# Embedded NiTi Wires for Improved Dynamic Thermomechanical Performance of Silicone Elastomers

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Section

#### 2.1. Materials and Specimen

_{55.34}Ti

_{44.66}; indicated fractions in wt.%) was selected with a diameter of 760 µm. A thin diameter was preferred in order to have high compliance under compressive loading while the stiffness in tension was preserved. A volume content of 5% was selected to study the dynamic thermomechanical properties of PDMS/SMA composite. The SMA wire was investigated in the as received state with an oxide free surface finish and straight annealed.

#### 2.2. Dynamic Thermomechanical Analysis (DTMA)

_{0}is the instantaneous modulus, τ

_{i}the relaxation time and to this corresponding the Prony series coefficient is given by g

_{i}= (E

_{i−1}− E

_{i})/E

_{0}. From Equation (1) the mechanical loss factor tanδ = E″/E′ can be directly derived:

_{T}is obtained and can be mathematically expressed by the well-known WLF-function [21]. The temperature-dependent shift factor a

_{T}is given by:

_{PT}is the lowest modulus (phase transformation), E

_{A}is the modulus of austenite dominant state of the alloy, E

_{M}is the respective modulus of the martensite dominant state, T is the temperature, T0

_{1}and T0

_{2}are the temperatures related to the inflection points of the curves, and h

_{1}and h

_{2}are dimensionless constants of the exponential functions. This function will be utilized for the NiTi alloy under investigation. In addition, we desired to model the temperature- and frequency-dependent modulus parameter of the PDMS-SMA composite. Considering the viscoelastic behavior of PDMS by applying Prony series Equation (1) and the Equation (4) for NiTi alloys, the following coupled model was proposed:

_{0}and its temperature dependency are represented by the biphasic function, while the frequency-dependent behavior is expressed by the real part of the Prony series. Equations (1)–(5) will be utilized to describe the measured and evaluated dynamic thermomechanical properties of the investigated materials and their correlations are also discussed in the following.

## 3. Results and Discussion

^{2}) to the experimental data. At low and high frequencies the fit of the Prony series to the tanδ master curve is not as good as in the other frequency range. As the Prony series was optimized to the storage modulus, this misfit could be related to the earlier mentioned opposite temperature dependency of tanδ and E′ at low and high frequencies (cf. Figure 4a vs. Figure 4b). The macroscopic storage modulus and the tanδ of the NiTi alloy are shown in Figure 5b. In contrast to the earlier discussed neat PDMS, the time–temperature superposition principle is not applicable to the NiTi alloy. However, a pronounced temperature dependency can be observed for both dynamic mechanical properties. In addition, the mechanical loss factor seems to be loading frequency-dependent, while the storage modulus is almost independent. The varying mechanical properties are mainly caused by the diffusionless phase transformation of the microstructure from austenite to martensite passing through an intermediate phase (rhombohedral-phase). From low to high temperature, the storage modulus declines until a minimum of 12.5 GPa, followed by a steep increase to a rather plateau with small variations around 20 GPa. The tanδ behavior is opposite within the investigated temperatures, showing an increase until the peak is reached and declines subsequently. The peak of the martensitic phase transformation is measured at around the same temperature of 310 K as the minimum of the storage modulus. This seems to be reliable, as the damping is higher the lower the storage modulus is. From modeling point of view, we have not found any constitutive law to describe (predict) the macroscopic behavior of NiTi alloys in the literature. Therefore, some of the authors conducted an investigation focusing on the dynamic thermomechanical behavior of NiTi alloys [22]. The frequency discrepancy was highlighted and reported there, including an empirical model for the temperature-dependent modulus of NiTi alloys. It was found that the biphasic function according to Equation (4) is capable of predicting the storage modulus characteristic. The fit is demonstrated in Figure 5b as a dashed line and the determined model parameters are listed in Table 3.

^{2}) of 97.75% is achieved by this approach and the corresponding model parameters are summarized in Table 4. For the model parameter determination, the relaxation times were predefined in order to reduce the number of dependent variables and the well-known Levenberg-Marquardt algorithm was utilized. The evaluated standard errors for the derived parameters are presented in Table 4.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Positioning plate with the shape memory NiTi alloy wires prepared for the cast mold of a barbell-shaped specimen; (

**b**) Actuation principle of the barbell-shaped composite specimen of Polydimethylsiloxane (PDMS) (Sylgard 184, base polymer:crosslinking agent 20:1, DowCorning Inc., US) and 4.4 vol% NiTi (Memry GmbH, D).

**Figure 3.**Experimental setup to characterize the dynamic thermomechanical behavior including the dimensions of the barbell specimen in mm.

**Figure 4.**Temperature- and frequency-dependent dynamic thermomechanical behavior of neat PDMS. (

**a**) frequency-dependent storage modulus E′ determined at various temperatures; (

**b**) frequency-dependent mechanical loss factor tanδ determined at various temperatures; (

**c**) wicket-plot; (

**d**) temperature-dependent time–temperature shift factor a

_{T}including the WLF-function (dashed line).

**Figure 5.**Modulus characteristics of the neat PDMS and the NiTi alloy determined by DTMA. (

**a**) green data points show the master curve of neat PDMS at glass transition temperature for the storage modulus E′ and the orange data points show the corresponding master curve of the mechanical loss factor tanδ. The dashed lines represent the 5th order Prony series (Equations (1) and (2)) prediction with the parameters shown in the inserted table. (

**b**) temperature-dependent storage modulus as well as mechanical loss factor tanδ characteristic of the NiTi alloy. Dashed blue line is the temperature dependent modulus modeled by Equation (4). The full orange line is the over the frequency averaged tanδ curve; the dashed orange lines indicate the maximum as well as the minimum tanδ trend.

**Figure 6.**Illustration of the DTMA results and performance of PDMS-SMA composite. (

**a**) The mean level as well as dynamic amplitude sweep data of neat PDMS (circle) in comparison with PDMS-SMA (square) depicted in the wicket-plot. (

**b**) The temperature- as well as frequency-dependent results of PDMS-SMA. (

**c**) 3D-plot of the temperature- and frequency-dependent storage modulus E′ of PDMS-SMA (red points); blue data points…projection to E′ vs. temperature; green data points…projection to E′ vs. frequency; grey area…prediction according to Equation (5).

**Table 1.**Experimental parameters for the investigated materials during dynamic thermomechanical analysis (DTMA).

Material | Dyn. Ampl. | Mean Level | Frequency | Temperature |
---|---|---|---|---|

PDMS5XL | 0.75 mm | 2 mm | 1 Hz–46.5 Hz | −30 °C–+40 °C |

0.5 mm–3 mm | 0.5 mm–3 mm | 10 Hz | +22 °C | |

NiTi | 8 MPa | 25 MPa | 1 Hz–21.5 Hz | −30 °C–+80 °C |

PDMSSMA | 0.75 mm | 2 mm | 1 Hz–90 Hz | −30 °C–+80 °C |

0.5 mm–3 mm | 0.5 mm–3 mm | 10 Hz | +22 °C |

E_{0} | g_{1} | g_{2} | g_{3} | g_{4} | g_{5} | τ_{1} | τ_{2} | τ_{3} | τ_{4} | τ_{5} |
---|---|---|---|---|---|---|---|---|---|---|

MPa | - | - | - | - | - | s | s | s | s | s |

15 | 0.0513 | 0.0642 | 0.0952 | 0.108 | 0.322 | 4.85 × 10^{−11} | 7.66 × 10^{−10} | 1.70 × 10^{−10} | 3.86 × 10^{−9} | 6.60 × 10^{−8} |

E_{PT} | E_{A} | E_{M} | T0_{1} | T0_{2} | h_{1} | h_{2} |
---|---|---|---|---|---|---|

MPa | MPa | MPa | K | K | - | - |

12,020 | 17,810 | 19,657 | 266.55 | 315.75 | 0.06 | 0.87 |

**Table 4.**Model parameters of the biphasic function coupled with the 3rd order Prony series according to Equation (5) for the PDMS-SMA composite.

Parameter | Unit | Value | Standard Error |
---|---|---|---|

E_{PT} | MPa | 7.248 | 0.3033 |

E_{A} | MPa | 8.771 | 0.7537 |

E_{M} | MPa | 8.696 | 0.3047 |

T0_{1} | K | 253.135 | 10.0159 |

T0_{2} | K | 326.720 | 3.3931 |

h_{1} | - | 0.083 | 0.0541 |

h_{2} | - | 0.078 | 0.0266 |

g_{1} | - | 0.045 | 0.0031 |

g_{2} | - | 0.055 | 0.0051 |

g_{3} | - | 0.642 | 0.0119 |

τ_{1} | s | 0.063 | predefined |

τ_{2} | s | 0.009 | predefined |

τ_{3} | s | 0.001 | predefined |

R^{2} | % | 97.75 |

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**MDPI and ACS Style**

Çakmak, U.D.; Graz, I.; Moser, R.; Fischlschweiger, M.; Major, Z.
Embedded NiTi Wires for Improved Dynamic Thermomechanical Performance of Silicone Elastomers. *Materials* **2020**, *13*, 5076.
https://doi.org/10.3390/ma13225076

**AMA Style**

Çakmak UD, Graz I, Moser R, Fischlschweiger M, Major Z.
Embedded NiTi Wires for Improved Dynamic Thermomechanical Performance of Silicone Elastomers. *Materials*. 2020; 13(22):5076.
https://doi.org/10.3390/ma13225076

**Chicago/Turabian Style**

Çakmak, Umut D., Ingrid Graz, Richard Moser, Michael Fischlschweiger, and Zoltán Major.
2020. "Embedded NiTi Wires for Improved Dynamic Thermomechanical Performance of Silicone Elastomers" *Materials* 13, no. 22: 5076.
https://doi.org/10.3390/ma13225076