Adrian’s attic: stress birefringence in an optically sensitive gel
Posted by apgaylard on August 3, 2008
Digging through boxes in my attic recently, I unearthed my A-level Physics project (c.1982). As it covers some interesting physics and has some pretty pictures, I thought that I’d use some of the material for a blog post. I’ve also unearthed some other old project work, so this will be the first of a short, occaisional, series that I’ll call “Adrian’s attic”.
Now, I’m not making any claims that this is particularly good stuff; it’s just something I did. However, it is an interesting bit of physics and I am sure that it could be re-worked into an even better project (for example, I used a pretty poor, wet-film, 35mm camera to take the pictures).
The aim of the work was to devise a gel that was optically sensitive to stress and then examine stress distribution in blocks and beams under different loads. This was achieved by illuminating the gel between crossed polarisers. Internal stresses in the gel cause some of the incident light to be refracted; allowing particular wavelengths (colours) to pass the second polariser (analyzer). This generates complex, and beautiful, fringe patterns. These describe the distribution of stress within the sample.
I got the idea from a passage in the well-known text “Optics” by Hecht and Zajac,
“In 1816 Sir David Brewster discovered that normally transparent isotropic substances could be made optically anisotropic by the application of mechanical stress. The phenomenon is variously known as mechanical birefringence, photoelasticity, or stress birefringence. Under compression or tension the material takes on the properties of a negative or positive uniaxial crystal, respectively. In either case the effective optic axis is in the direction of the stress, and the induced birefringence is proportional to the stress. Clearly then, if the stress is not uniform over the sample, neither is the birefringence.”
Eugene Hecht and Alfred Zajac, Optics, (1974) Addison-Welsey Publishing Co. p315
The birefringence varies from point to point through a solid; retardance at any point is proportional to the difference between the (orthogonal) principal stresses (σi – σj). The loci of points for which (σi – σj) is constant will, under white light illumination, produce a region of a particular colour (isochromic regions). Superimposed on these will be a system of black, isoclinic, bands: the result of light passing though the sample unaltered (the E-field of the incident wave being parallel to the local principal stress axis) and thus being absorbed by the analyzer. These processes cause the complex fringe pattern which reveals the internal stresses.
I found the idea that you could “see” the internal stresses in a material fascinating. Hect and Zajac mention that gelatine blocks could be used to demonstrate stress patterns – so I set about determining a suitable recipe.
I ended up deciding that gelatine mixed with glycerol and water would give me something with the optical and structural properties I was looking for. I made up various mixes and counted the number of fringes that I could see under a standard load, rated the relative clarity of the sample and tested its load-bearing capacity (to failure).
|Sample||Glycerol¹ (%)||Water¹ (%)||Gelatine²/ kg.m-3||Setting Time /h||³No. fringes||Relative Clarity Ranking||
Load Capacity /kg X 10-3
|¹Percentage by volume. ²Mass density in solution. ³Under 10 X 10‑3 kg load.|
I chose potion ‘B’ for its good birefringence, setting time, relative clarity and reasonable load bearing capacity. Having selected my material, measured its specific rotation (using a polarimeter) I set about capturing stress patterns (I also found household furntiure polish to be an adequate release agent when casting the blocks – though this could be improved upon).
Sometimes the casting and de-moulding process didn’t go particularly well. The picture above shows the stress distribution around various production cracks and flaws. Still, it illustrates that cracks in materials tend to concentrate stress.
I also didn’t feel too bad about testing this block to destruction! Here (above) is the result of applying a point-poad to the centre of the top face. It’s interesting to see that the centre of the block is still un-stressed; as shown by the large isoclinic region.
This contrasts with the pattern shown for even loading (above).
Inclining a block to the horizontal (above) results in a stress pattern caused by the action of gravity. Here stresses act troughout most of the block -even into the centre; in contrast with the other load cases.
During the project I was able to run through some interesting load cases – analogues for basic practical structures – and say something about the internal stresses. I even tried to do some quantitative work using a calibration based on an applied load versus number of fringes.
With the benefit of 26 years hindsight I think that some of my fringe ‘counting’ was dubious: I saw what I wanted to see and hence got a nice straight-line calibration. This kind of expectation bias is not uncommon in the history of science: we see what we want to see. Blondlot and his infamous N-Rays come to mind. That’s why blinding and automated measurement systems are such an important part of scientific practise. That’s why I take issue on this blog with people pushing non-blinded (and not well blinded) trials as good evidence.
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