Spherulites affine deformation

At very small strains within the viscoelastic region (e<0.5%), deformation within the PP solid is confined to disordered amorphous regions [97,98) due to their inherently low stiffness at temperatures above their Tg (-10 °C). In this deformation region, spherulites undergo affine deformation on the whole. Inside the spherulites, rotation of lamellae occurs [101]. The resulting orientation of lamellae depends on their position within the spherulite in respect to the orientation of the external deformation [102-104],... 

The change in scattering patterns upon deforming polyethylene was observed by Stein and Rhodes. The analysis of these patterns was carried out for two-dimensional spherulites by Gough et a/." and subsequently extended to three dimensions." The theory involves an affine deformation of the spherical spherulite to an ellipsoid of revolution, accompanied by the rotation of the optic axes which are assumed to be initially oriented at an angle Po to the radius, and at a twist angle oj... 

Assuming the unaxial deformation of the polyethylene spherulite to follow an affine deformation hypothesis keeping its volume constant, as has been postulated by several authors,the number of crystallites orienting in a range from 6 to (0 -hd0 ) is given by equation (35), where Nq is the total number of crystallites within a spherulite and X is the extension ratio of the spherulite along the X3 axis. 

---