So far you havn't got any answer, so I'll give you one.
You can't weld hardened SAE 1040 steel without taking some precautions. After removing the old weld by means of a grinding wheel, first thing you've got to do is to normalize the piece to get rid of the residual stresses resulting from hardening. To do this, heat it up to a temperature above 723 Celsius (called transformation temperature) preferrably into an oven or furnace (using a torch is not recommended). Maintain the piece at said temperature until you're sure that the whole metal has reached it. At this point, take the piece out from the oven or furnace and let it cool down naturally in a closed room, AWAY FROM AIR DRAFTS.
Now you can prepare it for welding, making a bevel or opening a groove, whichever is indicated in your case.
The selection of a stick electrode (or TIG rod) isn't easy. SAE 1040 is a medium carbon steel and there are few electrodes which will suit it. I'd suggest using a low chrome (1,25 percent) stick electrode of E70XX B2 classification, a ferritic structure able to be hardened. A hardfacing electrode must be also suitable, but I havn't got time now to investigate which one.
After the weld is complete, you've got to flame harden it, following the usual methods applied in this operation.
Giovanni S. Crisi
Sao Paulo - Brazil