Page 362 - Fiber Fracture

344 J.W.S. Hearle

Table 2. Parameters for analysis of mechanics of a simplified model
Features of the polymer
Molar mass of the repeat unit *
Length of repeat unit in crystal a
Crystal density a
Amorphous density, stress-free a
Number of equivalent free links per repeat
Degree of polymerisation
Features of jne structure
Fractional mass crystallinity
Number of repeats in crystallite length *
Number of repeats across crystallite *
Series fraction of amorphite a
Fraction of sites with crystallographic folds
Fraction of sites with loose folds
Length factor for free ends
Length factor for loose folds
Relative probability of connector types
Other parameters
Bulk modulus of amorphous material
Stress at which chains break
Temperature
Mass of proton
Boltzmann’s constant
* Is required to characterise two-phase structure.
Is required to characterise connectivity.
Is required to analyse mechanics.

tension, which acts against the resistance to volume reduction. A large-scale analogue
would be a collection of rigid blocks linked together by rubber bands under tension.
The general picture of the stress-strain response in the melt-spun synthetics is thus
one of elastomeric extension of a rubbery network, which is constrained by being tied
to the crystallites, as well as by internal bonding, up to stresses that cause a plastic
disruption of the structure by further yielding of crystalline regions.

Fracture
A consequence of the above account of the deformation behaviour is that, for what is
in practice a fully drawn fibre but is strictly an almost fully drawn fibre, the fibre strength
is given by the yield stress. The break load, which corresponds to the true stress at
break, is almost independent of the initial state. An unoriented fibre will fail at the same
tension as an oriented fibre, but at a much higher extension. The critical question is what
prevents a continuation of drawing to higher extensions. At some point, the structure
locks. Yielding is prevented and rupture occurs instead. Alternatively, one can say that
continued yielding would require a greater stress than is required to break molecules.
The likely explanation for this is that there is an underlying entangled network of
molecules, and when this reaches a critical strain it cannot be further extended.