# Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters

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## Abstract

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## 1. Introduction

^{®}BG R20) and EVA (EVALAM

^{®}80-120) in particular, are examined in this study. A brief review of current approaches focusing on the modeling of mechanical properties of polymers opens, in Section 2.1, the theoretical part of the paper. The generalized Maxwell model is outlined next in Section 2.2, and the effect of temperature on the stiffness of the interlayer is discussed in Section 2.3. Finally, the formulation of the identification method of the material parameters fitting the experimental data obtained from a cyclic loading is described in Section 2.4. The experimental program is introduced in Section 3, and the experimental data together with the performance of the generalized Maxwell model are presented in Section 4. The main findings and concluding remarks are then summarized in Section 5.

## 2. Material Model

#### 2.1. Overview

#### 2.2. Generalized Maxwell Model

#### 2.3. Temperature Shifting

#### 2.4. Parameter Identification

## 3. Experimental Methods

#### 3.1. Dynamic Single-Lap Shear Test

#### 3.1.1. Test Setup

#### 3.1.2. Method of Results Evaluation

#### 3.2. Dynamic Torsion Tests

#### 3.2.1. Test Set-Up

#### 3.2.2. Method of Results Evaluation

## 4. Results

#### 4.1. Linearity Validation

#### 4.2. Comparison of Obtained Results

#### 4.3. Identification of the Maxwell Model

## 5. Conclusions

^{®}BG R20 and EVA-based EVALAM

^{®}80-120, enabling the description of their time- and temperature–dependent behavior. To this purpose, sets of small-scale cyclic single-lap shear tests in an MTS loading device and torsional tests in a rheometer were performed for the range of temperatures from $-10{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C to $+60{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C and the range of frequencies from 0.001 Hz to 50 Hz .

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Time–temperature superposition principle master curve [29], ${T}_{1}<{T}_{2}<{T}_{3}<{T}_{4}$.

**Figure 3.**Comparison of PVB shift factors defined by the WLF equation and Arrhenius equations [26] for ${T}_{g}=10{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$.

**Figure 4.**(

**a**) MTS machine metal jaws of a single-lap shear test, (

**b**) climatic chamber for dynamic mechanical thermal analysis (DMTA) in shear and Dewar vessel, (

**c**) specimen with potentiometric linear transducers.

**Figure 7.**Measured force in time during the test; during the time interval ${t}_{1}$, the sample is displacement controlled, and during the time interval ${t}_{2}$, the sample is force controlled.

**Figure 8.**Viscoelastic loop of dynamic stress–strain relation in a loading cycle: (

**a**) illustrative scheme showing all important points, (

**b**) example of EVA stress–strain relation observed during cycling.

**Figure 10.**PVB and EVA linearity check for the selected amplitude sweep at a frequency of 1 Hz in the single-lap shear test.

**Figure 11.**PVB linearity test at $60{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C for the dynamic torsion test.

**Figure 12.**Storage modulus–frequency relations for a selected EVA (

**a**,

**c**) and PVB (

**b**,

**d**) specimen: (

**a**,

**b**) dynamic torsion test, (

**c**,

**d**) single-lap shear test.

**Figure 13.**Comparison of all EVA and PVB shear and torsion measurements for temperatures of $20{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C and $40{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C (solid lines correspond to the dynamic torsion test, dashed lines to the single-lap shear test).

**Figure 14.**Representative master curves constructed at $20{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C with both experimental methods: (

**a**) EVA interlayer, (

**b**) PVB interlayer; rheo indicates the dynamic torsion test, shear indicates the single-lap shear test.

**Figure 15.**Master curves fitted to all experimental data at $20{\phantom{\rule{0.166667em}{0ex}}}^{\circ}$C for the EVA and PVB interlayers.

**Table 1.**Parameters for the generalized Maxwell model for PVB (TROSIFOL

^{®}BG R20) and EVA interlayers (EVALAM 80-120).

Polymer | PVB | EVA | |||||

Long-term shear modulus | 232.26 | 682.18 | kPa | ||||

Reference temperature | ${T}_{0}$ | 20 | 20 | ${}^{\circ}\mathrm{C}$ | |||

Parameters | ${C}_{1}$ | 8.635 | 339.102 | – | |||

${C}_{2}$ | 42.422 | 1185.816 | ${}^{\circ}\mathrm{C}$ | ||||

PVB | EVA | PVB | EVA | ||||

$\mathit{p}$ | θ_{p} | G_{p} | G_{p} | $\mathit{p}$ | θ_{p} | G_{p} | G_{p} |

[s] | [kPa] | [kPa] | [s] | [kPa] | [kPa] | ||

1 | ${10}^{-9}$ | – | 6933.9 | 12 | ${10}^{2}$ | 587.2 | 445.1 |

2 | ${10}^{-8}$ | – | 3898.6 | 13 | ${10}^{3}$ | 258.0 | 300.1 |

3 | ${10}^{-7}$ | – | 2289.2 | 14 | ${10}^{4}$ | 63.8 | 401.6 |

4 | ${10}^{-6}$ | – | 1672.7 | 15 | ${10}^{5}$ | 168.4 | 348.1 |

5 | ${10}^{-5}$ | 1,782,124.2 | 761.6 | 16 | ${10}^{6}$ | – | 111.6 |

6 | ${10}^{-4}$ | 519,208.7 | 2401.0 | 17 | ${10}^{7}$ | – | 127.2 |

7 | ${10}^{-3}$ | 546,176.8 | 65.2 | 18 | ${10}^{8}$ | – | 137.8 |

8 | ${10}^{-2}$ | 216,893.2 | 248.0 | 19 | ${10}^{9}$ | – | 50.5 |

9 | ${10}^{-1}$ | 13,618.3 | 575.6 | 20 | ${10}^{10}$ | – | 322.9 |

10 | ${10}^{0}$ | 4988.3 | 56.3 | 21 | ${10}^{11}$ | – | 100.0 |

11 | ${10}^{1}$ | 1663.8 | 188.6 | 22 | ${10}^{12}$ | – | 199.9 |

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**MDPI and ACS Style**

Hána, T.; Janda, T.; Schmidt, J.; Zemanová, A.; Šejnoha, M.; Eliášová, M.; Vokáč, M. Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters. *Materials* **2019**, *12*, 2241.
https://doi.org/10.3390/ma12142241

**AMA Style**

Hána T, Janda T, Schmidt J, Zemanová A, Šejnoha M, Eliášová M, Vokáč M. Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters. *Materials*. 2019; 12(14):2241.
https://doi.org/10.3390/ma12142241

**Chicago/Turabian Style**

Hána, Tomáš, Tomáš Janda, Jaroslav Schmidt, Alena Zemanová, Michal Šejnoha, Martina Eliášová, and Miroslav Vokáč. 2019. "Experimental and Numerical Study of Viscoelastic Properties of Polymeric Interlayers Used for Laminated Glass: Determination of Material Parameters" *Materials* 12, no. 14: 2241.
https://doi.org/10.3390/ma12142241