Nanoindentation

There has been considerable recent interest in the mechanical characterisation of thin film systems and small volumes of material using depth-sensing indentation tests with either spherical or pyramidal indenters. Usually, the principal goal of such testing is to extract elastic modulus and hardness of the specimen material from experimental readings of indenter load and depth of penetration. These readings give an indirect measure of the area of contact at full load, from which the mean contact pressure, and thus hardness, may be estimated. The test procedure, for both spheres and pyramidal indenters, usually involves an elastic—plastic loading sequence followed by an unloading. The validity of the results for hardness and modulus depends largely upon the analysis procedure used to process the raw data. Such procedures are concerned not only with the extraction of modulus and hardness, but also with correcting the raw data for various systematic errors that have been identified for this type of testing. The forces involved are usually in the millinewton (10⁻³ N) range and are measured with a resolution of a few nanonewtons (10⁻⁹ N). The depths of penetration are on the order of microns with a resolution of less than a nanometre (10⁻⁹ m). In this chapter, we consider the general principles of elastic and elastic—plastic contact and how these relate to indentations at the nanometre scale.

The goal of the majority of nanoindentation tests is to extract elastic modulus and hardness of the specimen material from load-displacement measurements. Conventional indentation hardness tests involve the measurement of the size of a residual plastic impression in the specimen as a function of the indenter load. This provides a measure of the area of contact for a given indenter load. In a nanoindentation test, the size of the residual impression is often only a few microns and this makes it very difficult to obtain a direct measure using optical techniques. In nanoindentation testing, the depth of penetration beneath the specimen surface is measured as the load is applied to the indenter. The known geometry of the indenter then allows the size of the area of contact to be determined. The procedure also allows for the modulus of the specimen material to be obtained from a measurement of the “stiffness” of the contact, that is, the rate of change of load and depth. In this chapter, we review the mechanics of the actual indentation test and, in particular, the nature of the indenters used in this type of testing.

As described in Chapter 2, estimations of both elastic modulus and hardness of the specimen material in a nanoindentation test are obtained from load versus penetration measurements. Rather than a direct measurement of the size of residual impressions, contact areas are instead calculated from depth measurements together with a knowledge of the actual shape of the indenter. For this reason, nanoindentation testing is sometimes referred to as depth-sensing indentation testing. In this chapter, methods of the analysis of load-displacement data that are used to compute hardness and modulus of test specimens are presented in detail. It is an appropriate introduction to first consider the case of a cylindrical punch indenter — even though this type of indenter is rarely used for this type of testing, its response illustrates and introduces the theory for the more complicated cases of spherical and pyramidal indenters.

In conventional indentation tests, the area of contact between the indenter and the specimen at maximum load is usually calculated from the diameter or size of the residual impression after the load has been removed. The size of the residual impression is usually considered to be identical to the contact area at full load, although the depth of penetration may of course be significantly reduced by elastic recovery. Direct imaging of residual impressions made in the submicron regime are usually only possible using inconvenient means and, for this reason, it is usual to measure the load and depth of penetration directly during loading and unloading of the indenter. These measurements are then used to determine the projected area of contact for the purpose of calculating hardness and elastic modulus. In practice, various errors are associated with this procedure. The most serious of these errors manifests themselves as offsets to the depth measurements. Others arise from environmental changes during the test and the non-ideal shape of the indenter. In addition to the above, there are a number of materials related issues that also affect the validity of the results. The most serious of these are an indentation size effect and the phenomenon of piling-up and sinking-in. The sensitivity of nanoindentation tests to these phenomena and others is a subject of continuing research.¹ In this chapter, we review some of the most commonly encountered sources of error and methods of accounting for them.

The methods of analysis described in Chapter 3 can be used to provide a useful computation of simulated load-depth curves, where the mechanical properties of both the specimen and indenter are given as input parameters. A simulated load-depth curve allows comparisons to be made with actual experimental data. For example, such comparisons may yield information about non-linear events such as cracking or phase changes that might occur with an actual specimen during an indentation test. In this chapter, the procedure for generating a simulated load-depth curve is described in detail and a comparison is made with experimental data from materials with a wide range of ratio of modulus to hardness.

An interesting fundamental approach to the analysis of load-depth data is provided by dimensional analysis.^1–9 Consider the indentation of an elastic—plastic specimen with a rigid conical indenter.

In the previous chapters, the indentation process has been implicitly assumed to be quasi static, and no time-dependent or rate effects were considered. In this chapter, the basic theory underlying various dynamic modes of testing is presented. Techniques such as oscillatory motion, impact, and scratch testing are covered in sufficient detail to provide an understanding for the interpretation of the results obtained.

The ISO (the International Organization for Standardization) has recently issued a draft international standard ISO 14577 entitled “Metallic materials — Instrumented indentation test for hardness and materials parameters.”¹ The standard covers depth-sensing indentation testing for indentations in the macro, micro and nano depth ranges.

Interest in nanoindentation has spawned a number of nanoindentation instruments that compete on a world market. Purchasers of such instruments are universities, private and government research organisations, and quality control laboratories. There is particular interest within the semiconductor industry that is concerned with the mechanical properties of a wide range of thin films. All of the products described in this chapter are depth-sensing devices. The instruments typically measure depth of penetration using either a changing inductance or capacitance displacement sensor. A typical nanoindentation test instrument has a depth resolution of less than a tenth of a nanometre and a force resolution of less than a nanonewton. The load can be applied by the expansion of the piezoelectric element, the movement of a coil in a magnetic field, or electrostatically. Maximum loads are usually limited to the millinewton range. The minimum load is usually less than a micronewton.

Nanoindentation finds a wide application. The test results provide information on the elastic modulus, hardness, strain-hardening, cracking, phase transformations, creep, fracture toughness, and energy absorption. Since the scale of deformation is very small, the technique is applicable to thin surface films and surface modified layers. In many cases, the microstructural features of a thin film or coating differs markedly from that of the bulk material due to the presence of residual stresses, preferred orientations of crystallographic planes, and the morphology of the microstructure. The proceedings of annual symposiums are a rich source of information about the applications of nanoindentation. In this chapter, we present some rather straight forward examples of analysis of nanoindentation test data using the methods described in the previous chapters.