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Indentation in the sample of a solid of the known shape (indenter) followed by the observation of the effects on the material (print on its surface) is the most common way of measuring the hardness. Depending on the shape of the tip and test reporting features distinguished are the measuring methods, e.g. Vickers, Brinell, Knoop etc. Hardness under these methods is determined as the ratio of the applied load to the area of the print visible.
The indentation basics known in the USSR as a "method of kinetic hardness" was developed by the Soviet scientists S.I.Bulychev and V.P.Alekhin in 1960-1970. . In the following two decades the instruments for mechanical testing as well as new models describing the interaction between the indenter and material for indentation were keenly developed [2-4]. However, the method became widespread after publishing an article by the American scientists U. Oliver and J. Farr  who had offered the most coherent model for the analysis of experimental data and implemented that method in one of the first commercial nanohardness testers.
In 2002, the International Organisation for Standardisation (ISO) adopted the ISO 14577 standard which at that time consisted of three parts and regulated the measurement of hardness and other mechanical properties based on the analysis of the dependence of the applied load on the depth of indentation.  The method had the established name, instrumental indentation. The first part of ISO 14577 sets out the general principles of the method, provides advice on selecting indenters and addresses measurement uncertainty questions. The second part  focuses on the calibration of the tools and devices used to perform the measurements. The third part  contains hardness measure requirements, the samples used for indirect calibration of tools and validation of their metrological characteristics.
In 2007 the fourth part of the standard ISO 14577-4  dedicated to the characteristics of the application of the instrumental indentation to measure the mechanical properties of thin films and coatings was adopted. That same year, the American Society of Testing and Materials (ASTM) adopted the standard E2546-07  that repeats all of the key provisions of ISO 14577 1–3 in a compressed form. In 2011, the Russian Federation introduced GOST R 8.748-2011  that corresponds to the first part of ISO 14577 as amended in 2002 by its content.
In 2015, the new version of ISO 14577 [12–14] to update and supplement many measurement aspects of the instrumental indentation method was adopted. The draft of the new fourth part, which does not yet have any official status, was also published.
International standard ISO 14577
The idea behind the indentation procedure in accordance with ISO 14577 is that the indenter is pressed into the surface in accordance with a given law of force increase or penetration depth. After reaching a predetermined criterion, the maximum load or penetration depth, the indenter is held for some time and then taken away until a complete loss of contact with the sample. The load and indenter displacement values are recorded during the entire indentation procedure.
The normal conditions of measurement according to the standard are as follows, the temperature of 23 ± 5°C and relative humidity less than 50%. If there are substantial prerequisites for the thermal drift of a device, it is recommended to hold the indenter for 60 seconds in the end of the unloading section at a level corresponding to 10% of the maximum load. Later in this section the amount of thermal drift should be determined and taken it into account during processing of the experimental data.
Description of the method and key ratios are available for measurement by nanoindentation are presented in the first part of the standard. The hardness HIT and elastic modulus measurements are regulated:
where σs – Poisson’s ratio, EIT – Young's modulus. IT Index indicates that these two values are measured by the instrumental indentation methods and may be different from the hardness H and elastic modulus E of real materials, if the properties do not match the assumptions used in the model. It should be noted that the calculation of HIT and EIT requires knowing only three values from the "load-introduction" diagram F (h): the amount of the maximum load Fmax, the slope of the unloading curve at the point of maximum load S and the maximum depth hmax (fig.1).
Further calculations are based on formulas:
The index tip means that the value of the elastic modulus and Poisson’s ratio correspond to the material of the indenter. The indenter shape function A (hc) shows the dependency of the cross-sectional area on the contact depth and should be known by the time of measurement.
Naturally, these ratios have their limitations. For example, due to the neosymmetry of the indenter, a correction factor β is introduced into the right part of the elastic modulus, the values of which were calculated in a number of numerical experiments  and were in the range from 1.0226 to 1.085. Furthermore, it is assumed that the indent print has not plastic pile-up or elastic surface level sink-in, the material is homogeneous and elastic-plastic, the elastic and plastic properties being independent from each other. Attempts to consider these effects [16,17] have not yet led to the development of a standardised approach.
ISO 14577 and GOST R 8.748-2011
In 2011, Russia finally adopted the national standards GOST R 8.748-2011 to perform measurements by the instrumental indentation method; and in late 2014 the corresponding state standard of hardness was set up. This will greatly facilitated the life of scientists and process people by formalising the studies related to the measurement of mechanical properties at depths of less than 1 µm.
