Eddy Current Measurements
on Case-Hardened Steel

It is well known that steel components are often heat treated and carburized to produce a case-hardened surface layer that improves resistance to wear. This is an important industrial process that we all derive direct benefit from. Crankshafts, valves, gears, piston cylinders and so on, last much longer because of the benefits of case hardening. However, it is always possible that the process will go wrong, hence, there is a need to check the results to be sure that products will be wear resistant. A test that is fast and nondestructive is preferable. Although both ultrasonic^[1] and electromagnetic^[2] methods have been developed for the task, the quest for a better solution, like the search for a better mousetrap, continues. At the request of Eaton, a participant in CNDE's National Science Foundation Industry/University consortium, Marcus Johnson, Nicola Bowler, and Haiyan Sun undertook a project to develop a nondestructive device for the measurement of carburized case depth. 

Diffuse case hardening is usually carried out by packing the steel with carbonaceous material and raising the temperature to around 920C for a time depending on the desired case depth^[3]. This is followed by quenching and tempering. The initial treatment temperature is above the point at which carbon steel undergoes a phase transition from ferrite, which has a body-centered-cubic structure, to austenite, which is face-centered-cubic. In the austenite phase, it readily absorbs more carbon so that after quenching, the steel develops a case of different carbon content, able to be hardened to higher hardness. It also forms a martensitic structure due to thermal stresses near the surface as the steel is plunged back to room temperature^[4]. After quenching, it is usually too brittle for most purposes but tempering brings some of the carbon out of solution and improves the toughness.

From this brief glimpse of the case hardening process, it is evident that a number of things can go wrong. For example, a delay between carburizing and quenching will cause the temperature of the steel to fall before it is quenched, leading to a reduction in the hardening effect. If the tempering is not effective, then the part may remain brittle with undesirable consequences. In these circumstances, brittle gear teeth can break off causing an engine or gearbox failure. If the temperature is not properly maintained while carbon diffuses into the steel, then the case depth will be incorrect and there could be a presence of the high temperature phase called retained austenite. Such potential problems demonstrate the need for NDE. 

Estimates of case depth can be made using ultrasonic time-of-flight measurements. These rely on reflections from the transition zone between the case-hardened layer and the core. Multi-frequency eddy current methods have also been used to determine case depth and, in addition, they can give estimates of hardness. The usual technique relies on measuring eddy-current probe signals first on a sample batch with known properties whose pretreatment properties are similar to those of the test samples. The batch data is used to establish a statistical correlation between eddy current signals and the post treatment material properties. These are then used to estimate the properties of an unknown sample. The work presently being conducted at CNDE attempts to get around the need for a sample batch of known properties by finding material parameters by matching probe signal measurements with model predictions. Initial results are for cylindrical steel rods.

Figure 1: Case hardened layer on a cylindrical steel rod.

The basic model assumes that the material consists of a single layer with no transition zone between the layer and the core (figure 1). Probe signals are predicted from the eddy current probe parameters and five material parameters; the conductivity and permeability of layer and core plus the layer thickness^[5]. Eddy current measurements have been made on rod specimens, provided by Eaton Corporation^[6]. These are 50 cm long and 11mm in diameter and can be used for both inductive eddy current measurements (figure 2) and for potential drop measurements (figure 3), the latter providing independent data on the conductivity. In fact, the potential drop measurements have been carried out using both direct and alternating current with consistent results.

Figure 2: Case hardened rod and an encircling coil.

The theoretical approach adopted here requires precise control of all relevant parameters in order to be successful. The probe must be well-characterized and the number of unknown sample parameters must be reduced to a minimum. By choosing specimens with cylindrical geometry, it is possible to measure the material conductivity directly. This reduces the number of unknowns sufficiently to allow model-based parameter fitting to work successfully.

Eddy current coil impedance measurements were first made on a demagnetized rod that had been heat-treated without a curburized case and, hence, had the same microstructure in the core as the carburized rod (referred to, hereafter, as the reference) whose conductivity, 3.9 MS/m, was measured using the four-point approach (figure 3). The value of permeability was adjusted in the model until a good fit was obtained between theoretical impedance data and experimental measurements. The best-fit value for the relative permeability was 70.

Impedance measurements were then made on demagnetized, case-hardened steel rods. Assuming that the core has the same conductivity and permeability as the reference rod (3.9 MS/m and 70 respectively), the surface-layer depth, surface conductivity and permeability parameters, were adjusted to obtain the fit to experimental data shown in figure 4.

Figure 3: Measurement of conductivity using alternating current potential drop measurements.

The very good fit between theory and experiment shown in figure 4 is obtained by assuming that the conductivity and permeability of the substrate are the same as those for the reference steel rod, obtained by experiment on a soft steel rod.  This approximation allows two of the five material parameters in the theoretical model to be constrained so that only the remaining three must be adjusted to obtain a good fit between theory and experiment.  The method is apparently successful since the value obtained for the surface layer depth, 1.5 mm, agrees with the nominal value for the specimen.

Figure 4: Comparison between theory and experiment for eddy current impedance measurements on a case hardened steel rod. The theoretical curves shown here are obtained by fixing the conductivity and permeability values of the substrate to be the same as those found for the reference steel rod. The thickness, permeability and conductivity of the layer are then adjusted to obtain the best fit to the experimental data, as shown.

In summary, the depth of a case hardened layer in a steel rod has been determined by adjusting relevant parameters in a theoretical model and comparing calculated impedance values with experimental data obtained from a coil encircling the rod. These results indicate that the simple, single-layer model adopted here is sufficient to describe the structure of casehardened steel. In future work, however, a more complicated model may be considered. For example, the material properties could be allowed to vary continuously with depth^[7].

This eddy current procedure shows promise as a way of measuring case depth in case hardened steel. An advantage of the present eddy current method is that no comparison samples are required for reference. Tests on rod specimens have been successful but further work is needed to apply the procedure to samples with different shapes.

1.  http://www.sonix.com/ndt/products/umapaper.htm

2.  http://www.foerstergroup.de/ct/e_ct.html

3.  http://www.newmex.com/ebear/metal/heattreat6.html

4.  http://www.mintek.ac.za/Physmet/intermet/heatreat.htm

5.  Dodd, C. V. and Deeds, W. E., J. Appl. Phys. 39, 2829 (1968).

6.  Our thanks to A.Ahmad, Eaton Co., Southfield, MI, for providing the specimens.

7.  Theodulidis, T. P., Tsiboukis, T. D. and Kriezis, E. E., IEEE Tans. Mag.,31(3) 1995).

For further information, contact John Bowler. 

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