Viscous, deformation

The viscosity given by Eq. (3.98) not only follows from a different model than the Debye viscosity equation, but it also describes a totally different experimental situation. Viscoelastic studies are done on solid samples for which flow is not measurable. A viscous deformation is present, however, and this result shows that it is equivalent to what would be measured directly, if such a measurement were possible. 

In contrast to the behavior of most glasses, the elastic moduli of vitreous siUca increase with temperature, reaching a maximum at 1100—1200°C. The maximum is approximately 10% higher than the room temperature value (153). The high temperature values, however, are probably not accurate readings of the instantaneous moduli because viscous deformation is possible above 1000°C. 

The stress has an isotropic contribution due to fluid pressure and dilatation, and a deviatoric contribution due to viscous deformation effects. The deviatoric contribution for a Newtonian fluid is the three-dimensional generalization of Eq. (6-2) ... 

Viscous deformations, at a fixed deforming stress, increase rapidly with temperature whereas elastic deformations change much more slowly. For this reason the high elastic deformation component tends to be more important at lower processing temperatures than at high processing temperatures. 

A deformation due to slippage of polymer molecules past one another (viscous deformation Dvisc)- H often assumed that such viscous deformation rates do not change with time if the applied stress is constant. However, in long-term deformations chemical and morphological changes may occur which affect the rate of chain slippage. 

In Figure 9.7 stresses are imposed on a body showing ordinary elastic deformation only, a second body showing high elastic deformation only and a third body showing viscous deformation only. The stress is imposed at time to and held at a constant value until time t, when it is removed. Deformation... 

Because of the difficulty in explaining the observed U-series excesses by time-independent models, interpretations of how disequilibria are created have evolved into models based on residence times. In these models, a melt phase coexists with the solid mantle but moves relative to it due to a driving force, most typically buoyancy. The physical situation under ridges can be referred to as two-phase flow because both the solid and the liquid flow. McKenzie (1984) and Scott and Stevenson (1984, 1986) derived the equations describing flow in a viscously deforming porous media. McKenzie... 

The total deformation in the four-element model consists of an instantaneous elastic deformation, delayed or retarded elastic deformation, and viscous flow. The first two deformations are recoverable upon removal of the load, and the third results in a permanent deformation in the material. Instantaneous elastic deformation is little affected by temperature as compared to retarded elastic deformation and viscous deformation, which are highly temperature-dependent. In Figure 5.62b, the total viscoelastic deformation is given by the curve OABDC. Upon unloading (dashed curve DFFG),... 

Cracks at fillets, liner separation, viscous deformation, dewetting (blanching)... 

Fig, 25. Distribution of purely elastic, viscoelastic and viscous deformations correlated to a decrease of stress at a constant deformation rate 70, with all deformation processes coupled, (a) 7(f). (b) ° )... 

During aging, there are changes in most textural and physical properties of the gel. Inorganic gels are viscoelastic materials responding to a load with an instantaneous elastic strain and a continuous viscous deformation. Because the condensation reaction creates additional bridging bonds, the stiffness of the gel network increases, as does the elastic modulus, the viscosity, and the modulus of rupture. 

According to results reported in the literature [1-13] if the shear stress is canceled out after steady-state conditions are reached, the time dependence of the recoverable deformation [er(t)—cre(t)/r ] is obtained where e(t) is the shear strain, a is the stress and r is the viscosity (2.6). The higher temperature, the greater the unrecoverable contribution to the shear deformation i.e. the viscous deformation. Figure 2.3 shows the effect of temperature on the strain. 

Transportation of a molten polymer through a converging channel, e.g. with extrusion, goes accompanied with elongational flow when the rate of elongation is high, next to the viscous deformation also a considerable elastic component may be present. After the polymer leaves the channel, the elastic deformation will spontaneously recover, which is apparent as an increase in diameter of the extrudate, the so-called die-swell. 

As the amount of deformation increases, viscous phenomena become increasingly important. At a given moment the specimen may show yielding, i.e. rapid viscous deformation. 

After the stress has been removed (point D in Fig. 13A), the recovery phase follows a pattern mirroring the creep compliance curve to some degree First, there is some instantaneous elastic recovery (D-E return of spring 1 into its original shape Fig. 13A, B). Second, there is a retarded elastic recovery phase (E-F slow movement of the Kelvin unit into its original state Fig. 13A, B). However, during the Newtonian phase, links between the individual structural elements had been destroyed, and viscous deformation is non-recoverable. Hence, some deformation of the sample will remain this is in the mechanical model reflected in dash-pot 2, which remains extended (Fig. 13B). 

This work is equal to the energy dissipated by internal friction during viscous deformation ... 

An interesting observation is that in the course of the FRP the curvature of a free plate reverses and a permanent warping results. This is because, after the CRP, the unsaturated portion of the gel is compressed less than the saturated (non-drying) side. The fact that the warping is permanent means that viscous deformation of the unsaturated part of the gel is possible after the critical point even during the FRP2. 

The simplest physical situation that involves both chemistry and deformation is a cylinder that is being thinned radially and elongated axially in a uniform way by slow viscous deformation. The cylinder is in two parts that meet in the middle at an interface. First we suppose that the two materials are polymorphs, both capable of slow continuous deformation (creep) with different viscosities but the same composition. Then we extend to a situation where the materials are like sphalerite and wurtzite— both having formula (Fe, Zn)S but having different structures and hence different creep viscosities, and also having different Fe/Zn ratios. 

The other starting-block is emphasis on deformation processes that are dissipative rather than elastic. Links between a material s chemistry and elastic deformation have been widely sought, but the simpler links between change of chemistry and creep or dissipative or viscous deformation have been treated only more recently by G. B. Stephenson ( Deformation during interdiffusion, Acta Metallurgica et Materialia, 36 (1988) 2663-2683). This book is an attempt to combine the ideas of Ramberg with those of Stephenson. 

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