Advice on which grade of steel

John You will need to heat treat the finished collets for them to have the required strength and springiness. I have made small ones in silver steel but have done well with EN8 in larger ones. I would also say that it is not all that easy to make a good true running collet but my method is this- 1 chuck the bar in the lathe and turn the outside profile in one setting 2 counterbore the reverse if needed 3 drill the hole undersize 4 bore the hole 5 ream the hole 6 part off about 3/8" too long 7 hold in chuck in dividing head and mill the slits but do not take them ino the 3/8" wide band at the front, in this way the collet is still rigid 8 heat treat 9 grind front face to release the segments. PM me if you dont understand Peter

Try the shanks of high tensile bolts.
jsw

I like EN24T (Pre-hardened EN24 to about 24HRC). It machines nicely because it's hard enough not to be gummy. If you can quench it in oil from 850C, it'll give you 62HRC with no significant distortion (I couldn't measure any in the test pieces I've done).
Mark Rand RTFM