# Development of an Advanced Dynamic Microindentation System to Determine Local Viscoelastic Properties of Polymers

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Consideration

_{r}and the indenter contact area A:

_{r}depends on moduli and Poisson’s ratios of indenter (E

_{i}, ν

_{i}) and sample (E

_{s}, ν

_{s}), respectively:

_{s}:

_{i}>> E

_{s}), the second term in the denominator is a small quantity and can be neglected [1,6,7,8,9]:

_{b}is the truncation length of the indenter tip defect.

## 3. Materials and Methods

#### 3.1. Materials

_{g}) below room temperature, PBT is a semi-crystalline polymer with T

_{g}above room temperature, PC represents an amorphous polymer with T

_{g}above room temperature, and thermoplastic polyurethane (TPU) is an elastomeric polymer with T

_{g}below room temperature. All were chosen to show a broad range of thermo-mechanical properties.

#### 3.2. Apparatus

#### 3.3. Measurements

## 4. Results and Discussion

^{2}, all measurements show higher values at different loads. This discrepancy might result from the fact that the Young’s modulus from the material datasheet represents the mean value of a bulk property from tensile testing, whereas the values obtained in this study represent a local surface property.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Specially developed x-y-stage with a laser positioning system for spatial resolution of microindentations.

**Figure 4.**Evolution of raw applied signal force and raw response signal amplitude (both processed with fast Fourier transformation (FFT)) for various tungsten cone indenters.

**Figure 5.**Complex modulus across the cross-section of unannealed HDPE; second order polynomial fit as a trend (dotted) line.

Polymer | Standard | Young’s modulus ^{1} (MPa) | Young’s modulus range [27,28] (MPa) | Poisson’s ratio [29] |
---|---|---|---|---|

PBT (Vestodur, Evonik, Essen, Germany) | Injection molded tensile test bar ISO 527-2: 1A | 2600 (ISO 527-1/-2) | 2500–2800 | 0.42 |

PC (Makrolon, Bayer, Leverkusen, Germany) | Injection molded tensile test bar ISO 527-2: 1A | 2400 (ISO 527-1/-2) | 2200–2600 | 0.41 |

HDPE (Lupolen, LyondellBasell, Wesseling, Germany) | Injection molded tensile test bar ISO 527-2: 1A | 900 (ISO 527-1/-2) | 600–1400 | 0.46 |

TPU (Desmopan, Covestro, Leverkusen, Germany) | n.a. | 29 (ISO 6721-1/-4) | 20–400 | 0.49 |

^{1}Values according to the material datasheet.

Cone indenter | Diameter (mm) | Tip angle (°) | Tip radius (µm) | Abbreviation |
---|---|---|---|---|

Tungsten electrode, W > 99.9% | 1.0 | 28 | 8 | Green |

Tungsten electrode + 2% lanthanum | 1.0 | 28 | 5 | Blue |

Tungsten electrode + rare earth elements | 1.0 | 28 | 5–10 | Lymox |

**Table 3.**Overtones of the first order resonant frequencies of various tungsten cone indenters and complex moduli of high-density polyethylene (HDPE) measured under different loads.

Green Indenter | Lymox Indenter | Blue Indenter | ||||
---|---|---|---|---|---|---|

Load (N) | Overtones (%) | E* (MPa) | Overtones (%) | E* (MPa) | Overtones (%) | E* (MPa) |

0.5 | 7.5 ± 0.8 | 1732 ± 167 | 6.6 ± 3.1 | 3487 ± 335 | 4.0 ± 0.6 | 1780 ± 162 |

0.75 | 8.4 ± 1.9 | 1565 ± 243 | 6.8 ± 2.0 | 1843 ± 409 | 5.3 ± 1.8 | 1643 ± 126 |

1.0 | 8.4 ± 1.0 | 1652 ± 151 | 8.8 ± 2.0 | 1387 ± 237 | 5.7 ± 1.1 | 1343 ± 428 |

1.25 | 6.8 ± 0.9 | 1082 ± 114 | 8.7 ± 1.1 | 1117 ± 92 | 5.0 ± 2.3 | 1119 ± 88 |

Polymer | Tungsten cone indenter (MPa) | Vickers diamond indenter [5] (MPa) | Berkovich diamond indenter [5] (MPa) | Rockwell diamond indenter [5] (MPa) | DMA three-point bending [5] (MPa) | Young’s modulus literature [27,28] (MPa) |
---|---|---|---|---|---|---|

PBT | 2890 ± 378 | 1919 ± 353 | 1737 ± 358 | 1821 ± 78 | 2787 ± 84 | 2500–2800 |

PC | 2726 ± 386 | 2289 ± 156 | 1957 ± 317 | 2142 ± 351 | 2380 ± 19 | 2200–2600 |

HDPE | 1053 ± 175 | 1381 ± 339 | 1929 ± 302 | 1553 ± 75 | 1565 ± 33 | 600–1500 |

TPU | 38 ± 2 | 24 ± 2 | 26 ± 3 | 24 ± 3 | 73 ± 3 | 20–400 |

HDPE | Gate far | Gate near |
---|---|---|

Unannealed | 791 ± 132 | 1095 ± 76 |

Annealed | 1073 ± 231 | 1073 ± 156 |

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**MDPI and ACS Style**

Ramakers-van Dorp, E.; Haenel, T.; Ciongwa, D.; Möginger, B.; Hausnerova, B.
Development of an Advanced Dynamic Microindentation System to Determine Local Viscoelastic Properties of Polymers. *Polymers* **2019**, *11*, 833.
https://doi.org/10.3390/polym11050833

**AMA Style**

Ramakers-van Dorp E, Haenel T, Ciongwa D, Möginger B, Hausnerova B.
Development of an Advanced Dynamic Microindentation System to Determine Local Viscoelastic Properties of Polymers. *Polymers*. 2019; 11(5):833.
https://doi.org/10.3390/polym11050833

**Chicago/Turabian Style**

Ramakers-van Dorp, Esther, Thomas Haenel, Dominik Ciongwa, Bernhard Möginger, and Berenika Hausnerova.
2019. "Development of an Advanced Dynamic Microindentation System to Determine Local Viscoelastic Properties of Polymers" *Polymers* 11, no. 5: 833.
https://doi.org/10.3390/polym11050833