Affine deformation anisotropy

Shape Change of Structural Entities. In many cases the growing anisotropy is not only a phenomenon of rotating structural entities, but also goes along with a deformation of the structural entities themselves. This case will be studied here. Only affine deformations shall be discussed. In practice, such processes are observed while thermoplastic elastomers are subjected to mechanical load, but also while fibers are spun. 

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 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]. 

Strain affinely deforms the tube. This creates a directional anisotropy of the enclosed molecule, and a resulting stress. The stress relaxes by reptative escape from the distorted tube. The viscosity is the product of the plateau modulus and the disengagement time r, sori cc M. ... 

H. G. Kilian, M. Pietralla (Polymer 7P, 664-672, 1978) derive from the anisotropy A of the thermal diffusivity a = X/cpp of oriented polyethylenes that the intrinsic anisotropy Ai of the orienting, partly crystalline lamellar clusters increases with the degree of crystallinity (Aj = 7 to 26, linear extrapolation yields Aj = 2 for the fully amorphous and Aj = 50 for a completely crystalline cluster) the average degree of orientation of the lamellae, , as determined from thermal measurements agrees very well with X-ray data the observed increase of orientation with draw ratio is more rapid than it would be in affine deformation. 

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