Viscoelastic relaxation linear

The premise of the above analysis is the fact that it has treated the interfacial and bulk viscoelasticity equally (linearly viscoelastic experiencing similar time scales of relaxation). Falsafi et al. make an assumption that the adhesion energy G is constant in the course of loading experiments and its value corresponds to the thermodynamic work of adhesion W. By incorporating the time-dependent part of K t) into the left-hand side (LHS) of Eq. 61 and convoluting it with the evolution of the cube of the contact radius in the entire course of the contact, one can generate a set of [LHS(t), P(0J data. By applying the same procedure described for the elastic case, now the set of [LHS(t), / (Ol points can be fitted to the Eq. 61 for the best values of A"(I) and W. 

The EMT analysis indicated that the stress relaxes in proportion to the number of bonds removed. The initial linear decrease of E/Eq with is intuitively appealing and is the basis for many linear constitutive theories of polymers. An example is the Doi-Edwards theory of viscoelasticity of linear polymer melts [49] in which... 

Initial indications are that a multi-mode version of Eqs. (50) and (51) can be useful at a quantitative level in modelling an extensively-investigated LDPE for all geometries of flow [82]. Matching only the linear viscoelastic relaxation spectrum, and adding a segment priority distribution consistent with that derived... 

The investigation of viscoelasticity of dilute blends confirms that the reptation dynamics does not determine correctly the terminal quantities characterising viscoelasticity of linear polymers. The reason for this, as has already been noted, that the reptation effect is an effect due to terms of order higher than the first in the equation of motion of the macromolecule, and it is actually the first-order terms that dominate the relaxation phenomena. Attempts to describe viscoelasticity without the leading linear terms lead to a distorted picture, so that one begins to understand the lack of success of the reptation model in the description of the viscoelasticity of polymers. Reptation is important and have to be included when one considers the non-linear effects in viscoelasticity. 

Pokrovskii VN, Volkov VS (1978b) The calculation of relaxation time and dynamical modulus of linear polymers in one-molecular approximation with self-consistency. (A new approach to the theory of viscoelasticity of linear polymers). Polym Sci USSR 20 3029-3037... 

These relaxation time equations together with Eqs. (2), (15), and (19) can be utilized in analyzing the experimental measurements of volume relaxation and recovery, of linear and nonlinear viscoelastic relaxations, and of yield behavior and stress-strain relationships. 

In the solid state deformation, the nonlinear viscoelastic effect is most clearly shown in the yield behavior. The type of stresses applied to a system has little effect on the linear viscoelastic relaxation, but becomes very important as the stress level increases. At high stress levels, the contribution from the external work done on a lattice cell has to be included in the nonlinear viscoelastic analysis. By taking into account the long range cooperative interaction, the external work can,... 

Here a(t,s) is the value of the stress at time t and strain e, E(t) is the relaxation modulus of linear viscoelasticity and /(e) is a function of strain alone. The physical implication of strain-time factorization is that the viscoelastic relaxation processes are independent of strain, a plausible idea for small to moderate deformations. 

Sawada, T., X. Qiao, and H. Watanabe. 2007. Viscoelastic relaxation of linear polyiso-prenes Examination of constraint release mechanism.. Soc. Rheol. Japan (Nihon Reoroji Gakkaishi) 35 11-20. 

ANALYSIS OF THE LINEAR VISCOELASTIC RELAXATION OF A LIQUID HYDROCARBON. 

Detiora number Dielectric relaxation Enthalpy relaxation Linear viscoelasticity Non-equilibrium thermodynamics... 

Ilie anomalous behaviour in the linear viscoelasticity has been explained by the tube model.Figure 7.26 shows schematically how the stress relaxation takes place in star polymers. In the crude theory, it is assumed that the centre of the star is fixed during the viscoelastic relaxation time and that the relaxation takes place only by the contour length fluctuation, i.e., by the process that the polymer retracts its arm down the tube and evacuates from the deformed tube as shown in Fig. 7.26. 

The subject of relaxation has been illustrated by several case studies in the previous section slowed down motion, occurring reaction, RC circuit, dielectric relaxation, and viscoelastic relaxation. Depending on the peculiarity and tradition of each domain (linearity, measurability, use of forced... 

Table 3. Viscoelastic relaxation data for linear high molecular weight polymers... 

This square-root dependence on tw is a fundamental featme of linear chains in the Rouse model. The shear modulus at intermediate frequencies is a signature of the internal, intra-chain dynamics, which is determined by the topology of the GGS. As stressed before, the viscoelastic relaxation forms can be expressed through the relaxation spectrum H r), see Eq. 27. Here one finds [3] ... 

For a viscoelastic liquid in shear, the ratio oz t)/y in equations 56 to 58 is sometimes treated as a time-dependent viscosity J (r) which increases monoton-ically (provided the viscoelasticity is linear) to approach the steady-state viscosity Meissner has pointed out that, in an experiment involving deformation at constant strain rate followed by stress relaxation at constant deformation, viscoelastic information can be obtained without imposing the restriction in equation 11 of Chapter 1 that the loading interval is small compared with the time elapsed at the first experimental stress measurement. ... 

Stress relaxation for step squeezing of polystyrene at 180°C. (a) Stress versus time for increasing strain steps. Stress increases at short times, 2-10 ms because the plates take a finite time to close. The horizontal stress response signifies transducer overload. The rapid drop for strains e > 1 indicates loss of lubricant, (b) Stress relaxation data plotted as relaxation modulis. Solid line is the linear viscoelastic relaxation modulus calculated from shear dynamic data. Adapted from Soskey and Winter (1985). 

Ramkumar, D. H. S., Caruthers, J. M., Mavridis, H., Shroff, R. Computation of the linear viscoelastic relaxation spectrum from experimental data. /. Appl Polym. Scl (1997) 64, pp. 2177-2189... 

Figure 6 Normal mode relaxation processes in linear polymers (a) motion of a polymer molecule when subjected to an oscillating shear field (b) diagrammatic representation of the motion of an ideal flexible chain when in an oscillating shear field (c) viscoelastic relaxation of a polymer in solution, ri is the high frequency limiting value, tjq is the zero frequency and...

Figure 36 is representative of creep and recovery curves for viscoelastic fluids. Such a curve is obtained when a stress is placed on the specimen and the deformation is monitored as a function of time. During the experiment the stress is removed, and the specimen, if it can, is free to recover. The slope of the linear portion of the creep curve gives the shear rate, and the viscosity is the appHed stress divided by the slope. A steep slope indicates a low viscosity, and a gradual slope a high viscosity. The recovery part of Figure 36 shows that the specimen was viscoelastic because relaxation took place and some of the strain was recovered. A purely viscous material would not have shown any recovery, as shown in Figure 16b. 

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