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Austenitic shape memory alloy has potential applications in self-centering seismic resistant structural systems due to its superelastic response under cyclic tension. Raw austenitic SMA needs proper pretreatments and pretraining to gain a stable superelastic property. In this paper, tests are carried out to investigate the effects of pretraining, pretreatments, loading rate, and strain amplitude on the mechanical performance on austenitic SMA rods with a given size. The tested rods are to be used in a new concept self-centering steel link beam. Customized pretraining scheme and heat treatment are determined through the tests. The effects of loading rate and strain amplitude are investigated. A simplified stress-strain model for the SMA rods oriented to numerical simulations is obtained based on the test results. An example of using the simplified material model in numerical analysis of a self-centering steel link beam is conducted to validate the applicability of the model.

Besides the well-known shape memory effect, shape memory alloy at the austenite state exhibits a superelastic effect due to crystallographic transformation between austenite phase and martensite phase under certain conditions [

Recognizing the similarity between the flag-shaped stress-strain loop exhibited by the superelastic SMA and the flag-shaped hysteresis loop observed in typical self-centering systems, the superelastic SMA, especially in the form of rods, has recently been studied for use as recentering components in self-centering connections [

In this paper, tests on SMA rods with a given size are reported. The purpose of the tests is to determine the optimal pretreatments for the SMA rods and extract a simplified material model for the SMA rods compatible with available commercial FE packages. The layout of the paper is as follows: Section

The raw SMA rods used in this paper were provided by a commercial special metal supplier. The alloy was manufactured in accordance with the Standard Specification for Wrought Nickel-Titanium Shape Memory Alloys for Medical Devices and Surgical Implants (F2063) issued by ASTM. As reported in the “Certification of Product Quality” provided by the supplier, the weight percentage of nickel, carbon, hydrogen, and oxygen in the alloy are 56.01%, 0.009%, 0.0006%, and 0.024%, respectively, and the weight percentage of nitrogen in the alloy is below 0.003%. The nominal diameter of the raw SMA rods is 20 mm. The nominal austenite start temperature of them is −20°C which guarantees that they are in austenite state in the room temperature. No heat treatment has been conducted on them by the manufacture. The raw SMA rods are machined to dog-bone-shaped coupons, as shown in Figure

Test coupon.

To simplify the identifications of the specimens, each specimen is notated by an identifier starting with the diameter of the work section, followed by the heating temperature and duration, and ending with the sequence of heat treatment and machining work. HM and MH were used to represent heat treatment conducted before machining work and heat treatment conducted after machining work, respectively. For example, specimen 14-350-30-MH indicates that the specimen was machined down to the dog-bone shape with 14 mm diameter over the working segment and is then heated by 350°C for 30 minutes. If there is no heat treatment applied on the specimen, the identifier for it will be 14-N-N.

Nine specimens were used in this study to investigate various characteristics of the rods and the details of them are given in Table

Summary of specimens used in this study.

Specimen number | Specimen codes | Loading protocols | Numbers |
---|---|---|---|

1 | 14-N-N | LP (I-0.03, II-0.03-25) | 1 |

2 | 14-300-30-MH | LP (I-0.03, II-0.03-25) | 1 |

3 | 14-350-30-MH | LP (I-0.03, II-0.03-15, II-0.03-10) | 1 |

4 | LP (I-0.03, II-0.03-15, II-0.15-10) | 1 | |

5 | LP (I-0.03, II-0.03-15, II-0.30-10) | 1 | |

6 | LP (I-0.03, II-0.03-15, I-0.03) | 1 | |

7 | 14-400-30-MH | LP (I-0.03, II-0.03-25) | 1 |

8 | 14-450-30-MH | LP (I-0.03, II-0.03-25) | 1 |

9 | 14-450-30-HM | LP (I-0.03, II-0.03-25) | 1 |

A 250 kN INSTRON 8802 servo-controlled hydraulic test machine was used to perform the tests. Since the SMA specimens were round and hard, the test machine failed to grip them directly by its jaws once the tension reached 70 kN. As a result, a set of rectangle steel heads were used to facilitate gripping of the specimens. A 50 mm length MTS extensometer was used to monitor the strain of the tested specimen. Test setup is shown in Figure

Test setup.

