This rifle. 5.56 mm, came in with a head separation.
I tried all the typical methods: Reversing a cleaning brush, broken case extractor, language arts, heat, Kroil, etc.to no effect. I finally turned to the ultimate broken case extractor:

BrokenCase by jakefromclemson, on Flickr

Good trick to add to the bag of tricks. I've always had good results with bismuth alloy (cerrosafe).

Nice job! For some jobs like this (when we can't dismount the barrel easily), we use a shop made tool. It is a length of mild steel rod that we grind a 30 degree +/_ tip and shape to a half cone on the polishing wheel to a razor-sharp tip. Then we carefully drive the tip between the brass case and the chamber wall, making sure you drive parallel to the chamber wall. This will push brass in and pull it away from the chamber wall without damage. Eventually, the case will loosen and fall out or you can run a rod down from the muzzle and push it out.

I have used a regular tap slightly smaller than the OD of the case, twisted into the case just far enough into the case to get a grip and pushed out with a cleaning rod or some such.

I have only had to do it once, but I used a tap like Jim.

THERE IS A TOOL AT TIRE SHOPS THAT WORKS LIKE A CHARM, YOU INSERT IT, INCREASE THE TENSION BY SCREWIN IT INESIDE THE CASE AND OUT IT COME, BUT I CANT RECALL THE NAME OF IT? I SAW IT WORK YEARS AGO,
maybe ONE OF THE MECHANICS CAN. ITS USED TO TAKE THE WHEELS APART.

How does taking wheels apart relate to stuck case removal ? I was in the automotive world for some time, never heard of the tool you're talking about.

Ray, your caps lock has been on for a week.

Rays screaming at us.

Place a little wad of cloth or paper towel in the case, back when bullets were cheap I'd just drop a bullet in there. Then fill about 3/8"-1/2" of either molten lead, solder, cerrosafe, or just some epoxy. when it has hardened up just drive out with a rod.

I've seen it used many moons ago, it went in the case then screwed tight raising arms to pressure the inside walls then pulled out best I recall sort of like a picture hanger expanding screw in drywall does. You may have to drill out the base depending on the circumstances. It's used best I know to push in something to remove it, that's all I know thought someone might be smart enough to tell us what it is called? It might be a claws foot puller is the best I've come up with.

My caps are on because I'm going blind at last Old age aint for sissies my friend!