No, dont get the wrong idea, im not going to tell you a pattern for enhancing. My bf has spent over 1 gold enhancing things and he's fair certain it's random... which makes sense to me. He's got a whole bunch of conspiracy theories about enhancing which would take too long to even dot point here.
But one thing he did notice: when you click on 'begin enhancement' your stone disappears from your inventory before the enhancement finishes... thats not all, if your weapon is going to be destroyed it too
will disappear from your inventory before the enhancement finishes.
So no more sitting on the edge of your seat wondering if it will be destroyed, you can now find out imediately. Sad thing is, as you should know, theres no way to stop enhancing once you've started.

so now do what my bf does and while the enhancement is going and he knows its going to fail, he runs around looking for another green item to destroy XD
I will try to submit some screenies of the failed enhancement if you want me to.