Hey Dave, First, Three layers of 1/4" oak is tough to cut, But it is doable. Most importantly is the grain direction. Chances are the tree broke because the grain was running against the weakest area. Next time orient the grain so it runs with the weakest point. If I were cutting these ( I cut about fifty of these last year) I would only stack two layers of 1/4".
Good luck!
I guess Sheila and I were typing at the same time!