Cryogenically treated axle shafts 1

Although this may sound like a red herring it isn't, you must search for and read all information on cryogenic conditioning of materials. From the information you obtain you will be able to make your own conclusions on the benefits, as you say it is very unlikely anyone is going to give you figures at this early stage of the technology.
Br
B

There are different types of torque capacity for axles. If you are testing by twisting until the material yields, cryogenic processing will not have much affect. However, if you are testing for life under multiple repeated loads, the typical life values are double or triple. We find that a lot of axle failures in racing are failures of the splines, which is another story all together. In some cases, just getting the heat treat right will create a significant increase in life and is necessary if you want any increase in life due to cryogenics.

The numbers that you are looking for depend upon the steel alloy in question and a detailed description of the heat treatment that it received. The main benefit of a cryogenic treatment is to complete the transformation of austenite to martensite. Most tool steels develop their hardened structure, martensite, during the quench as the temperature falls between about 600 F and 200 F. For some steel alloys, transformation to martensite may not be complete even at room temperature. In this case there is a significant amount of the high temperature microstructure called austenite that is retained after normal heat treating is completed. As an example, A2 and D2 are two tool steels that may retain more than 20% austenite after normal heat treating, and retained austenite may be undesireable for a number of reasons. Cryogenic treatments can sometimes transform much of the retained austenite to martensite, and this newly formed martensite is similar to the as-quenched microstructure. Since newly formed martensite is brittle and under great stress, cryogenic treatments must also include at least one temper after freezing. And often the cryo cycle may be performed in between normally scheduled multiple tempers. Due to the possibility of cracking, the material should be tempered at least once before performing any cryogenic treatments.


Maui

Maui is correct that the Austenite to Martensite transformation is important, but there is a lot more to cryogenic processing than that, and it does not explain the huge increase in fatigue life created by cryogenics. It also does not explain why cryogenics works on non ferrous metals.