Solution to Design Problem IV

The quantity (C/AN° ) turns out to be a constant for all polymers. Thus,/am is proportional to Aa, which arises during flow. We must remember that stresses relax when the flow is stopped so that unless the cooling is rapid enough, we will lose a considerable amount of the orientation. For shear flows the same stress/optic law holds that is. 

With the assumption that the principal directions and the optical directions coincide—that is. 

The reason for the discussion of orientation is because physical properties are closely tied to orientation. Our goal is to point out that molecular orientation and morphology are related to flow and deformation history, and hence physical properties are related to processing history. Our discussions of orientation serve only to quantify and define orientation. Likewise they serve to show that at least for amorphous polymers and for polymer melts there is a direct correlation between stress and orientation. 

from the stress field generated during flow we can estimate the degree of molecular orientation. In particular, we find from Eqs. 5.186 and 5.187 that 

In extensional flow it is assumed that Xopt = Xstress = x = 0, and hence Xxx — yy = y — cr2 = AN/C. So in extensional flow, the molecules are oriented in the flow direction. Values of C for several polymers are listed in Table 5.19. 

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