Elastic Properties of a rubber band

[woodsy2k]

Hi all.

I have something of a problem in my understanding of a current lab experiment that I am doing in my second year.

The experiment is set such that we explore the elastic properties of an elastic band through small and large deformations and measure the force that it exerts on the mountings (that are moveable in order to defore the material). We are to observe a stress/strain curve, and work out the young's modulus, The hysterisis curve, and ultimate deviations from Hookean behaviour.

The later part of the lab is to observe how the elastic properties change when at different temperatures. (I.E., hold a constant deformation, and vary the temperature)

Note: the band is deformed linearly along its length, no force is applied in the plane of the cross section.

My question is this.
The stress/strain curve exhibits three stages, each having an almost perfect fit to a linear line along that part. The first i know is a Hookean type behaviour, where F=-kX.
The second and third stage I have no idea what property of the band they represent. Does anyone know what they are meant to reveal?

I understand that there are two dependancies that a band has in terms of its elasticity, those being an energy and entropic depenance. Can anyone shed some light on this problem for me? I would very much appreciate it :)

Woody

PS, this isn't homework, it is simply a question of understanding.

 

[vanesch]

My question is this.
The stress/strain curve exhibits three stages, each having an almost perfect fit to a linear line along that part. The first i know is a Hookean type behaviour, where F=-kX.
The second and third stage I have no idea what property of the band they represent. Does anyone know what they are meant to reveal?

Warning: what I'm going to write is a guess. It doesn't have to be the purpose of your lab experiment. But in general, ductile materials (non-brittle materials) show indeed roughly 3 domains in their tension/deformation relation. The first, you noticed, is linear elasticity.
The second is non-linear elasticity - usually the material "hardens". This can be accompagnied or not, by a kind of hysteresis (you have permanently changed the material or not). In this region, the force increases MORE with displacement than was the case in the linear region if it hardens (or less if it softens).
Finally, the third region is the one of failure: the force DECREASES with increasing deformation (so the more you deform, the easier it becomes to deform even further). This is in fact an artifact due to the effective cross section diminishing due to the large deformation. So the tension per unit of cross section doesn't really diminish, but the cross section itself diminishes (in other words, your material is breaking up!).

 

[woodsy2k]

What you are saying i understand, But it seems that my experiment is showing otherwise. I am plotting stress on the Y axis and Strain on the X axis. Stress is force over area (in this case, the cross section of the band) So in the Second section, as the gradient is less than that of the Hookean section, whether or not the material is hardening or softening, the force per unit change in strain is decreasing, (shallower gradient). This is what is puzzeling me.

Woody

 

[vanesch]

What you are saying i understand, But it seems that my experiment is showing otherwise. I am plotting stress on the Y axis and Strain on the X axis. Stress is force over area (in this case, the cross section of the band)

The actual cross section during the experiment ?

 

[woodsy2k]

I am not measuring the cross section during the experiment, only when the band is relaxed.

I am simply measuring the force for different extensions. Hence i am puzzled by the decrease in gradient for the middle stage.

 

[woodsy2k]

Does anyone else know what these stages mean?

Id really aprpeciate any help people can offer.

Woody

 

[brewnog]

Vanesch touched on a clue which you didn't pick up on.

If you're not measuring stress, but load (over a fixed, nominal cross sectional area), what would you expect to happen to the cross sectional area when the band stretches, or approaches the end of its linear elastic region? How does your graph of force/extention compare with your stress/strain graph?

 

[PerennialII]

What you are saying i understand, But it seems that my experiment is showing otherwise. I am plotting stress on the Y axis and Strain on the X axis. Stress is force over area (in this case, the cross section of the band) So in the Second section, as the gradient is less than that of the Hookean section, whether or not the material is hardening or softening, the force per unit change in strain is decreasing, (shallower gradient). This is what is puzzeling me.

Woody

So do I get it right that after yield your stress measure decreases for a while and after it starts to increase again as a function of strain (for a while at least)? Some polymers after yield (breakdown of the initial structure) exhibit as a function of strain a sort of a "re-organization" phase, followed by a phase one could refer to as "orientation strengthening" (or molecular alignment). The re-organization phase can have a stress drop within it as the structure adjusts itself to applied loading. Or is the behavior 'just' "typical" nonlinear as described above...

 

[PerennialII]

How repeatable is this measurement ? At first sight, I'd say that you're talking about measurement fluctuations...

Likewise, looks like a pretty typical 'kink' often have in stress-strain curves.

 

[woodsy2k]

It is repeatable easily enough. But these are the best readings recorded yet, according to others that have done the same experiment. The band only conforms to hookean behaviour when at small strains. You'll notice that the graph goes up to a strain of 2, that is way beyond where hooks law holds until. Either way, the original question still stands. Is there a reason for the drop in gradient?

 

[PerennialII]

... would be interesting to see an overlap like plot of couple of results in order to be able to evaluate the experimental scatter. Other than that, in principle the explanations given above are valid for behavior in the non-linear strain regime. In order to to refine the micromechanism based description a bit, it's a "typical" rubber band (you know anything else about the material, it's properties and/or spec)?

 

[woodsy2k]

Im affraid not. Its a bit cheeky really as we were given a bog standard band that could have come from anywhere really. I think given a higher quality material, the experiment might have produced better results, but such is life i suppose.