Most materials deteriorate or degrade as they age. It is assumed that most things fail when their degradation reaches a specified threshold. However, the material condition assessment using nondestructive tests is, in most cases, still an open problem, especially when we are faced with situations that are at the limit of the detection capabilities of the commercial equipment currently available.
This paper proposes a technique to surpass this problem. It proofs the possibility to inspect a material in a stretched geometry with an eddy current method (ECM) using a formulation of the scale invariance principle theory. In the scale transform domain, the stretch factor of signals can be manipulated in order to compute quantities invariant to changes in that stretch factor.
Let’s detail the idea by assuming possible scenarios. For example, if the aim is to detect a crack on the surface of a metallic plate by inspecting the material through the opposite surface. We may start by performing measurements at the laboratory with a scaled model to detect a crack with a given length in a plate of the same material having a thickness k times smaller than the original one, using a probe with a given geometry where the excitation current with a specified amplitude and frequency runs. If tests within this reduced model are successful then, this paper proves, that it is possible to perform the targeted inspection of the metallic plate to detect a crack having a k times length using a scaled probe increased the same k scale factor with the excitation current increased k times and the frequency reduced k2 times.
Another application of this field dilation invariance can be the use of ECM for the characterization of the microstructure transformation that occurs in the reforming furnace columns used in the petroleum refineries. Again the idea is to evolve from successful tests performed at the laboratory with a coil with reduced dimensions to the inspection of large tubes using a scaled coil that keeps the magnetic field invariant in the scaled domain.