Page 312 - Fiber Fracture

294 Y. Termonia

BRITTLE N ECKl N G MICRO-NECKING HOMOGENEOUS
FRACTURE DEFORMATION
Fig. 5. Typical deformation schemes obtained from the model at different molecular weights. From left to
right: M = 1900; M = 8500; M = 20,000 and M = 250,000.

Effect of Density of Entanglements

The results of Figs. 4 and 5 clearly show that the molecular weight has a weak influence
on the drawability of flexible polymers. The largest draw ratio value h = 6, obtained
in Fig. 4, is indeed much too small to attain enough orientation, hence acceptable
mechanical properties through tensile drawing. It is now well accepted that the density
of entanglements in a polymer network can be easily controlled through a spacing factor
4 defined as
4 = (Me/M,melt)- I

in which Me denotes the actual entanglement molecular weight value used in our
simulations. Fig. 6 shows a series of nominal stress-strain curves calculated for
monodisperse polyethylene of M = 475,000 at 5 different values of the entanglement
spacing factor 4 (1, 0.1, 0.04, 0.02 and 0.004). The figure shows a dramatic dependence
of polymer drawability on the entanglement spacing factor. At 4 = 0.02, the draw
ratio at break reaches values as high as 45 which are in the range of those required
for the attainment of good orientation, hence acceptable mechanical strength. At much
lower 4 = 0.004, the elongation at break shows a sudden drop and brittle failure is
observed. The latter is due to the fact that at 4 = 0.004, the molecular weight between
entanglements is now comparable to that for the entire chain.