Indentation deflection curve

Figure 5.16 (a) Tip and fiber interaction during indentation measurement, (b) Indentation deflection curve. Reprinted with permission from M. Wang et al. (2004a). Copyright 2004. Elsevier. 

The CFD (compression force deflection) as well as IFD (indentation force deflection) curves of these foams are relatively linear in comparison with slabstock foams, as shown in Figures 10 and 11. 

However E must be obtained at the same temperature and time conditions as the fracture test because of the viscoelastic nature of polymers. In order to avoid the associated uncertainties, it is considered preferable to determine Gy or G. (subject to the validity criteria of AV) directly from the load versus deflection curve up to the same load point as used for Ay or A l. determination (see Fig. 3). The energy should be corrected for speeimen indentation (suffered under loading and support pins) by deducing the energy of indentation. ( j from t y. Therefore ... 

Carman et al. [ 18] developed a test called the meso-indentation test which used a hard spherical ball indenter to apply a compressive force to a surface of the composite perpendicular to the fiber axis. The indenter was much larger than the diameter of a single fiber therefore, when the ball was forced into the end of the composite, it made a permanent depression in the material. From the size of the depression and the force-deflection curve, they calculated a mean hardness pressure as a function of strain in the coupon. Qualitative differences have been reported in tests conducted on carbon fiber-epoxy composites where the fiber-matrix adhesion had been varied systematically. 

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 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... 

Indentation force measurements utilize the indentation part of a force-displacement curve (Fig. 4.19). In the case of a non-compliant sample surface, the SFM tip does not indent the sample and hence the deflection vs. piezo position curve in the contact region has a slope of 1.0. For compliant samples, the slope is <1.0 and can be used to obtain the elastic modulus of the sample by fitting the measured... 

The slope of a force curve on an infinitely stiff substrate is by definition one thus, the deflection equals the piezo z travel. In measurements of soft samples, the deflection is reduced by the indentation 8. Thus, employing the cantilever force constant k (which must be chosen appropriately in AFM indentation measurements),... 

FIGURE 4.25 Force versus displacement curves on PNiPAAm gel in pure water at 10 and 35°C and on mica in pure water at room temperature. The same z-piezo displacement results in a smaller cantilever deflection on the soft gel surface in comparison with the hard mica sample because of elastic indentation. Source Matzelle et al. [55]. Reproduced with permission of American Chemical Society. 

Once the tip is in contact with the surface, cantilever deflection will increase as the end of the cantilever is brought closer to the sample. If the cantilever is sufficiently stiff, the probe tip may indent the surface at this point. In this case, the slope or shape of the contact part of the force curve can provide information about the elasticity of the sample surface. Extending the tip (along line C-D) results in loading (repulsive) forces to the surface. These repulsive forces are usually used as a feedback parameter for the AFM system to obtain surface morphology. 

Fig. 1 Force mode of AFM. (a) A schematic view of single molecule stretching, (b) Relation between piezo distance, D, cantilever deflection, d, and sample extension, E. The approach of the cantilever starts from position 1 on the tight to position 2 where the probe touches the sample surface. When the sample surface is rigid, the cantilever is pushed up to position 3 where the cantilever movement is reversed and the cantilever traces back to position 1 without hysteresis. When the sample surface is soft, cantilever deflection follows a curve from position 2 to 3 indenting the sample with the maximum depth of I. In the retraction regime, when a part of the sample is adhered to the probe, the cantilever shows a gradual or immediate downward deflection due to the tensile force from the sample. In this figure, the tensile material adhered to the probe is assumed to be a flexible polymer like material so that the downward deflection of the cantilever is inititdly small but rapidly increases to position 5 where the adhesion bond of the sample to the probe is broken abruptly (Reproduced from [66] with permission)...

Figure 13 Idealized force-distance curve describing a single approach-retraction cycle of the AFM tip. Modified from Shahin, V. etal. J. Cell. Scl. 2006, f f9,23-30. The AFM tip is approaching the sample surface (a). The initial contact between the tip and the surface is mediated by the attractive van der Waals forces (contact) that lead to an attraction of the tip toward the sample (b). Hence, the tip applies a constant and default force upon the sample surface that leads to sample indentation and cantilever deflection (c). Subsequently, the tip tries to retract and to break loose from the surface (d). Various adhesive forces between the sample and the AFM tip, however, hamper tip retraction. These adhesive forces can be taken directly from the force-distance curve (e). The tip withdraws and loses contact with the sample upon overcoming the adhesive forces (f). Inset experimental approach curve recorded fora silicon surface electrografted by poly(/V-succinimidyl acrylate) (PNSA) (from a 0.1 M NSA solution in DMF) with a silicon nitride tip.

However, the fact that AFM is sensitive to these weak forces can be turned into an advantage. One of the most common ways to measure the interactions is a force-distance curve measurement, in which the scanner starts to move vertically to make contact with the probe and surface and then reverse to make them separated. During the process, the cantilever deflection is recorded as a function of vertical scanner movement. One can obtain the relation between normal load P and indentation depth 8 using simple relations (the detailed procedure is discussed later). Applying an appropriate contact mechanics theory, one can estimate the mechanical properties of the sample surfaces. 

The indentation versus time curves for each scan rate from the contact point to the zero cantilever deflection point cire converted from Figure 9(a) and plotted in Figure 10(a). The indentation versus -Z is given in Figure 10(b), which reveals the viscoelastic effects more clearly. 

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