I had the exactly same kind of crack develop in my favorite bow. I super glued the crack, wrapped it serving thread and soaked the thread with superglue. Here is the fix.
Well, the fix lasted a year, killed a deer with the bow, shot a bunch of tournaments with it, then I noticed the patched limb had gotten weak. A close examination revealed the crack had extended almost an inch on either side of the patch. Here is the current fix, a new limb spliced into the bow to save it.