Application of the Aggregate Model

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 

In a series of related publications, Hennig has reported the measurements of elastic constants for oriented polymers which are either amorphous or of low crystallinity. In his earliest work. Hennig showed that in polyvinyl chloride and polymethylmethacrylate the relationship 3/Eo = S33 + 2S11, where is the modulus of the isotropic polymer, holds to a good approximation. Results for the anisotropy of the linear compressibility y in polyvinyl chloride, polymethylmethacrylate, polystyrene and polycarbonate were also reported. In this experiment Hennig measured the linear compressibility parallel to the draw direction 7ii, and that in the plane perpendicular to the draw direction Vi. For uniaxially oriented polymers yn = 2Si3 + S33 = S i -I-Si2-I-S 3. It was 

On the aggregate model, it can readily be shown that for the compliance averaging 

In a further paper Hennig showed that the linear compressibility results for polyvinyl chloride stretched in the temperature range 90-120 C fitted this relationship very well, with values of cos 0 calculated from the draw ratio using the pseudo-affine deformation scheme. It was also found 

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Northolt and Sikkema [62] also noted that yielding is most pronounced in lower modulus LLCP fibers and that this phenomenon is less apparent in samples that have increased modulus. Furthermore, they quantified yield strain values of 0.7% for poly(p-phenylene benzobisthiazole) (PBTZ), 0.8% for poly(p-phenylene benzobisoxazole)(PBO), and 0.5% for poly(p-phenylene terephthalamide) fibers. The similarity of these levels with that of HBA/HNA TPCP suggests that these materials are governed by a common deformation process. This supports the application of the aggregate model to describe elastic extension of this less-crystalline TLCP. 

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