Page 46 - Fiber Fracture

MODELS OF FIBRE FRACTURE 31

PE CRYSTAL FIBER

-0.741 " m i
Fig. 1. Unit cell of a perfect crystal fibre of polyethylene (Bunn and Garner, 1947).

Strong Bonds in One Dimension: Polymer Fibres

In organic polymer fibres the intra-chain bonding is always covalent, a strong bond,
but the nature of the inter-chain bonding is weaker; in polyolefines the chains are linked
by van der Waals bonds, and in polyamides and polyesters inter-chain cohesion is
augmented by hydrogen bridging.
A very rough estimate of the theoretical tensile fracture stress of a fully aligned
polymer can be made quite easily by multiplying the strength of a covalent carbon-
carbon bond (about 6 x N; see, for example Kelly and Macmillan, 1986) by the
number of bonds that can be broken by unit area.
Consider, as an example, polyethylene; if the chains are packed as in the crystal
(Fig. l), there are 5.5 x 10'' per m2 in the plane perpendicular to their length. Hence
the tensile fracture stress would be 33 GPa. Variants of this approach, using simple
Morse potentials, provide values ranging from about 19 to 36 GPa. Other calculations
using Hartree-Fock self-consistent field methods yield values of 66 GPa at 0 K (Crist
et al., 1979). This last value seems a bit high and may be due to inaccuracies of the
Hartree-Fock approximation at large atomic separations.