Measuring Visco-Elastic Properties of Polymers with Nanoindentation

Spherical indentation is generally used for determining the properties of materials like hardness, elastic modulus and elastic/plastic properties. With the help of a spherical indenter, low loads elastic deformations could be achieved. The contact issue can be overcome by solving Hertz equations, thus making it easy to calculate the elastic constants of the material.

In this application note, various aspects of low load spherical indentation and a way to determine visco-elastic characteristics from these measurements are explored in detail.

Advanced Indentation Systems

Lack of suitable instruments hinders the use of low load spherical indentation. To address this issue, advanced indentation systems such as the CSM Instruments Ultra Nanoindentation Tester (UNHT) with active top referencing principle can apply forces from the micronewton range and calculate the displacement from nanometer range with adequate resolution. The phenomenon of thermal drift is yet another critical problem and becomes particularly important in the low depth and low load creep measurements.

Moreover, to remain in the visco-elastic standard, the defects should be reversible and the indenter displacement must be relatively small. This aspect makes the problem of thermal drift more important when compared to other types of measurement, where shorter indentation times and larger depths are needed.

A detailed view of the UNHT measurement head. The indenter is on the left-hand side, the ball reference is on the right-hand side.

Figure 1. A detailed view of the UNHT measurement head. The indenter is on the left-hand side, the ball reference is on the right-hand side.

Viscoelastic Model

The process for acquiring visco-elastic characteristics of the tested material was built on fitting the displacement evolution during a hold period at the peak load. The indentation was deliberately carried out at extreme loading rates with load rise duration of 5 s

Subsequent to the load increase, the hold period was set to 30 min. The duration of the hold period was longer than in many other instances, thus reproducing real life conditions where the creep times are significantly longer.

Utilizing a formula recommended by Mencik et al., the displacement signal was fitted and the material in question was modeled by a range of dashpots, springs, and Kelvin-Voigt bodies. This model can be adjusted to suit different types of materials and measurement conditions.

Experimental Framework

For the experiment, polymethyl-methacrylate (PMMA) was used a sample material, which was in the form of a large block. With the help of CSM Instruments’ UNHT system, the indentation experiments were conducted.

The UNHT system is integrated with a spherical indenter made of ruby, which has a small radius of 100 mm. The actual radius of this spherical indenter was confirmed on fused silica by a range of indentations at increasing peak loads.

It was observed that the radius was inconsistent in the range of 0 nm to ~20 nm from the tip of the indenter, and reached its nominal value above this distance from the tip. Hence, the fitting formula can be utilized in its simple form with R = const.

Albeit the forces employed in the experiments may seem fairly high, the related depth growth during the 30 minutes hold period differed between 7 nm and 180 nm. Therefore, superior resolution in displacement measurement and long-term stability of this signal was an important factor in this study.

In spite of the fact that the UNHT had excellent thermal stability, its thermal drift was confirmed by a range of measurements at the same conditions as the creep experiments on PMMA.

The experiment results show that the thermal stability is exceptional and the thermal drift does not exceeds 0.2 nm/min.

Evolution of the displacement signal during hold period on fused silica

Figure 2. Evolution of the displacement signal during hold period on fused silica

The above figure displays a normal evolution of displacement signal during a 30 min long creep period on fused silica at 10 mN load. This value is negligible during traditional measurements and hence the thermal drift of the UNHT does not need to be rectified.

Creep Measurements and Fitting

The entire creep measurements were carried out with the same loading time of 5 s equation, except for the 50 mN load. Thus, the loading rate was changing according to the peak load from 12 mN/min to 200 mN/min.

On the other hand, the hold period remained constant for all measurements. Therefore, the visco-elastic properties can be measured for a larger set of loading conditions.

Indentation depth increase during a 30 minutes hold at 5 mN. The initial depth (hi) after 5 s load rise was 240 nm.

Figure 3. Indentation depth increase during a 30 minutes hold at 5 mN. The initial depth (hi) after 5 s load rise was 240 nm.

The above graph displays an average evolution of indentation depth growth during the hold period, along with thermal drift calculated at the same conditions.

Conclusion

Instrumented indentation is a suitable technique for determining very soft gels, which exhibit similar structure and characteristics like biological tissues. This technique determines small samples in a nondestructive manner and produces indentation information that can be studied to determine the sample’s mechanical properties.

Moreover, the UNHT can be employed for such measurements without involving any hardware modifications. With special design, superior force stability, and thermal drift-free features, the UNHT system offers a quick and convenient way for testing very soft materials.

This information has been sourced, reviewed and adapted from materials provided by Anton Paar TriTec SA.

For more information on this source, please visit Anton Paar.

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