Polymer Elasticity in Various Deformations

In Chapter 7, we studied polymer melts and solutions as viscous liquids, and in Chapter 8, we introduced the idea of viscoelasticity to describe both the viscous and elastic properties of polymeric liquids. For the case of cross-linked polymers, amor-phons glassy materials, and materials that exhibit flow under stress, it is easier and profitable to describe their mechanical properties as elastic solids whose characteristic parameters are somewhat time dependent. Some fanuliar mechanical properties are summarized in Table 9.1. 

Other quantities are also used. For example, true stress is sometimes used as force/(actual area) rather than the more conventional definition of force/(original area). In ordinary calculations for steel, wood, and other materials of construction, the materials are regarded as linearly elastic and the modulus is a material property. In the case of polymers subject to larger deformations, the modulus is a function of deformation, deformation rate, and time. It is therefore no longer a material property and various formulas from theory or empirical practice are required to describe polymer elasticity. 

From the definition of Poisson s ratio, in Table 9.1, it is easily seen that when the volume of a material V = abL) does not change on stretching, v = 0.5. 

5 for incompressible liquids, most rubbers Cantilever beam, end-loaded (b = width)  

If the changes in a and b with L are proportionately the same and V does not change withL, 

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