Displacement curves contact deformation

Figure 6. Contact diameter and contact deformation displacement curves.

Figure 13. Experimentally determined contact deformation displacement and calculated curves for POM.

Since the force-displacement curve contains information about the whole indentation process, the elastic deformation of the sample can be measured and used to calculate the stiffness S=dFldh at h=hmax, where F is the force and h is the indentation. As already explained in Sect. 3.1.1., in order to relate the stiffness to the Young s modulus, it is necessary to make assumptions about the contact area. The depth of the permanent indentation (plastic deformation), i.e. the depth DFdi shown in Fig. 26b, and the maximum indentation (sum of the plastic and of the elastic deformation) can be used to calculate a parameter that describes the relative weight of the elastic and of the plastic response. 

Fig. 7. (a) Load-displacement curve of a typical elastoplastic material and (b) the schematic of the indentation model of Oliver and Pharr [40]. S—contact stiffness he— contact depth /imax—indenter displacement at peak load hf—plastic deformation after load removal hs—displacement of the surface at the perimeter of the contact. 

A typical load-displacement curve is shown in Fig. 2. The loading portion of the curve results from both plastic and elastic deformation response of the contact, while the unloading portion of the curve is related to the elastic recovery of the contact. If the indenter geometry and materials properties are known, the modulus can be obtained by fitting the unloading curve to determine the contact stiffness at maximum load (i4, 17). In this case,... 

Figure 7.9b shows the typical force-displacement curve of a cylindrical Y-A1203 a omerate. At the beginning of loading the contacts are elastically deformed. The elastic force-displacement hne up to the yield point F can be described using an elastic contact model (Antonyuk and Tomas, 2008) ... 

During compression testing of the layered structure, the high tensile stress, which is perpendicular to the direction of loading, leads - as before - to the formation of meridian cracks. According to Fig. 7.22, the shell first deforms around the contact point. Then, a crack (1) is released and reaches the surface that separates the stiff nucleus (2) from the shell (3). The force-displacement curve of Fig. 7.23 shows that, after the formation of a meridian crack in the shell (Point Bi), deformation and then... 

PFT Mode AFM Related to this dynamic pulsed force mode is the so-called PFT mode. Using a cantilever with intermediate spring constant ( lN/m), a somewhat altered intermittent contact mode experiment is carried out during which the entire force-displacement curve is being captured. Unlike the intermittent contact mode, however, in which the amphtude is used as the feedback parameter, in this mode the force is controlled directly by using the maximum exerted force, the peak force, as the feedback parameter. This mode allows exquisite control of the force exerted with the tip/cantilever and provides information on sample deformation, stiffness, and adhesive forces from an analysis of the force-displacement curve (Fig. 6.8). 

The point-by point analysis was used to gain the loading-point displacements, i.e. deflections of the notched beams, of the photographic plates of all load intervals of the specimens. The elastic deformations of the loading frame and the supports and the contact deformations between the specimens and supports were deducted from the total deformations measured by using the speckle photography and the point-by-point analysis. As the results, the load vs. loading-point displacement P-6 curves of all tested specimens were obtained. The P-5 curves were drawn in Fig.3. 

The particle deformation and breakage behavior can be illustrated by means of the measured force-displacement curves. A typical force-displacement curve for the investigated sugar pellets is shown in Fig. 9. The force F characterizes the contact force between stamp and particle. The distance 5 shows the corresponding displacement of the particle. AH compression tests were carried out up to a compressive strain of 20%. 

Force curve gives the relationship between the z-piezo displacement and the cantilever deflection as shown in Figure 21.10b. When a cantilever approaches to a stiff sample surface, cantilever deflection. A, is equal to the z-piezo displacement, z — Zo- The value of zo is defined as the position where the tip-sample contact is realized. On the other hand, z-piezo displacement becomes larger to achieve the preset trigger value (set point) of the cantilever deflection in the case of an elastic sample due to the deformation of the sample itself. In other words, we can obtain information about a sample deformation, 8, from the force-distance curve of the elastic surface by the following relationship ... 

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