Hello doyenofcastle:

I'm no expert and I hate to be an "armchair" consultant on something like this, but since you asked, I'll do my best.

Make sure the shaft is in the annealed condition before attempting to weld it. Use a hand file on the shaft to make sure you can "take a cut". If the file glides over the surface of the steel without cutting, it is too hard to weld in the current condition. A hand file will give you a good feel for the hardness of the shaft.

Verify the  entire crack is removed by using wet fluorescent magnetic particle testing to test the excavation before beginning your preheat. The excavation should extend pass the crack tip by about 50 mm. While grinding, don't let the shaft heat up be more than 80 C. Grind from beyond the crack tip toward the center-line and repeat from the opposite crack tip. Grinding hard and heavy can cause the shaft to heat up locally and cause the crack to propagate.

It appears you are welding it with low hydrogen shielded metal arc electrodes. That is good, but the AISI 4140 is highly hardenable if the preheat isn't sufficiently. Hydrogen introduced into the weld puddle is one of many enemies you have to control. To minimize the diffusible hydrogen, I would suggest that any low hydrogen electrode be baked before use. I would suggest the bake-out temperature to be about 400 degree C for one hour before use. A rather short window for exposure is recommended. No more than 1 hour out of the "hot box" or electrode holding oven. An alternative to low hydrogen shielded metal arc electrodes is to use GMAW spray mode transfer or GTAW (very uncomfortable welding) due to their use of bare filler metal, i.e., no flux coating to absorb moisture, thus they are considered to be low hydrogen welding processes.

The AISI 4140 has a very high CE, so high preheat is required. The diameter is large as well, so it offers high restraint, thus a second reason to use very high preheat. I would consider something on the order of 370 degrees C and a stress relief post weld heat treatment. SR would entail heating the entire weldment to about 620 degrees C for about 25 hours (1 hour plus 1 additional hour for each 25 mm of thickness). Slow cool after stress relief. Preheat must be maintained during the entire welding cycle.

You are contending with very high restraint. From a strength standpoint, you want the weld to be as strong as the base metal you are welding, but the residual stresses are causing transverse cracks. I would suggest considering using a lower strength low hydrogen electrode such as an E9018-H4 or ER90S-X. This is a repair, so something is better than nothing. The lower strength electrode will allow the weld metal to yield as it cools without over stressing the 4140 shaft and causing transverse cracks to form. Something has to "give" when you make a weld. Either the weld has to yield, the shaft has to yield, or a crack is going to form. The shaft isn't going to yield, it is too thick and too strong. You have to allow the weld to yield without the weld or shaft cracking as a means of accommodating the residual stresses in the base metal that are of the same magnitude as the yield strength of the base metal (C4140) at temperature (a moving target as the base metal cools and the magnitude of the residual stress increases).

This shaft isn't a good candidate for a field repair. A shop where proper annealing can be performed, oven preheating, and stress relief capabilities are needed to ensure a successful repair. A field repair is very difficult to do because of the high preheat and soak times (let me repeat myself; soak time) required to ensure the entire shaft is uniformly heated to the minimum preheat temperature. You should consider wrapping the shaft with insulation to retard cooling and to make life a little more bearable for you (the welder) during the welding cycle.

The Ms is about 350 C and the Mf is about 330 C, so a preheat of about 370 C is about right to ensure the austenite doesn't decay to form hard martensite. The idea is to retard the cooling rate from the highest temperatures attained while the weld bead is still liquid and the HAZ is austenized down to the preheat temperature which is above the Ms temperature. Hopefully the cooling rates are sufficiently slow to allow the austenite to transform (decay) into something more benign, i.e., not as hard or as brittle as the martensite.

One last thought. Use run-off tabs at the end of the crack excavations so that you can initiate and terminate individual weld beads on the tabs that can be cut off when the weld is completed. The run-off tabs are welded to the shaft after the shaft is preheated to the proper temperature. See attachments below.

You have a Tiger by the tail my friend.

There may be someone reading this that has ideas of their own. Their council may be worth considering. Good luck.

Best regards - Al