Nanoindentation is a method of measurement of the mechanical properties of small volumes of materials using an instrumented indentation technique. Elastic modulus, hardness, fracture toughness, creep and dynamic properties such as storage and loss moduli can be measured. In this and subsequent articles, we will look at some of the issues facing the user of a nanoindentation instrument. Our purpose is to educate and inform the prospective user of this type of equipment as to what can be measured and what factors influence the results obtained.
Figure 1. The IBIS Nanoindentation system from Fischer-Cripps Laboratories.
Issues that Can Affect Nanoindentation Data
Naturally as with any scientific experiment, things can go wrong and the inexperienced scientist may have some difficulty in knowing if the results actually mean anything. Your results, especially when plotted as a function of penetration depth, can be affected by compliance, area function, kickback, Poisson’s ratio, piling-up, and surface roughness. Once you have an understanding of these issues, only then can you have confidence in your results as they apply to the mechanical properties of your specimen.
Issues which can lead to misleading conclusions in your results include:
- Frame Compliance
- Area function
- Tip sharpness
- Unloading analysis
- Specimen Poisson’s ratio
- Other issues
These factors will be discussed in the following sections
The reaction force of the indenter load causes the depth sensor to include deflection of the load frame. The deflection is usually a linear function of indenter load. The best way to check that the compliance correction has been correctly applied is to perform tests on a standard specimen with a high elastic modulus. Sapphire is a good choice since it has an elastic modulus of about 450 GPa. A series of tests over a range of loads will soon show up problems with the compliance correction factor being used. An alternative is to plot self-corrected data from fused silica.
Look for obvious “shape” in the depth data. Errors in the area function will transfer directly to your results. The most common cause of error is the use of equations to fit the area function data. This practice is to be avoided. Real indenters have a nominal shape, e.g. a pyramid, but of course also contain imperfections in the geometry. It is highly unlikely that an indenter’s departure from perfect geometry will follow that imposed by an equation, even one with a large number of fitting parameters. Area function data should be used either raw, as a look up table, or lightly filtered with a running average. The slightest “shape” imposed by a fitted equation will follow through into variations in E and H in the test data.
Look for evidence of developing plastic zone in hardness data. Choice of indenter and maximum load is important when testing on a nanometre scale. Thin film testing is particularly prone to errors in interpreting the hardness values. If the indenter load is too low, or the indenter too blunt, then a fully developed plastic zone will not be achieved and the measured value of H will be in error (see Lesson 5). The sharpest possible tip, and the highest possible load lead to be best results, but the depth of penetration should be not too high, or too low since substrate properties and surface roughness respectively will be important limitations.
Look for higher than expected values of E and H. Piling-up of material around the indentation is not accounted for in the analysis of nanoindentation data. The amount of piling up depends on the ratio of E/H of the specimen. There is not one particular method to overcome this. The most accurate method is to use AFM imaging to determine the area of contact, but this is an expensive option. For materials which are expected to pile up, many metals, it is important to treat the results with caution. Errors up to 100% high can be obtained in some materials.
Check the data selected for fitting and fitting method. Too often users apply the analysis but do not look at the fitting. The instrument software should allow the facility for displaying the raw data and the fitted curve to the unloading. In some materials, a judicious selection of the amount of unloading data to include in the fitting has to be made. For example, in silicon, there is usually a sharp phase change in the material on unloading and if these data were to be included in the fitting, then the slope of the tangent at the initial unloading will be in error. It is important to look at the data graphically first before deciding on the fitting parameters for analysis. Automated methods of calculating results where the operator cannot see the data are not recommended.
Specimen Poisson’s Ratio
Check value of Poisson’s ratio used for specimen. The theoretical analysis actually calculated the combined elastic modulus of the specimen and the indenter E* according to:
1 1-v2 1-v'2
—— = ——— + ———
E* E E'
What is required in most cases is E of the specimen. This means that the modulus and Poisson’s ratio of the indenter must be known beforehand, and the Poisson’s ratio of the specimen also known. Usually the indenters are made from diamond and these properties are well known. For the specimen, a reasonable guess can often be made. A value of about 0.3 for metals, and about 0.2 for ceramics is a reasonable starting point.
Consider the differences in results when analysis is done on a load-displacement curve taken from silicon:
Figure 2. Load-displacement curve for silicon at 10 mN load. The kink in the unloading arises from a pressure induced phase change in the crystal structure of the material.
1. Effect of % unloading data selected for fitting
|% unloading data
||Elastic modulus E
*ISO 14577 recommendation
2. Effect of % data used for fitting
|Fitting method 70%
||Elastic modulus E
3. Effect of Poisson’s ratio
||Elastic modulus E
Note the large error introduced by including the data after the phase change in the unloading fitting. An incorrect choice of Poisson’s ratio can also have a large effect as well as the fitting algorithm. The correct value of E for this material is 172.5 GPa.
Other materials-related issues that can affect the data are: residual stress, size effect, and surface roughness.
Much more valuable information about nanoindentation can be found in Fischer-Cripps' free downloadable IBIS Handbook of Nanoindentation
This information has been sourced, reviewed and adapted from materials provided by Fischer-Cripps Laboratories.
For more information on this source, please visit Fischer-Cripps Laboratories.