The development of mechanical anisotropy with molecular orientation

3 The development of mechanical anisotropy with molecular orientation 

In particular polymers either the Reuss or the Voigt averages or a mean of the two lie closest to measured values. It is likely that these differences relate to details of the stress and strain distributions at a molecular level, which should in turn be related to the strueture. 

Kausch, who has applied the aggregate model to a range of both crystalline and 

In summary it is evident that despite the highly simplistic nature of the assumptions made the aggregate model provides an appropriate model for a number of important pol3miers. For such materials details of the crystal structure can play no more than a subsidiary role in the development of mechanical anisotropy, and the deformation is essentially that expected for a single-phase texture or a distorted network. 

3 The Development of Mechanical Anisotropy with Molecular Orientation 

Fibres and films of intermediate molecular orientation are often produced by a two-stage process in which the first stage consists of making an approximately isotropic specimen, which is then uniaxially stretched or drawn. The aggregate model can be extended to determine the mechanical anisotropy as a function of the draw ratio. 

On this model, the birefringence Att of a uniaxially oriented polymer is given by 

In these equations, 5i 1,5i2 etc. are the compliance constants and Ci 1, C12 etc. are the stiffness constants for the anisotropic elastic unit, which in practice means those of the most highly oriented specimen obtained. The terms h, I2, h, h and h, are the orientation functions, defining the average values of 

The aggregate model predicts only that the elastic constants should lie between the Reuss and Voigt average values. In polyethylene terephthalate, it is clear that the experimental compliances lie approximately midway between the two bounds. For cold-drawn fibres, it has been shown that this median condition applies almost exactly [87]. 

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