There is a phenomenon with plastic in which it changes color to white in areas where stress is applied. When I bend a plastic rod the area in the centre, it turns white or loses colour. Why does this occur with plastic materials?
[Physics] Why does plastic turn white in the area of stress
material-sciencestress-strain
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Ok, so figuring that stress is defined to be the force per unit area around a point, I'd like to know why it's defined that way, rather than say force per unit volume enclosing a point.
Here is the intuitive explanation.
Suppose you have a string S from which a weight W is hanging. We will suppose that the amount of weight is so much that the string is near the regime where it would snap, but is not quite there yet. We're going to think about what happens when we add another length of string S.
If you add it in parallel, so there are two strings holding W, then it seems obvious that you could then increase the mass to about 2W before the combined two-string system would be near-breaking.
By contrast, if you add it in series (W hangs from S hanging from S), then we know that the tension force is the same in both strings, and it seems likely that they'd simply both be near-breaking. The top string might even break, if the weight of the string underneath it is enough to put it past breaking.
This tells us that the material properties which concern us (like when a string breaks) respond to stresses, defined as forces divided by an area perpendicular to that force. The direction that lies alongside the force doesn't matter, qualitatively because it propagates the force rather than responding to it.
You can also examine this two-string thought-experiment with much smaller forces not near breaking, where Hooke's law should hold for lengthening, to find that if the original deforms by $\delta L = \ell$, the two-strings-in-parallel should deform by $\ell/2$ while the two-strings-in-series should deform by $2\ell,$ so that there seems to be a constant "stress / strain" relationship where the "strain" is defined as $\delta L / L.$ In other words you can look at a system with the normal spring-constant $F = k ~ \delta L$ relationship, but it is more helpful from a materials perspective to divide by the length of the "spring" $L$ and also its cross-sectional area $A$ to find $$\sigma = \frac FA = \frac {kL}{A} ~ \frac{\delta L}{L} = \lambda ~ \epsilon.$$ The elastic modulus $\lambda$ then also has units of pressure (force per unit area) and is more fundamental to the material (a material-property) that you're studying than the spring constant (a property of both the material and the setup) is.
Since the elastic modulus is a material-property, this hints that "stress" is the right definition of "force" and "strain" is the right definition of "displacement" at the more-microscopic level when we're peeking inside the substance.
In turn, it becomes very common in materials science to show the "stress/strain" curve of various materials. This starts out of course as a straight line through the origin with slope $\lambda$, but then as a substance deforms it will describe some sort of curve as added stress leads to further strain. So for example the plastic bags from the supermarket will curve upwards; they get stiffer as they stretch more.
Once you know that the stress is the right way to "microscopically" define force, elastic systems start to show off a similar problem: the simplest stretching of a beam consists in that beam not only lengthening but also narrowing. Microscopically, a little box inside the substance is not only feeling a force $+\sigma~dA$ on one side and a force $-\sigma~dA$ on the other side (so it is in force balance and provides tension), but it must also be feeling some forces on its other sides which "pinch" it smaller. So: the force is direction-dependent, and we therefore have not a stress vector (which we already didn't quite have -- the stress is in opposite directions on the top and bottom of the box), but a stress tensor: give me a direction and I'll give you the stress vector on a plane normal to that direction. (This also solves nicely the "stress on the top of the box is negative the stress on the bottom of the box" problem.)
Usually this simplifies a lot because there are eigenvectors of the stress tensor: directions where the stress points exactly normal to the plane it deforms. Those are called the "principal stresses". However there is no reason why they'd have to be orthogonal, especially, for example, in a crystal lattice which is not cubic.
At least a part of this comes from understanding where the stress-strain curve comes from. Normally from a physics background we think of applying a force to a sample and seeing how it responds. Instead, experimental results like what you show are done differently in materials science - the sample is mounted in the testing machine (Instron for example), and the strain (distance between the jaws holding the test piece) is linearly increased at some rate, and the resulting force across the test piece is measured. So, you need to warp your thinking from physics to materials science. Now, In the elastic regime, this difference really doesn't mean much - you pull it and it extends, or you extend and it pulls back on you. However, once plastic deformation starts things are different.
So, what is plastic deformation? At the simplest, of course, it means the test piece isn't going to be the same length/shape as it was before hand. This is a somewhat slippery slope, because the engineering definition of the start of the plastic regime is actually that a small, measurable deformation has occurred (hint to mechanical engineers - if you really want no change stay well away from the elastic 'limit').
How does the material plastically deform? That might take several books to describe, but I will focus on one mechanism - dislocation generation and motion. At some applied stress various mechanisms in crystals come in to play to generate dislocations. These dislocations can move, and their motion results in plastic deformation. The softening from Y1 to Y2 is where these dislocations are moving. At Y2, however, the dislocations start interacting with each other, so they no longer move as easily. Thus, more elongation requires more stress than it did before, so one heads uphill toward the ultimate tensile strength.
At the UTS, well, things go pretty much all wrong. The dislocation tangles break up, dislocation sources pump out lots more dislocations, shear bands rapidly form, and the material more or less falls apart. Yes, the cross section has (likely) been thinning all along, but now it all goes non-linear and poof, it breaks.
One might think this is really bad for engineering materials - why would you want any material to have a stress-strain curve as you have shown? One thing to consider is that the material has absorbed a great deal of energy - You want the materials making up the engine compartment of your car to behave as shown - in a crash they will deform and absorb a tremendous amount of energy before they fail. That means that you don't have to absorb much energy, which is a good thing.
Best Answer
This colour change effect occurs when the strands of plastic material, the polymers in the plastic, start to stretch as you twist the plastic. As they do so, this changes the way the light is reflected from the plastic. Say for example, you chew a biro top, by doing so, the Refractive Index of the plastic is altered, from its original colour, to a whitish colour. Once the light is scattered, you start to lose the original colour the plastic had.
From Why does stressed plastic turn white? gives a fuller explanation of the colour change effect
Here is the formula of polyethylene, the plastic that makes up mineral water bottles, it's 2 carbon atoms and 4 hydrogen ones, linked together in long hydrocarbon chains, for the exact chemical formulas of various plastics you could look up Wikipedia or ask on ChemistryStackExchange, but I would imagine it's the same physical process that occurs to change the colour, which is the physics part of your question:
and this is a bit of the polymer chain, join enough of these together and you have a plastic bottle: