Being far from expert on wooden bows, I'l throw in my .02c.
Did I understad correctly that you backed the oak board with poplar?
White oak is a tremendously strong wood in compression, while poplar is soft and not really a bow wood I'd use if I'd have other options. The belly overpowered the soft backing and the limb broke in tension, as seen in the pictures.
Hickory and bamboo would be more suitable woods for backing a white oak board. Especially if you're aiming for a reflexed bow. Sometimes one can find large bamboo staves in garden centres.
I've made a couple of board bows backed with rawhide, which is probably the easiest. And while the rawhide backing does not keep any reflex, it does keep bows in one piece.