ASME's acceptance criteria is not as stringent as that used by AWS D1.1. For instance, ASME Section IX has no criteria for undercut, overlap, excessive face or root reinforcement, porosity, etc. Likewise ASME Section IX acceptance criteria for guided bend tests is not as stringent as that of AWS D1.1.
Few Engineers that understand the differences between the two welding codes would accept Section IX qualification in lieu of AWS D1.1 for structural steel applications.
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