Stiffening behavior

This extreme capacity for deformation mainly results from the highly nonlinear properties of the coiled-coil structures by sacrificing individual protein filaments [65]. Also, the flaw-tolerant characteristic results from the stiffening behavior during the secondary structural transitions for a single filament. In addition to the properties of a single filament, the crosslinks between intermediate filaments are also critical to the mechanical behavior of the intermediate filament network [42]. 

The c/ dependence indicates that the chains become progressively harder to stretch. As seen in Figure 13.28, this simple model based on (infinitely extensible) Gaussian chains fails to explain the extreme stiffening behavior at very high strains near the maximum possible chain extension. 

Another issue that turns out to be very important for the sandwich-blade stiffener, but not at all important for the hat-shaped stiffener, is shear in the vertical web. Not shear in the plane of the web, but shear in the plane perpendicular to the web. This transverse shear stiffness turns out to dominate the behavior or be very important in the behavior of the sandwich blade, but simply is not addressed at all in the hatshaped stiffener. You can imagine that the transverse shearing stiffness would be more important in the sandwich blade when you consider the observation that the sandwich blade is a thick element and the hatshaped stiffener is a thin element. That is, bending and in-plane shear would dominate this response, whereas transverse shear, because the sandwich blade is thick, can very easily be an important factor in the sandwich blade. For both stiffeners, appropriate analyses and design rationale have been developed to be able to make an optimally shaped stiffener. 

An important observation is that the fiber volume fraction at zero compaction pressure can differ significantly between different fabrics [8], This represents a lower limit to the range of fiber volume fractions that are acceptable. A lower nominal fiber volume fraction can result in movement of the reinforcement during filling and incomplete impregnation. Another typical feature of the compaction behavior is that all fabrics behave like nonlinear (stiffening) springs and that the possible increase in fiber volume fraction from the value at rest is limited [8] (Fig. 12.4). 

In spite of their high contents of grafted and ungrafted PVC, the behavior of the raw graft copolymer and of the poly(ethylene-g-vinyl chloride) is not very different from that of low-density polyethylene. The stiffening action of this PVC is thus rather low. 

Rolling friction is often found to be proportional to the velocity, but more complex relationships may be observed, depending on the combination of the bodies. For a soft, viscoelastic sphere on a hard substrate, Brilliantov et al. [464] predicted a linear dependence of rolling friction on speed. For a hard cylinder on a viscous surface, a much more complex behavior was found [465,466], At lower speeds, the rolling friction increases with speed to reach a maximum value and then decreases at higher speeds. The reason is an effective stiffening of the substrate at higher speeds. 

The light-scattering behavior of those polysilanes studied indicates that they are slightly extended and stiffened compared with typical polyolefins. One measure of chain flexibility is the characteristic ratio C, which is also shown in the table. The values of C for most polysilanes of about 20 are larger than those for typical hydrocarbon polymers (—10), indicating that the polysilanes are somewhat less flexible than polyolefins. However, poly(diarylsilylene)s are much more rod-like and inflexible, with persistence lengths greater than 100 46... 

The type and amount of filler affects not only the final properties of the vulcanizate but also the processing behavior of the compound. Since the compounds stiffen very soon after mixing, only relatively small amounts of fillers, typically 10 to 30 phr (parts per hundred parts of rubber), can be used.24... 

Transient dynamic mechanical data on the DGEBA-TETA and high performance M-5208 epoxy based systems have been obtained and compared with "equilibrium" data.. The transient data have demonstrated that moisture can act not only to plasticize an epoxy network but also to restrict and stiffen molecular chain movement. The behavior observed was explained by examining the synergistic effects that moisture and temperature have on the particular epoxy network structure. 

The 6FDA/BDAF polyimide was modified using PPD in an effort to "stiffen" the polymer backbone and improve thermal performance (Tg). A better overall property balance was achieved in several of these 6FDA/BDAF/PPD copolyimides. A series of random copolymers was prepared in which the level of PPD was varied from 0% to 100% based on the total moles of diamine. The incorporation of PPD had little effect on the dielectric constant but did result in improved thermal performance and was accompanied by increased moisture uptake (Figures 1,2, and 3). This behavior is consistent with the overall reduction in the amount of bound fluorine in the polymer backbone however, additional work is required to establish a direct correlation. A reasonable property balance was realized over a range of 40 to 60 mole% PPD which displayed dielectric constants from 2.85 to 2.90, moisture absorption from 1.5% to 2.0%, and Tg from 280°C to 290°C. In addition, the 6FDA/BDAF/PPD copolyimides displayed somewhat less solvent sensitivity than the 6FDA/BDAF homopolymer as described above. 

Fluoropolymers, as well as other thermoplastics, exhibit a complicated nonlinear response when subjected to loads. The behavior is characterized by initial linear viscoelasticity at small deformations, followed by distributed yielding, viscoplastic flow, and material stiffening at large deformations until ultimate failure occurs. The response is further complicated by a strong dependence on strain rate and temperature, as illustrated in Fig. 11.1. It is clear that higher deformation rates and lower temperatures increase the stiffness of the material. 

Aromatic substituents at the chains of vinyl polymers influence the behavior of these materials. Aromatic units as part of the main chain exert a profound influence on virtually all important properties of the resulting polymer. Aromatic polyamides are formed by the repetitive reaction of aromatic amino group and carboxyl group in the molar ratio of 1 1. In aromatic polyamides as well as aromatic polyesters, the chain-stiffening aromatic rings are separated from each other by three consecutive single bonds ... 

As we have seen, the presence of fibers in the matrix has the effect of stiffening and strengthening it. The tensile deformation behavior of fiber-reinforced composites depends largely on the direction of the applied stress in relation to the orientation of the fibers, as illustrated in Figure 3.48. The maximum strength and modulus are achieved with unidirectional fiber reinforcement when the stress is aligned with the fibers (0°), but there is no enhancement of matrix properties when the stress is applied perpendicular to the fibers. With random orientation of fibers the properties of the composite are approximately the same in all directions, but the strength and modulus are somewhat less than for the continuous-fiber reinforcement. 

---