Is it right to cut a slot on some material before bending? I made a suggestion to my boss to cut a thin, shallow slot on a metal sheet on the side we wanna make 90°, so that the machine could bend it. However, the outcome was "The metal broke". 
My boss was disappointed. I believe other people cut a slot to help bending too. I want to find some theories to support my idea that it was not incorrect. Please help if you're interested...
 A: Bending a material causes plastic deformation in it. More ductile the material, more easier it is to bend.
If you cut a slot in it, the stress concentration will increase in the region around the slot, which in turn decreases the ductility. So, bending after cutting a slot will cause the material to break.

I believe other people cut a slot to help bending too.

Yes, cutting a slot does make the bending easier because the material has "space" to bend. But the right way to do this is not by cutting a slot.
Ideally you would want to make the same slot by other methods, which do not increase the stress concentration (forming, etc.)
A: I would suggest that you repeat the experiment by cutting a slot on the inside of the bend. There are two thoughts that go into this:
1) materials break when a crack propagates through them
2) crack propagation is a result of stress initiation with tension at the tip of the crack
Now when I cut a slot, I create a natural place for stress concentration to occur. First of all there is the macroscopic scale (the notch), then there's the microscopic scale (the cutting causes additional subsurface cracking). The result - just as you observed.
If instead I cut the notch on the inside of the bend, I do not create conditions for stress concentration on the outside - instead, by making the material thinner where I want it to bend, I reduce the potential for high tensile stress which leads to bending.
A separate consideration (and this depends on the material) is the yield curve of the material in question. A metal, for example, will start to yield (plastic deformation) long before it breaks. This happens when the stress reaches a certain magnitude. Again, when you create a point of stress concentration, the amount of bending needed for the material to yield is less. Now to an extent this is desirable - because bending the material permanently requires it to yield, and scoring the material was supposed to make the bending easier, and it did for the reasons above. But slotting the inside of the bend would have made the material thinner in the same way, but would have created the stress concentration on the inside of the bend; quite likely this would improve your ability to bend it without breaking.
Either way it may take some experimentation to get right. There is some advice on http://www.cooksongold.com/forum/showthread.php?t=5749 that specifically says

in the trade when we make boxes that require sharp 90 degree corners we always score the inside of the bend.

See also http://sheetmetal.me/design-guidelines/ for some interesting pointers on how to bend sheet metal - it's an entire branch of skill.