Two basic loading protocols LPI and LPII were used in the tests. Loading protocol LPI consists of increasing strain cycles of 1–6% by increments of 1%, as shown in Figure ^{−1}. For loading protocol LPII, three different strain rates 0.03% s^{−1}, 0.15% s^{−1}, and 0.3% s^{−1} were adopted depending on the cases. For each specimen, the practical loading protocol applied was a combination of the basic ones. To simply indicate the practical loading protocol used for a given specimen, a loading protocol code consisting of the abbreviations of the basic loading protocols and the corresponding parameters (i.e., strain rates and cycle numbers) lined in time order was adopted. For example, loading protocol LP (I-0.03, II-0.15-15, and I-0.03) means that the specimen will be loaded with the basic loading protocol LPI at a strain rate of 0.03% s^{−1}, then loaded with the basic loading protocol LPII at a strain rate of 0.15% s^{−1} for 15 cycles, and finally loaded with the basic loading protocol LPI at a strain rate of 0.03% s^{−1} again. The loading protocol codes for each specimen are given in Table

Two basic loading protocols. (a) LPI and (b) LPII.

Previous studies showed that the stress-strain response of SMA rods under each load cycle varied from each other when no prestraining or inadequate pretraining was imposed on the SMA rods [_{Ms} between adjacent cycles.

The forward transformation stress _{Ms} is defined as the starting stress for the transformation from austenite to martensite, as shown in Figure _{Ms}. Accordingly, elastic modulus _{A} of the SMA material was defined as the tangent of the secant connecting the origin and the conditional point.

Diagram for the simplified stress-strain curve of superelastic SMA material.

Diagram for the stress-strain response of real SMA material.

If SMA rods without pretraining or with inadequate pretraining are used in a self-centering system, considering that the number of loading cycles and the strain amplitude in each loading cycle would being experienced by the SMA rods during an earthquake event could not be predicted in advance, the behavior of the self-centering system will become unpredictable. In another aspect, since the forward transformation stress _{Ms} significantly decreases as the number of cycles increases, the linear strength of the self-centering system will decrease after an earthquake event. In another word, the strength of the self-centering system is not recovered and even the residual deformation of them is negligible. Whether the postearthquake recentered system with decreased strength could be used as before will be in question. This fact will contradict the original design philosophy of a self-centering system which is aimed to be reusable after designed earthquake without repairmen or with limited repairmen. Previous experimental studies also showed that there was an amount of unrecoverable deformation in the self-centering system caused by the incremental residual strain between the loading cycles of the SMA rods without pretraining [

To determine a proper pretraining scheme for the given SMA rods, four specimens with different heat treatment temperatures were firstly loaded with the loading protocol I and then loaded with the loading protocol II by 25 constant cycles, at a strain rate of 0.03% s^{−1}, that is loaded with loading protocol LP (I-0.03 and II-0.03-25). The stress-strain responses of the specimens under the aforementioned loading protocol are shown in Figure _{Ms} also happens in the first several cycles and approaches stable as the number of constant cycles increases. To quantify the development of the residual strain, the accumulated residual strain at typical load cycles are given in Table _{0}, _{5}, _{10}, _{15}, and _{25} denote the accumulated residual strains after 0, 5, 10, 15, and 25 constant loading cycles, respectively. It shows that more than 80% accumulated residual strain had been taken place after 15 constant cycles for each specimen. A similar quantification on the forward transformation stress _{Ms} is given in Table ^{−1} are chosen as the prestraining loading scheme for the SMA specimens.

Stress-strain responses under loading protocol LP (I-0.03 and II-0.03-25).

Accumulated residual strains at typical loading cycles.

Specimens | Accumulated residual strains | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

After incremental cycles | After 5 constant cycles | After 10 constant cycles | After 15 constant cycles | After 20 constant cycles | After 25 constant cycles | ||||||

_{0} (%) |
_{0}/_{25} (%) |
_{5} (%) |
_{5}/_{25} (%) |
_{10} (%) |
_{10}/_{25} (%) |
_{15} (%) |
_{15}/_{25} (%) |
_{20} (%) |
_{20}/_{25} (%) |
_{25} (%) | |

D14/14-N-N | 3.56 | 89.67 | 3.87 | 97.48 | 3.93 | 98.99 | 3.95 | 99.50 | 3.96 | 99.75 | 3.97 |

D14/14-300-30 | 1.38 | 60.00 | 1.91 | 83.04 | 2.10 | 91.30 | 2.20 | 95.65 | 2.27 | 98.70 | 2.30 |

D14/14-350-30 | 0.49 | 40.50 | 0.76 | 62.81 | 0.93 | 76.86 | 1.06 | 87.60 | 1.16 | 95.87 | 1.21 |

D14/14-400-30 | 0.53 | 38.13 | 0.84 | 60.43 | 1.03 | 74.10 | 1.16 | 83.45 | 1.31 | 94.24 | 1.39 |

D14/14-450-30 | 1.61 | 53.67 | 2.49 | 83.00 | 2.73 | 91.00 | 2.86 | 95.33 | 2.93 | 97.67 | 3.00 |

Forward transformation stress at typical loading cycles.

