Plug Welds - Size

You are going to want to put down a 1/4" bead so a 1/2" hole is going to be too small, 3/4" would be better in the 1/2" plate. Also, 3/32" rod is pretty small to be messing around with 1/2" plate.
6013 puts down a thick slag coat that cannot be over welded without slag inclusions. (as you already know!) Plus 6013 does not like to be run as a big puddle, you will get a lot of porosity.
Try 6011 or even 6010 (this is a DC only rod) Doing this in one pass is still going to be iffy unless you go up to 5/32" rod and 200 amps or so.
Robert Snyder wrote:

1/8" 6011 or 6010 would work much better. Run either one at around 110 amps
6013 has very low penetration.
3/32" 6013 is what I would use for seam welds on 1/8" sheet.

To plug weld properly you really need a half inch diameter hole in half inch material at a minimum. A three quarter inch diameter hole with a 3/8 fillet weld around at the bottom of your hole would be best. Whether you fill the hole up is irrelevant. I am wondering what the half inch flat bar is welded to. Sometimes it is more efficient to be plug welding through the possibly thinner material that takes the half inch flat bar? I think using 6011 or 6010 1/8th is a good choice. I have done 5/8 diameter holes in half inch material using E 7018 but there is a trick to it to keep the slag on top floating as you fill the hole up. With ten or eleven the flux is thin. Start by running a fillet around the bottom corner dragging your rod. Keep going around putting your rod into a vertical position and slowly moving around the edge as the weld pool rises in the hole. Let us know which way you go and how well it worked out for you. Randy

Randy,
I tested a 1/8" 6011 DC+ at 120 amps with a 1/2" diamter hole. My test was simply to hit the two 1/2" bars after welding with a hammer to see if they were solid. It appeared very good so I cut it in half with my bandsaw. 100% penetration into the base and full core in the drilled hole. I noticed some porocity near the mid-height of the drill line but generally very good.
I think I need to work on technique because the 1/2" hole is small for my skill level.
Bob

The porosity you mention is irrelevant.. The "strength comes from the bond in the bottom corner all around. By the time you get one quarter inch up the hole and in the center the metal is not being stressed. A good test if you are joining flat bar to flat bar is to do one plug weld and then rotate the bars relative to each other until failure. Examine the break for porosity or slag inclusions. This test will duplicate failure tests done on spot welded sheet metal. It sounds like you have a good plug weld but need to satisfy yourself more. If you need more "stength" then you will have to consider another method of joining. Can you stitch weld teh edges. If the fillets get inthe way then bevel the bar at each weld location before welding. Randy