Force-penetration curve

Mercury porosimetry is governed in each pore by an equilibrium force/surface tension balance (the Washburn equation) that relates the diameter of a cylindrical pore to the pressure needed to force mercury into it. The pressured step-by-step invasion of a pore network is then controlled by a pattern of pone accessibly at each given pressure. Systematic penetration, starting from an empty network surrounded by mercury, can be readily performed. Results for the network in Fig. 5 are given in Fig. 6, showing both the penetration curve and the retraction curve. Stochastic pore networks implicitly predict hysteresis between penetration and retraction as well as a residual final entrapment of mercury. In Fig. 6, the final entrapment is about 45%, with much of the retained mercury entrapped in the larger pores [11]. More details of the pore-by-pore calculation have been published [4]. 

Punch displacement measurements are easily done on a single station press by attaching LVDT to the punch. On a rotary press, such measurements can be done by means of slip ring, telemetry, or instrumented punch. Punch displacement profiles may be used in conjunction with compression force to estimate work of compression and work of expansion (measure of elasticity). Because capping tendency increases with the punch penetration depth, it may be desirable to monitor actual punch movement into the die. The shape of a force-displacement curve is an indication of the relative elasticity or plasticity of the material whereas plastic deformation is desirable for stronger tablets, excess plasticity usually results in tablets that tend to cap and laminate. ... 

The forces operating between tip and sample in the liquid may be distinctly different from the situation in ambient conditions. As mentioned capillary forces are absent and hence weaker interactions may become significant in liquids. Electrostatic repulsion may also occur between tip and sample, which has an impact on the selection of proper imaging conditions. The situation is exemplified in Fig. 3.39, where force-displacement curves obtained in different media are compared. For the same preset deflection (i.e. setpoint) the z-position corresponds to a different value. At the point where the repulsion is overcome, the tip penetrates through the bilayer. 

Typical force - penetration depth curves can be obtained, as shown in Fig. 4.24, together with a comparison of nanoindentation and bulk mechanical tests. Using the approaches as reported by Tranchida et al. a good correspondence between surface and bulk values of the Young s modulus can be achieved. 

Cumulative pore penetration curves are obtained by measuring the volume of mercury forced into the solid at difierent pressures. Figure 7.14 shows a typical mercury porosimeter and Fig. 7.1S a cumulative penetration curve. Derivative distribution data are also given in Fig. 7.15. Until recently, most porosimeters were limited to pressures of 3.5 x 10 atm. From Table... 

At a very low rate of penetration (curves 1 and 2), the concentration Cm does not differ appreciably from Cq due to the small Peclet number (Pe = v// D) and predominance of diffusion. At very high values of K, the concentration close to the meniscus tends to zero. This also takes place in the case of forced penetration under the action of an external pressure [19], when Pe > > 1. In this case, surfactant molecules cannot reach the meniscus and influence the contact angle. The effect of capillary radius is similar the smaller the values of r, the more pronounced is the influence of surfactant adsorption. An increase in Z)s2 values leads to some decrease in Cm due to the enhanced diffusion along the nonwetted capillary surface. 

Figure 4. (a) Force penetration and (b) stress strain curves of the indentation on GCs with 100 mN terminal force. 

For the elevation of heat-treatment temperature of GCs, it is seen that the penetration by the indentation is deeper and the hysteresis loop is larger. The area of the hysteresis loop on the force-displacement curve corresponds to energy loss during the deformation of the substrate by the indentation. 

In the penetration test, force is measured when a probe is pushed at a constant speed into a food or plastic fat that is contained in a small container. The probe can be round, rectangular, or conical. Usually the maximum force is recorded at a specified depth. Force is usually expressed as newtons per square centimeter. The shape of the penetration curve can reveal characteristics about the sample... 

For some types of wetting more than just the contact angle is involved in the basic mechanism of the action. This is true in the laying of dust and the wetting of a fabric since in these situations the liquid is required to penetrate between dust particles or between the fibers of the fabric. TTie phenomenon is related to that of capillary rise, where the driving force is the pressure difference across the curved surface of the meniscus. The relevant equation is then Eq. X-36,... 

Fig. 33—Typical scratch curve of Sample 4, Fn is the normal load. Ft is the measured tangential force, Pd is the penetration depth, Rd is the residual depth. The critical load is 86.63 mN.

Figure 33 shows a typical scratch test curve of Sample 4. Both the penetration depth and the residual depth as well as the tangential force can be obtained from this curve. The critical load can be found from the transition stages plotted in the three curves. The critical load (L ) of Sample 4 is 86.63 mN. 

Figure 34 shows the critical load of all the samples. For the monolayer samples, Sample 1 has a higher critical load than Sample 2. The multilayers Samples 4, 5, and 6 have higher critical loads than monolayer Samples 1 and 2. Samples 5 and 6 have excellent scratch resistant properties. Only extremely small cracks are found in the scratch tracks of Samples 5 and 6. Therefore, there is no sudden change found in the force and penetration depth curves. Sample 7 has the lowest critical load, similar to the monolayer Sample 2. 

FIGURE 9.14 Typical approach force curve (solid line) for a sample which is penetrated by the scanning probe microscope (SPM) tip. Also shown is the force curve (dashed line) when the tip encounters a hard surface (glass) and schematic drawings of the relative positions of the SPM tip and the sample surface as related to the force curves. (From Huson, M.G. and Maxwell, J.M., Polym. Test., 25, 2, 2006.)... 

Figure 9.14 shows a typical approach force curve along with schematic drawings of the relative positions of the SPM tip and the sample surface, as related to the force curve. At the start of the experiment, i.e., position A on the right-hand side of the figure, the tip is above the surface of the sample. As it approaches the surface the Z value decreases until at position B the tip contacts the surface. With further downward movement of the piezo the cantilever starts to be deflected by the force imposed on it by the surface. If the surface is much stiffer than the cantilever, we get a straight line with a slope of — 1, i.e., for every 1 nm of Z travel we get 1 nm of deflection (Une BC in Figure 9.14). If the surface has stiffness similar to that of the cantilever, the tip wUl penetrate the surface and we get a nonlinear curve with a decreased slope (line BD in Figure 9.14). The horizontal distance between the curve BD and the line BC is equal to the penetration at any given cantilever deflection or force. The piezo continues downward until a preset cantilever deflection is reached, the so-called trigger. The piezo is then retracted a predetermined distance, beyond the point at which the tip separates from the sample.

The hardness of wood varies markedly from soft balsa to hard ironwood with pine, oak, and maple in between. It is measured either by determining the force needed to push a hard ball (diameter = 0.444 in) into the wood to a depth equal to half the ball s diameter (Janka hardness) or by the initial slope of the force vs. penetration-depth curve (Hardness modulus). Average values of Janka hardnesses for typical woods are listed in Table 13.1. The data are from Green et al., (2006), and are for penetration transverse to the tree axis. The values are for moisture contents of about ten percent. The first set of five items are hardwoods, while the second set are softwoods. To roughly convert Janka hardnesses to VHN multiply by 0.0045. 

Mercury porosimetry is based on the fact that mercury behaves as a nonwetting liquid toward most substances and will not penetrate the solid unless pressure is applied. To measure the porosity, the sample is sealed in a sample holder that is tapered to a calibrated stem. The sample holder and stem are then filled with mercury and subjected to increasing pressures to force the mercury into the pores of the material. The amount of mercury in the calibrated stem decreases during this step, and the change in volume is recorded. A curve of volume versus pressure represents the volume penetrated into the sample at a given pressure. The intrusion pressure is then related to the pore size using the Washburn equation... 

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