3/8" thick A36 is pretty dang hard to screw up(via too much heat input from welding).....however if the welder is welding with the machine too cold, you can have coupon problems when welding with wire.
In my experience the grinding marks can start or initiate the cracks that you see, so just because they are deep doesn't rule out that they didn't come from the improper grinding direction. Coupon preparation can make or "break" the welder's test. Also the heat from improper grinding can cause surface cracking.
Hello spots, there are a number of things which could possibly give the indications that you are seeing as you have described them. First off, are you certain of the grain of the test pieces? If the grain is running the same direction as the weld joint you may see some "cracking" and in some cases you might even find some serious fractures. As you mentioned additionally, the grinding lines/marks, if they are ground with the marks in the same direction as the weld joint you could see additional possible indications/fractures. If the test pieces are being made from plate and the direction of rolling isn't apparent/known you could very well have issues come from this that aren't the fault of the tester. If you are using flat bar, even if it is correctly oriented it may exhibit some of this surface tearing due to the manufacturing process, in some cases, due to the size of the bar it will be subjected to a more rapid cooling rate than plate would be and this can have an effect on how it might bend or it's level of brittleness (a possible contributor to surface cracks).
There are some of the folks on the forum that have done some testing concerning arc strikes and such and have polished up bars with arc strikes on them and shown the effects of these problems regarding tearing (if you have seen arc strikes outside of weld zone, these would very likely show up as discontinuities and would justify a break-out), there have been others that have bent pieces with the grain going the wrong direction, I have bent pieces that I have ground the wrong way and found issues, I have also scribed lines across pieces and found issues with cracking related to that practice and many of these pieces didn't even have a weld in them they were simply a piece of flat bar of the same size as a test piece. I would leave you with one final thought, consider that cracks outside the area of the weld deposit are typically not an indication of the welders level of electrode application and manipulation skills. If there are cracks that are there due to excessive heat/incorrect prep and such then these might be due to not following the WPS that has been provided, this might lead you to question their skills with following this document and might justify a break-out. Personally, I tend to disregard indications outside of the actual weld zone as long as I can determine that they aren't related to the fusion line between the weld metal and the parent metal or have anything to do with an arc strike. Even though you are using A36 material, I wouldn't allow or get used to doing any rapid cooling of the test pieces, in other words I wouldn't dunk them in water. Technically speaking this shouldn't effect the test pieces due to their relatively low carbon content, yet, I believe you will find this to not always be the case. In D1.1 I believe there is a statement that speaks to cracks that don't exhibit any slag or lack of fusion and allows an additional coupon to be taken. So depending on your interpretation of this you might take this into consideration as well. I believe you will be receiving additional comments on this topic so stay tuned and make your best call after you have considered all of them. My $.02 Best regards, Allan