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Sometimes we have to do High Frequency Eddy Current (HFEC) or Low Frequency Eddy Current (LFEC) inspections. My question is: what are the major differences between these two types of inspection? Which one is preferable and more economical? Which type of inspection is required in which cases?

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In general, higher frequency gives better resolution of potential defects but with lower penetration into the material (depth). So HFEC is used to detect surface defects and near-surface defects, but LFEC will be required to detect deeper defects.

From this page on the NDT Resource Center website:

The depth that eddy currents penetrate into a material is affected by the frequency of the excitation current and the electrical conductivity and magnetic permeability of the specimen. The depth of penetration decreases with increasing frequency and increasing conductivity and magnetic permeability. The depth at which eddy current density has decreased to 1/e, or about 37% of the surface density, is called the standard depth of penetration (d). The word 'standard' denotes plane wave electromagnetic field excitation within the test sample (conditions which are rarely achieved in practice). Although eddy currents penetrate deeper than one standard depth of penetration, they decrease rapidly with depth. At two standard depths of penetration (2d), eddy current density has decreased to 1/e squared or 13.5% of the surface density. At three depths (3d), the eddy current density is down to only 5% of the surface density.
Since the sensitivity of an eddy current inspection depends on the eddy current density at the defect location, it is important to know the strength of the eddy currents at this location. When attempting to locate flaws, a frequency is often selected which places the expected flaw depth within one standard depth of penetration. This helps to assure that the strength of the eddy currents will be sufficient to produce a flaw indication.

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