Nanoindentation Testing

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Nanoindentation testing

Classification within nanoindentation testing

Nanoindentation plays a key role in the testing and evaluation of the mechanical properties of miniature components (see: testing microcomponents) [1]. This indentation testing method is one of the instrumented hardness testing methods, i.e. it can be used to determine hardness values, moduli of elasticity and fracture mechanics parameters (see: fracture mechanical testing) [2]. The distinctive feature of this method lies in its high resolution in terms of load and indentation depth.

Technical data

Typical technical specifications for a nanoindenter are given below as an example:

Maximum load:	500 mN
Load resolution:	50 nN
Penetration depth resolution:	0.02 nm
Maximum penetration depth:	>> 40 µm
Positionig accuracy:	1 µm, some instruments achieve measured value accuracy of up to 0.2 µm
Indenter shapes:	Berkovich, Vickers (see: indenter), cone, special shapes
Minimum load rate:	$\leq$ 1 mN s^-1
Maximum load rate:	$\geq$ 7 $\cdot$ 10¹⁰ µN s^-1.

Material Parameter

This provides the experimental capability to determine, directly within complex components composed of different materials, the hardness, modulus of elasticity and, in some cases, the fracture toughness K_Ic of the individual materials. Furthermore, these instrument systems offer additional applications for continuous stiffness measurement, in which an additional oscillation is superimposed on the load-penetration depth signal; this enables scratch functions to be implemented and allows the measurement of normal and tangential loads.

In addition to determining the material properties of individual components within a part, this method can be used to determine interfacial properties. For this purpose, the application of the indentation fracture mechanics method – or, for low loads, nano-fracture mechanics – has proven effective.

Indentation fracture mechanics

However, the conventional approach, which relies on measuring the radial cracks formed beneath the indenter, reaches its limits, as certain critical loads are required to generate radial cracks. When using indenter shapes in accordance with the Vickers or Berkovich methods, these loads depend on the material and the indenter geometry. However, the resulting penetration depths are too great for the testing of thin and ultra-thin layers, meaning that the elastic-plastic zone can reach the substrate. It is also very difficult to measure the radial cracks at very small penetration depths using a scanning electron microscope (SEM). The fracture toughness K_Ic can be determined according to Eq. (1).

K_{Ic}\,=\,0{.}016\,\left({\frac {E}{H\,V}}\right)^{\frac {1}{2}}\cdot {\frac {F}{c^{\frac {3}{2}}}}

(1)

with

HV		Vickers hardness
c		crack length (measured from the centre of the indentation)

Based on findings in the literature [3–7], a method for determining interlaminar fracture toughness (see also: interlaminar shear strength) is described and tested using the example of a thin polystyrene (abbreviation: PS) layer on a glass substrate; to generate sufficient elastic strain energy in the PS, a polymethyl methacrylate (abbreviation: PMMA) layer was additionally applied as a ‘superlayer’.

Example of nanoindentation testing on a multilayer system

The Figure shows a schematic representation of an applied PMMA superlayer, used to determine the interfacial adhesion between PS and glass by means of a penetration test. This procedure is necessary because, in the presence of a ductile layer on a brittle substrate, it is very difficult or impossible to achieve layer delamination, as insufficient elastic strain energy is generated within the layer. The use of a conical indenter (90°) with a tip radius of 1 µm results in the desired separation of the interfaces in the PS/glass system.

The fracture process in a multilayer system proceeds in three stages, which can be observed in a load (F)-penetration depth (h) curve. In stage 1, the first annular cracks are observed through the layer due to the high stresses in the contact zone. Stage 2 is characterised by the delamination and bulging of the layer due to the high lateral compressive stresses (see: compression test). Stage 3 is caused by the layer being breached and results in a jump in the loading curve.

For Stage 3, the fracture toughness (see: fracture mechanics) can be calculated according to Eq. (2)

K_{Ic}\,=\,\left[\left({\frac {E}{\left(1-\nu ^{2}\right)\cdot 2\,\pi \,c_{R}}}\right)\cdot \left({\frac {U}{h}}\right)\right]^{\frac {1}{2}}

(2)

where, for very thin layers, the crack length c_R is usually determined using a scanning electron microscope (SEM), and the energy released U is calculated, as shown in the Figure, as the area enclosed by A, B and C.

Fig.:

Schematic cross-sectional structure for demonstrating phase adhesion at a PS/glass interface with a PMMA superlayer (a) and a schematic load-penetration depth curve showing the stages of the fracture process for determining the energy released (b)

References

[1]	Michel, B., Walter, H.: Mikroprüftechnik. In: Grellmann, W., Seidler, S. (Eds.): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edition, pp. 707–709 (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see AMK-Library under A 23)
[2]	Grellmann, W., Seidler, S. (Eds.): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edition, pp. 196 ff (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see AMK-Library under A 23)
[3]	Li, X., Bushan, B.: Measurement of fracture toughness of ultra-thin amorphous Carbon films. Thin Solid Films 315 (1998) 214–221; https://doi.org/10.1016/S0040-6090(97)00788-8
[4]	Li, M., Carter, C. B, Hillmyer, M. A., Gerberich, W. W.: Adhesion of polymer-inorganic interfaces by nanoindentation. J. Mater. Res. 16 (2001) 3378–3388; https://doi.org/10.1557/JMR.2001.0466
[5]	Lu, Y., Shinozaki, D. M.: Microindentation induced debonding of polymer thin films from rigid substrates. J. Mater. Science 37 (2001) 1283–1293; https://doi.org/10.1023/A:1014506823464
[6]	Li, M., Palacio, M. L., Carter, C. B., Gerberich, W. W.: Indentation deformation and fracture of thin polystyrene films. Thin Solid Films 416 (2002) 174–183; https://doi.org/10.1016/S0040-6090(02)00613-2
[7]	Rosenfeld, L. G., Ritter, J. E., Lardner, T. J., Lin, M. R.: Use of microindentation technique for determining interfacial fracture energy. J. Appl. Phys. 67 (1990) 3291–3296; https://doi.org/10.1063/1.345363