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I have a question or two about what you are finding out about your welds. First, Is the nut failing and thereby not meeting requirements?
Second, Is the weld failing (or the base material failing) to hold the nut and thereby not meeting the requirements?
I have ran into fastener problems and found that high strength fasteners can fail when welded due to the heat changing the heat treat of the high strength bolt/nut.
John Wright
PS. Also supply the process used and filler material/base material ASTMs and thicknesses and what parameters you have tried and does not work.