Tube wall loss from phase angle

In bobbin coil tube testing depth is read from the phase angle of the flaw signal, not from its amplitude. Eddy current phase lags progressively with depth, so an OD-initiated flaw signal is rotated relative to an ID-initiated one of the same severity. Amplitude, by contrast, is dominated by the volume of missing metal and by fill factor, so a long shallow OD groove and a small deep pit can give the same height on the screen while sitting tens of degrees apart in phase.

The relationship between phase and depth is real physics but it is not a straight line, and it is not the same for every tube size, frequency, probe or instrument. That is why every procedure requires a calibration curve to be constructed from the reflectors machined into the applicable calibration standard: the signal from each known-depth reflector is rotated to the required convention, its phase recorded, and a curve of phase against percent through-wall built for that exact set-up.

Depth is then read by interpolating between the two calibration points that bracket the measured angle. Interpolating between adjacent points is standard practice and is acceptable because the curve is smooth over a short span, but extrapolating past the shallowest or deepest calibration reflector is not - the curve flattens at both ends and an extrapolated depth can be badly wrong in the direction that matters.

Use this at the analysis station to convert a phase reading into a reportable percent through-wall and a remaining wall, and to check by hand a depth that automated software has assigned. If the measured angle falls outside the calibration bracket, the answer is to re-run the calibration standard at a frequency that brackets it, not to extrapolate.

%TW = d_a + (theta - theta_a) x (d_b - d_a) / (theta_b - theta_a)
depth [mm] = wall x %TW / 100
remaining wall [mm] = wall - depth
cross-check from first principles: theta [deg] = 57.3 x depth / delta