ToFD flaw through-wall height

A planar flaw that is not surface-breaking produces two diffracted signals: one from its upper tip and one from its lower tip. Each is converted to a depth with the standard ToFD relation d = sqrt((c*t/2)^2 - S^2), and the through-wall height is the difference between them. The lower tip arrives later and, for a crack-like flaw, is normally in phase opposition to the upper tip signal. That phase change is the main confirmation that the two arrivals belong to the same flaw rather than to two separate features.

Working from the two depths, rather than from the time difference alone, is essential because the time-to-depth relation is non-linear. The same time interval represents a much larger height near the scanning surface than it does near mid-wall, so any height obtained by simply scaling a time difference is only valid deep in the wall.

Through-wall height is the parameter that drives acceptance in ISO 15626 and in fitness-for-service assessment, so record the ligament to each surface as well as the height. If the upper tip signal merges into the lateral wave, the flaw is either surface-breaking or lies inside the near-surface dead zone; height must then be measured from the scanning surface or by a complementary technique, and reported as such.

Both signals must be taken from the same probe position, ideally at the apex of the flaw arc in the D-scan. Cursors placed on different scan positions mix in the off-axis error and overstate the height.

S = PCS / 2
d_upper = √( (c × (t_upper − t_delay) / 2)² − S² )
d_lower = √( (c × (t_lower − t_delay) / 2)² − S² )
h = d_lower − d_upper