BevanSmith,
There is no such thing as a "typical" ball bearing. As flash3780 noted, a common thru-hardening steel alloy is E52100. But since steel cleanliness can have a huge effect on bearing life, and because there is significant cost pressure on production ball bearings, each bearing manufacturer carefully selects and customizes the exact steel alloy they use for any particular bearing. It is a compromise between material cost and required fatigue life.
Very high grade double vacuum melt E52100 CEVM (AMS 6444) bearing steel will give the best fatigue life, but is very costly. M50 (thru hardening) or M50-NiL (case hardening) will give good performance at temperatures up to about 600degF, versus about 350degF for 52100. 440C is a thru hardening stainless alloy. Sometimes 9310 (carburizing) steel alloy is used where a race needs to be part of a structure, like a gear shaft. And other steel alloys such as 4150 are used on large bearings where the race surface is locally induction hardened.
Tensile strength specifically, is generally not a concern with rolling element bearings. The most common failure mode in a properly lubed and maintained rolling element bearing is a sub-surface initiated race spall. These spalls are due to fractures that propagate up from sub-surface shear failures, so technically shear strength is what matters. The nucleation point of these shear fractures are usually microscopic inclusions (such as non-metallic oxides) within the steel. Vacuum melt steels are mostly free from these inclusions, which is why they tend to perform so much better in fatigue than air melt steels.
Retained austenite can also result in soft spots in the race structure with thru hardening bearing steels. So their heat treat usually includes a sub-zero treatment immediately after the initial quench.
Depending upon how your bearing is loaded (ie. which race is fixed with regards to load) and due to differences in relative contact geometries, one race will always have less fatigue life than the other. In most cases the inner race will be the limit. So having contact geometries and materials that equalize the elastic strains between the balls and races is very important.
Sorry for the long-winded post, but the answer to your question is that with regards to bearing fatigue life, properties like tensile strength and poisson's ratio are relatively meaningless. So maybe you might want to ask a different question.
Hope that helps.
Terry
ps. flash3780- could you elaborate on how manufacturers "thermodynamically" induce compressive stress in a race surface. Is it something similar to what nitriding does? And maybe give an explanation, if possible, of how this surface compression is not relieved by the repeated mechanical strains resulting from the rolling element contacts? It's something I've not heard of before, but sounds very interesting.