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Why does it take such a small incision for the glass to break at that spot? Why is the structural strength of the material influenced by such a small imperfection?

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Well, because glass is uniform in thickness and the force needed to break it is proportional to the thickness - or some increasing function, whatever it is. An incision means that the thickness at that point could be 1% or 10% smaller so the fource needed to break it at that point is 1% or 10% smaller than elsewhere. If one continuously increases the force - and any realistic contact has a nonzero time when the force is continuously increasing - it's therefore guaranteed that the glass will break at that point. –  Luboš Motl Dec 15 '12 at 10:42
    
i'm not sure if the force needed is proportional with the thickness. Could the glass start to crack at one end and sort of unzip itself to the other end. For a normal unscored glass this unzipping couldn't take place because it doesn't have a clear path. If this unzipping is really happening then the force should be just enough to start the crack, which I believe is much small then the force needed to break the whole length of glass at the same time as it would happen with a normal pane of glass –  titus Dec 15 '12 at 10:57
    
What is wrong with the description at Fracture Mechanics? –  RedGrittyBrick Dec 15 '12 at 11:03
    
Right, of course, I meant the force needed to start the crack. Once the shape begins to change and bonds are broken, the situation and required forces for further steps change - and have to be recalculated again. Yes, it's then very likely that the breaking will continue along a path. –  Luboš Motl Dec 15 '12 at 11:03
    
@RedGrittyBrick thanks for the reference, I was not aware of 'fracture mechanics' terminology/field –  titus Dec 15 '12 at 11:27
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1 Answer

Suppose you bend a perfect, i.e. unscratched, piece of glass, the forces on it look like:

bend glass

The top of the glass is in tension and the bottom in compression, but the stress is spread over a large area of glass so the local stress at any point isn't enough to break the glass.

Now put a scratch in the top surface and bend it again:

bend scratch

This time the stress is concentrated at the leading edge of the scratch so you get a high local stress and the glass breaks at the tip of the scratch. This means the crack grows until it breaks through the glass. That's why putting a scratch on the glass causes it to break when bent. The scratch focusses the stress at the scratch.

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