Why is packing tape nearly impossible to tear when intact, but easily shreds if you cut the slightest nick into it?
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OOh! I actually remember this one from an engineering course I took!
A nick forms a stress concentrator at the tip of the nick, which easily propagates if the two halves are pulled apart. But without the stress concentrator, the material is able to resist the typical stresses encountered when the material is held under tension. To give you an idea of how much the stress concentrator concentrates stress, look at [the finite element analysis of various geometries under tension](https://www.google.com/search?q=stress+concentrator+FEA&tbm=isch). You can see that bends that come to a sharp corner have extremely high stress at the tip of nicks and corners, whereas gentle curves spread the stress out to levels that the material can withstand.
The same sort of effect is the reason why airplanes with pressurized cabins do not have square windows, but rather, have rounded windows. There were a handful of tragic accidents where a pressurized cabin tore the skin of the plane, and the tear propagated from the corners of square windows cut into the skin of the plane, blowing out a massive hole and causing the plane to crash. The corners concentrate the stress to a single point, making an otherwise resilient material to tear easily.
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