Fragmentation and the Critical Length
Besides the weakest link mechanism, there is
another mechanism known as the fragmentation
process which relates to, but acts differently from,
the weakest link mechanism. It was observed
during the fracture process of both composites61
and yarns45 that the constituent fibers break repeatedly
along the length with increasing strain
of the structure before overall material failure.
This phenomenon indicates a fact that, contrary
to common assumption, a broken fiber can again
build up tension, carry load, break into even
shorter segments, and contribute toward overall
system strength. Also, the fiber breaks will not
stop, as long as the whole structure does not collapse,
until the length of the breaking segments
reaches a minimum value at which its load can no
longer build up to its segment breaking strength.
This length is well known as the critical length lc.
If sb is the tension that causes the fiber segment
to break, it follows that the minimum length on
which a broken segment can no longer build up its
tension again from the broken position or the