Nanoindentation
For nanoindentation experiments which include a holding period at constant load (i.e. the flat, top area of the load-displacement curve),
It consists into overlapping a very small, fast (> 40 Hz) oscillation onto the main loading signal and evaluate the magnitude of the resulting partial unloadings by a lock-in amplifier, so as to quasi-continuously determine the contact stiffness.
The harmonic amplitude of the oscillations is usually chosen around 2 nm (RMS), which is a trade-off value avoiding an underestimation of the stiffness due to the "dynamic unloading error"[5] or the "plasticity error"[6] during measurements on materials with unusually high elastic-to-plastic ratio (E/H > 150), such as soft metals.
The ability to conduct nanoindentation studies with nanometre depth, and sub-nanonewton force resolution is also possible using a standard AFM setup.
Utilizing optical fiber Fabry-Perôt interferometry, nanoindentation studies can be performed with unparalleled precision, achieving micro-mechanical characterization of soft biomaterials.
[8] Optical interferometry, allows for nanomechanical studies of biomaterials alongside topographic analyses without the need for dedicated instruments.
Additionally, some advanced systems offer the capability to integrate optical imaging with micro-mechanical characterization, enabling a comprehensive understanding of the relationship between structure and stiffness in biomaterials.
The Indentation Grapher (Dureza) software is able to import text data from several commercial machines or custom made equipment.
[9] Spreadsheet programs such as MS-Excel or OpenOffice Calculate do not have the ability to fit to the non-linear power law equation from indentation data.
An automatic software technique finds the sharp change from the top hold time to the beginning of the unloading.
The Doerner-Nix method is less complicated to program because it is a linear curve fit of the selected minimum to maximum data.
For nanoindentation experiments performed with a conical indenter on a thin film deposited on a substrate or on a multilayer sample, the NIMS Matlab toolbox[10] is useful for load-displacement curves analysis and calculations of Young's modulus and hardness of the coating.
[11] Finally, for indentation maps obtained following the grid indentation technique, the TriDiMap Matlab toolbox[12] offers the possibility to plot 2D or 3D maps and to analyze statistically mechanical properties distribution of each constituent, in case of a heterogeneous material by doing deconvolution of probability density function.
For instance, Alexey et al [13] employed MD to simulate the nanoindentation process of a titanium crystal, dependence of deformation of the crystalline structure on the type of the indenter is observed, which is very hard to harvest in experiment.
Tao et al [14] performed MD simulations of nanoindentation on Cu/Ni nanotwinned multilayers films using a spherical indenter and investigated the effects of hetero-twin interface and twin thickness on hardness.
All of the MD-obtained results are very difficult to be achieved in experiment due to the resolution limitation of structural characterization techniques.
An interaction potential and an input file including information of atom ID, coordinates, charges, ensemble, time step, etc are fed to the simulator, and then running could be executed.
Another interesting Matlab toolbox called STABiX has been developed to quantify slip transmission at grain boundaries by analyzing indentation experiments in bicrystal.
[19][20] The reduction in sample size requirements has allowed the technique to become broadly applied to products where the manufactured state does not present enough material for microhardness testing.
[21] Alternative uses of the technique are used to test MEMs devices by utilizing the low-loads and small scale displacements the nanoindenter is capable of.
[22] Conventional nanoindentation methods for calculation of Modulus of elasticity (based on the unloading curve) are limited to linear, isotropic materials.
Nanoindentation of soft material has intrinsic challenges due to adhesion, surface detection and tip dependency of results.
[24] Two critical issues need to be considered when attempting nanoindentation measurements on soft materials: stiffness and viscoelasticity.
However, there may be softer materials with moduli in the Pa range, such as floating cells, and these cannot be measured by an AFM or a commercial nanoindenter.
[27] However, the storage and loss moduli obtained this way are not intrinsic material constants, but depend on the oscillation frequency and the indenter probe geometry.
[28] In this method, a constitutive law comprising any network of (in general) non-linear dashpots and linear elastic springs is assumed to hold within a very short time window about the time instant tc at which a sudden step change in the loading rate is applied on the sample.
Fitting such a relation to experimental results allows this lumped value to be measured as an intrinsic elastic modulus of the material.
kl across this leads to the Tang–Ngan method of viscoelastic correction [29] where S = dP/dh is the apparent tip-sample contact stiffness at the onset of unload,
Postulated explanations include the need to create very high gradients of plastic strain with small indents, requiring "geometrically necessary dislocations".
However, no systematic, universal correction can be made for such "size effects" and it is not normally possible with nanoindenters to deform a volume that is large enough to be representative of the bulk material.
