## 1. Introduction

The history of hardness characterization goes back for almost 200 years. Initially, when quantitative characterization of hardness has not yet been defined, qualitative hardness measurement was based on observing which material deforms the other, showing intuitively which material is harder than the other one. A more advanced qualitative hardness measurement, a 10-step scratch hardness scale, still used today in mineralogy, was proposed by Friedrich Mohs in 1822 [

1]. Later, more sophisticated, quantitative hardness measuring methods became necessary, which came in the form of indentation tests. The first theory of elastic contact of solids was reported by Hertz in 1881 [

2]. In an indentation test a very hard body (indenter) with a well-defined geometry is pushed into the surface of the investigated sample. The hardness is defined as the ratio of the applied force,

F on the indenter and the projected area,

A of the contact surface. This surface was measured optically after the removal of the indenter, however, as the demands shifted towards smaller loads, in order to investigate small samples, thin films or to obtain local hardness values, the size of the residual indentations was reduced so that it could no longer be measured with sufficient accuracy by a simple optical method. The development of depth-sensing indentation (DSI) or instrumented hardness measurements, where the indentation load and indentation depth are continuously registered, offered a solution to this problem by methods which used the unloading stage of the indentation curves for determining the size of the residual indentation. Further, it has become possible to determine additional mechanical parameters of materials, such as the Young’s modulus [

3]. It should also be emphasized that by setting the loading rate, the average deformation rate of the deformed volume under the indenter can also be controlled, allowing also the study of several characteristics of plastic deformation.

The basic applications of the DSI method are based on the calculations developed by Oliver and Pharr [

4,

5], which enable the determination of the hardness (

H) and Young’s modulus (

E) of the measured material from the loading-unloading indentation curve (

Figure 1) without the need of optical measurement of the residual impression. The basic equations of this procedure come from contact mechanics, giving the so-called reduced modulus,

E_{r} as:

and the relationship for calculation of the modulus,

E of the investigated material, as:

where

$S=\frac{dF}{dh}$ is the contact stiffness measured as the slope of the tangent of the unloading curve at the maximum load,

F_{max},

A is the projected area of the elastic contact,

E and

E_{i} are the Young’s moduli,

$\nu $ and

${\upsilon}_{i}$ the Poisson’s ratios of the sample and indenter, respectively. Furthermore, the hardness,

H of the sample is given by the following equation:

During the indentation, the value of the projected area is depending on the contact depth,

h_{c}, where the indenter tip is actually in contact with the surface of the sample. In the Oliver-Pharr evaluating procedure [

4], the contact depth can be calculated by the following equation:

where

${h}_{max}$ is the maximum penetration depth measured experimentally, and

$\epsilon $ is an indenter-constant (for conical indenter

$\epsilon =0.72$, for Berkovich and Vickers tips

$\epsilon =0.75$, and for flat punch

$\epsilon =1$). For the conventional–conical, Berkovich, Vickers–indenters, the projected area can be given as:

It should be noted that in fact, Oliver and Pharr [

4,

5] have improved the suggestions of Doerner and Nix [

6], who assumed that the initial part—at

F_{max}—of the unloading curve is linear. Oliver and Pharr, however, have observed that not even the initial part of the unloading curves are linear and they found that the unloading curves can be described rather by a power law function. In this approach, there is no restriction on the unloading data being linear and the contact stiffness is determined only at peak load.

Over the past nearly 30 years, since the publication of the Oliver-Pharr method, DSI has been used to investigate a number of new phenomena and properties in addition to measuring the basic mechanical characteristics. Especially, the introduction of nanoindentation methods has given new impetus to the application of DSI techniques. The purpose of this paper is to present some of the results of (nano)indentation techniques beyond the determination of (nano)hardness and Young’s modulus.

## 3. Summary

More than 100 years after the introduction of quantitative hardness measurement, the invention of depth-sensing indentation measurements and their further development in nanohardness testing have opened up new possibilities in studying the mechanical properties of materials. Depth-sensing measurements routinely allow the determination of the hardness and Young’s modulus of micron-sized samples. In addition, a number of further new research possibilities have been opened up, including e.g., the determination of the hardness and Young’s modulus of even nanoscale components of multiphase systems, due to the high lateral resolution of nanoindenters. Dynamic transformations and mechanical instabilities that occur during indentation can also be studied, and the new area of micromechanics, examining the plasticity of micrometer-size or even smaller bodies, is emerging. In this review, we have presented some examples in which the application of depth-sensing indentation measurements, eventually supplemented by other methods, has led to the study of new mechanical features or phenomena, with the following main points:

- (1)
During a nanoindentation measurement, the pressure under the tip of the indenter may be so high that it may induce structural phase transition in the investigated sample. This phenomenon may manifest itself as pop-out events or elbows appearing on the unloading stage of the indentation curve.

- (2)
The Portevin-Le Chatelier type plastic instabilities, as the phenomenon of discontinuous yielding during plastic deformation, can be studied by using indentation method. During indentation, the phenomenon of plastic instability manifests itself as step-like indentation depth–load curves, indicating discontinuous indentation process. The occurrence and the development of the instability-steps depends strongly on both the loading rate and the composition of the investigated materials.

- (3)
Beside the investigation of plastic instabilities, other dynamic characteristics, such as strain rate sensitivity or viscoelastic behavior can also be studied by using indentation. Furthermore, deformation mechanisms, such as slipping in individual atomic planes, or grain boundary sliding can be observed and investigated by combining indentation with atomic force microscope and/or with scanning electron microscopy.

- (4)
It has also been shown that indentation can be applied for studying micro-plasticity. As today’s devices are getting smaller and smaller, there is an urgent need to understand the deformation processes of small-size samples, where most of the conventional methods are very hard to apply. Typical examples have been shown to demonstrate the advantages of investigating micro-plasticity by compression of micro-pillars using nanoindentation.