Stiffness response

We have recently been exploring this technique to evaluate the adhesive and mechanical properties of compliant polymers in the form of a nanoscale JKR test. The force and stiffness data from a force-displacement curve can be plotted simultaneously (Fig. 13). For these contacts, the stiffness response appears to follow the true contact stiffness, and the curve was fit (see [70]) to a JKR model. Both the surface energy and modulus can be determined from the curve. Using JKR analyses, the maximum pull off force, surface energy and tip radius are... 

Fig. 13. Load vs. stiffness response for diamond hemisphere (R = 5.3 irm) vs. silicone polymer. Solid line is JKR Hi.

The stiffness response of RPs can be identified as viscoelasticity. RPs is nearly elastic in behavior and tends to reduce the importance of the time-dependent component of viscoelastic behavior. Also, the stiflhess of fiber reinforcements and the usual TS resin matrices are less sensitive to temperature change than most URPs. The stiffness of both the fibers and the matrices are frequently more stable on exposure to solvents, oils, and greases than TPs although for certain composites water, acids, bases, and some strong solvents still may alter stiffhess properties significantly. 

It ean be shown [15] that the linear displaeement boundary condition gives an "over-stiff response, and the constant traction boundary condition an "under-stiff response. These results thus give upper and lower bounds for the problem. 

FIG. 8-75 Frequency response curves for a pneumatic positioner/actuator (a) input signal to stem travel for a 69-inch spring and diaphragm actuator with a 1.5-inch total travel and. 3-15 psig input pressure (h ) dynamic stiffness for the same positioner/actuator. 

Figure 9-10. Map of response frequencies plotted against bearing stiffness.

A very practical way to infer the contact area was later developed by Carpick et al. [65] and Lantz et al. [66]. In these experiments, a small (up to nanometer) lateral modulation, djc, is applied to the sample, and torsion of the cantilever is monitored with a lock-in amplifier to detect the lateral force response, dF (Fig. 5). In this way, the lateral stiffness, [51], given by... 

Fig. 7. Voigt model analysis of (a) lateral contact stiffness and (b) the response time, t, for a silicon nitride tip vs. poly(vinylethylene) as a function of frequency and polymer aging times. Reprinted with permission from ref [71].

It is an unfortunate fact that many students and indeed design engineers are reluctant to get involved with plastics because they have an image of complicated materials with structures described by complex chemical formulae. In fact it is not necessary to have a detailed knowledge of the structure of plastics in order to make good use of them. Perfectly acceptable designs are achieved provided one is familiar with their perfonnance characteristics in relation to the proposed service conditions. An awareness of the structure of plastics can assist in understanding why they exhibit a time-dependent response to an applied force, why acrylic is transparent and stiff whereas polyethylene is opaque and flexible, etc., but it is not necessary for one to be an expert... 

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