Rheologically, the BCC phase behaves as a solid, as expected, i.e. the dynamic elastic modulus is independent of frequency at high frequency in the linear [Pg.42]

In materials which are highly attenuating, the particle velocity and particle displacement are out of phase, so the elastic modulus and density of the material are complex and dynamic ( .e. frequency dependent). For many materials, the attenuation coefficient is fairly small ( .e. a co/c), so the particle velocity and displacement are in phase and Eq. 9.4 can be replaced with [Pg.312]

Fig. 14. Amplitude dependences (y0 is the amplitude of cyclic deformations) of the elastic modulus for frequency a) = 63 s 1 13% dispersion of acetylene carbon black in low- (/) and high-molecular (2) poly(isobutylene)s |

The peculiarities of dynamic properties of filled polymers were described above in connection with the discussion of the method of determining a yield stress according to frequency dependence of elastic modulus (Fig. 5). Measurements of dynamic properties of highly filled polymer melts hardly have a great independent importance at present, first of all due to a strong amplitude dependence of the modulus, which was observed by everybody who carried out such measurements [3, 5]. [Pg.93]

We can consider the friction coefficient to be independent of the molecular weight. At times less than this or at a frequency greater than its reciprocal we expect the elasticity to have a frequency dependence similar to that of a Rouse chain in the high frequency limit. So for example for the storage modulus we get [Pg.199]

Some specimens have withstood over 500 cycles. Untreated specimens of these concretes commonly failed the test at approximately 80 cycles. The elastic modulus criterion (less than 60% of original by resonant frequency analysis) was used to determine failure. Specimens often failed the test with no visible cracking or spalling. Strength retention in these specimens was usually high (50% or more). [Pg.139]

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). [Pg.21]

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