Low-frequency incremental permeability for the evaluation of deep carburization treatments: Theoretical understanding

Abstract

Precise evaluation of deep carburization treatments is essential to prevent degradation of high-performance mechanical components. A nondestructive magnetic method called low-frequency incremental permeability testing appears to be particularly suitable for this purpose. This method consists of slowly magnetizing the specimen to be controlled and then superimposing a relatively low-frequency eddy current testing process on the specimen (<2 kHz). The sensor’s coil impedance is monitored along with the magnetization cycle. When plotted versus the magnetic excitation, the impedance produced butterfly-shaped curves that were dependent on the carburization depth. Operating at low frequency increases the scanned layer thickness up to the untreated inner part of the specimen and induces characteristic variations in the butterfly-shaped curves. A model to solve for the indirect relationship between the magnetic properties and the carburization treatment properties is presented in this manuscript. This model combines the Dodd and Deeds analytical expression for a flat sensor coil above a two-layer conductor with Jiles-Atherton theory for consideration of the hysteresis. The magnetic and electromagnetic responses are well considered, providing accurate reconstructions of experimental data. The model predictions reveal magnetic indicators that are highly correlated with the carburization depth and provide optimal conditions for nondestructive testing observation.