Thursday, March 29, 2012

Thurs-Demo: The Photoelastic One

Our department has an iPad. It's a lonely first-generation device: it doesn't get as much use as we hoped due to it's limited flexibility with computer projectors and video. Perhaps the newer versions would be more useful. That's not the point of my comment - the polarized light emitted by the iPad is. Last week I was able to use the iPad to view deformation in gelatin. Here's a quick movie of me rotating the iPad in front of my laptop's built in camera. The polarized light from the iPad is extinguished by the polarized filter I have in front of the laptop camera. All you see is a shiny reflection of the computer screen as a result.

My buddy Todd is (hopefully) putting together a post on light and polarization - perhaps he'll include some discussion on the orientation of the polarization of smart phones and sunglasses and such.

video


So this week, I tried something a little different. I pulled out some circular polarizers and used them to shoot some video of a steel ball dropped onto a dish filled with gelatin. I think the effect is both easier to see and easier to film due to the increased light coming from the setup.


That blue square in the background is one of the circular polarizing filters. There's another one in front of the camera.

The colored bands are a result of interference produced when the gelatin deforms. The spacing of the bands is proportional to the magnitude (amount) of strain/deformation in the material. Here's the experiment with a much larger ball (hence more stress, producing more strain):


For comparison, here's the same experiment in plane-polarized light:


In the write-up above, I've been using stress and strain somewhat interchangeably. That's because the gelatin deforms easily when subjected to pressure. The magnitude of the applied force/area (pressure) is the stress and the amount of deformation is the strain. So when we apply a little stress, we see a small amount of strain. With a lot of stress, a lot more strain develops. But in gelatin, it doesn't take much stress to produce strain. In more rigid solids, stress can develop without any observable strain. But that's a topic for later.

If you like, you could place a square block on the gelatin and see how the stress is distributed beneath and away from the base of the block (much like how stress spreads below and outward from a load placed on soil). Or you could take plaster or food coloring and inject a liquid into the gelatin and see how the shape of the fractures depends on the stress field around the intrusion (Callan has done this and there's a set of neat labs from a prof in Hawaii that talks about this technique in great detail).

I've found that using a gelatin mixture that's about 150% thicker than recommended for "finger jello" works best - and holds up reasonably well to the increased heat of the lights used for filming.

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