I got a few short lengths of three-quarter inch thick round bars of 4140 steel lying about, thinking of making an axe head or something with them. Can I work these in a forge?

Yes.  But they might make better tooling.

It is done all the time! 3/4" round bar is too small for most axes though! I would likely begin with about 1" for tomahawks... bigger for most other axes! People do make tomahawks from railroad spikes, which are only 5/8" square... but I think they are too skinny at the eyes!

So size aside, there is nothing wrong with the grade of steel?

4140 forges nicely as long as you pay attention to temp. If forged too cool it cracks rather badly. My big demo anvil for striking demos is a forged 4140 axle intended for a rough terrain loader. It has a 20" flange about 3" thick forged in 4 hits on a 10" upset forge machine.

makes great tooling and not as great blades; I prefer higher carbon contents to have more carbides for edge retention myself for blades---even axes

One has to define the use of an axe, first is it intended as a tool of a weapon? A tomahawk intended as a "woodsman axe" would do well with a 24" handle, and a head 6" long, 4" edge and 1/4" threw most of its length. Weighing somthing like 2 1/2#. But frankly this would be to heavy for a weapon. A batle axe with a 32" handle only sported a 1 1/4# head (same outside dementions of the above head but much thiner) Making it neir as weildy as a sword. A tomahawk intended for fighting would be somthing like 18" handle, 4" edge to center of eye, edge 2 1/2" orso 3/16-1/8" thick. If one splits and drifts a spike, it can be drawn thiner and deaper on the drift, as most end up with the cheaks of the eye being to thick. The tomihawk pictured is not a spike hawk, but it is what I moddel my fighting haks on. Wile I model my woodsman hawks on a swedish military 3/4 axe. I would model a batle axe on the larger head, but it would be much thiner.
So you can make a wepon, out of that stock, but to what perpose? It is a better piece of stock used for tools.

You have to keep it in perspective. 4140 is MUCH BETTER axe stock than railroad spikes! 1095 is probably a bit better though! I could be quite happy with a 4140 axe for rough work around the farm! I would much prefer a higher carbon steel for my carving axes! I use lower grade steel for my ice axes that I chop holes in the water troughs with! So much depends on the intended uses and user preferences! The blade design is also an important factor... My ice axes have small very thin blades with integral handles. Ice is very hard and a steep bevel on a thick blade makes for a lot more work! I make the ice axes with fairly long handles so that I can reach through the fences to cut the ice... Small light heads allow for easy wrist swings that can hit the same slot over and over... Cutting even a foot of ice in just a couple minutes!

I have made several axes out of 4140, but you have to understand the limitations of the steel. It can theoretically get to mid-50 RHC, and I pretty much temper it at 375 just to stress relieve. I used it because I had it. If I had had 5160, or 1050, I would have used that first.

I used to go winter camping allot more than I do now, and frequently chipped knives and axes chopping though frozen wood. That's where I used my 4140 axe. It's tough as hell, and easy to sharpen in the field.

Thanks for the replies guys, appreciate it :) .

4140 rounds, 2" dia (which I have  B) ) is more like axe material.  But you'd better have a hefty power hammer to forge it down ^_^

you could make a leaf hammer, 4140 is good steel for a lot of tools.

4140 is a great steel, used for a multitude of uses.  if you had enough of it in all the various sizes/lengths....you really wouldn't need any other steel

Yes it would make a good leaf hammer! In larger sizes it's a good choice for many types of hammers! Works well for punches, headers and such, as well!

the thing to remember is 4140 is a medium carbon steel. For a good edge you want a high carbon steel. 3/4" stock would make some very nice tongs.

Clifton Ralph has said that in the steel mill blacksmiths shop he worked in, 4140 was the default tool steel, they made almost all the tools out of 4140. They would forge or fabricate the tools and would use it just normalized or they would harden and then temper to nearly 1000... If I remember correctly, seems they were more worried about something fatiguing and exploding in their faces, than the prospect of having to make a new one.  This was for struck tools, hacks, flat backed fullers, side sets, "furniture", swages, and spring fullers.  A lot of the tongs were made out of coil spring.

one of the best tongs I have was made by JJ (Jim Joyce) out of sucker rod..........wished he woulda made me a full set....... :unsure: