gearcutter,
The limiting factor with your unlubricated, steel-on-steel gear mesh is not one of bending or contact stress. So core strength or case properties are not really an issue. With steel-on-steel contact and no lubricated interface, the coefficient of friction will be very high (ie. >.30). That means a large percentage of the force (work) being transmitted at the pitch line will be converted to heat in the gear teeth and rim. Unless you have some way of removing that heat, the (thermally isolated) gear teeth and rim will heat up and lose their temper, and ultimately ending up in a very soft, annealed condition. So unless you have designed your gears to have adequate durability in an annealed condition, they will likely fail fairly rapidly.
Having said that, to maximize life in a steel-on-steel mesh without lubrication, I would do everything I could to minimize friction. You could try low friction coatings like hard chrome, DLC (Diamond Like Coatings) or Titanium Nitride. You could also try superfinishing the gear working surfaces. I would also recommend modifying the gear geometry to get full recess action at the gear mesh. Recess action has less friction loss than approach action meshing.