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## Über dieses Buch

Nanoindentation, Third Edition gives a detailed account of the most up-to-date research in this important field of materials testing. As in previous editions, extensive theoretical treatments are provided and explained in a clear and consistent manner that will satisfy both experienced and novice scientists and engineers. Additionally, numerous examples of the applications of the technique are provided directly from manufacturers of nanoindentation instruments. A helpful series of appendices provides essential reference information that includes a list of frequently asked questions.

The new edition has been restructured to provide results of the latest research and developments in the field of mechanical testing while retaining the essential background and introductory, but authoritative nature, of the previous editions. The new edition also expands on the instrumentation and applications chapters by including material sourced direct from the instrument manufacturers in this field.

Aimed at graduate student level, this book is designed to fill a need associated with the use of nanoindentation as a quantitative test method for mechanical properties of small volumes of materials.

## Inhaltsverzeichnis

### Chapter 1. Contact Mechanics

Abstract
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.
Anthony C. Fischer-Cripps

### Chapter 2. Nanoindentation Testing

Abstract
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.
Anthony C. Fischer-Cripps

### Chapter 3. Analysis of Nanoindentation Test Data

Abstract
As described in Chap. 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.
Anthony C. Fischer-Cripps

### Chapter 4. Factors Affecting Nanoindentation Test Data

Abstract
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.
Anthony C. Fischer-Cripps

### Chapter 5. Simulation of Nanoindentation Test Data

Abstract
The methods of analysis described in Chap. 3 can be used to provide a useful computation of simulated load-displacement curves, where the mechanical properties of both the specimen and indenter are given as input parameters. A simulated load-displacement 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-displacement 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.
Anthony C. Fischer-Cripps

### Chapter 6. Scaling Relationships in Nanoindentation

Abstract
An interesting fundamental approach to the analysis of load-displacement data is provided by dimensional analysis [1–9]. Consider the indentation of an elastic–plastic specimen with a rigid conical indenter. The mechanical properties of the specimen can be approximated by a uniaxial stress–strain response given by Eqs. 4.28 and 4.29, here repeated for convenience:
\begin{aligned} \sigma &= E\varepsilon \qquad\quad\varepsilon\le {\rm{Y/E}} \\ \sigma &= K{\varepsilon ^x}\qquad\;\; \varepsilon\ge {\rm{ Y/E}} \end{aligned}
(6.1)
where σ is the applied stress and e is the resulting strain and K is equal to:
$$K = Y{\left[ {\frac{E}{Y}} \right]^x}$$
(6.2)
Anthony C. Fischer-Cripps

### Chapter 7. Time-dependent Nanoindentation

Abstract
In general, materials can resist deformation in a solid-like or viscous-like manner. Solid-like materials store energy under deformation, and upon removal of stress, returns to its original state. Viscous materials dissipate energy during deformation and upon removal of stress, remains in its deformed state. Materials with combined solid-like and viscous-like properties are said to be viscoelastic. Nanoindentation can be used to quantitatively determine the viscoelastic properties of materials. In one method, a small oscillatory force or displacement is imparted to the indenter. The resulting load and displacement signals provide a method whereby the elastic and viscous components of the specimen response can be calculated. In another method, the load or displacement is held at a fixed value and the change in displacement (creep) or load (relaxation) recorded over a period of time. Application of an appropriate mechanical model can yield values for the elastic and viscous properties of the specimen.
Anthony C. Fischer-Cripps

### Chapter 8. Nanoindentation of Thin Films and Small Volumes of Materials

Abstract
One of the most popular applications of nanoindentation is the determination of the mechanical properties of thin films. In nanoindentation tests, the properties of the film may be measured without removing the film from the substrate as is done in other types of testing. The spatial distribution of properties, in both lateral and depth dimensions, may be measured, and a wide variety of films are amenable to the technique, from ion-implanted surfaces to optical coatings and polymer films. Apart from testing films in-situ, nanoindentation techniques can also be used for films made as free-standing microbeams or membranes [1].
Anthony C. Fischer-Cripps

### Chapter 9. Other Techniques in Nanoindentation

Abstract
Nanoindentation has proven to be a very versatile method of mechanical testing. It is often considered to be non-destructive in the sense that the indentations are in general, too small to be visible to the naked eye and, for the most part, the test does not impair the structural integrity of the specimen. Compared to the previous chapters, we now turn to a discussion of various unusual and advanced methods of testing that illustrate the versatility of the method.
Anthony C. Fischer-Cripps

### Chapter 10. Nanoindentation Test Standards

Abstract
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].” This draft standard covers depth-sensing indentation testing for indentations in the macro, micro and nano depth ranges and also covers the testing of coated material systems.
The ISO is a worldwide federation of national standards bodies. Preparation of international standards is normally carried out through ISO technical committees. Member bodies interested in a subject for which a technical committee has been established have the right to be represented on that committee.
Anthony C. Fischer-Cripps

### Chapter 11. Nanoindentation Instrumentation

Abstract
Interest in nanoindentation has spawned a number of nanoindentation instruments that compete on a world market. Purchasers of such instruments are usually 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.
Anthony C. Fischer-Cripps

### Chapter 12. Applications of Nanoindentation

Abstract
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, some rather straightforward examples of analysis of nanoindentation test data are presented using the methods described in the previous chapters.
Anthony C. Fischer-Cripps

### Chapter 13. Appendices 1–7

Abstract
The methods of analysis of nanoindentation test data rely heavily on the elastic unloading response of the system. It is of interest therefore to have some appreciation of the equations for elastic contact and the associated indentation stress fields. The following assumptions are an essential component of the analytical equations:
• The radii of curvature of the contacting bodies are large compared with the radius of the circle of contact.
• The dimensions of each body are large compared with the radius of the circle of contact. This allows indentation stresses and strains to be considered independently of those arising from the geometry, method of attachment, and boundaries of each solid.
• The contacting bodies are in frictionless contact. That is, only a normal pressure is transmitted between the indenter and the specimen.
Anthony C. Fischer-Cripps

### Backmatter

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