Hi,
I think it broke because: it's oak, it's not an optimal piece for a self bow, and it was not well tillered. These are usually the reasons any bow breaks in the tillering process. You're asking too much of too little. Oak is fine, but for a piece like that, back it. Hickory, linen, silk, rawhide... take your pick. Go get another piece, and start again! If you're not breaking stuff, you're not pushing the envelope! There is only one way to find out how far you can push...
Bye the way, your design looks good.