The max stretching of a rubber band

[John Melody]

Hello! There was a question about the maximum stretching of the rubber band. For example, the Oxford Textbook provides a graph attached below. Can someone share if there is a more detailed schedule? Does the fluidity begin there? Or is it just tearing up? What is the stretching limit? And can we say that tga with line is Young's module at a given tension?

[studiot]

Hello John.

Glad to see you are thinking about this.

All materials break at some point.

Consequently the force extension graph only goe so far and the stops at the break so it never increases without limit.

Secondly at the sort of extensions shown here the material will be 'necking' significantly.

Now Young's Modulus is stress/ strain not load / strain as you have here so it is necessary to try to interpret this.

 

Look carefully and you can see that the curve is turning over towards an asymptote (it never gets there as it breaks)

This means that for a given % increase in extension there is a greater increase in load required as the rubber stretches.

This is because the very long molecules are originally coiled and twisted up but the loading gradually straightens them up .

Until you get to the point that to achieve fracture you have to start pulling molecules apart - a definitely harder process.

 

A second consideration is that for the necking that occurs at these levels of extension the stress is considerably increased as the stressed cross sectional area is greatly  reduced.

So for this type of material tthe modulus is only correct as the slope of the curve at or near zero.

 

 

 

[studiot]

Good  Morning @John Melody

 

I was rather pushed last night so here is some more info and a better (more up to date theory)

Note Hayden, Moffat and Wulff use stress strain curves not load /extension %  , as I already noted.

 

 

Edited October 10 by studiot