By its nature, our standard is almost a verbatim repetition of the first part of ISO 14577-1:2002 but there are differences, the main of which is that in ISO hardness has the dimension N/mm2 (MPa), and in the Russian GOST is determined in units of the appropriate scale. This difference appears to be associated with the national metrological school tradition to use ordinal scales for hardness. In this sense, evading in the new standard from the SI values continues the long-standing dispute of domestic scientists and metrology experts about the physical nature of hardness as the average contact pressure under the indenter.  At the same time, in daily practice, both use quite simple ratios or tables for the conversion of hardness values from one scale to another.
In general, we can say that the standardisation of nanomechanical testing is high in demand by the materials scientists and equipment developers. It is hoped that the remaining parts of GOST will come up in the near future, and they will include 2015 additions to the ISO standard.
The 2015 edition of ISO 14577 accounted for many of the features identified by the joint efforts of engineers designing nanohardness testers and scientists using them. In particular, the procedure for measuring and recording temperature drifts in the hardware component is clarified; the procedure for preparing and fixing the samples is spelled out more carefully; the sources of errors and their contribution to the overall uncertainty of the measurements are described in more detail as well as the procedures for instrument standardisation and calibration are finalised.
In general, we can say that a vast experience in the application nanohardness testers for a variety of materials in a wide range of measurement conditions was gained for 13 years. It became clear that the devices could be used to assess not only the basic mechanical properties such as hardness and elastic modulus but also a number of other specific properties, e.g. viscous, time-dependent etc. Therefore, the dedicated technical committees are actively working on the development of the ISO 14577 standard; Part 5 will focus on creep measurements, Part 6 concerns the dynamic indentation methods (the so-called method of continuous stiffness measurements, CSM), Part 7 is about measurement of the mechanical properties in the extended temperature range.
NanoScan scanning nanohardness testers
The only Russian serial device that implements the instrumental indentation method is the nanohardness tester NanoScan-4D [19-22] (fig.2). The device makes it possible to carry out tests by the sclerometry method, measurement of hardness and elastic modulus by the instrumental indentation method as well as to implement a number of atomic force microscopy methods. The nanohardness indentation module allows you to apply loads ranging from several micronewtons to a few newtons and measure displacements in the range of several nanometers to a millimetre. The device can be equipped with various types of tips which include the pyramidal Berkovich and Vickers indenters, spherical indenters as well as tips in the form of a flat die.
Nanohardness testers of the NanoScan family fully meet all the requirements and recommendations of ISO 14577.
It should be noted that the standard has three levels of measurement depending on the values of the applied load F or indentation depth h:
macro (F < 30 kN);
micro (F < 2Н; h > 0.2 µm);
nano (h < 200 nm).
In practice, the "macro" range is not used in contemporary nanohardness testers because in the macroscale measurement tasks are successfully solved with the help of more simple and accessible instruments following the long-established methods.
Particular attention should be paid to the fact that in NanoScan-4D the "micro" and "nano" ranges are implemented in a single measurement module; in order to change to higher loads it is enough to select the appropriate mode in the software of the device. In the devices of other manufacturers this problem is usually solved by adding additional costly modules.
It should also be noted that the standards govern the single measurement performance but in the real work the measurements with samples of large series are carried out. Therefore, to expand the NanoScan research capabilities a wide range of functions implemented in the software of the device including as follows:
high-performance batch processing of the experimental data using the latest parallel computing methods;
the macrocommand language that allows you to implement the necessary sequence of measurements in the automatic mode;
construction of two-dimensional (topographic) and three dimensional (volumetric) maps of the hardness and elastic modulus distribution depending on spatial coordinates.
Fig.3 shows the example of a three-dimensional (tomography) hardness map based on the results of processing 225 multicycle injections. Silver coating on the glass, the average thickness of which was about 175 nm, obtained by magnetron sputtering was used as the sample. Indents were both in the film coating area and outside it.
The NanoScan-4D devices were implemented by the method of dynamic contact stiffness measurement (CSM) based on the measurement of the quadrature components of displacement in the application of harmonic forces in addition to the monotonous deepening of a probe into the sample. Based on the components calculated are the values of real and imaginary stiffness components, and then the values of the elastic modulus E’ and loss modulus E’’ corresponding to the in-phase displacement component and the displacement component shifted by 90є are determined. As an example, fig.4 shows the values measured for the fused quartz and bitumen. The typical operating frequency range is up to 50 Hz but in the case of measurements in the pre-loaded condition it can operate at frequencies up to 300 Hz.
As noted above, it is planned to standardise the dynamic measurement in the seventh part of ISO 14577 over the next few years; however, the developers of NanoScan are already implementing this method and others in their devices. This applies in particular to temperature measurements.
As you can see, it is really easy to make measurements with the NanoScan in accordance with ISO and GOST R!