Strain amplitude, defined

The stresses used in a creep test are chosen in two ways. First, a value is chosen from oscillatory tests (specifically stress or strain amplitude sweeps at 1 Hz or 10 rad/sec unit hs.i) to define the linear region. Using two to five different values, the sample is taken from a linear viscoelastic response to the onset of... 

For a small amplitude oscillatory shearing flow, the strain is defined as,... 

These are most easily represented by the equation E = E + iE". where E is the ratio between (the amplitude of the in-phase stress component strain, a/e) and E" is the loss modulus (the amplitude of the out-of-phase component. strain amplitude). Similarly for (7 and K and the ratio between the Young s modulus E and the shear modulus C includes Poisson s ratio u, for an isotropic linear elastic solid with a uniaxial stress. (Poisson s ratio is more correctly defined as minus the ratio of the perpendicular. strain to the plane strain, or for one orthogonal direction 22 which equals the. 3.3 strain if the sample is... 

The rheological properties of liquid-crystalline elastomers strongly depend on the mes-omorphous order [95, 98, 102, 113-118], even for strains that are too small to induce macroscopic orientation of the mesogens (strain amplitude <10%). This is mirrored by the thermal evolution of the storage modulus (Fig. 30), defined for very small... 

In attempting to predict the direction that future research in carbon black technology will follow, a review of the literature suggests that carbon black-elastomer interactions will provide the most potential to enhance compound performance. Le Bras demonstrated that carboxyl, phenolic, quinone, and other functional groups on the carbon black surface react with the polymer and provided evidence that chemical crosslinks exist between these materials in vul-canizates (LeBras and Papirer, 1979). Ayala et al. (1990, 1990) determined a rubber-filler interaction parameter directly from vulcanizatemeasurements. The authors identified the ratio a jn, where a = slope of the stress-strain curve that relates to the black-polymer interaction, and n = the ratio of dynamic modulus E at 1 and 25% strain amplitude and is a measure of filler-filler interaction. This interaction parameter emphasizes the contribution of carbon black-polymer interactions and reduces the influence of physical phenomena associated with networking. Use of this defined parameter enabled a number of conclusions to be made ... 

A further difficulty with this method is that for many soils, the behavior in a laboratory test does not lead to a well-defined failure condition. Rather, the sample simply strains progressively with increasing number of cycles. This difficulty is overcome by defining failure of a laboratory test specimen in terms of developed strain amplitude. Five percent single amplitude is a common criterion, but other strain amplitudes have also been used. The strain amplitude refers to the cyclic strain developed in a laboratory test specimen imder-going the simulated cyclic field stresses superimposed on static-field consolidation stresses. The F.S. at each element is therefore a comparison between the dynamic-induced stress in the field and the cyclic stress required to cause 5% strain in a laboratory test specimen. 

Fig. 3. Critical current as a function of the number of fatigue cycles between zero stress and the maximum stress indicated on each curve, et refers to the total strain of the maximum stress, Ac refers to the peak-to-peak strain amplitude as defined in Fig. 4. Critical current was measured by stopping the cyclic loading at maximum.

The final experiment that may be of value in characterizing the flow characteristics of LCP is that of stress relaxation following a suddenly imposed shear strain. In this experiment various strain amplitudes are imposed very rapidly. In this way no flow occurs. At low strain levels intermolecular forces which can result in yield stresses may be more readily identified. From this type of experiment we determine the strain dependent relaxation modulus defined as follows ... 

Work on the effect of flow on block copolymer melts has been reviewed [1,5,39,40]. Due to the convenience and well defined nature of the shear geometry most model studies have exploited this type of flow. The application of shear leads to orientation of block copolymer microstmctures at sufficiently high shear rates and/or strain amplitudes (in the case of oscillatory shear). Depending on shear conditions... 

Fig. 15. Viscoelastic material stress (—) and strain (—) amplitudes vs time where S is the phase angle that defines the lag of the strain behind the stress.

The resulting strain signal is analyzed in terms of its amplitude (y) and shift 8. Due to linear viscoelasticity, the stress amplitude is proportional to the strain amplitude, and a complex modulus is defined as the ratio of the sinusoidal stress to the strain. The complex modulus E comprises the contribution of both the elastic component and the viscous component ... 

As indicated earlier the ER particle may form a network structure instead of the nbrillaled chain structure once the particle volume fraction exceeds the critical volume fraction 162,83], due to the percolation transition. Under a large amplitude shear field the formation and destruction of network junctions may happen one after the other, and thus the type III LAOS behavior may best describe ER suspensions. Figure 43 shows the simulated storage and loss moduli vs. strain amplitude at different frequencies, using an idealized electrostatic polarization model of ER fluids that was implemented in the particle-level dynamics simulation. Tlie storage modulus G and loss modulus G" remain constant up to a certain strain amplitude (/() 0.4), which defines the linear response region. With further increase... 

The modulus G"iw) is defined as the stress 90° out of phase with the strain divided by the strain it is a measure of the energy dissipated or lost as heat per cycle of sinusoidal deformation, when different systems are compared at the same strain amplitude. It is plotted with logarithmic scales in Fig. 2-4. 

Figure 6.2 (a) Variation of the stress drop as a function of the cumulative viscoplastic strain, p, obtained after integration with time of the ahsoiute value of the viscoplastic strain rate for different total applied strain amplitudes (steel grade 91, 550°C) [41]. This drop is defined hy the difference between the amplitude measured at the first cycle and the amphtude measured at the Vth cycle (b) stress variation during cyclic load at very low total strain (grade 91, 0.15%, 550°C, 3.3 million cycles). 

Hyun and Wilhelm propose a mechanical nonlinear coefficient Q(co) 45). Note that Q(co) is defined in terms of the strain amplitude yo and relative amplitude /3/1 of the third and first harmonics as... 

Fig. 5 a Frequency dependence of Qq for PI-84k, Qq is defined as the plateau value of at small strain amplitudes (Eq. 5 with n = 3). The lines are linear regressions with a fixed slope of 2. The fine for the ARES-G2 black) and the DHR-3 light and dashed) overlap. The DHR-3 data match, if the motor mode is set to stiff, a setting to auto instead caused severe deviations as shown by the open circles, b Frequency dependence of Qq for PIB. The DHR-3 A data was recorded using the correlation acquisition mode, whereas for the DHR-3 B-data, the transient acquisition mode was used. At low angular frequencies Qo is proportional to (Uq. Additionally, the ratio of the sample torque amplitude to the raw torque amphtude Mso/Mro for the DHR-3 A data is shown. When Mso/Mro reaches approx. 0.8, i.e. the inertia contribution makes up 20 % of the total torque, pronounced deviations in Qo are observed when no inertia correction is applied. Data reprinted from [31], copyright 2014, Springer... 

Note 2 Viscoelastic properties are usually measured as responses to an instantaneously applied or removed constant stress or strain or a dynamic stress or strain. The latter is defined as a sinusoidal stress or strain of small amplitude, which may or may not decrease with time. 

Note 4 Unlike the strain in forced uniaxial extensional oscillations, those in forced flexural deformations are not homogeneous. In the latter modes of deformation, the strains vary from point-to-point in the specimen. Hence, the equation defining the displacement y in terms of the amplitude of applied force (/q) caimot be converted into one defining strain in terms of amplitude of stress. 

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