Extraction of Flow Behavior and Hall–Petch Parameters Using a Nanoindentation Multiple Sharp Tip Approach

Significance Statement

Mechanical characterization of materials through elementary measurements has attracted attention in engineering disciplines for decades. Nanoindentation offers an opportunity to obtain a variety of mechanical properties on the nano- or micro-scale. Nanostructured elements are in the focus of many researchers owing to their excellent strength and functionality. Their mechanical characterization, therefore, appears to be of ultimate interest.

Obtaining stress-strain curves from nanoindentation that are conform with uniaxial flow curves is of great interest. Stress-states with a high hydrostatic part allow to test materials with low ductility, where rate dependent behavior could not be obtained with conventional uniaxial tests. In addition, it enables to study the hardening behavior of single crystals. Unfortunately, the method has not yet been asserted as a standard testing approach.

In view of the existing literature, there are still a number of uncertainties. The analysis of typical hardness tests compared to instrumented indentation yields to considerable varying values. Basic observations reveal that the stress significantly correlates with hardness while strain depends on the geometry of the indenter tip.

Alexander Leitner, Verena Maier-Kiener and Daniel Kiener at the Montanuniversität Leoben conducted a detailed comparison of nanoindentation and Vickers micro-hardness tests. Furthermore, they followed Tabor’s work analyzing the method of establishing stress-strain curves through nanoindentation by implementing four sharp indenter tips with different opening angles. Their work is published in the peer-reviewed journal Advanced Engineering Materials.

The authors investigated four samples each of nickel and tungsten where the specimen had microstructures reaching from single crystalline to nanocrystalline dimensions, thus ending up in a large interval of Young’s modulus to stress ratios and significantly different work-hardening attributes. The authors also extracted the flow behavior and Hall-Petch parameters for both materials in a bid to examine whether hardness tests were appropriate and comparable to parameters obtained from uniaxial tests.

The authors observed that when a Berkovich tip was used for nanoindentation, hardness values were in agreement with typical Vickers hardness tests. However, they had to apply a series of corrections in the analysis as hardness is defined differently for the two methods. Testing nickel and tungsten with varying grain sizes allowed for obtaining Hall-Petch parameter at four varying strains. All the obtained values coincided well with those reported in literature although those are typically extracted from uniaxial testing. The profiles of KHP and σ0 indicated expected trends in dependence of the strain for both materials but were sensitive to indentation size effect.

Verena Maier-Kiener states that: ‘Implementing the method with varying sharp tips allowed for the description of the flow behavior of metals and owing to the high hydrostatic component of the stress filed even brittle materials could be tested at higher strains. Through precise calibration of the tips, local indentation flow curves could be extracted and are in good agreement with literature values of uniaxial tests.’

In summary, the authors illustrated that nanoindentation is an excellent method for obtaining mechanical properties of metals, particularly if sample volume is limited, difficult to machine, or when high lateral resolution is needed. This study demonstrates that Hall-Petch parameters and the flow behavior can be extracted using a multiple sharp tip method, and the outcomes can be compared to data obtained by uniaxial testing.

About the author

Alexander Leitner received his master’s degree 2014 in Material Science at the Montanuniversität Leoben, Austria, and is currently employed as a doctoral candidate at the Department of Materials Physics at the Montanuniversität. Starting with nanoindentation in his master thesis, he performed advanced high temperature nanoindentation experiments on nanoporous gold to study its thermo-mechanical deformation behavior.

Main goal of the current PhD project is to gain further insights in dynamic nanoindentation testing in order to develop new protocols for the extraction of mechanical flow curves utilizing sharp and spherical indenter tips.

About the author

Verena Maier-Kiener is group leader for “High Performance Materials” at the Department of Physical Metallurgy and Materials Testing at the Montanuniversität Leoben, Austria. During her PhD position at the Friedrich-Alexander Universität Erlangen-Nürnberg, Germany she laid the foundation for the investigation of thermally activated deformation mechanisms by implementing nanoindentation strain-rate jump techniques. Following post-doc positions at Montanuniversität Leoben and Erich Schmid Institute allowed scientific deepening in terms of understanding the mechanical behavior of high performance materials by nanoindentation.

Currently, her main research themes are in-situ high temperature nanoindentation experiments to achieve novel insights in the thermo-mechanical behavior of advanced materials, and a scale-bridging understanding of the interplay between global and local properties studied with high resolution microscopy techniques.

About the author

Daniel Kiener is associate professor at the Department of Materials Physics at the Montanuniversität Leoben. After receiving his PhD in Leoben in 2007 and post-doc positions at Ludwig-Maximilians-University Munich, Lawrence Berkeley National Laboratory, California and Erich Schmid Institute, Leoben he received his venia docendi in the field of nanoscale plasticity in 2013. Among others, he was awarded the Fritz-Kohlrausch, the Adolf-Martens and the Georg Masing award for his pioneering work in the field of small-scale testing, nano- and micromechanics as well as deformation mechanisms.

His current research interests are focused on advanced nano- and micromechanical characterization techniques to assess atomistic deformation and fracture mechanisms in nanostructured materials.


Alexander Leitner, Verena Maier-Kiener and Daniel Kiener. Extraction of Flow Behavior and Hall–Petch Parameters Using a Nanoindentation Multiple Sharp Tip Approach. Advanced Engineering Materials 2017, 19, No. 4, 1600669.

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