Specimens | Forward transformation stress | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

After incremental cycles | After 5 constant cycles | After 10 constant cycles | After 15 constant cycles | After 20 constant cycles | After 25 constant cycles | ||||||

_{0} (MPa) |
_{0}/_{25} |
_{5} (MPa) |
_{5}/_{25} |
_{10} (MPa) |
_{10}/_{25} |
_{10} (MPa) |
_{10}/_{25} |
_{10} (MPa) |
_{10}/_{25} |
_{10} (MPa) | |

D14/14-N-N | 674 | 1.06 | 657 | 1.04 | 650 | 1.03 | 644 | 1.02 | 640 | 1.01 | 633 |

D14/14-300-30 | 605 | 1.10 | 578 | 1.05 | 568 | 1.04 | 557 | 1.02 | 551 | 1.01 | 548 |

D14/14-350-30 | 399 | 1.65 | 313 | 1.29 | 275 | 1.14 | 258 | 1.07 | 244 | 1.01 | 242 |

D14/14-400-30 | 360 | 1.95 | 253 | 1.40 | 216 | 1.19 | 202 | 1.12 | 188 | 1.04 | 181 |

D14/14-450-30 | 210 | 1.44 | 175 | 1.20 | 163 | 1.12 | 155 | 1.06 | 150 | 1.03 | 146 |

As mentioned in Section

A specimen without heat treatment and four specimens annealed with different temperatures ranged from 300°C to 450°C were tested using a same loading protocol as that used in Section

Effect of heat temperatures on the mechanical properties. Effect on (a) EVD, (b) average residual strain, (c) elastic modulus, and (d) forward transformation stress.

Note that the effects of heat temperature (duration = 30 mins) on the mechanical properties of the SMA rods found in this paper differ from those reported by Wang et al. [

As reported by Wang et al. [

Cyclic responses of specimens using different pretreatment sequences. Cyclic responses of specimen (a) 14-450-30-MH and (b) 14-450-30-HM.

It is found that the specimen 14-450-30-HM exhibits a comparable response to its counterpart reported in the previous study [

Effect of heat and machining sequence on the mechanical properties. Comparison on (a) EVD and (b) accumulated residual strain.

To investigate the effect of strain rates on the mechanical properties of the SMA rods, three identical specimens 14-350-30-MH are pretrained at 0.03% strain rate and then loaded 10 constant cycles at 0.03%, 0.15%, and 0.30% strain rates, respectively. The cyclic responses of them are shown in Figure

Stress-strain responses under different loading rates. Stress-strain response under loading rate (a) 0.03%, (b) 0.15%, and (c) 0.3%.

Effect of loading rate on mechanical properties. Effect on (a) EVD, (b) energy dissipation, (c) elastic modulus, and (d) forward transformation stress.

A specimen 14-350-30-MH is loaded by the protocol LP (I-0.03, II-0.03-15 and I-0.03) to investigate the effect of strain amplitude on the mechanical properties of the prestrained SMA rods. The stress-strain response of the specimen under different strain amplitudes is shown in Figure

Stress-strain responses under different strain amplitudes.

Effect of strain amplitude on mechanical properties. Effect on (a) EVD, (b) energy dissipation, (c) elastic modulus, and (d) forward transformation stress.

Since the strain plateau has not fully developed in the cycles with strain amplitudes smaller than 4%, there is a skip in the elastic modulus and the forward transformation stress between the cycle with 4% strain and the cycle with 5% strain. For the cycles above 5% strain, both the elastic modulus and the forward transformation stress gradually decrease as the strain amplitude increases. This may not be purely caused by the increasing of the strain amplitude. There may be also contribution from the increasing of the number of cycles as that observed in the constant loading cycles.

The optimal pretreatment determined by the tests will be adopted for the SMA rods that will be applied in self-centering link beams. FE-based numerical simulation is a well-accepted method to predict the response or parametric study of the performance of a structural system/component before or after test study. Aurichhio’s model [_{Ms}, _{Mf}, _{As}, and _{Af}), Young’s modulus (_{A}), and the maximum transformation strain (_{L}) to define Aurichhio’s model for the SE SMA. A typical six-parameter model for SMA material is shown in Figure

Derivation of simplified SMA material model from test data.

As mentioned in Section

The simplified model for the pretrained specimen 14-350-30-MH is determined using the above principle, and the corresponding characteristic parameters are given in Table

Characteristic parameters of simplified model for specimen 14-350-30-MH.

