Indentation curves

Kharrat, M., Chateauminois, A., Carpentier, L. and Kapsa, P., On the interfacial behavior of a glass/epoxy composite during a micro-indentation test assessment of interfacial shear strength using reduced indentation curves, Composites, A, 28, 39 (1997). 

The shape of the force versus indentation curve depends on surface adhesive and elastic properties. Variations in these parameters affect the ultrasonically induced deflection. Conversely, the variations in the shape of the ultrasonically induced normal deflection contain information on surface adhesive and elastic properties. Figure 13.3 illustrates how the threshold amplitude should depend on the normal force value. If the normal force is set at a higher value F2 > Fi, then the threshold amplitude a2 = h2) needed to reach the pull-off point should be higher than the threshold amplitude (fli = hi) for Fi. If the threshold amplitude values (fli and a2) are measured for two different normal force values (Fi and F2), the contact stiffness is... 

Apart from repulsive and attractive forces between a given polymer sample surface and an AFM tip, surface mechanical properties can be measured in contact mode AFM. This requires the acquisition of force-displacement curves and their conversion into force—indentation curves. The subsequent analysis is based on theoretical models and provides access to surface elastic moduli, among others. Since the AFM tip is typically very sharp, moduli can be obtained with high spatial resolution. 

In addition to indentation curves, the residual imprints after the application of a defined load force can be images using intermittent contact mode AFM. This is shown below for indentation tests performed on PE, in which the size of the imprint was shown to be reduced to the level of individual lamellae (Fig. 4.23). 

Fig. 4.30 Approach parts of the f-d curves recorded on poly(n-butyl methacrylate) samples at various rates and temperatures. The different slopes of the indentation curves represent different moduli of the polymer (Tg = 22°C) (reproduced with permission from [61]. Copyright 2005 American Chemical Society)...

Force-Indentation Curves on Systems of Controlled Surface Chemistry and Controlled Mechanical Properties... 

Figure 2. (a) An example of the indentation curve measured on a 5 pm thick layer of ncTiN/aSi3N4. and are the maximum applied load and indentation depth, Aplastic is the depth of the remanent, plastic deformation. The arrows — and denote the loading and unloading part, (b) Measured values of the hardness against the maximum applied load, (c) Indentation depth at a constant appUed load of 50 mN against time which shows the absence of creep. 

Modern indentometers for the measurement of the hardness of thin films use a computer controlled step-wise increase of the load up to a chosen maximum Zvmax followed by a step-wise unloading. Instead of measuring the diagonal of the plastic deformation, the indentation depth, h, is measured electronically and the indentation curve evaluated (see Fig. 2a). The plastic hardness is calculated from the maximum load, Lmax> d the depth of the plastic indentation. Aplastic,... 

AFM has become the method of choice for measuring cellular elasticity. Harris and Charras et al. [8] have shown that in AFM elasticity measurements, experimental force-indentation curves are analyzed using contact mechanics models that infer the tip-cell contact area from the tip geometry and indentation depth. However, values of cellular elasticity reported in AFM measurements are large compared to those reported by other methods, and measurements affected using spherical tips give significantly lower elasticity than pyramidal tips [8]. 

Du and co-workers (256) analyzed SFM force indentation curves according to the method by Oliver and Pharr (104). For PS and PC thin films, good agreement between theory and experiment required the introduction of a correction factor that accounts for the asymmetry to the SFM indentation (256). 

Figure 2.12. Indentation curves of (a) elastic materials, from equation (2.16), (b) rigid-plastic materials, from equation (2.17), and (c) experimentally determined curve, from equation (2.18).

The indentation curves also showed that Sample 5 shows a very soft near-surface region revealed by shapes of loading curves i.e. plastic flow at low indentation pressures, as has been seen on amorphous Si. 

Force-Curves and Force-Modulation Calibration. In figure l(a b), typical force-indentation curves obtained respectively on a rigid ( = 610 MPa) and a soft (E = 27 MPa) polymer are presented. The elastic modulus derived from the analysis of the force-indentation curves is compared to the bulk elastic modulus measured by DMA in figure 1(c). For this analysis, the used tip geometry was adapted to the maximum indentation depth reached during the experiment, Smax- For Smax Rj the spherical geometry was considered while, for Smax the conical one was used. For intermediate values, the paraboloid model was used. 

Figure 1. Typical force-indentation curves obtained respectively (a) on a rigid polymer (E = 610 MPa) and (b) on a soft one(E = 27 MPa), (c) Comparison l tween the surface Young s modulus deduced from the analysis of the force-indentation curves and the volume modulus measured by dynamic mechanical analysis, DMA, using the Hertz elastic model ( ) and using the JKR model (A).

Figure 17.4 Displacement-deflection curves and load-indentation curves theoreticaUy produced by the the DMT-M model (a), (b) and the JKR model (c) (d).

The mentioned heterogeneities were also visible in the mechanical analysis of the nano indentation experiments [63, 75, 77]. We calculated the hardness H and the elastic modulus E from the indentation curves following the model by Oliver and Pharr [80, 81]. In the case of the dense amorphous structure, the mechanical modulus of the sample was homogeneous over the tested area. In contrast, strong scattering of the data was observed in the case of the polycrystalline sample. The latter result reflects the intrinsic structural heterogeneity of the sample. 

Sharp indentation curves of time-dependent materials can be modelled using the Oyen and Cook (2003) viscous elastic-plastic (VEP) model which extends the Sakai (1999) representation of elastic-plastic (EP) materials (Chapter 8). 

Shown in Figure 3 is a representative force-indentation curve using the two-section model. This microgel is composed of sodium alginate studied in soybean oil. ... 

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