Tightening bolts occurs in stages. At first, you’re only using the bolt to remove slack between two separate pieces; you’re probably able to tighten the bolt with your fingers at this stage. At a certain point, though, all of the slack is gone and now the bolt is pressing the two objects together. This is when the bolt becomes more difficult to tighten; you’re not just pressing two objects together, you’re actually stretching the bolt in this stage.
And then it happens.
You over tighten and the bolt head breaks off. Now you have nowhere to grip the bolt and no way to remove it- or so you thought:
First, grind the surface of the bolt until it is as smooth as possible. Next, center punch the bolt as near to its center as possible. It is important to be as accurate as you can, since in the next few steps you’ll be drilling into the middle of the bolt.
Select a drill bit that 1/4th as wide as your bolt. For instance, if you are using a ½ inch bolt, use a 1/8th inch drill bit. Press the tip of the drill bit into the center punch and slowly drill all the way down the center of the bolt. Go slowly so that you do not damage your tools or get your drill bit stuck.
Now select a drill bit that is twice the size of the first bit. Following the previous example, you would now need a 1/4th inch drill bit. Slowly drill halfway down the center of the bolt.
You will now need to thread a nut over the exposed threads of the bolt. First, clean the bolt’s threads. Then firmly screw on a nut, loosening it about one half turn after you have tightened it.
Use a wire welder, or MIG welder, to weld up the hole in the bolt. Start as close to the bottom of the hole as you can and work your way up, finishing by welding the nut to the bolt.
After the bolt has cooled, work it back and forth with a wrench, not making full turns in either direction until it has loosened. After you have loosened the bolt, remove it. At this point, the bolt may be loose enough to remove with your fingers.
The process can be applied to any broken bolt, but tends to work better with short bolts size ¼ inch or larger.