9/16" annealed 4140 will bend almost as easily as cold rolled.

BTW: there is a major advantage to the annealed 4140 in impact strength
.......... but it only shows up in the -40F and below range. Sorta doubt
you will be out on a motorcycle at that temp.

Jordan wrote:
I made a rear axle for my rigid-framed motorcycle out of 4140 steel, and
the thing bent in use. I was advised that heat-treatment was optional,
but not really necessary, so I didn't do that. Was this advice wrong?
The axle diameter is 9/16", and bike weight = 375 lbs. I do sometimes
hit the odd pothole, but nothing major.

Jordan