# A Non-Destructive Methodology for the Viscoelastic Characterization of Polymers: Toward the Identification of the Time–Temperature Superposition Shift Law

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## Abstract

**:**

## 1. Introduction

## 2. Mechanical Behavior of Viscoelastic Materials

## 3. Non-Destructive Viscoelasticity Evaluation: VESevo

- Several acquisitions at ambient temperature;
- Cooling to −30 °C employing a climatic cell or a freezing spray and then performing VESevo acquisitions during the natural heating process up to ambient temperature;
- Forced heating up to 100 °C through a thermal blanket or a professional heating gun and then carrying out acquisitions down to ambient temperature.

## 4. Methodology: Virtual Model, Sensitivity Analysis, and Experimental Validation

## 5. Results

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Phase lag between stress and strain (

**b**) Stress-Strain curves at different phase angles. $0<\delta <\pi /2$.

**Figure 2.**(

**a**) Viscoelastic moduli as a function of frequency (

**b**). Viscoelastic moduli as a function of temperature.

**Figure 7.**(

**a**) Rod displacement signal as a function of time for the three indenter masses. (

**b**) Rod velocity signal as a function of time for the three indenter masses.

**Figure 11.**Normalized spring constants as a function of the normalized indenter masses for a target velocity of 2.3 m/s.

**Figure 12.**New values of impact-free surface and velocity as a function of the material stiffness for each indenter mass.

**Figure 13.**Normalized frequency of the indentation phenomenon as a function of the semi-spherical indenter mass.

**Figure 16.**Values of impact-free surface and velocity with the newly designed sensor modules. Mass ${m}_{1}$ is shown in black, ${m}_{2}$ is shown in blue, and ${m}_{3}$ is shown in red.

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**MDPI and ACS Style**

Sakhnevych, A.; Maglione, R.; Timpone, F.
A Non-Destructive Methodology for the Viscoelastic Characterization of Polymers: Toward the Identification of the Time–Temperature Superposition Shift Law. *Sensors* **2023**, *23*, 9213.
https://doi.org/10.3390/s23229213

**AMA Style**

Sakhnevych A, Maglione R, Timpone F.
A Non-Destructive Methodology for the Viscoelastic Characterization of Polymers: Toward the Identification of the Time–Temperature Superposition Shift Law. *Sensors*. 2023; 23(22):9213.
https://doi.org/10.3390/s23229213

**Chicago/Turabian Style**

Sakhnevych, Aleksandr, Raffaele Maglione, and Francesco Timpone.
2023. "A Non-Destructive Methodology for the Viscoelastic Characterization of Polymers: Toward the Identification of the Time–Temperature Superposition Shift Law" *Sensors* 23, no. 22: 9213.
https://doi.org/10.3390/s23229213