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.