Modulus viscous flow

Mechanical Behavior of Materials. Different kinds of materials respond differently when they undergo basic mechanical tests. This is illustrated in Eigure 15, which shows stress—strain diagrams for purely viscous and purely elastic materials. With the former, the stress is reheved by viscous flow and is independent of strain. With the latter, there is a direct dependence of stress on strain and the ratio of the two is the modulus E (or G). 

Fig. 23.7. A modulus diagram for PMMA. It shows the glassy regime, the gloss-rubber transition, the rubbery regime and the regime of viscous flow. The diagram is typical of linear-amorphous polymers.

Elastic modulus Up to the fracture stress, glass behaves, for most practical purposes, as an elastic solid at ordinary temperatures. Most silicate-based commercial glasses display an elastic modulus of about 70GNm", i.e. about 1/3 the value for steel. If stress is applied at temperatures near the annealing range, then delayed elastic effects will be observed and viscous flow may lead to permanent deformation. 

The model of a viscoelastic body with one relaxation time used above has one principal disadvantage it does not describe the viscous flow of the reactants before the gel-point at t < t. Thus it is important to use a more general model of a viscoelastic medium to interpret the results obtained. The model must allow for flow and may be constructed by combining viscous and viscoelastic elements the former has viscosity rp and the latter has a relaxation modulus of elasticity Gp and viscosity rp,... 

In the case of polymer networks there is not possibility of viscous flow irrespective of the increment on the temperature. The network when reach a temperature higher than Tg, the modulus is like that for a rubber with a constant value (see curves 3 and 4) in Fig. 2.5. 

For elastic bodies, the shear stress is related to the shear strain by the shear modulus. For viscous fluids, the shear stress is related to the shear strain rate by the viscosity. We note that for laminar viscous flow in a Margules viscometer (Figure 10.7), radial fluid displacement is zero (gr = 0). Thus, differentiating with respect to time ... 

The frequency correlation time xm corresponds to the time it takes for a single vibrator to sample all different cavity sizes. The fluctuation-dissipation theorem (144) shows that this time can be found by calculating the time for a vertically excited v = 0 vibrator to reach the minimum in v = 1. This calculation is carried out by assuming that the solvent responds as a viscoelastic continuum to the outward push of the vibrator. At early times, the solvent behaves elastically with a modulus Goo. The push of the vibrator launches sound waves (acoustic phonons) into the solvent, allowing partial expansion of the cavity. This process corresponds to a rapid, inertial solvent motion. At later times, viscous flow of the solvent allows the remaining expansion to occur. The time for this diffusive motion is related to the viscosity rj by Geo and the net force constant at the cavity... 

In the same way as our dashpot represents the whole range of linear viscous flow, the spring represents the whole range of linear elastic behavior. If you are having a bad day and haven t wrapped your mind around the idea of a picture representation of a type of mechanical response, imagine that you have an unlimited supply of springs (or dashpots), each with a different value of the modulus (or viscosity), so that you can model any-... 

A generalized kinetic model of cure is developed from the aspect of relaxation phenomena. The model not only can predict modulus and viscosity during the cure cycle under isothermal and non-isothermal cure conditions, but also takes into account filler effects on cure behavior. The increase of carbon black filler loading tends to accelerate the cure reaction and also broadens the relaxation spectrum. The presence of filler reduces the activation energy of viscous flow, but has little effect on the activation energy of the cure reaction. 

The activation energy of viscous flow will be decreased by an increase in filler loading and, therefore, the viscosity and modulus of filled polymer systems are less temperature dependent. On the other hand, filler loading has little effect on the activation energy of cure. 

The Poisson-MaxweU theory that the viscous flow of a hquid is analogous to the yieldihg of a solid under forces exceeding the elastic limit ( 3.IX F) has received much attention recently. According to Maxwell, if P is the shearing force per unit area, i the time, 6 the deformation, n the shear modulus ( 4.IX F), then for a solid free from viscosity ... 

Figure 4. The high-temperature shear storage and loss moduli of Halthane 73-14 and 73-19 adhesives are controlled by the presence or absence of the cross-linking agent quadrol in the hard segments. In the linear urethane (73-14), viscous flow follows the melting of the hard segments, whereas in the cross-linked urethane (73-19), the modulus drops only when the polymer begins to degrade.

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