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Polishing the surface, not just the edges removes stress raising hair line cracks. A crack likes a place to begin, like a stone chip on your window, watch how that little chip spreads.
After polishing another good thing to do is shot pean. This expands the surface putting those hairline cracks you missed into compression further preventing stress risers.
Another way, if you pull a rubber band it stretches, knick it with a nife and it breaks.
When a part is forged or even cast if you were to look at the surface under a scope you would see very rough edges. These rough edges are where the cracks start. Stress risers are in the steel and the crack starts very small and under load will get larger eventually causing a failure. When you polish the rod or whatever you eliminate these small stress risers and therefore making the rod less prone to cracking or braking. That is it in very basic terms, I'm sure an engineer can explain it in more detail.
I learned this in my engineering class last semester:
quick answer: crack growth depends on strength of the material and size(geometry) of the crack. I don't have the exact formula on hand, but from what i remember crack growth occurs faster the bigger the crack(depending on shape of the crack eg. "pointiness" of the point of the crack). So, by polishing, you're trying to minimize the size of the crack and thus inhibit crack growth.
A simple visualisation is to get a sheet of clear perspex & gently bend it in a well lit area & watch how the light reflections behave. Then put a scratch in it, bend it again & you'll see how the scratch affects it Or.... think about how you cut glass to size - you scratch it where you want it to break.