Application Note | Nanoindentation CSM
Cyclical Nanoindentation Stress-Strain Measurement
Elastic Limit, Hardness and Modulus Versus Depth from Over 100 Load Oscillations
Research & Experimental Testing
Jonathan Thomas & Pierre Leroux
Visual Design & Editorial
Andrew Shore
Introduction
Continuous stiffness measurements (CSM) obtained by nanoindentation reveal the stress-strain relationship of materials with minimally invasive methods. Unlike traditional tensile testing methods, nanoindentation provides stress-strain data at the nanoscale without the need of a large instrument. The stress-strain curve provides crucial information on the threshold between elastic and plastic behavior as the sample is subject to increasing loads. CSM gives the capability to determine the yield stress of a material without dangerous equipment.
Importance of Nanoindentation
Nanoindentation provides a reliable and user-friendly method to quickly investigate stress-strain data. Furthermore, measuring stress-strain behavior on the nanoscale makes it possible to study important properties on small coatings and particles in materials as they get more advanced. Nanoindentation provides information on elastic limit and yield strength in addition to hardness, elastic modulus, creep, fracture toughness, etc. making it a versatile metrology instrument.
The stress-strain data provided by nanoindentation in this study identifies the elastic limit of the material while only going 1.2 microns into the surface. We use CSM to determine how mechanical properties of materials develop as an indenter travels deeper into the surface. This is especially useful in thin film applications where properties can be depth dependent. Nanoindentation is a minimally invasive method of confirming material properties in test samples.
The CSM test is useful in measuring material properties versus depth. Cyclical tests can be performed at constant loads to determine more complex material properties. This can be useful to study fatigue or eliminate the effect of porosity to obtain true elastic modulus.
ℹ️ Learn more about nanoindentation lab services.
Measurement Objective
In this application, the NANOVEA mechanical tester uses CSM to study hardness and elastic modulus versus depth and stress-strain data on a standard steel sample. Steel was chosen for its commonly recognized characteristics to display the control and accuracy of the nanoscale stress-strain data. A spherical tip with a 5-micron radius was used to reach high enough stresses beyond the elastic limit for steel.
NANOVEA PB1000 Large Platform
Mechanical Tester
Test Procedure
The following indentation parameters were used:
| Parameter | Value |
|---|---|
| Maximum force | 300 mN |
| Loading rate | 150 mN/min |
| Unloading rate | 600 mN/min |
| Creep | 0 s |
| Computation method | ASTM E2546 and Martens hardness |
| Indenter type | 5 µm spherical tip |
| Amplitude | 2 mN |
| Frequency | 10 Hz |
Table 1: Indentation parameters.
Results and Discussion
Increase in load during oscillations provides the following depth versus load curve. Over 100 oscillations were conducted during loading to find the stress-strain data as the indenter penetrates the material.
We determined stress and strain from the information obtained at each cycle. The maximum load and depth at each cycle allows us to calculate the maximum stress applied in each cycle to the material. Strain is calculated from the residual depth at each cycle from the partial unloading. This allows us to calculate the radius of the residual imprint by dividing the radius of the tip to give the strain factor. Plotting stress versus strain for the material shows the elastic and plastic zones with the corresponding elastic limit stress. Our tests determined the transition between the elastic and plastic zones of the material to be around 0.076 strain with an elastic limit of 1.45 GPa.
Each cycle acts as a single indent so as we increase load, we run tests at various controlled depths in the steel. So, hardness and elastic modulus versus depth can be plotted directly from the data obtained for each cycle.
As the indenter travels into the material we see hardness increase and elastic modulus decrease.
Conclusion
We have shown the NANOVEA mechanical tester provides reliable stress-strain data. Using a spherical tip with CSM indentation allows for material property measurement under increased stress. Load and indenter radius can be changed to test various materials at controlled depths. NANOVEA mechanical testers provide these indentation tests from the sub mN range to 400N.
Frequently Asked Questions About Nanoindentation Stress-Strain Testing
Can nanoindentation produce a stress-strain curve?
Yes. Continuous stiffness measurement (CSM) applies small load oscillations during loading; each cycle gives a maximum stress and, from the residual depth after partial unloading, a strain, revealing the elastic and plastic zones.
What elastic limit was measured on steel?
The transition between elastic and plastic behavior occurred around 0.076 strain, with an elastic limit of 1.45 GPa, while the indenter went only 1.2 µm into the surface.
Why use a spherical tip?
A spherical tip, here of 5 µm radius, loads the material progressively so that stresses rise from elastic to beyond the elastic limit, which is needed to capture the full stress-strain response.
What else does CSM measure?
Each cycle acts as a single indent, so hardness and elastic modulus can be plotted directly against depth; in this steel, hardness increased and modulus decreased with depth.
How does this compare with tensile testing?
Nanoindentation gives stress-strain data at the nanoscale without a large instrument or dangerous equipment, and works on thin films, small coatings and particles where properties can be depth dependent.
Which test parameters were used?
A maximum force of 300 mN, loading at 150 mN/min and unloading at 600 mN/min, with 2 mN amplitude oscillations at 10 Hz, analyzed per ASTM E2546 and Martens hardness.
