Page 286 - Fiber Fracture

FRACTURE OF HIGHLY ORIENTED. CHAIN-EXTENDED POLYMER FIBRES 269

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Fig. 3. Simple theory of idealised strength and modulus. Crystal lattice shows planes of failure in tension
AB and shear CD. Upper graph shows free energy versus strain. Lower graph shows force versus strain
with initial modulus from the equilibrium zero force, minimum-energy position and peak force at point of
inflection on energy diagram. From Morton and Hearle (1993).

Structure, Modulus and Strength

The highest polymer fibre strength would presumably come from a perfectly oriented
assembly of infinitely long molecules, though in practice some disorder probably helps
lateral cohesion and makes the material more robust. The free energy and force-
extension relations of such a material would have the form of Fig. 3 and would give
estimates of an upper bound for stiffness and strength. The modulus, which depends on
the first A(x - x,)* term in the free energy equation, can be calculated with confidence.
The predicted maximum strength, which depends on the determination of the point of
inflection resulting from higher-order terms, is less certain. It is commonly calculated
from the modulus as the stress at 2% extension.