1. (a) DSC curve for NiTi wire with diameter of 2.16 mm annealed at 500ºC for 5 minutes. Two peaks are observed during cooling, which is an evidence of an R-phase; (b) DSC curve for NiTi wire with diameter of 1.78 mm annealed at 500ºC for 5 minutes. It was concluded that heat treatment must be performed in order to obtain superelastic behavior. A parametric study on these wires was conducted by heat treating them at different temperatures and testing them to determine the ideal temperature and time for optimizing the superelastic behavior [12, 13]. The samples were heat treated at temperatures ranging from 375°C to 500°C for time periods from 5 to 15 minutes. The results of the parametric study at 400°C for the wires with diameter of 2.16 mm are shown in Figure 2. It can be seen that the material heat treated for 5 minutes shows best pseudoelastic response. It undergoes complete reverse phase transformation, characterized by the elastic portion of the stress-strain curve during the late stages of unloading. The results for the other two specimens, heat treated at 10 and 15 minutes at 400°C, as well as the results for heat treatment at 500°C, which are not shown in this work, do not exhibit clear elastic unloading portion. Thus, based on this parametric study, 400°C heat
Figure 2. Parametric study of the effect of heat treatment time at 400°C on the pseudoelastic behavior of wires with diameter of 2.16 mm. After the optimal heat treatment parameters were established, the wires were mechanically tested to obtain their stress-strain response. The tests were performed on an MTS servo-hydraulic loading frame fitted with a custom made heating chamber. The chamber is equipped with heating elements and a temperature controller, which maintains an accuracy of 0.5°C. The temperature of the specimens was continuously monitored using a thermocouple attached to each specimen’s surface. The strain during the experiments was measured using both the crosshead displacement of the MTS frame and an Epsilon extensometer attached to the wire. The load was measured using a Transducer Techniques load cell. The experimental setup is shown in Figure 3. As a part of the research effort, different gripping techniques for the large diameter wires were investigated. Jaw grips with perforated jaws create regions of stress concentrations on the surface of contact. These regions become points where the specimen fractures. Grips with flat gripping surfaces lead to slipping of the specimen at high load levels. Thus, custom grips were designed and fabricated. The grips
2
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were designed to prevent slip while at the same time provide capabilities of gripping wires of various diameters without any stress concentrations. The grips are shown in Figure 4.
close to saturation after 20 cycles. Another effect of the cycling is the decrease of the area enclosed by the hysteresis loop. Table 1. Test matrix for cyclic mechanical loading of large diameter NiTi wires.
Load cell
Heating Chamber Custom Grips Extensometer
Thermocouple Temperature controller
Figure 3. Experimental setup for mechanical testing of the wires.
Test # Number of Loading tested type specimens Maximum 1 2 strain Maximum 2 2 strain Maximum 3 2 stress Maximum 4 2 stress Maximum 5 2 strain Maximum 6 2 strain Maximum 7 2 stress Maximum 8 2 stress
Wire Limit diameter
Temperature
Number of cycles
1.78mm 6%
70°C
20
2.16mm 6%
70°C
20
1.78mm 750 MPa
70°C
20
2.16mm 650 MPa
70°C
20
1.78mm 6%
80°C
20
2.16mm 6%
80°C
20
1.78mm 800 MPa
80°C
20
2.16mm 800 MPa
80°C
20
Figure 4. Manufactured grips. Also shown is a gripped wire. 3. EXPERIMENTAL RESULTS The wires of both diameters were tested under isothermal conditions above the austenitic finish temperature. Tests at different temperatures and loading patterns were performed. The first temperature for both wires was chosen to be 70°C. The second temperature was 80°C for the 2.16 mm wire and the 1.78 mm wire. Two loading patterns were chosen: cyclic loading up to a constant maximum strain level and cyclic loading up to a constant maximum stress level. A study was performed to examine the effect of loading rate on the test results. It was noticed that strain rate of 10-4 s-1 results in quasistatic response. Thus, this loading rate was chosen to ensure constant temperature of the wire during forward and reverse transformation. The test matrix for both wire diameters is summarized in Table 1. Figure 5 shows the results of two wires of 1.78 mm diameter, tested at 70°C for 20 cycles to a constant maximum strain of 6%. The results indicate a good correlation between the test results of the two wires. The initial curve shows a sharp transition in the slope, which indicates transformation from austenite to martensite. However, as the number of cycles increases, the transformation becomes more gradual. The residual strain that accumulates in this case is approximately 0.7% to 0.8%. The accumulation of this permanent strain slows down with the increasing number of cycles and the strain is
Figure 5. Test results from cyclic mechanical loading at 70°C for 1.78 mm diameter NiTi wires: loading up to maximum strain of 6%. Figure 6 shows the results of two wires of 2.16 mm diameter, tested at 70°C for 20 cycles to a constant strain of 6%. The test results shown indicate a gradual accumulation of residual strain as the number of cycles increase. However the accumulated permanent strain is 0.23%, which is less than what is observed in the 1.78 mm diameter wire. Similar to the previous case the strain is close to saturation after 20 cycles.
