Amorphous viscous flow deformation

Although PBT fiber also has a plateau region in the stress-strain curve [4], the crystalline chains do not respond to external strain in the first few percent of deformation. They increased in length only when the strain is above 4% (see Figure 11.13). Therefore, initial macroscopic deformation involved viscous flow of the amorphous phase. Furthermore, PBT undergoes strain-induced crystal transformation at moderately low strains of 15-20% [75], The differences in their microscopic crystalline chain deformation explained why PTT has a better elastic recovery than PBT even though both have contracted chains and knees in their stress-strain curves [4, 69],... 

The complete stress-strain relation requires the six as to be written in terms of the six y components. The result is a 6 x 6 matrix with 36 coefficients in place of the single constant, Twenty-one of these coefficients (the diagonal elements and half of the cross elements) are needed to express the deformation of a completely anisotropic material. Only three are necessary for a cubic crystal, and two for an amorphous isotropic body. Similar considerations prevail for viscous flow, in which the kinematic variable is y. 

The situation for amorphous linear polymers is sketched in Fig. 2.8a. If a polymeric glass is heated, it will begin to soften in the neighbourhood of the glass-rubber transition temperature (Tg) and become quite rubbery. On further heating the elastic behaviour diminishes, but it is only at temperatures more than 50° above the glass-rubber transition temperature that a shear stress will cause viscous flow to predominate over elastic deformation. 

Finally, at a still higher temperature the polymer starts to deform homogeneously by viscous flow. For amorphous polymers the stress levels are very low in this case. 

The four-parameter model provides a crude quahtative representation of the phenomena generally observed with viscoelastie materials instantaneous elastie strain, retarded elastic strain, viscous flow, instantaneous elastie reeovery, retarded elastie reeovery, and plastic deformation (permanent set). Also, the model parameters ean be assoeiated with various molecular mechanisms responsible for the viscoelastic behavior of linear amorphous polymers under creep conditions. The analogies to the moleeular mechanism can be made as follows. 

Unlike elastic deformation in which the atoms maintain their nearest neighbors, flow involves changes in nearest neighbors and is a process of shear. This process is also dependent on time, so that one is concerned with the change of strain with time. The ease of flow in a liquid is characterized by its viscosity. Viscous flow is usually associated with liquids but it can occur in amorphous solids. For such materials, elastic and viscous processes can coexist. This is termed viscoelasticity and one can view elastic and viscous deformation as the limiting conditions of such behavior. Flow processes, such as creep, can also occur in crystalline materials. In this situation, the deformation processes involve different mechanisms but they can mimic viscoelastic behavior. 

Because amorphous materials, such as glasses, have no grain boundaries, their neck growth and densification are caused by viscous flows and the deformation of the particles. In practice, the paths of matter flows are not clearly defined. The geometrical changes caused by the viscous flow could be complex, in which the equations for matter transport can only be established with significantly simplified assumptions. The sintering mechanisms of polycrystalline and amorphous solids are summarized in Table 5.2. 

J(t) has a characteristic shape composed of several parts. Subsequent to the glassy range with a solid-like compliance in the order of 10 N m, an additional anelastic deformation emerges and eventually leads to a shear compliance in the order of 10 N m. The latter value is typical for a rubber. For a certain time a plateau is maintained but then there finally follows a steady linear increase of J, as is indicative for viscous flow. The displayed creep curve of polystyrene is really not a peculiar one and may be regarded as representative for all amorphous, i.e. noncrystalline polymers. One always finds these four parts... 

From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then the re-forming of bonds with new neighbors as large numbers of atoms or molecules move relative to one another upon removal of the stress, they do not return to their original positions. The mechanism of this deformation is different for crystalline and amorphous materials. For crystalline solids, deformation is accomplished by means of a process called slip, which involves the motion of dislocations as discussed in Section 7.2. Plastic deformation in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism, which is outlined in Section 12.10. 

For solid phase sintering, there are fonr ways of diffusion i) surface diffusion, ii) volnme diffusion (often called lattiee diffusion), iii) vapor phase transport (evaporation-eondensation), and iv) grain boundary diffusion the boundaries are very disturbed areas, which allow diffusion short-circuits . For liquid phase sintering, we must add dissolution-reprecipitation effects or a vitreous flow. Finally, for pressure sintering the pressure exerted allows the plastic deformation of the crystallized phases and the viscous flow of the amorphous phases. 

In the molten state polymers are viscoelastic that is they exhibit properties that are a combination of viscous and elastic components. The viscoelastic properties of molten polymers are non-Newtonian, i.e., their measured properties change as a function of the rate at which they are probed. (We discussed the non-Newtonian behavior of molten polymers in Chapter 6.) Thus, if we wait long enough, a lump of molten polyethylene will spread out under its own weight, i.e., it behaves as a viscous liquid under conditions of slow flow. However, if we take the same lump of molten polymer and throw it against a solid surface it will bounce, i.e., it behaves as an elastic solid under conditions of high speed deformation. As a molten polymer cools, the thermal agitation of its molecules decreases, which reduces its free volume. The net result is an increase in its viscosity, while the elastic component of its behavior becomes more prominent. At some temperature it ceases to behave primarily as a viscous liquid and takes on the properties of a rubbery amorphous solid. There is no well defined demarcation between a polymer in its molten and rubbery amorphous states. 

True liquids, in contrast, do not show an extensive order. Even with very slight stresses applied for a short time, they deform so completely that they very quickly adopt the form of the surrounding container. Low-molar-mass liquids thus behave in a purely viscous way under normal conditions. When stress is applied, the molecules are displaced irreversibly in relation to one another. In high-molar-mass substances above the glass transition temperatures, flow can be produced relatively easily. Deformations are much more difficult below the glass transition temperature of amorphous polymers. For this reason, and because of their lack of order, amorphous substances below their glass-transition temperatures are often termed supercooled liquids. 

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