Orientation Growing from the Isotropic State

Straining of isotropic materials is a common method of testing or processing. During such treatment uniaxial orientation is frequently growing (Fig. 10.1). 

Rigid Structurai Entities. If the initial structure is described by rigid, anisotropic structural entities which are oriented at random, the evolution of anisotropic scattering is readily studied by means of the methods presented in Chap. 9. A practical example is the study of growing orientation in fiber-reinforced materials. 

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. 

If the intended evaluation can be carried out on isotropic material, and thus the observed anisotropy is rather an obstacle than an advantage, the fiber pattern can be isotropized (cf. Sect. 8.4.2). This may, in particular, be helpful if lamellar structures are analyzed. If the focus of the study is on the anisotropic structure, the multidimensional CDF (cf. Sect. 8.5.5) may be a suitable tool for analysis. Several studies have demonstrated the power of the CDF method for the study of structure evolution during straining [174,177,181-183]. 

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