Page 310 - Fiber Fracture

292 Y. Termonia

relaxation steps, the Monte-Carlo process of bond breakings and chain slippage is
restarted for another time interval 6t. And so on and so forth, until the network fails.

Oriented Fiber

Our model representation of the oriented fiber is given in Fig. 3. The nodes in
the figure represent the elementary repetition units of the polymer chains, i.e. methyl
units for polyethylene. For very long chains, each node is made to correspond to more
than one repetition unit (Termonia et al., 1985). The nodes are joined in the x- and
z-directions by secondary bonds having an elastic constant Kz. These bonds account
for the intermolecular vdW forces in polyethylene or hydrogen bonds in nylon. Only
nearest-neighbor interactions are considered. In the y-direction, stronger forces with
elastic constant K1 account for the primary bonds, Le. C-C bonds in polyethylene.
The network of bonds in Fig. 3 is deformed at a constant temperature T and strain
rate i. using a Monte-Carlo process similar to that described for the unoriented case.
Both primary and secondary bonds are allowed to break using the Eyring chemical

Y

X
Fig. 3. Model representation of an oriented polymer fiber. KI and K2 are the elastic constants for the
primary and secondary bonds, respectively.