MAGNETIC NONDESTRUCTIVE CHARACTERIZATION OF CASE DEPTH IN SURFACE-HARDENED STEEL COMPONENTS C. C. H. Lo, E. R. Kinser, Y. Melikhov and D. C. Jiles Center for NDE, Iowa State University, Ames, Iowa 50011
ABSTRACT. The magnetic hysteresis properties and Barkhausen effect signals in a series of induction hardened steel rods were studied through measurements and model simulations, with the objective of developing the measurement techniques for nondestructive evaluation of case depth. It was inferred from the measured hysteresis loop that magnetization reversal proceeded in two stages which took place in the core and the case of the hardened rods. The case depths of the samples were estimated by considering the hysteresis loops as a weighed sum of signals from the case and the core. The results were in good agreement with the nominal case depths determined from the hardness depth profiles. Keywords: Magnetic hysteresis, Barkhausen effect, induction hardened steel, case depth PACS: 75.60.Ch, 75.60.Ej, 75.60.Jk, 81.40.Rs, 81.65.Lp, 81.70.Ex.
INTRODUCTION Surface hardening is commonly applied to improve mechanical properties of industrial components by achieving increased strength and toughness at the surface while still retaining ductility at the core. This offers advantages over no heat treatment by increasing service life of a component, and over through hardening by reducing heat treatment cycle time and cost. The use of nondestructive evaluation (NDE) techniques for measurements of case depth in surface hardened components has increased in importance for quality control of both new and remanufactured industrial components. Increased quality control via NDE leads to improved safety, which in turn results in fewer warranty claims and thus higher profits. Magnetic measurements, such as magnetic hysteresis and Barkhausen effect (BE) signal [1,2], have the potential to serve as effective methods for determining case depth in surface-hardened steel [3-5] since both techniques are sensitive to microstructure. Analysis of magnetic hysteresis and BE data for quantitative information on structural conditions (e.g. case depth of hardened steels) has nevertheless remained a long standing challenge due to the complex dependence of the detected signals on microstructure which, in the case of surface-modified materials, may vary with depth [6]. In this study, the magnetic properties of a series of induction hardened steel rods with various case depths were studied through magnetic hysteresis and Barkhausen effect measurements, with the objective of providing insight into how magnetic NDE techniques can be used for quantitative case depth measurements. Magnetic properties of samples CP820, Review of Quantitative Nondestructive Evaluation Vol. 25, ed. by D. O. Thompson and D. E. Chimenti © 2006 American Institute of Physics 0-7354-0312-0/06/$23.00
1253
obtained from each rod at different depths were measured in order to better understand how magnetic properties vary with depth in surface hardened steels. The present results indicate a high degree of correlation between the depth profiles of hardness and magnetic properties. Hysteresis loop measured from the entire hardened rods shows a two-stage magnetization reversal process which took place in the core and the case under different applied field strengths. Case depths were estimated by approximating the hysteresis loop as a weighed sum of signals from the case and the core, and were found to agree with the nominal case depths measured from the hardness depth profile. EXPERIMENTAL PROCEDURES A series of AISI 1045 steel rods 500 mm long and 11 mm in diameter was induction hardened to produce various case depths. All the samples were found to have a microstructure consisting of a hardened surface layer of martensite and a soft ferrite/pearlite core. Depth profiles of hardness were measured using micro-hardness tester. The measured nominal case depths (the depth corresponding to hardness of 50 in the Rockwell C scale) and the mid-points of the hardness depth profiles (determined by fitting an error function to the hardness depth profiles) are shown in Table 1 for comparison. Hysteresis loops and BE signals were measured from the rods using a 2 Hz magnetic field of amplitude 350 Oe (27.9 kA/m). An encircling induction coil was used to detect the magnetic signals. The induced emf was either integrated to obtain the hysteresis loop, or filtered (frequency passband: 10 kHz to 100 kHz) and amplified (total gain: 50 dB) to obtain BE signals. Rectangular strip samples, 20 mm long, 1 mm wide and 0.4 mm thick were cut from each rod at different depths using an electric discharge machine (EDM). Hysteresis loop and BE measurements were performed on individual strips in order to study depth profiles of magnetic properties of the hardened rods. RESULTS Magnetic Hysteresis Loops and Barkhausen Effect Signals As shown in Fig. 1, the hysteresis loops measured from the induction hardened rods show a systematic change in shape that becomes more prominent for samples with larger case depths. This can be interpreted in terms of a two-step magnetization reversal process that took place inside the samples under different applied fields. The hardened rods consist of a martensitic case layer characterized by highly dense dislocations which strongly impede magnetic domain walls, and a softer ferrite/pearlite core having a much lower dislocation density and hence a lower pinning strength for domain walls. Under a large applied magnetic field both the case and the core were magnetized along the field direction. As the applied field was increased from negative saturation and was reversed (as indicated by the dotted arrow in Fig. 1(c)), domain magnetization of the core switched first due to weaker domain wall pinning, resulting in a sudden change in magnetization (indicated by the single arrow in Fig. 1(c)) in the low field regime. As the reverse field was further increased, the domain walls in the martensitic layer became unpinned. As a result domain magnetization of the case reversed, giving rise to an abrupt change in magnetization (indicated by the double arrow in Fig. 1(c)).
