Let me describe a couple of golf-ball caliber mortars of mine for a reference point.
First, although I have some that are MORE robust, is a hand-held chunk of 4140 - overbuilt.
Bore 1.70, depth of 3.3"
OD 2.7" Length: about 7"
Fuse hole .2" dia.
Powder chamber of about 3/4" x 3/4".
Range from 100-200 yards with one or two .45acp cases filled with FFFg.
Kick is about like a .38 special with a golf-ball.
Firing 2 at a time - top golf-ball will go further.
Second, made as a part of our mortar building contest, is made from 1144 stressproof DOM tubing and a 'round' of 1144SP cut to fit into the muzzle and moved to the rear containing the powder chamber. Fuse hole is drilled through both, taken apart and cleaned after each use.
Bore 1.70, depth of 4.38"
OD 2.0" Length: about 7"
Fuse hole .15" dia.
Powder chamber of about 7/8" x 3/4".
Considerations:
1. range - 400 yards is do-able but with golf balls would be tough to track them. To get longer range keep bore diameter to 1.7" (not 1.75), keep fuse hole to minimum diameter. For strength (safety) use a powder chamber. Plan on some idot using a steel or lead ball and build it accordingly. The second one may well be questionable with anything else other than a golf-ball.
Making the length of the bore perhaps a foot long should make achieving 400 yards easy with lower pressure (use FFg or Fg powder to utilize longer burn time).
2. Plans for the second one are in the thread on the mortar-making contest. I may be able to dig up another set of materials (less the oak) if you want to cover my shipping costs (I just mailed one out today.).
3. Inexpensive and DOM don't fit together, unless you find some scraps. I get mine out of the scrap box at work, it varies from week to week and the pieces are generally about 7" long and need to be bored out to 1.7" ID.
4. We've had extensive discussions about proofing - check the search function and read up. To me, proofing is a testing of the DESIGN. Use a good design and the right materials you won't go wrong. (Add welding and/or casting and life is more complicated.) IF you REALLY want to know where the failure point is build 3. Keep increasing the charge until the first one blows up. Reduce the charge and repeat it MANY times on the second until it fails. Then you know how much you can abuse the third one.
5. Books - hmmm. THere are a number of articles (See the REFERENCES sticky) about using mild steel in cannons (1840-1860 vintage) when the strengths of mild steel were first discovered. There is a LOT out there, spread between MANY sources. Suggest reading up on work hardening, charpy notch tests as well as tensile strenghts, hoop tests.
1.7" bore diameter will require a little cleaning between rounds and there are some odd size golf-balls that are a little big for it.