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Figure 6. Test results from cyclic mechanical loading at 70°C for 2.16 mm diameter NiTi wires: loading up to maximum strain of 6%. Figure 7 shows the results of two wires of 2.16 mm diameter, tested at 80°C for 20 cycles to a constant strain of 6%. The results indicate that the material is not completely transformed to martensite at that temperature and strain level. In the former result the 2.16 mm wire tested at 70°C under the exact same conditions showed clear sign of complete transformation with the end of the plateau region and start of the second elastic region. The residual strain in this case is much higher compared to the test at 70°C. Similar to the earlier cases, the onset of transformation is initially sharp and smoothens as the number of cycles increase. The results shown in Figure 7 indicate that there is significant discrepancy between the two identical specimens, tested under the same conditions. Similar discrepancies are also observed for other test case, as discussed below. Test results shown if Figure 8 and 9 correspond to 1.78 mm and 2.16 mm wires tested to constant stress levels of 750 MPa and 650 MPa respectively at a temperature of 70°C. As in the previous cases there is permanent strain accumulation (1.0% to 1.2% for the 1.78 mm diameter wire and 1.0% to 1.5% for the 2.16 mm diameter wire) and saturation of this strain is observed towards the end of 20 cycles. While the residual strain in the wires with diameter of 1.78 mm is attributed to the development of plastic strains due to the phase transformation, in the case of the wire with diameter of 2.16 mm some of the residual strain may be due to incomplete reverse phase transformation. This conclusion is based on the observation on the stress-strain curve upon unloading for the wire which response is presented on Figure 9 with the dashed line.
Figure 7. Test results from cyclic mechanical loading at 80°C for 2.16 mm diameter NiTi wires: loading up to maximum strain of 6%.
Figure 8. Test results from cyclic mechanical loading at 70°C for 1.78 mm diameter NiTi wires: loading up to maximum stress of 750 MPa. It should be noted from the results in Figures 8 and 9 that there is a pronounced deviation in the response of the wires, which were heat treated and tested under the same conditions. As seen from Figure 8, after 20 cycles one of the wires exhibits larger transformation strain (the results indicated by the dashed line) than the second one (the results plotted in solid line). In addition, the value of the accumulated residual strain after 20 cycles differs for the two wires. Even if the accumulated residual strain is not completely due to plasticity, still the response of the two wires suggests that the material behaves
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differently even after identical heat treatment and testing under the same conditions.
Figure 10. Test results from cyclic mechanical loading at 80°C for 1.78 mm diameter NiTi wires: loading up to maximum stress of 800 MPa. Figure 9. Test results from cyclic mechanical loading at 70°C for 2.16 mm diameter NiTi wires: loading up to maximum stress of 650 MPa. Figure 10 shows the results for 2 wires of 1.78mm diameter tested to constant stress level of 800MPa at 80°C. The residual strain reached approximately 1.5% in both wires. The results obtained indicate that the residual strain in the wires in this case is much higher than for the same wires tested at 70°C (Figure 8). Unlike in the 2.16mm wires the plateau is not flat and sharp. Comparing it to the results in Figure 8, the inconsistency in the results clearly shows up. The deviation at 80°C is less pronounced compared to the former case. To examine the effect of the incomplete reverse phase transformation, the wires with diameter of 2.16 mm are tested at higher temperature of 80°C, which is well above the austenitic finish temperature. Thus, complete reverse phase transformation is ensured. The results of these tests are shown in Figure 11 for two wires for 20 cycles up to a constant stress level of 800 MPa. The results are compatible with the results obtained at 70°C and shown in Figure 9. However, the residual strains for this case are slightly higher, compared with the strains in the previous test. The residual strain for one of the wires is 1.4% while the second wire exhibits residual strain of 2%. Based on these observations, it can be concluded that the incomplete reverse phase transformation does not play major role in the results for 70°C, shown in Figure 9. It is again noted that the results for two identical specimens show significant discrepancies. Both the initial and final responses (after 20 cycles) are different.
