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Nanoindentation: Cutting-edge Hardness Measurement for Advanced Materials

Hardness or ability of a material to resist external forces has always played a significant role in determining its application for practical purposes. In materials science, hardness is often defined as the resistance to localised deformation. The deformation can be from indentation, scratching, cutting, or bending. The hardness of metals, alloys, ceramics, and most polymers typically associates to plastic or permanent deformation of the surface. The hardness of elastomers and some polymers, on another hand, is associated with elastic or recoverable deformation of the surface.

Various hardness tests and measurement techniques are used to check the quality of the material, maintain structural integrity, and determine the material’s functional and optimal working range and conditions.

Indentation: The conventional way

Various indentation tests like Vickers hardness test, Knoop hardness test, Rockwell hardness test, etc, depending on the material under consideration, are often used to determine the hardness of the material and testing its other mechanical properties. In these tests, a hard tip (usually of diamond) whose mechanical properties are known is pressed into a sample whose properties are unknown. The load placed on the indenter tip is increased as the tip penetrates further into the specimen to reach a user-defined value. The load may be held constant for a period or removed after this point is reached. The area of the residual indentation in the sample is measured and the hardness H, is calculated by dividing the maximum load, Pmax, by the residual indentation area, A [1, 2]:


These indentation tests worked well for thick homogeneous samples but failed for materials with thin coatings or thin films deposited over them since they require the application of large amounts of loads and thus, the large overall area of indentation. To resolve the issue and to promote scientific advancement, the need was felt to minimize the area of indentation during the test while precisely determining the mechanical properties of the material. This led to the development of the nanoindentation technique in the mid 1970s.

Nanoindentation: The rescue route

Nanoindentation improved on the conventional macro and micro-indentation tests by indenting on the nanoscale with a very precise tip shape, high spatial resolutions, and by providing real-time load-displacement (into the surface) data while the indentation is in progress [3].

In nanoindentation experiments, small loads and tip sizes are used to yield net indentation area in nm2. An indenter with a geometry known to high precision (generally a Berkovich tip) is employed, a record of the depth of penetration is made, and the area of the indent is determined using the known geometry of the indentation tip. While indenting, various parameters, such as load and depth of penetration can be measured to obtain load-displacement curves. The load-displacement curves can further be used to determine (a) The displacement relative to the initial undeformed surface, h, (b) maximum displacement, hmax, (c) Permanent depth of penetration after the indenter is fully unloaded, hf, and (d) S is the elastic unloading stiffness.

Minimum probing maximum information

Nanoindentation seems to have an upper hand over many conventional indentation methods as it allows for precise determination of many mechanical properties other than just hardness. Hardness can be derived by dividing the maximum load, Pmax, by indentation area, A. Young’s modulus and strain rate sensitivity are two important properties that can be obtained from nanoindentation tests which are important for material selection and component design.

Young’s modulus

Young’s modulus, or the ability of the material to withstand dimensional changes when subjected to tension or compression, is a measure of the stiffness of a solid material. The slope of the load-depth curve, dP/dh, upon unloading is indicative of the stiffness, S, of the material being tested. This includes a contribution from both the material being tested and the response of the indenter itself. The stiffness of the contact can be used to calculate the reduced Young's modulus Er [4, 5]:


Where Ap is the projected area of the indentation at the contact depth hc and β is a geometrical constant whose value is generally taken as unity. The reduced modulus Er is related to Young's modulus Es of the test specimen through the following relationship:


In the above equation, the subscript “i” and “s” indicates the property of the indenter material and specimen respectively and υ is the Poisson's ratio. For a Berkovich diamond indenter tip, Ei is 1140 GPa and υ is 0.07. Poisson’s ratio of the specimen generally varies between 0 and 0.5 for most materials and is typically around 0.3.

Strain rate sensitivity

Strain rate is the rate of change in strain (deformation) of a material with respect to time. A material is sensitive to strain rate if its stress-strain relationship is dependent on the rate of loading. In nanoindentation experiments, strain rate sensitivity of the material is studied using strain rate sensitivity exponent m, which is the material’s resistance to prevent necking during deformation of a material. Mathematically, it is the slope of hardness versus equivalent strain rate graph plotted on a log-log scale.

Equivalent strain rate can be derived from the loading rate and applied maximum load P using the equation below:


Strain rate sensitivity exponent m is defined as:


Various deformation models rely on strain rate sensitivity exponent to explain the principal deformation mechanism in a material like the grain boundary affected zone mediated plastic deformation and the grain boundary assisted partial dislocation emission mechanism [6, 7]. The strain rate sensitivity of the material is a useful tool for material selection for environments involving different stress and strain levels.

Nanoindentation: The future view

Nanoindentation has eased up our efforts to determine various mechanical properties. It is time-saving, material conserving, and highly reliable approach used for a range of materials from bulk to thin films. Some nanoindentation equipment like Hysitron Tl 950 Triboindenter also have inbuilt software that calculates hardness, Young's modulus, and other relevant properties which minimises the chances of human error during calculations. In the future, this technique can be used for quick and easy assessment of new generation materials.


The article is written by Jay Amrish Desai, Ph.D. in Materials Science and Engineering with a special interest in 2-D Materials.


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[2] Oliver, Warren C., and Pharr, Georges M., Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology, Journal of materials research, 3, 2004.

[3] Minor, Andrew M., Asif, S. A. Syed, Shan, Zhiwei, Stach, Eric A., Cyrankowski, Edward, Wyrobek, Thomas J. and Warren, Oden L., A new view of the onset of plasticity during the nanoindentation of aluminium, Nature materials, 697, 2006.

[4] Li, Xiaodong, and Bhushan, Bharat, A review of nanoindentation continuous stiffness measurement technique and its applications, Materials characterization, 11, 2002.

[5] Ehtemam-Haghighi, Shima, Cao, Guanghui, and Zhang, Lai-Chang, Nanoindentation study of mechanical properties of Ti based alloys with Fe and Ta additions, Journal of Alloys and Compounds, 892, 2017.

[6] Gu, C. D., Lian, J. S., Jiang, Q., and Zheng, W. T., Experimental and modelling investigations on strain rate sensitivity of an electrodeposited 20 nm grain sized Ni, Journal of Physics D: Applied Physics, 7440, 2007.

[7] Desai, Jay A., and Kumar, Alok, Effect of iron alloying in the evolution of nanostructure and microstructural stability in nickel, Metals and Materials International, 451, 2016.