Yeah, I agree with EdDanzer, AISI 4140/4130 are typically used in the oilfield, but the condition is HRc 18-22.
I've designed and manufactured many of these for various downhole equipment usage in the past fifteen (15) plus years, no problems.
A word to the wise, pay attention to bending stress at the root of the fingers around the collet base. Ensure a very healthy fillet to keep stress concentrations down, the predominant mode and location of failure. You can very easily compute stresses using Circular Beam Theory or get an estimate from cantilever analysis and using end beam or tip deflection as your variable input. I have found that my mathematical analysis, particularly pull-out force, stab-in load, etc mimick reality in lab experiments.
Good luck with the design!
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada