The pseudo-affine aggregate model

Rg. 11.7 A comparison between experimental moduli for low-density polyethylene filaments and values calculated using the pseudo-affine aggregate model E, extensional modulus Ei, transverse modulus and G, torsional modulus (a) experimental, (b) calculated and (c) experimental and calculated. (Reprinted by permission of Kluwer Academic Publishers.)... 

Deduce whether the affine rubber or the pseudo-affine aggregate model better describes these data. Given that the birefringence observed for a very highly uniaxially oriented sample of the polymer is 0.078, deduce what numerical information you can about a sample with draw ratio 3.0. 

In a somewhat later study of mechanical anisotropy, Hennig and Kausch-Blecken von Schmeling have both independently considered the application and possible development of the aggregate model. Kausch reviewed the applicability of compliance and stiffness averaging predictions for several polymers. He noted that the compliance averaging predictions with the pseudo-affine deformation scheme were close to the experimentally observed behaviour for nylon 66, Dacron and regenerated... 

The pseudo-affine deformation scheme gives a reasonable approximation to experimental data for low-density polyethylene (Figure 7.15(b)), nylon, polyethylene terephthalate and polypropylene, despite ignoring the distinction between crystalline and disordered regions. It thus provides a basis for extending Ward s aggregate model to predict the compliance constants s y and stiffiiess constants c y of the partially oriented polymer in terms of the constants sy and Cy for the anisotropic elastic unit (in practice, those of the most highly oriented sample obtainable). 

The orientation functions can be calculated on the pseudo-affine deformation scheme, and Figures 8.18-8.22 show that the aggregate model then predicts the general form of the mechanical anisotropy. It is particularly interesting that the predicted Reuss average curves for low-density polyethylene show the correct overall pattern, including the minimum in... 

For amorphous polymers, Ward et al. [96] and Kausch [88] and later Rawson and Rider [95] are in agreement that the mechanical anisotropy can be discussed very satisfactorily by the aggregate model. Moreover, the development of anisotropy with draw ratio can often be described by the pseudo-affine deformation scheme [94]. 

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