Introduction: Fix a Broken Stud / Remove a Broken Bolt
So you used gorilla strength and not monkey strength. Something snapped when it should have snugged. Yeah it sucks. Lets fix it so you can get on with your repair.
In my most recent situation, it was the intake manifold bolt on a small motorcycle engine. Steel bolt into aluminum. It was tightened too far into bad threads and bottomed out. Snap!
There was about 1/4" of bolt sticking out so I first tried a Dremel tool with a cutting disk to make a slot. I hoped to un-screw it with a slotted screw driver. It didn't work. Next option was to use a broken bolt removal tool - this one was called GraBit. First you chuck it up in your drill and drill into the broken bolt. Once you have the hole drilled, you use the other end of the GraBit and it's left handed threads pull as you screw it into the drilled hole. If the planets are aligned in your favor and it's the third Tuesday of a month ending in R, it will work effortlessly. Sometimes these methods don't work. It worked for me on a 2nd Tuesday, so maybe I'm lucky! All kidding aside, breaking a bolt or stud really sucks. Good luck to you!
Step 1: Celebrate Your Success!
If either of these methods worked, pat your self on the back. Good Job!
If not, adding heat from a torch sometimes helps. More rust penetration chemicals may help. Drilling the bolt completely through and removing the bolt material and re-tapping is another option. Another method for larger bolts is to actually weld a nut onto the protruding section from the inside and backing it out once it has cooled down.
Dremel rotary tool with cutting wheel - http://amzn.to/2vkUOvK
Dewalt Cordless Drill - http://amzn.to/2fs2AQO
GraBit extraction tool - http://amzn.to/2fs2AQO
SeaFoam Deep Creep - http://amzn.to/2fs2AQO