Modelling polymers with a single-crystal texture

53 Modeling Polymers with a Single-Crystal Texture 

The Takayanagi models were remarkably successM in providing a simple interpretation of the dynamic mechanical behaviour of crystalline polymers and polymer blends. The theoretical basis is contained in Equations (9.1) to (9.6) of Section 9.2, and is deficient in two respects. First, only tensile deformations are considered and shear deformations are ignored. Secondly, as emphasised in Chapter 8, Voigt and Reuss schemes (i.e. parallel and series) only provide bounds to the true behaviour. 

In contrast with the Takayanagi model, which considers only extensional strains, a major deformation process involves shear in the amorphous regions. Rigid lamellae move relative to each other by a shear process in a deformable matrix. The process is activated by the resolved shear stress a sin y cos y on the lamellar surfaces, where y is the angle between the applied tensile stress a and the lamellar plane normals, which reaches a maximum value for y = 45° (see Chapter 12 for discussion of resolved shear stress in plastic deformation processes). 

Gupta and Ward found crossover points in the extensional moduli for be and ac sheets similar to those found by Takayanagi in high-density polyethylene, but at lower temperatures 

Other applications of the Takayanagi model to oriented polymers have included linear polyethylene that was cross-linked and then crystallised by slow cooling from the melt under a high tensile strain [55], and sheets of nylon with orthorhombic elastic symmetry [56]. A fuller discussion is given in the previous edition of this text by Ward [57]. 

3 Modelling polymers with a single-crystal texture 

Gupta and Ward found cross-over points in the extensional moduli for be and ae 

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