Lecture 12 Considere Criterion and Geometric Condensation 100520

Course on Nonlinear Polymer Rheology. See the beginning minute for the content.

[@lixiangyoung5518]

Thanks for sharing. Does causality reversal mean chain disentangament is not included in considere criterion as a cause for the necking? As you said, only engineering stress is considered here.

[@marijhorn]

thank you.. still baffled a bit about this generic criteria Considere already bring to life in 1885... very interesting for many cases.

[@polymerphysics2242]

The logic of Considere is questionable. Perhaps one ought to first find out how the tensile force would start to drop (i.e., identify the material physics responsible for it). To say that the force maximum implies necking misses point: the force decline is the effect (we should identify the structural/mechanical cause for the force decline) rather than the cause for neck. At two different levels of description, you see the cause and effect switched! Just say this comment and thought I should reply.

[@marijhorn]

@@polymerphysics2242 there's much more than that, however the fact it's still mostly* valid. Is correct and it really does corresponds to the material point of necking. Also I would not refer it as force than Stress. Because it's uses True stress and strain by definition. Not just force. Because the force is not quite correctly determined in such way as the stress is. And yes in that sense the inclination/is corresponding to the localization of deformation in true sense and because I do quite a lot of testing I really can say it does and you might easily observe it. The facts Why's that and why there are quite a couple of mechanisms, which might be involved is the really tricky part. What Considere' did not take in account are reversible changes for instance. Not these elastic or plastic but recoverable inelastic. Therefore, it's relatively genius thing for most everyday used material and cases but not suitable for more complex materials or composites.

[@polymerphysics2242]

@@marijhorn there cannot be any confusion regarding force vs. stress. By definition, engineering stress is nothing but normalized (by initial cross-sectional area) total force. Indeed, I suppose that the force decline could arise from the specimen being non-uniform, either geometrically or structurally. I am not considerably such cases. For polymer melts, it is possible to rule out such a case, yet the engineering stress shows a peak. See the counter example in J. Rheol. 55, 1247 (2011); doi: 10.1122/1.3626416 - Figures 4 to 6 show force maxima without necking at all!

[@marijhorn]

@@polymerphysics2242 will look at the article. Truly interested in to the results. The major problem in the theory is that it's working only with the plain (recalculated) stress-strain. Not True* (real true) cross section reduction. But even that even if corresponding to some particular response at the S-S curve it doesn't mean that place will be necessarily the ultimate necking area. Will look t the publication thanks.

[@marijhorn]

@@polymerphysics2242 Not working with polymers myself, however regarding these data in 4-6 in above mentioned article my first guess would be some form of "natural drawn ratio" in action.. therefore getting first some gradual change in the polymers either by forming more uniformly elongated chains or some form of defect accumulation. The "similar" can be observed even for metallic materials. Regardless of that with engineering stress recalcualted to the "True stress" you imidietely switch these two peaks and the higher (and closer to the failure) truly corresponds to the Considere' criterion therefore the formation of final necking prior failure.