Mechanical properties shear modulus

The dynamic mechanical properties (shear modulus and loss tangent) of polymer composites prepared from carbon fiber and thermosetting and thermoplastic resins were studied in the frequency range 0.01-5.0 Hz. The stxrface of the fiber was covered by the interlayer from styrene-co-maleic anhydride polymer. It was estabhshed that different interphase composition causes a difference of dynamic mechanical behavior and that the interphase contributes both to glass transition and to energy dissipation. 

Table 19.6 Mechanical properties (elastic modulus ( ), shear modulus (G), Poisson s ratio (v), hardness Hz), and fracture toughness Klc) of composites sintered by SPS...

There is an increase in the polymer strength when the polymers are formed within a gradient of shear stresses, known to result in the alteration of the macromolecular conformation. For example, polyethylene produced by melt extrusion through capillaries rmder high pressure possesses unique physical-mechanical properties—its modulus of elasticity is of the same order as that of glass fiber (7 x 10 ° Pa) [116],... 

The procedure described above is an application of the time-temperature correspondence principle. By shifting a set of plots of modulus (or compliance) versus time (or frequency) at any temperature (subscript 1) along the log t axis, we obtain the value of that mechanical property at another time and temperature (subscript 2). Using the shear modulus as an example, the time-temperature correspondence principle states... 

Rheology. The rheology of foam is striking it simultaneously shares the hallmark rheological properties of soHds, Hquids, and gases. Like an ordinary soHd, foams have a finite shear modulus and respond elastically to a small shear stress. However, if the appHed stress is increased beyond the yield stress, the foam flows like a viscous Hquid. In addition, because they contain a large volume fraction of gas, foams are quite compressible, like gases. Thus foams defy classification as soHd, Hquid, or vapor, and their mechanical response to external forces can be very complex. 

As one example, in thin films of Na or K salts of PS-based ionomers cast from a nonpolar solvent, THF, shear deformation is only present when the ion content is near to or above the critical ion content of about 6 mol% and the TEM scan of Fig. 3, for a sample of 8.2 mol% demonstrates this but, for a THF-cast sample of a divalent Ca-salt of an SPS ionomer, having only an ion content of 4.1 mol%, both shear deformation zones and crazes are developed upon tensile straining in contrast to only crazing for the monovalent K-salt. This is evident from the TEM scans of Fig. 5. For the Ca-salt, one sees both an unfibrillated shear deformation zone, and, within this zone, a typical fibrillated craze. The Ca-salt also develops a much more extended rubbery plateau region than Na or K salts in storage modulus versus temperature curves and this is another indication that a stronger and more stable ionic network is present when divalent ions replace monovalent ones. Still another indication that the presence of divalent counterions can enhance mechanical properties comes from... 

Torsion property As noted, the shear modulus is usually obtained by using pendulum and oscillatory rheometer techniques. The torsional pendulum (ASTM D 2236 Dynamic Mechanical Properties of Plastics by Means of a Torsional Pendulum Test Procedure) is a popular test, since it is applicable to virtually all plastics and uses a simple specimen readily fabricated by all commercial processes or easily cut from fabricated products. 

For a Hookian material, the concept of minimum strain energy states that a material fails, for example cell wall disruption occurs, when the total strain energy per unit volume attains a critical value. Such an approach has been used in the past to describe a number of experimental observations on the breakage of filamentous micro-organisms [78,79]. Unfortunately, little direct experimental data are available on the Young s modulus of elasticity, E, or shear modulus of elasticity G representing the wall properties of biomaterial. Few (natural) materials behave in an ideal Hookian manner and in the absence of any other information, it is not unreasonable to assume that the mechanical properties of the external walls of biomaterials will be anisotropic and anelastic. 

Contrary to the phase separation curve, the sol/gel transition is very sensitive to the temperature more cations are required to get a gel phase when the temperature increases and thus the extension of the gel phase decreases [8]. The sol/gel transition as determined above is well reproducible but overestimates the real amount of cation at the transition. Gelation is a transition from liquid to solid during which the polymeric systems suffers dramatic modifications on their macroscopic viscoelastic behavior. The whole phenomenon can be thus followed by the evolution of the mechanical properties through dynamic experiments. The behaviour of the complex shear modulus G (o)) reflects the distribution of the relaxation time of the growing clusters. At the gel point the broad distribution of... 

The crystallization kinetics of commercial polyolefins is to a large extent determined by the chain microstructure [58-60]. The kinetics and the regime [60] of the crystallization process determine not only the crystalline content, but also the structure of the interfaces of the polymer crystals (see also Chapter 7). This has a direct bearing on the mechanical properties like the modulus, toughness, and other end use properties of the polymer in fabricated items such as impact resistance and tear resistance. Such structure-property relationships are particularly important for polymers with high commercial importance in terms of the shear tonnage of polymer produced globally, like polyethylene and polyethylene-based copolymers. It is seen that in the case of LLDPE, which is... 

Fig. 10. Estimated viscoelatic properties in a normal human breast in vivo. (A) T2 anatomical image. (B) Shear modulus image of the same slice. (Q Young s modulus image of the same slice. Grey scale bars are in kPa. Images B and C are extracted from 3D data sets of reconstructed elasticity parameters, obtained with the subzone based method used in Fig. 8. Note the good contrast in image C, even though the mechanical parameters are not obviously correlated to the structural properties depicted in image A (reprinted with permission from Ref. 48 2000 IOP Publishing Ltd.).

Most polymers are applied either as elastomers or as solids. Here, their mechanical properties are the predominant characteristics quantities like the elasticity modulus (Young modulus) E, the shear modulus G, and the temperature-and frequency dependences thereof are of special interest when a material is selected for an application. The mechanical properties of polymers sometimes follow rules which are quite different from those of non-polymeric materials. For example, most polymers do not follow a sudden mechanical load immediately but rather yield slowly, i.e., the deformation increases with time ( retardation ). If the shape of a polymeric item is changed suddenly, the initially high internal stress decreases slowly ( relaxation ). Finally, when an external force (an enforced deformation) is applied to a polymeric material which changes over time with constant (sinus-like) frequency, a phase shift is observed between the force (deformation) and the deformation (internal stress). Therefore, mechanic modules of polymers have to be expressed as complex quantities (see Sect. 2.3.5). 

The Physical Properties are listed next. Under this loose term a wide range of properties, including mechanical, electrical and magnetic properties of elements are presented. Such properties include color, odor, taste, refractive index, crystal structure, allotropic forms (if any), hardness, density, melting point, boiling point, vapor pressure, critical constants (temperature, pressure and vol-ume/density), electrical resistivity, viscosity, surface tension. Young s modulus, shear modulus, Poisson s ratio, magnetic susceptibility and the thermal neutron cross section data for many elements. Also, solubilities in water, acids, alkalies, and salt solutions (in certain cases) are presented in this section. 

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