Measuring nanoindentation hardness at high sustained strain-rates

Conference Dates

September 29-October 4, 2019


Dynamic pyramidal nanoindentation, performed at a constant strain-rate, is a popular nanomechanical method for accessing the local strength of complex materials. However, with currently available testing systems using continuous stiffness measurement (CSM), nanoindentation is so far limited to strain-rates of s-1, which precludes it from ballistic applications. Here, we show that the current limitation derives primarily from a plasticity issue related to the continuous stiffness measurements.

Increasing the harmonic frequency would allow for a corresponding extension of the strain-rate range. Unfortunately, this is usually prevented by machine resonance effects, which become prominent above several multiples of the natural frequency of the measurement system. Here, we show the existence of so-called “sweet spots” frequencies, one order of magnitude higher than the standard harmonic oscillation, which are nonetheless unaffected by undesirable resonance phenomena and can be selected for performing valid hardness measurements.

In order to access even higher deformation rates, we also show how the Oliver-Pharr evaluation method can be modified, so as to avoid the need for a measurement of the contact stiffness. Specifically, provided the elastic modulus is known from a prior measurement, the hardness can be calculated as a function of the indentation depth from quasi-static indentation loading data. As the new evaluation method strongly relies on the load and displacement input data, the experimental upper strain-rate limit is mostly determined by the time constants of the hardware components in the nanoindentation system. With most current commercial systems, valid measurements are shown to be possible up to strain-rates of s-1.

These improvements enable the characterization of the small-scale mechanical properties of materials over a much larger strain-rate range than previously achievable with standard CSM testing, as will be illustrated by an application to the superplastic alloy Zn22Al.


[1] B. Merle, V. Maier-Kiener, G.M. Pharr. Influence of modulus-to-hardness ratio and harmonic parameters on continuous stiffness measurement during nanoindentation. (2017) Acta Materialia, 134, pp. 167-176.

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