Limit frequency for rod and tube testing

Encircling coil testing of rod, bar and tube behaves the same way for every diameter and every material once the frequency is expressed as a ratio to the limit frequency fg, defined by Forster as the frequency at which the dimensionless group a^2 . omega . mu . sigma equals 1 for a solid cylinder of radius a. In engineering units that becomes fg = 5066 . rho / (mur . d^2) hertz, with resistivity in uohm.cm and diameter in mm. At the limit frequency the standard depth of penetration is d/sqrt(2), so the whole cross-section is still strongly energised.

The point of the normalisation is that it predicts behaviour. Forster’s impedance-plane diagrams for rods and tubes are plotted against f/fg, so once the ratio is known you can read off where the operating point sits, how the crack signal is oriented relative to the diameter and permeability directions, and whether raising or lowering the frequency will improve separation. In practice bar and tube lines run at several times the limit frequency, because at low ratios the coil sees mostly conductivity and diameter and the crack response is buried in them.

For a tube the second parameter is the wall: the diagrams are indexed by f/fg computed from the outside diameter together with the diameter ratio di/do. A thin-wall tube (ratio near 1) behaves very differently from a heavy-wall tube at the same frequency ratio, so both numbers have to be quoted.

Use this when setting up an in-line encircling coil, when comparing a proven set-up on one product size to a new one, and when a signal that worked on one heat of material collapses on another – a permeability or resistivity change moves fg, and therefore the operating point, without anything on the instrument having been touched.