1254
TABLE 1. Normal case depth, mid-point of hardness depth profile, coercivity and hysteresis loss of an untreated (case depth = 0 mm) and a series of induction hardened steel rods.
Nominal case depth (mm)
Mid-point of hardness depth profile (mm)
Mid-point of coercivity depth profile (mm)
Mid-point of BE signal depth profile (mm)
0.00
—
—
—
0.38
0.42
0.59
0.51
1.03
1.07
1.10
0.88
1.49
1.51
1.40
1.40
1.90
1.93
1.85
2.19
0 mm
20000
(b)
20000
0.38 mm
15000
0 -50
0
50
-5000
100
150
1.49 mm
0
-150
-100
-50
100
150
Field (Oe)
-150
0 -100
-50
0 -5000
-10000
-10000
-15000
-15000
-15000
-20000
-20000
-20000
1.90 mm
15000
0 -5000
100
150
Field (Oe)
15000 10000
0 -50
50
20000
(e)
50
100
Field (Oe)
150
Induction (G)
Induction (G)
50
5000
-10000
5000
-100
0 -5000
10000
-150
15000 10000
5000
Field (Oe)
20000
(d)
Induction (G)
Induction (G)
5000
-100
1.03 mm
10000
10000
-150
20000
(c)
15000
Induction (G)
(a)
5000 0 -150
-100
-50
0 -5000
-10000
-10000
-15000
-15000
-20000
-20000
50
100
150
Field (Oe)
FIGURE 1. Measured hysteresis loops of (a) the untreated rod (0 mm case depth), and the induction hardened rods with nominal case depths of (b) 0.38 mm, (c) 1.03 mm, (d) 1.49 mm and (e) 1.90 mm. The single and double arrows in (c) indicate the changes in magnetization as a result of domain wall processes taking place in the core and the case respectively.
The measurement parameters extracted from the hysteresis loop in general vary monotonically with case depth. Examples are given in Fig. 2, which shows that the coercivity and hysteresis loss of the hardened rods increase while the maximum permeability decreases with case depth. As the case depth increases, an increasing fraction of domain magnetization reversal takes place in the martensitic case. This requires a higher reverse field to unpin domain walls and contributes to higher energy loss. As a result the coercivity and hysteresis loss increase while the permeability decreases.
1255
(a) 30
3
Hysteresis loss (ergs/cm )
Hysteresis loss
25 20 15
100000
Coercivity
10 50000 5 0 0.5
1.0
1.5
1500
1000
500
0
0 0.0
2500
2000 Maximum permeability
150000 Coercivity (Oe)
(b)
200000
0.0
2.0
Nominal case depth (mm)
0.5
1.0
1.5
2.0
Nominal case depth (mm)
FIGURE 2. Plots of (a) coercivity and hysteresis loss, and (b) maximum permeability as a function of the nominal case depth of the induction hardened rods. 0 mm
0.38 mm
FIGURE 3. Differential permeability and Barkhausen effect signal versus applied field over half of a hysteresis cycle for (a) the untreated rod and (b) the induction hardened rod with a nominal case depth of 0.38 mm.
As a result of surface hardening, the BE signal profiles (i.e. plot of BE signal as a function of applied field) exhibit systematic changes which are closely related to the observed changes in the differential permeability profiles. The permeability of the unhardened rod shows a sharp peak near zero applied field where the Barkhausen signal also shows a maximum (Fig. 3(a)). In contrast the permeability profiles of all the surface hardened rods consist of two peaks, namely the initial and final peaks. These results are consistent with the findings of Theiner et al [7]. An example is given in Fig. 3(b), which shows the permeability and BE signals for the sample with a nominal case depth of 0.38 mm. The initial peak position (labeled I) coincides with the coercivity of the unhardened rod (10.4 Oe), whereas the final peak (labeled F) occurs at a higher reverse field (50 Oe). As the case depth increases, the initial peak of the permeability profiles gradually shifts to a higher field and decreases in magnitude, while the final peak height increases. The BE signals of all surface hardened rods show low-amplitude pulses near zero field and a narrow peak (e.g. Fig. 3(b)) which coincides with the final peak of the permeability profile. The effects of surface hardening on BE signals can be interpreted as follows. For the unhardened rod which has a ferrite/pearlite structure magnetization reversal proceeded mainly by irreversible domain wall processes near the coercive field, giving rise to a sharp peak in the permeability profile and strong BE signals in the low field region (< 19 Oe, Fig.