Figure 11. Test results from cyclic mechanical loading at 80°C for 2.16 mm diameter NiTi wires: loading up to maximum stress of 800 MPa. 4. DISCUSSION The results of the cyclic testing of wires with two different diameters are presented in this work. Some of the differences in the behavior of the specimens with two different diameters can be observed from the test results. Most notably, there is a sharp transformation point in the case of wires with larger diameter (2.16 mm), while the transformation is more gradual in the case of wires with smaller diameter of 1.78 mm. In addition, the width of the hysteresis loop is larger for the wires with diameter
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Figure 12. Model simulations and experimental data for cyclic loading up to a maximum stress of 650 MPa at 70°C for 2.16 mm diameter NiTi wires: the experimental results are used to calibrate the model. 800
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of 2.16 mm. These differences have been consistently observed for all of the reported tests. In general, the results presented in this work are consistent with the results presented in the literature for tensile SMA specimens [15,16]. However, some of the specifics of the current results must be pointed out. The main difference between the current results and the results previously reported in the literature is the observation that the results for identical specimens tested under the same conditions exhibit discrepancies, which in some cases are significant (see Figures 9 and 11). This observation has strong implications on the modeling of the response of these alloys. It is clear that if one test is used for calibration of the material parameters of a deterministic SMA constitutive model, discrepancies will be observed in the predictions of other testing results. These discrepancies may be significant, since in the case of SMAs small variations in the input material parameters may lead to large variations in the output results, such as stress-strain response. To briefly show this, consider that the critical stress for phase transformation at given (constant) temperature varies between two identically treated and tested specimens. This small variation will lead to significantly different output results. This difference is due to the nonlinearity of the material response during the martensitic phase transformation, where small changes in the stress lead to large changes in the strain. Thus, a situation is possible where at given stress level one of the specimens is still in the austenite phase, while the second specimen is already in advanced stages of the martensite transformation (see, for example, the first loading cycle in Figure 11 for an illustration of the above discussion). To further illustrate the implications of the material uncertainties in the modeling approach, the stress-strain response presented in Figure 9 with solid line is used to calibrate the material parameters for an SMA model, which can take into account the evolution of plastic strains [16]. The results from the model simulation are shown in Figure 12 with the corresponding experimental results, used in the calibration of the material parameters. It can be seen that the model can capture the material behavior very well. Next, the model simulation results are compared with the second set of experimental results for the same wire diameter and identical heat treatment and loading conditions (see the stress-strain curve shown with dashed line in Figure 9). The comparison is shown in Figure 13, where it can be seen that the discrepancies between the model simulations and the experimental results are substantial. It must be mentioned that the discrepancies observed in Figure 13 are not due to the model used. The different response of seemingly identical specimens is due to the differences in their microstructure. Since the microstructure is not taken into account by the existing phenomenological models, the variation of the stress-strain response for different specimens could not be reproduced.
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Figure 13. Model simulations and experimental data for cyclic loading up to a maximum stress of 650 MPa at 70°C for 2.16 mm diameter NiTi wires: the experimental results are obtained for a specimen with identical heat treatment and loading conditions as in Figure 12. Based on the results presented in this work, an argument can be made that a new approach to modeling may be required. Future model development should focus on the description of the statistical distribution of the material parameters and its effect on the constitutive modeling of the SMAs. The SMA model predictions must also be interpreted with the understanding of the limitations of current models, which
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cannot take into account the observed uncertainties of the material response. 5. 5. SUMMARY AND CONCLUSIONS Large diameter SMA actuators were tested under cyclic loading in this work. Before testing the actuators were heat treated to reveal the pseudoelastic effect. The wires were tested under two different loading patterns: cyclic loading up to a maximum value of strain and cyclic loading up to a maximum value of stress. In both cases twenty loading/unloading cycles were performed. It was observed that during testing relatively large unrecoverable plastic strain accumulated. During the initial cycles the strain accumulates with a higher rate, while at later stages the rate of accumulation slowed down and the plastic strain was close to saturation. Other effects of the cyclic loading also include decrease of the critical stress for onset of the stress-induced martensitic transformation, increase of the transformation hardening and decrease of the area enclosed by the hysteresis loop. In addition, after approximately 10 cycles the pseudoelastic response of the material stabilizes and the stress-strain response during subsequent cycles is repeatable. These observations are compatible with results observed by other researchers and presented in the literature. Another important observation is the difference in the stress-strain response and in the accumulation of plastic strain of identical specimens, tested under identical conditions. These uncertainties in the material response need further investigation and must be taken into account in the modeling efforts, since small variations in material parameters may lead to large variations of the resulting modeling predictions. It is observed that the 2.16 mm wires have a much more even plateau of transformation in comparison with the 1.78 mm wires. In most cases the residual strains are larger in the 2.16 mm wires than the 1.78 mm wires. Observing earlier trends and test results in small diameter wires subject to cyclic loading and relating it with current test results, it is observed in small diameter wires that there is a rapid degradation in the hysteresis with the same number of cycles compared to the large diameter wires. The 2.16 mm wires have a significantly stable hysteresis compared to the 1.78 mm. Further microstructural investigation of the specimens is being carried out.
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ACKNOWLEDGMENTS The authors acknowledge the financial support of the Boeing Company by Contract No. Z10560 monitored by Edward White.
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