ACPD in Detail

Crack Sizing

Crack sizing using the ACPD technique is best carried out using theoretically-derived results applicable to real fatigue cracks. Use of notches in calibration blocks should be avoided if at all possible.

Thin-Skin Sizing

The simplest sizing procedure applies in the thin-skin case when the crack is long compared to both the crack depth and the voltage probe spacing. Long in this case means more than 5 times greater. In this case the electric field strength, E, is constant so that the reference voltage is given by:

Vr = EΔr

where Δr is the voltage probe spacing when measuring the reference voltage. The cross-crack voltage is given by:

Vc = E(Δc + 2d)

where Δc is the voltage probe spacing when measuring the cross-crack voltage, and 2d represents the extra current path length introduced by a crack of depth d.

Eliminating E from these two equations, the crack depth is thus given by the following simple formula:

d1 = Δr/2 (Vc/Vr - Δc/Δr)

The crack depth will be given in the dimensions used for the probe spacings. In most cases the two probe spacings will be equal (Δr = Δc = Δ) so that equation simplifies to:

d1 = Δ/2 (Vc/Vr - 1)

For example, for a probe of spacing 10mm, a cross-crack voltage of 800 and reference voltage of 400 indicates a crack depth of 5mm.

The subscript 1 indicates that this is the so-called 1-dimensional depth estimate. This first estimate of depth is only strictly true for the conditions of long cracks in a thin-skin, but it is also used as the starting point for all defects. In these cases, this initial estimate is modified to take account of the pertaining, such that the true depth d is given by:

d = Md1

The modifier, M, is in general a function of probe spacing, probe position relative to the crack, surface breaking crack length, 1-dimensional depth estimate, skin depth etc.

The most often used thin-skin modifiers are those for sizing short cracks. It is generally assumed that such cracks are semi-elliptical in shape, although circular arc or rectangular cracks can also be treated. Theoretical modelling has produced a series of graphs and look-up tables of the shape modifier M. Other modifiers are also available to take account of corner cracks, crack bridging etc.

Thick-Skin Sizing

A similarly simple equation for crack depth applies at the thick-skin limit when the crack is long compared to the depth and the probe spacing, and the skin depth is large compared to the crack depth. In this case:

d = Δ/2 (Vc/Vr - 1)(Vr/Vc)1/2

For example, for a probe of spacing 10mm, a cross-crack voltage of 800 and a reference voltage of 400 indicates a crack of depth 3.5mm.

The above depth estimate can be related to the 1-dimensional thin=skin depth estimate by d = Md1 in which M = (1 + 2d1/Δ)-1/2

In a similar way to the thin-skin case, modifiers have also been computed to take account of short cracks, inclined cracks etc.

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