Viscoelastic deformation processes

Micro-mechanical processes that control the adhesion and fracture of elastomeric polymers occur at two different size scales. On the size scale of the chain the failure is by breakage of Van der Waals attraction, chain pull-out or by chain scission. The viscoelastic deformation in which most of the energy is dissipated occurs at a larger size scale but is controlled by the processes that occur on the scale of a chain. The situation is, in principle, very similar to that of glassy polymers except that crack growth rate and temperature dependence of the micromechanical processes are very important. 

The most complete model to date for describing Case II diffusion is that of Thomas and Windle (13-16). They envision the process as a coupled swelling-diffusion problem in which the swelling rate is treated as a linear viscoelastic deformation driven by osmotic pressure. This model leads to the idea of a precursor phase propagating ahead of a moving boundary, as we have depicted in Figure 4. While Thomas and Windle have used numerical methods to examine in detail the predictions of their model, this model is difficult to test with the data obtained here. 

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) ° )... 

It is also known that the compression process can be described using static and dynamic models. In the case of static models, time is not considered, although it is a very important factor in the deformation process. The viscoelastic reactions are time dependent, especially for the plastic flow. 

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. 

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. 

The viscoelastic deformation is characterized by time-, temperature-, and velocity-dependent deformation processes. Relatively low levels of hardness and strength, high plasticity, low thermal conductivity, and high thermal expansion are effects of the weak secondary bonding forces between the macromolecules and their coiled structures. 

The onset of deformation mechanisms at particular temperatures indicated that it was appropriate to investigate viscoelastic relaxation processes by dynamic mechanical methods. Some preliminary studies were made in 1956 and 1957 by Hellwege et who demonstrated... 

These workers also showed that the apparent energy of activation of the failure process could be calculated assuming an Arrhenius mechanism. As illustrated in Table 10.3, addition of reinforcing filler raises the apparent activation energy of the viscoelastic failure processes. Halpin and Bueche ascribe the enhanced reinforcement to those processes that spread the viscoelastic motions of the filler-rubber complex over a much wider time scale, and concluded that the lower strength observed at elevated temperatures was due to the increased rate at which viscoelastic response to deformation... 

The fracture of practical adhesive joints involves two primary processes— cohesive or adhesive failure at or near the joint and work (reversible and irreversible) involved in plastic, elastic, or viscoelastic deformation of one or all of the components of the joint—one of the two solid surfaces or the adhesive (Fig. 19.4). As indicated in the preceding chapter on friction, cohesive failure of the weaker of two solids in contact is common. The same can be said for normal adhesive joints, in that actual adhesive failure (i.e., exactly at the interface) is less common that cohesive failure, of, for example, the adhesive material, near the interface. What, then, are the necessary conditions for obtaining good adhesion between two surfaces ... 

The discussion of mechanical properties comprises the various contributions of elastic, viscoelastic and plastic deformation processes. Often two characteristic stress levels can be defined in the tensile curve of polymer fibers the yield stress, at which a significant drop in slope of the stress-strain curve occurs, and the stress at fracture, usually called the tensile strength or tenacity. In this section the relation is discussed between the morphology of fibers and films, made from lyotropic polymers, and their mechanical properties, such as modulus, tensile strength, creep, and stress relaxation. 

The combinahon of high molecular weight and high concentration leads to a very dramahc increase in the viscosity of the soluhon. A theory elaborated by deGennes is presented in Sechon 7.7. In addihon, for rapid deformation processes, the concentrated soluhon displays viscoelastic behavior. One of the most challenging problems in polymer science is the full explanahon of the viscoelastic behavior of high-molecular-weight concentrated solutions. 

And although thermoforming is basically a rubbery solid deformation process, the viscoelastic character of the polymer may need to be understood, particularly for the plug-assisted forming process. Computer-aided design programs also may need polymer viscoelastic properties. This may be particularly true for crystalline polymers such as polyethylene and polypropylene when formed above their melt temperatures. This is discussed below. 

Figures 16.1-3 show Ryshkewitch-Duckworth plots for dicalcium phosphate or lactose mixtures with sodium dodecyl sulfate as well as the Ryshkewitch-Duckworth plots for each of the pure components. As previously observed by Wu et al. [20] and Tye et al. [10] no dependence on dwell time was noted. We did note that tablets were not formed for some materials when short dwell times, comparable to production conditions, were used. Presumably, insufficient time is given for viscoelastic deformation of the materials that is, in part, responsible for adhesion. Viscoelestic recovery upon decompression may also contribute to lamination of tablets on decompression. Figures 16.1-3 and Figme 16.6 show the importance of tablet porosity to tablet tensile strength. Porosity should be considered a measure of the outcome of the tableting process.

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