60 years ago I worked as a draftsman at an Axle manufacturing Plant in Spencer, Ohio. We made Axles for various Ford and GM Trucks, Jeeps, and large Axles for large Off-Road Equipment.
The typical Axle for the large Off-Road Equipment was around 3" diameter x 68" long. Both ends were upset forged. On one End was an SAE Spline. On the other End would be a Spur Gear about 5-1/2" OD with about 18 teeth (these are all rough numbers from memory). The splined End would enter the Differential Gearing. The Spur Gear would be the Sun Gear in a Planetary Gearing set-up in the Wheel Hub.
These shafts were made from SAE 8620 and 9310 Steels. The last two Digits on the SAE number lists the Steel's Carbon content (xx20 = 0.20% Carbon, xx10 = 0.10% Carbon). Note the normal Model Engineer's Cold Drawn Steel (or Bright Steel – a term not used over here) is 1018 (0.18% Carbon). A common leaded Steel is 12L14 (0.14% Carbon). Ball Bearing Races are made from 52100 which has 1.00% Carbon.
We would fully machine the Axle Shafts. We did not have Gear Grinding equipment but would use a Gear Shaver to improve the Gear Tooth finish, to bring the Gear to final size, and crown the Gear Tooth Profile. The end of the Shaft would be tapped 1/2", still preserving the Lathe Centers on both Ends. The Shafts were held vertically in the Carburizing Furnaces., say qty 80 at a time. It was always a sight to see them removed and quenched in the Oil Tank – lot of Flames. The Oil Tank had a large Screw (Propeller for the non-nautical Types) in the bottom which churned the Oil to eliminate hot spots.
As SOD says above the Carbon diffuses into the Steel (which is on the order of 97% Iron). The outside Surface would probably be in the Range of 0.90 to 1.00% Carbon. The Carbon would diffuse a good 3/16" into the material but the percentage would be less and less. After quenching, the Axles would be tempered. The 86xx and 93xx part of the SAE number indicates the Alloying composition – 10xx steels have no Alloy Constituents. The Issue arising during Quenching is the Heat Transfer Rate. Some Alloys reduce the required Heat Transfer Rate to obtain proper Grain Transformation. That is the reason many Alloy Steels can be Oil quenched. The advantage of Oil Quenching is slower Grain Transformation which leads to lower incidence of cracking. It also allows the Steel deeper in the part to harden where the Quench Rate is lower than near the Part Surface.
At this point a couple of Gear Teeth would be cut from a test Sample Shaft, about 1/4" thick. I would place the Sample in a Mold, pack it with some sort of thermosetting Plastic, heat it up and press a Plunger to encase the Gear Sample. I would then polish the exposed cross-section of the Gear Teeth on a Lapidary Wheel, Acid etch it and study the Microstructure under Microscope. I would them use a Diamond Point Rockwell Machine to find the location of the 50Rc point of the Case as it transitioned from 62 Rc on the Surface to 28 Rc in the Core. The distance from the Surface to the 50Rc point would typically be .06" (from memory). I made the measurement with the Microscope and recorded it with the Heat Treat Lot.
If the Heat Treat Properties were incorrect, it would be back into the furnace (which could create. another set of problems). Depending on the Manufacturer's Lot of the Steel, the Spur Gear would increase in size which led to annealing the Shaft and re-shaving the Gear Teeth – but that did not happen often. They would make that correction on all further Axles made from that Lot of Steel.
If an Axle required an area to be non-carburized, it would be copper-plated before going into the Carburizing furnaces. It was common for the Customer to specify the Outside Diameter of the Spur Gear to be non-carburized. This prevented chipping of the Gear Tooth Edges. In this Case the End of the Axle was copper-plated before cutting the Gear Teeth.