Alternating Current Potential Drop for Measuring the Case Depth of Hardened Steel

Transcription

1 Alternating Current Potential Drop for Measuring the Case Depth of Hardened Steel Mohammad R. Quddes a), Yuan Ji, and John R. Bowler Department of Electrical Engineering, Iowa State University and Center for Nondestructive Evaluation, Applied Sciences Complex II, Ames, IA 011, USA a) Corresponding author: Abstract. Multi-frequency alternate current potential drop measurements have been made to estimate the case depth of case hardened steels using four point probes. The probes have four parallel sprung loaded pins in a line with a 1.5 mm separation between the contact points. A printed circuit board has been used to ensure the electrical connections to the pins are close to the surface of the material. This has the effect of reducing the mutual induction between driver and pick-up pins. The case depth is estimated from measurements at frequencies typically from 10 Hz to 10 khz. The real part of the voltage phasor representing the AC potential drop is used to evaluate the case depth. The imaginary part includes the contribution due to mutual induction. To estimate the case depth of the hardened samples, the measured potential drop has been fitted to theoretical predictions. The substrate material properties of the hardened samples are extracted from multi-frequency potential drop measurements on non-harden samples. The estimated case hardened depths, deduced from potential drop measurements, are similar to those found from destructive measurements. INTRODUCTION The theoretical development of the alternating current potential drop (ACPD) technique has been established for over a decade to characterize materials [1]. While direct current potential drop techniques are in often use in NDT applications, geo-physics and in semiconductor technologies [2-4], the ACPD technique can also be applied to extract more information. Four point probe measurements have been carried out to demonstrate that the conductivity of a metal plate can be obtained accurately from low frequency measurements, for example in the range Hz [5,6]. A theoretical model of the field in a uniform half-space [1] has been extended to approximate the effect of a case hardened metal surface. Using predictions from this model, estimates of case depth have been determined [7]. There are advantages in reducing the pin separation to allow the measurement of the material properties of narrow specimens while limiting edge effects. In addition, the low frequency potential drop increases as the inverse of the pin separation with a consequent improvement in the signal to noise ratio. Reduction of pin separation is also advantageous in measuring the effect of small cracks at a metal surface. In this paper, experimental results using a four point probe will be given for two different specimen types; cylindrical specimens and cantilever bars. From these measurements the case depth has been estimated using single uniform layer model of the case hardened region [7]. PROBE DESIGN The probe, shown in figure 1, is housed in a stainless steel tube, length 120 mm and diameter 15 mm. The steel body reduces electromagnetic interference on the driver and pick-up cables. The key feature of the new probe is the pin separation of 1.5 mm. This dimension approaches the minimum distance that can be achieved easily while using

2 brass bushes to hold the spring loaded pins accurately in position. The bushes are soldered into a printed circuit board (PCB), figure 1. To hold the top end of the 4 pins, another PCB board has been used. PCB traces are used to connect to the pick-up pins near surface of the sample, which ensures the mutual inductance between the diver and pick-up circuits is kept within reasonable bounds. FIGURE 1. The proposed probe design, the probe, the driver and the pick-up pin assembly. MEASUREMENT SETUP AND PROBE PERFORMANCE The probe characteristics have been compared with those of a previously developed 3 mm pin separation probe. Using both of the probes, the material properties have been extracted for a non-case hardened cylindrical ferrous steel specimen. The measurement setup is been shown in figure 2. The heart of the measurement system is a lock-in amplifier from Stamford Research Systems. The signal voltage, supplied by the lock-in is connected to a transconductance amplifier whose output passes through a sampling resistor. The drive voltage is set to ensure that a 1 Amp alternating current is delivered to the probe. The two outer pins are used for current injection into the metal surface and the inner pins pick-up the potential drop, figure 1. The inner two pins are connected to the lock in amplifier to measure this voltage. A switch box is used to select either the voltage drop across the sampling resistor or the potential drop connection since both must be measured. In addition, the switch box reverses the connection to the lock-in to minimize the common mode error in the signal measurement. FIGURE 2. Measurement setup. Multi-frequency measurements of potential drop for a known current have been carried out on the specimens of pyrowear 53 and 9310 steel in the frequency range from 10 Hz to 10 khz. The real and imaginary parts of the measured potential drop are shown in figure 3. The real parts of the potential drop at the low frequency differ by a factor of 2 because of the reduction of pin separation by a similar factor in comparing results obtained using the 3.0 mm pin separation probe with that using 1.5 mm separation. Material properties are extracted from the analytical model by exploiting non-linear regression method of MATLAB. The quasi-dc region has the conductivity information [1] and the high frequency response depends on the product of conductivity and permeability. Thus the

3 two material parameters can be separately determined. The fitted curves match the measurement accurately for both probes, figure 3. The material properties obtained from each set of probe measurements are listed in Table 1. The electrical conductivity of the pyrowear sample has been found to be 3.19 MS/m and the relative permeability 114, using 1.5 mm probe. These material properties are close the values obtained by using 3 mm probe; 3.18 MS/m and 106 respectively. TABLE 1. Material properties of non-hardened region of a pyrowear specimen. Pin Separation 1.5 mm 3 mm Conductivity 3.19 MS/m 3.18 MS/m Relative Permeability Potential Drop [ V] Measured: 1.5 mm Cal.: 1.5 mm Measured: 3 mm Cal.: 3 mm Potential Drop [ V] Measured: 1.5 mm Measured: 3 mm FIGURE 3. Potential drop measurements on the non-case hardened region of a pyrowear specimen are shown: The real part of the potential as a function of frequency together with curves derived by fitting model predictions to experimental results The imaginary part. 80 Potential Drop [ V] FIGURE 4. To observe the edge effect, the measurement footprint from the edge, the real part of the potential drop. To have a good agreement between the theoretical model and the measurement, the edge effect need to be considered. To evaluate the edge effect on the pick-up potential drop, a series of measurements have been recorded for different distances, d [mm], from the edge of the specimen between the frequencies 10 Hz to 10 khz. For clear visibility, the data have been plotted from 10 Hz to 1 khz. The real part of the potential drop is been shown in figure 4. It is clear that the pin distance from the edge needs to at least 3 times the pin separation, while the error falls Distance from the edge, d [mm] 4 5

4 below 1% for all the frequency range. As the pin separation of the probe is 1.5 mm, the minimum distance from the edge required to be about 4.5 mm. CASE DEPTH ESTIMATION After validation of the new probe performance, measurements have been conducted for two different specimens and case depth information has been extracted. Cylindrical specimens of 9310 steel were provided by AlphaSense, Inc., shown in figure 5. And cantilever bars of pyroware 53 were supplied by Boeing, figure 5. To estimate the case depth of the specimens, two sets of measurements are needed, one is on the non-hardened specimen to obtain the substrate material properties and other is on the case-hardened surface to obtain the material properties and case depth for the hardened layer. All the measurements were taken at the center of the specimens to suppress the edge effect. The measurement frequency range was from 10 Hz to 10 khz. To obtain the best fit, MATLAB s non-linear regression function has been used. FIGURE 5. A cylindrical specimen of 9310 steel and cantilever bars of pyroware 53. Measurement on Cylindrical Specimens Among the cylindrical specimens, one of them was non-hardened and labeled as Fresh. All other specimens were heat treated for the case hardness. Multi-frequency measurements have been completed on all the specimens. To validate the eddy current estimation of case depth, case hardened profile has been obtained through sectioning and impact testing. The results are shown in figure 7. The Rockwell hardness depth profile has been obtained for all the specimens. It has been revealed that the substrate hardness has been changed to slightly harder than the Fresh sample. The specimen, , has been found was used to determine the substrate hardness. The measured potential drop has been normalized to that of the results found by fitting a smooth theoretic curve to the measurements. Figure 6 shows the normalized potential drop for two case hardened specimens. The fitted curves have reasonable agreement with the measured points.

