A canna’ change the laws of physics

Scotty, The Naked Time, stardate 1704.3, Episode 7

Adrian’s attic: stress birefringence in an optically sensitive gel

Posted by apgaylard on August 3, 2008


Stress pattern in a cast gelatine/glycerol block under white-light illumination between crossed polarisers

Stress pattern in a cast gelatine/glycerol block under white-light illumination between crossed polarisers

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 stressesi – 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

A 50 50 50 96 2 1 (best) 10
B 10 90 50 3 4 3 100
C 1 99 50 2 3 5 100
D 50 50 80 72 3 4 20
E 10 90 30 3 2 2 80
F 1 99 70 2 4 6 (worst) 200
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).

Distribution of stresses around cracks and other flaws in a cast gelatine/glycerol block

Distribution of stresses around cracks and other flaws in a cast gelatine/glycerol block

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.

A point load is applied in the centre of the top-face of a cast gelatine/glycerol block (note a production fault emanating from the lower face)

A point load is applied in the centre of the top-face of a cast gelatine/glycerol block (note a production fault emanating from the lower face)

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. 

Distribution of stresses caused by 0.2kg load load placed, on the upper surface, 25mm inboard from the left-hand face.

Distribution of stresses caused by 0.2kg load load placed, on the upper surface, 25mm inboard from the left-hand face.

The image (above) shows the results of eccentric loading (inboard of the left-hand face).  The stress pattern shows the results of the right-hand side of the block being pulled towards the left. 
Gelatine/glycerol block under even load on the top face.

Stress distribution in a gelatine/glycerol block caused by a 0.2kg even load on the top face.

 This contrasts with the pattern shown for even loading (above).

Stress pattern formed when a cast gelatine/glycerol block is inclined at 9 degrees to the horizontal

Stress pattern formed when a cast gelatine/glycerol block is inclined at 9 degrees to the horizontal

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.

5 Responses to “Adrian’s attic: stress birefringence in an optically sensitive gel”

  1. dvnutrix said

    I showed this to a relative who must have been a contemporary of yours albeit he took the Nuffield Board (which examining body were you with?). Anyway, he is impressed – if this were the USA, and you had access to firearms, you might have been a very early CSI, shooting into your gelatine mix.

    I should thank you for sparking some vastly entertaining Sunday lunch conversation as umpteen relatives dredged up memories of formal and informal experiments that they ran as children.

  2. pleick said

    Just for continental readers: A-levels are the british equivalent of a high-school degree, that is, the degree you need to qualify for university education?

    In any case, it’s nice stuff. I never had the opportunity to do anything that “cool” in my physics classes… kind of shows how science should be taught, but generally isn’t.

  3. apgaylard said

    dvnutrix: Thanks. I did Nuffield physics as well.
    pleick: Yes, the British A-level is the (ahem ‘gold’ ) standard pre-university qualification – usually taken at 18; though these days there are an increasing number of other routes.

    I think it was one of the strengths of the course I did that there was a project as well as a practical exam. We also did a preliminary project to get us into the approach.

    I think I’ll do something on one of the elements of our practical exam at some point.

    Once more, thanks both.

  4. jdc325 said

    Nice post. I liked the ‘moral of the story’ bit at the end of your post so much I just spent the afternoon reading up on the N Rays story [shame Wood’s Nature paper is behind a paywall] and checking out more of Langmuir’s talk. Interesting stuff. Cheers!

  5. apgaylard said

    jdc325: Thanks. Langmuir’s talk is very good.

Sorry, the comment form is closed at this time.

 
%d bloggers like this: