Undercut is term associated with welding. While providing circumferential weld on small bore pipes in field, welder usually stop and start welding at frequent intervals. Moreover the electrode angle is changed several times because it is difficult to weld small bore pipes with same electrode angle. Doing so there is a tendency to undercut the previous weld.
This tendency (undercut) can be eliminated by grinding the weld surface.
Note that weld with undercut have higher SIF values (refer B31.1 Appendix D Note 11).