5 Re(V) / Re(V 0 ) Measured Fitted Measured Fitted Sub FIGURE 6. Normalized experimental measurements and model fitted curves for cylindrical 9310 steel specimens. TABLE 2. Case depth estimation for cylindrical specimens: 9310 steel. Relative Conductivity Depth Estimation by ACPD Depth Estimation by Specimens Permeability [MS/m] technique [mm] Destructive way [mm] Substrate, The estimated material properties and case depth for 9310 steel specimens is listed in Table 2. The relative permeability of the substrate and conductivity are and 2.85 MS/m respectively. Using these substrate material parameters, the case depth has been estimated for the samples and , using a non-linear regression method. The case depth for has been estimated closely. In case of , case depth has been underestimated. The reason has been reveal after destructive measurement. The substrate of has been deformed and has much higher hardness than the substrate, Because of this mismatch, the extracted depth does not agree precisely with the depth found from destructive measurements. The implication is that accurate substrate material properties are needed to infer the case depth. Rockwell Scale [HRC] Rockwell Scale [HRC] Depth [mm] Depth [mm] FIGURE 7. Destructive hardness profile in Rockwell scale on the, cylindrical specimens and, cantilever bars.

6 Measurements on Pyrowear 53 Cantilever Bars Three cantilever bars of pyrowear 53, labeled as 345, 355 and 357, have been supplied by Boeing. At the end of the cantilever bars, the side surface was ground to remove 3.5 mm of the material and thereby expose the substrate, figure 5. Multi-frequency measurements were completed both on the exposed surface and on the hardened surface. All the measurements were normalized to the fitted substrate potential drop and plotted in figure 8. Measurements on specimens 345 and 355 in the quasi-dc region are noisy, figure 8, which led to errors in the parameter estimation. The substrate measurements for all the pyrowear specimens are take separately and they slightly differ from each other. As a result, the crossover point of the normalized data does not the same for different specimens, figure 8. For all the bars, the Rockwell hardness depth profiles have been obtained through destructively and the results shown in figure 7. In Table 3, the estimated depths are listed, both for those estimated from the ACPD technique and those found destructively. The estimated depths by ACPD technique are 2.4 mm, 1.8 mm and 1.4 mm for specimens 345, 355 and 357 respectively. The depth profile by Rockwell hardness scale has revealed that all the specimens have same case step, 2.2 mm. From figure 8, the measurement on cantilever bar, 357, has less randomness than others and the depth estimated 2.4 mm, which is of acceptable accuracy. Re(V) / Re(V 0 ) Measured 345 Fitted 345 Measured 355 Fitted 355 Measured 357 Fitted 357 Substrate 0.9 FIGURE 8. Fitted curves for cantilever specimens. TABLE 3. Case depth estimation for cantilever bars. Relative Conductivity Depth Estimation by Destructive Depth Specimens Permeability [MS/m] ACPD technique [mm] Estimation [mm] CONCLUSION Two 4-point ACPD probes, one with a 1.5 mm and the other with a 3.0 mm pin separation have been compared for the task of estimating case depth of hardened steel. The reduced size of the probe with the smaller pin separation made it possible to complete measurement on narrow cantilever bars and avoid edge effects. Case depth estimates have been made using ACPD nondestructive measurements on both pyrowear 53 and 9310 steel specimens showing reasonable agreement with results from destructive tests of hardness. It has been revealed that the electrical properties of the substrate changed somewhat during the hardening process. Therefore, to estimate the case depth accurately, substrate information needs to be corrected for changes during treatment.

7 ACKNOWLEDGMENTS This work was supported by an SBIR project with AlphaSense, Inc., 510 Philadelphia Pike, Wilmington, DE and performed at the center for NDE at Iowa State University. REFERENCES 1. N. Bowler, Theory of four-point alternating current potential drop measurements on a metal half-space, Journal of Applied Physics, 39, pp (2006). 2. D. K. Schroder, Semiconductor Material and Device Characterization (New York: Wiley) (1998) 3. Reynolds J M 1997 Introduction to Applied and Environmental Geophysics (Chichester: Wiley) 4. D. S. Parasnis 1997 Principles of Applied Geophysics 5 th edn (London: Chapman and Hall) 5. N. Bowler and Y. Huang, Model-based characterization of homogeneous metal plates using four-point alternating current potential drop measurements, IEEE Trans. Magn (2005). 6. N. Bowler and J. R. Bowler Theory of four-point alternating current potential drop measurements on conductive plates, Proc. Roy. Soc. Ser. A. Vol. 463 No. 2079, (2007) 7. N. Bowler and J. R. Bowler, Theory of four-point alternating current potential drop measurements on a layered conductive half-space, Electromagnetic Nondestructive Evaluation (XI) ed A. Tamburrino, Y. Melikhov, Z. Chen and L. Udpa (Amsterdan: IOS Press), pp (2008).