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.
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Figure 1. The IBIS Nanoindentation system from Fischer-Cripps Laboratories.
Testing With A Standard Specimen
Before undertaking tests on a specimen of unknown properties, it is essential to check that reliable and accurate readings are obtained on a sample of known properties using the indenter and the load that you intend to use on the unknown specimen.
Choosing an Indenter
Before proceeding with the test on the standard specimen, it will be necessary to choose the indenter to use with your own sample. Choice of indenter depends on the nature of the specimen. The most commonly used indenter shape is the three-sided Berkovich pyramidal indenter. This is preferred for nanoindentation work over the four-sided Vickers indenter because it is easier to ensure that the apex of the indenter is sharp with three sided geometry. For a four-sided indenter, there is an inevitable line at the apex which is detrimental to the measurements at this scale of deformation.
Calibration of the Indenter Tip Geometry
The most important calibration item of the whole apparatus is the calibration of the indenter tip geometry. Each indenter has its own calibration “area function”. This function is a geometrical measurement of the shape of the indenter. The shape must be known with some precision in order for the application of the theory to provide absolute measurements of material properties. The main practical difficulty is that the indenter may have been damaged by a previous user without anyone knowing, and unless an area function calibration procedure is performed, it will not be possible to have any confidence in the results on any other specimen. The area function calibration procedure is performed by making indentations into a sample of known elastic properties. The most common standard specimen for this purpose is fused silica. The elastic modulus for fused silica is 72.5 GPa with a Poisson’s ratio of 0.17.
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Figure 2. Standard fused silica specimen in position on stage ready for area function determination.
Determining the Calibration of the Instrument
The most accurate way to determine the calibration of the instrument from the readings on the standard specimen is as follows: First, perform an area function determination by running a series of tests with the indenter on the fused silica sample that spans the load range of the instrument. Then, create the area function calibration file from this data. Then, analyse the area function tests with this same area function calibration file enabled. The results for elastic modulus E should be uniform throughout the depth of penetrations measured. This checks that the software is correctly utilising the area function data. Now, the next step is most important. Plot the measured values of H (hardness) against penetration depth from this self-corrected data. The values of H should be fairly constant with depth, neither increasing or decreasing, and the values should be around 9 to 9.5 GPa. If there is an obvious upward or downward trend in H with penetration depth, then the chances are that the compliance correction factor for the instrument is not correct. If this is the case, then establishment of the compliance correction factor will be required.
Testing The Integrity of the Instrument
A very good test of the integrity of the instrument is found from the results on three standard specimens covering a range of elastic moduli. Fused silica, silicon and sapphire are commonly used. Consistent results for both E and H should be obtained an all three specimens before quoting results for tests on specimens of unknown material properties. Reasonable values are given below:
Fused silica: E = 72.5 GPa, H = 8 – 10 GPa, n = 0.17. Results should be very repeatable and fairly independent of depth although some rise in H may be observed at low loads due to partially developed plastic zone.
Silicon: E = 170 - 180 GPa, H = 10 – 12 GPa, n = 0.28. Results should be very repeatable and fairly independent of depth. Values for E should be > 170 GPa. Results can depend on presence of surface layer (eg. some samples are coated with SiN). Note presence of discontinuity in the unloading corresponding to a pressure-induced phase change in the material.
Sapphire: E = 420-520 GPa, H = 30 GPa, n = 0.25. Results for hardness may increase at low loads with increasing penetration depth due to partially developed plastic zone. This may be offset by surface hardening from polishing. Values for H should be quite repeatable. Values for E can vary quite a lot due to anisotropy in crystalline properties.
The Importance of Good Results from Standard Specimens
Once you are satisfied that the results are consistent for a series of standard specimens, you will have confidence in the readings taken on your specimen of unknown properties. You will be surprised how difficult it can be to obtain results on standard specimens over a range of moduli. Small errors in compliance correction or area function make a substantial difference to the results obtained. Without tests on a standard specimen to back up your data, you cannot have any confidence in your data, especially if you are using a public machine with an indenter that has not been recently calibrated.
Much more valuable information about nanoindentation can be found in Fischer-Cripps' free downloadable IBIS Handbook of Nanoindentation
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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.