hoop stress on a thin glass window

Question

A common problem with ultra-high vacuum viewport windows is that often the window material deforms, into a saddle or Pringles chip shape. .

An engineer from a viewport  manufacturer explained to me that this can happen when the hoop stress around the window is not fully symmetric. If it were symmetric, the window would simply bulge or cup in the middle. That seems intuitive, but why would an uneven stress cause a saddle-like strain in particular? What is a simple physical explanation for this? So far, the fact that uneven stress in x/y directions cause different curvatures seems intuitive. What is also important is that glass is a very stiff material and cannot stretch (so volume/thickness is assumed to be conserved).

Here is a rough illustration of a stressed window in a metal sleeve typically found in experiments:

EDIT: the brazing pad (thick black) is where the metal sleeve (thin black lines) is brazed to the braze adapter (red lines representing another cylinder). The glass is hermetically sealed to the bottom of the metal sleeve.

kamran · Answer

Your sketch is not clear, But any collapse and wrinkling is a process of least energy configuration.

If you had very fast video camera and reviewed the recording at normal speed, you would see every step of deformation follows the path of least strain energy.

Rick · Answer

The pringling is caused by the positive (compression) hoop stress causing buckling around the perimeter. The positive hoop stress is created by the radial tension trying to pull the edges towards the middle as the center is displaced axially. Since there's not enough space for all the glass to move inwards, some of it goes up and some down.

You can see the same effect take place if you lay a piece of paper on top of a drinking glass and then push down in the middle. The center will move down and then the paper will buckle / fold such that some parts go up and some parts go down allowing the perimeter to move inward. As the material get thicker, the resistance to buckling goes up and folds/ bends get less extreme. This is why you'll only get a saddle rather than folding/ shattering.

hoop stress on a thin glass window

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