Parameters |
_{A} (GPa) |
_{Ms} (MPa) |
_{Mf} (MPa) |
_{As} (MPa) |
_{Af} (MPa) |
_{L} |
---|---|---|---|---|---|---|

Values | 21.7 | 254.6 | 524.2 | 338.7 | 148.7 | 0.025 |

Note that a few stress-strain models for SMA rods have been proposed and used in the previous numerical studies on SMA-based self-centering systems [

Most of them were based on the first-cycle test data of SMA rods without prestraining. As we know, the SMA rods without prestraining are not able to repeat the response of its first cycle in the following loading cycles, while multicycle loading is unavoidable in a real earthquake event. There would be a considerable error between the numerically predicted response and the real response after the first cycle.

There is no clear equivalent principle having being stated for the derivation from the test data to the simplified model. As a result, different simplified models might be derived from the same test data.

Using the simplified SMA material model obtained in this paper and the analytical model for self-centering link beams using SMA rods given by Xu et al. [_{0} = _{Af} is used to get a high linear elastic strength. Grade Q345 hot rolled H-shape steel HM300 × 200 [

Prototype self-centering link beam considered in FE simulation: (a) self-centering link beam and (b) layout of SMA rods.

A virtual test setup which is similar to the real test setup used by Mansour et al. [

Virtual test setup.

Since the whole structural system is symmetry about the middle-thickness plane of the web of the link beam, only half of the structural system is modeled in the simulation. Solid elements were used for the SMA rods, the link beam, and the test beams. Line elements were used for the loading beams to reduce the number of elements and enhance the computing efficiency, as shown in Figure

FE model of self-centering steel link beam.

The general-purpose FE software package ANSYS v.12.1 [

The steel material was simulated by the bilinear kinematic hardening model built in ANSYS. Young’s modulus and yield strength mentioned above had been used in the simulation. The strain hardening modulus of the steel material was assumed to be 15 GPa. The six-parameter SMA model determined above was simulated by ANSYS’s built-in superelastic SMA model.

A loading protocol which cyclically loaded the link to a rotation of 0.02 rad, 0.04 rad, 0.06 rad, and 0.08 rad was employed.

The deformation as well as the distribution of the Von Mises stress of the structural system at the ultimate state (0.08 rad) is shown in Figure

Deformation and stress distribution at ultimate state (unit: MPa).

Shear force to link rotation response.

Stress-strain response of a typical SMA rod.

This paper has conducted a number of tests on pretrained large size SMA rods which are towards to be used in a new concept self-centering steel link beam. The pretraining scheme for the given SMA rods is determined based on the test results. The effects of quenching temperature, strain rate, strain amplitude, and processing sequence on the mechanical properties of pretrained SMA rods are investigated. The optimal quenching temperature and the proper processing sequence are determined. A simplified stress-strain model for the prestrained SMA rods oriented to apply in numerical simulations is obtained based on the test results. An example of using the simplified SMA material model in numerical analysis of a self-centering steel link beam is conducted to validate the applicability of the material model. More detailed conclusions of this study are given as follows:

The stress-strain response of the SMA rod under cyclic load significantly varies at the first a few cycles and then becomes stable after a certain number of cycles. Based on the test results, a pretraining scheme that consists of 6 incremental cycles and 15 constant cycles is determined.

The quenching temperature shows a significant effect on mechanical properties of the pretrained SMA rod specimens. By comprehensively investigating the effect of it on the residual strain, elastic modulus, energy dissipation, and forward transformation stress, 350°C (duration = 30 minutes) is deemed as the optimal quenching temperature.

Shifting the order of machining process and heat treatment results in significant degeneration on the mechanical properties of the SMA rod specimen. This is because the optimal quenching temperature for the SMA rod specimen is sensitive to the effective diameter of the SMA rod specimen at the heat treatment. Machining before heat treatment is preferred for ease of machining.

When the loading rate increases, the energy dissipation and the EVD decrease and the elastic modulus and forward transformation stress increase. Generally speaking, the decrements in energy dissipation and EVD and the increments in the elastic modulus and forward transformation stress are insignificant and may be negligible in most cases.

When the strain amplitude increases, the energy dissipation and EVD linearly increase. This indicates that the SMA rod should be designed to be loaded into high-strain levels to fully extract the energy dissipation capacity of it.

The applicability of the simplified stress-strain model for the pretrained SMA rods is verified by a numerical example. The numerical example shows that the prestrained SMA rods enable the self-centering link beam to be totally recoverable from a deformation up to 8% rotation.

The authors declare that there are no conflicts of interest regarding the publication of this manuscript.

This work is supported by the National Key Research and Development Program of China (Grant no. 2016YFC0800206) and the Fundamental Research Funds for the Central Universities.