If you look at the curve, where there is a sharp ramp up in stress vs position (linear), that is the elastic region. In other words if you stopped stretching anywhere at that point it would return back to the original length. Where you see the curve go flat, (departs from linear) that is the yield point. The bolt has yielded and is undergoing plastic deformation. The bolt it ruined at that point. The high point of the curve is the Ultimate tensile strength(UTS). Where the curve stops that is the failure point. They break at the threads since the stress area is smaller yes, but also because the thread is a stress riser at the root. Rolled threads have a radiused root and can therefore go higher.