1256
3(a)). In the hardened rods magnetization reversal first took place in the ferrite/pearlite core, and then in the martensitic surface layer at a higher reverse field due to a stronger domain wall pinning strength. This accounts for the formation of the initial and final peaks of the permeability profile (Fig. 3(b)). The low-amplitude BE pulses in the low field region and the strong BE signals observed at higher reverse field (Fig. 3(b)) are attributed to irreversible domain wall processes occurring in the core and the surface layer respectively. The relatively small contribution of the BE signals from the core can be explained by considering the fact that the signals generated in the core are more attenuated by eddy current damping than those generated in the surface layer. Depth Profiles of Magnetic Properties The coercivity and rms values of BE signal voltage measured from the strip samples which were cut from the rods at different depth are shown in Fig. 4 for comparison with the hardness profiles. All the hardened rods show a high coercivity and weak BE signals in the case layer due to a high density of defects (e.g. dislocations) which act as pinning sites for domain walls. The coercivity decreases while the BE signals sincrease significantly near the case depths of the samples where the microstructure of the sample transformed from martensite to ferrite/pearlite with a substantially lower dislocation density. It was evident in Fig. 4 that the magnetic properties correlate well with hardness except for the hardened rod with a nominal case depth of 0.38 mm. The mid-points of the magnetic property depth profiles, which were determined by fitting the data using the error function, are shown in Table 1. The midpoints of the coercivity and BE depth profiles agree reasonably well with the mid-point of the hardness depth profiles, except for the sample with a nominal case depth of 0.38 mm. In that case, the discrepancies probably result from the fact that the depth resolution of the profiling study is limited to 0.6 mm due to the finite thickness (0.4 mm) of the slices and material loss by EDM sectioning which was estimated to be 0.2 mm. ESTIMATION OF CASE DEPTH The fact that in the hardened rods magnetization reversal takes place in the core and case in different applied field regime offers an opportunity to estimate volume fractions of the case and hence the case depth. As shown in Figs. 5(a) and (c), the strip samples cut from the case layer of the hardened rods show basically the same hysteresis loops irrespective of the case depth, whereas those cut from the core region show the same hysteresis loops as the untreated rod. The result suggests that the bulk hysteresis loops measured from the entire hardened rods can be approximated as being composed of hysteresis loops of the case layer and the core region as illustrated in Fig. 5(b). i.e. the induction signal from the entire rod Brod(H) is approximated as the sum of the induction of the case Bcase(H) and that of the core Bcore(H) weighed by the corresponding volume fractions: Brod(H) = VC × Bcase(H) + (1-VC) × Bcore(H) ,
(1)
where VC is the volume fraction of the case and H is the applied field. The case depth dc can then be calculated from VC by:
1257
(a) 40
0.20
0.38 mm
(b) 40
Hardness (HRC) Coercivity Barkhausen signal
20 15
0.10
30
Coercivity (Oe)
0.15
25
0.15
25
Hardness (HRC) Coercivity Barkhausen Signal
20 15 10
5
0.05 0
1
2
3
4
5
5
0.05 0
1
Depth below surface (mm) 40
2
3
4
5
Depth below surface (mm)
(d) 40
0.20
1.49 mm
0.20
1.90 mm
35
25
Hardness (HRC) Coercivity Barkhausen signal
20
0.10
15
30
0.15
25
Hardness (HRC) Coercivity Barkhausen Signal
20 15
0.10
RMS BE voltage (V)
0.15
RMS BE voltage (V)
30
Coercivity (Oe)
35
Coercivity (Oe)
0.10
RMS BE voltage (V)
30
10
(c)
0.20
1.03 mm
35 RMS BE voltage (V)
Coercivity (Oe)
35
10
10 5
5
0.05 0
1
2
3
4
0.05 0
5
1
Depth below surface (mm)
2
3
4
5
Depth below surface (mm)
FIGURE 4. Depth profiles of micro-hardness (in Rockwell C scale), coercivity and rms BE signal voltage for a series of induction hardened rods with nominal case depths of (a) 0.38 mm, (b) 1.03 mm, (c) 1.49 mm and (d) 1.90 mm.
