Unfortunately bike axles don't have markings on them so you can't work backwards to easily ID their material.
As a general rule shafts, axles, studs, bolts are made from 4140 high tensile steel or it's various equivalents. This is the workhorse construction steel supplied in a hardened and tempered condition but able to be taken to much higher strength and hardness without reducing it's toughness or fatigue resistance when required.
Judging by the way it machines, many motorcycle wheel axles are made from 4140 HT or a proprietary equivalent. Highly loaded bolts, like the swingarm pivot fasteners on a linkage bike can be a lot harder and stronger- more like a socket head cap screw aka Allen bolt which are the strongest most fatigue, resistant commercial bolts available.
4140 is readily available but the suppliers get a bit sniffy for non account holders wanting less than a length; which is normally about 6 metres. Still, it's worth trying Bohler Steel, Global Metals, Steelmark Eagle and Globe, Ian Stansfield Smith in Melbourne, and the like for some- you might get an off cut, or a rod that is downgraded and put aside because it is bent. Typically 4140 would probably sell for about 4 to 5 bucks a kilo retail making 20 mm rounds for axle stock about $10 a metre.
