Another common problem with cukes and squash is the Squash Vine Borer. If you notice sawdust like pilings near the stems, it may be you have the SVB larvae inside your stems. This often causes stems to be prone to splitting. It is difficult to stop them once they've started. If you notice holes or sawdust like stuff near the stems, you can carefully slit it open with a razor blade lengthwise and try to remove the larvae. Then bury the damaged stems. Hopefully the plant will survive. If you have borers and they are left to continue chewing away, the plant will die.
It could be just split on their own. If you determine there are no pests or diseases, I would still bury the damaged parts in the soil. The vines should produce new roots to help the plant survive.
Greg- ND, Zone "4"