(
)
d C = 12 D 1 − 1 − VC , (2) where D is the diameter of the steel rods. By obtaining the best fit to the experimental Brod(H), dc were calculated for the hardened steel rods and the results are shown in Table 2. The estimated values of dc are remarkably close to the nominal case depths and mid-points of the hardness depth profiles. It should be pointed out that the case depths were estimated based on two simplifications: (1) the analysis does not consider the transition zone between the case and the core which is present as revealed in the hardness depth profile; and (2) it is assumed that domain magnetization in the case and the core switches independently. A more realistic picture is one in which the domains in the case are influenced by magnetization of the core and vice versa. CONCLUSIONS Relationships between magnetic property and hardness depth profiles were studied in detail for a series of induction hardened steel rods with different case depths. The depth profiles of magnetic properties, such as coercivity and Barkhausen effect signals, were found to follow closely the hardness profiles. The hysteresis loops measured from the rods show features indicative of two magnetization reversal stages that took place in the core and in the case. By assuming that the hysteresis loops measured from the entire hardened rods as a weighed sum of signals from the case and the core, the volume fractions of the
1258
case and hence the case depth were estimated. The estimated case depths are in good agreement with the nominal case depths, demonstrating the potential of hysteresis measurements for quantitative measurements of case depth in surface hardened steel components. (a)
20000
Induction (G)
Untreated rod 0.38 mm 1.03 mm 1.49 mm 1.90 mm
15000 10000 5000 0
-150
-100
-50
0
50
-5000
100
150
Field (Oe)
-10000 -15000 -20000
(b)
20000
Measured
Induction (G)
Fitted
0 -150
-100
-50
0
50
100
150
Field (Oe)
-20000
Induction (G)
(c)
-150
20000
0.38 mm 1.03 mm 1.49 mm 1.90 mm
15000 10000 5000 0
-100
-50
0 -5000
50
100
150
Field (Oe)
-10000 -15000 -20000
FIGURE 5. Hysteresis loops of the strip samples cut from (a) the core (at a depth of 4.2 mm) and (c) the surface layer (at a depth of 0.2 mm) of the hardened steel rods. The hysteresis loops measured from the entire hardened rods can be considered as a sum of the loops of the case and the core. An example is given in (b) which shows the measured hysteresis loops (circle) of the hardened rod with a nominal case depth of 1.90 mm and the best fit loop (solid line) using equation (1).
1259
TABLE 2. Comparison of the nominal case depth, mid-points of hardness depth profiles and the case depths estimated from the measured hysteresis loops for the hardened steel rods.
Hardness depth Estimated case depth Nominal case profile midpoint from fitting to depth (mm) (mm) hysteresis loops (mm)
Percentage difference between the midpoint of hardness depth profile and the estimated case depth (%)
0.38
0.42
0.54
29.9
1.03
1.07
1.03
-3.3
1.49
1.51
1.45
-3.6
1.90
1.93
1.95
0.6
ACKNOWLEDGEMENTS This work was supported by the NSF Industry/University Cooperative Research Program at the Center for Nondestructive Evaluation, Iowa State University. REFERENCES 1. Jiles, D. C., "Magnetic methods in nondestructive testing", D.C.Jiles, Encyclopedia of Materials Science and Technology, p. 6021. Ed. K.H.J. Buschow et al., Elsevier Press, Oxford, September 2001. 2. Lo, C.C.H., “A review of the Barkhausen effect and its applications to nondestructive evaluation”, Feature article in Materials Evaluation, July issue, pp. 741 – 748, 2004. 3. Bach, G; Goebbels, K; Theiner, W.A., “Characterization of Hardening Depth by Barkhausen Noise Measurement.” Materials Evaluation, Volume 46, November 1988, pp. 1576-1580. 4. Vaidyanathan, S; Moorthy, V; Jakakumer, T; Raj, B. “Evaluation of induction hardened case depth through microstructural characterization using magnetic Barkhausen emission technique”, Materials Science and Technology, Vol. 16, February 2000, pp. 202-208. 5. Moorthy, V; Shaw, B.A; Brimble, K., “Testing of Case Depth in Case Carburized Gear Steels Using Magnetic Barkhausen Emission Technique.” Materials Evaulation, May 2004 pp. 523-527. 6. M. Johnson, C. Lo, S. Hentscher, E. Kinser. “Analysis of Conductivity and Permeability Profiles in Hardened Steel.”, Electromagnetic Nondestructive Evaluation, Volume IX. IOS Press, 2005. 7. Theiner, W.A., Altpeter, I., Kern, R., “Determination of Sub-surface microstructure states by micromagnetic NDT”, presented at the 2nd International Symposium on Nondestructive Characterization of Materials, Montreal, Canada, July 1986.
1260
