I suspect the answer lies in thinking about what the failure mechanism is. If you imagine the PVC to be chains with side groups on that tangle or physi-bond with each other, then the strength may well depend on the size of the chain overlaps and so, ultimately, the chain length. There may also be a hidden rate dependence. If there is viscous elongation (creep) a typical mechanism is that the chains slip past each other; failure will depend on how long the chains are and how many and what size the side groups are to hinder the slipping of the chains. Cut the chains up and you get less time before it fails.
I have always thought break occurred in tensile tests when a flaw of sufficient size was encountered at the boundary of the growing yielded zone. If the material succeeds in yielding without breaking, the yielded material is much stronger, and so the boundary continues to move into un-yielded material. In an ideal, unflawed specimen, the yielded zone grows indefinitely to include all the specimen all the way to the grips. The flaws break at strengths that are roughly similar (though I agree they must vary somewhat according to size and nature of flaw). As degradation increases, the critical flaws become more numerous, so a critical flaw is encountered sooner as the yield zone begins to enlarge. In other words, fracture elongation is probabilistic, and related to flaw density. Fracture stress, in contrast, is related to nature of the critical flaws, which is often more constant.
I have seen this flaw-density scenario play out very clearly in patio chairs injection moulded from a compound of polyethylene filled with calcium carbonate, for stiffening. The calcium carbonate grade was poorly chosen as ground-up mineral, having an excessive topsize. The rare large grit particles acted as flaws. The chairs were generally tough, but a few fractured abruptly in brittle mode at quite low stress. The same happened when we machined tensile specimens and tested - most bars were tough, but a random few were very brittle.
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