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Magnetic field variation induced by cyclic bending stress
ARTICLE IN PRESS NDT&E International 42 (2009) 410–414
Contents lists available at ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Magnetic field variation induced by cyclic bending stress Jiancheng Leng a,b,, Minqiang Xu a, Mingxiu Xu a, Jiazhong Zhang a a b
School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China Department of Mechanical Science and Engineering, Daqing Petroleum Institute, Daqing 163318, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 8 October 2008 Received in revised form 18 January 2009 Accepted 22 January 2009 Available online 6 February 2009
Metal magnetic memory technique has provided a new arena for assessing stress status, especially for detecting early damage in ferromagnetic materials. To investigate the magnetomechanical effect of metal magnetic memory phenomenon, the rotary bending fatigue experiments under different stress levels were conducted. The normal components of magnetic field intensities induced by cyclic bending stresses on the surfaces of 45-steel specimens were measured throughout the fatigue process. The results show that surface magnetic fields generated contains reversible and irreversible process prior to failure, while there is a substantial increase just before fracture. Possible reasons for the variations of magnetic fields and corresponding signal characteristics to identify damage zones were discussed. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Magnetic field variation Cyclic bending stress Magnetomechanical effect Metal magnetic memory Transient fracture
1. Introduction More accurate inspection capability is required to evaluate stress status, in particular to detect stress concentration zones due to today’s heightened safety expectations in engineering structures. Most traditional magnetic methods such as magnetic particle inspection, magnetic flux leakage, and eddy current inspection [1] are oriented toward detection developed defects, thus providing little information on the early damage. In view of the limitations, a few studies using magnetic Barkhausen effect [2] and magnetoacoustic emission [3] to probe changes in magnetic properties with applied stress have emerged, but they require an externally applied magnetic field besides the earth’s magnetic field. Perhaps the recent advance in magnetic methods for nondestructive evaluation, already started but still in its infancy, is metal magnetic memory (MMM) technique pioneered by Russian researcher Dubov [4]. MMM phenomenon of ferromagnetic structures relies on self-magnetic leakage field, which is caused by magnetoelastic and magnetomechanical effects. Recently, this idea has attracted much attention [5–10] because special magnetizing devices are not required as compared to the known magnetic methods. Research on MMM technique is conducted by performing numerous static and fatigue experiments. The magnetic field distributions under both applied and residual stresses were measured, respectively [5], and a good correlation was Corresponding author at: School of Astronautics, Harbin Institute of Technol-
ogy, Harbin 150001, PR China. Tel.: +86 45186418020; fax: +86 45186402608. E-mail address: [email protected] (J. Leng). 0963-8695/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ndteint.2009.01.008
shown. Dong et al. reported the variation of stress-induced magnetic signals during static tensile test to investigate the coupling relationship between the stray field signals and stress [6]. Furthermore, the magnetomechanical effect induced by cyclic tensile stress within the elastic region was also discussed and a simple model was derived [7]. On the other hand, tension–tension fatigue [8] and tension–compression fatigue [9] are the most favorable fatigue experiments. However, physical fundamentals of MMM technique have appeared to be very complex. Previous work on the development of magnetomechanical effect concentrated on the magnetization changes under tensile stresses [10], nevertheless experimental research under cyclic loading is scarce, especially under bending moment. Indeed, many industrial components experience bending loads during service. Accordingly, bending fatigue experiments can yield a lot of useful information. The objective of the current work is to explore the change of magnetization induced by cyclic bending stress and to understand the magnetomechanical effect better. The magnetic field distributions at different stress levels throughout the fatigue process are given, and the possible reasons underlying the magnetic trends are discussed.
2. Experimental The material studied was tempered medium carbon 45-steel, which was first water quenched at 840 1C and then tempered at 510 1C. As-received material was in the form of 7.52 mm diameter rods with an annular groove of depth 0.1 mm and width 0.2 mm in
ARTICLE IN PRESS J. Leng et al. / NDT&E International 42 (2009) 410–414
the center to ensure fracture at a prefixed region, as shown in Fig. 1. The specified chemical composition and mechanical properties are shown in Tables 1 and 2, respectively. Due to its high strength and good cutting performance, there are wide applications in gears, main shafts, crankshafts, etc. The rotary bending fatigue experiments were conducted on a PQ1-6-type fatigue pure bending machine at a frequency of 47.5 Hz according to the Chinese Standard GB4337-84. Each specimen was clamped horizontally at both ends between the two clamps, and applied bending moments were 17.4 and 20.4 Nm, respectively. When the specimen under test rotated a predetermined number of cycles continuously, the testing machine was manually shut off and the normal components of the surface magnetic field intensities, Hp(y), of eleven points on top of specimens were immediately measured by a magnetic indicator TSC-1M-4, as shown in Fig. 1. Note that the sensor probe was always perpendicular to the specimen surface with a liftoff of 2 mm during testing.
3. Results and discussion The typical fatigue experiments under bending moments of 17.4 and 20.4 Nm are analyzed below, and the corresponding failure occured at 474,500 and 35,300 cycles, usually the cases in high-cycle and low-cycle fatigue. The whole process can be roughly divided into the following three stages.
411
3.2. Cyclic procedure The magnetic signal curves with counterclockwise rotation during the fatigue process are shown in Fig. 3. The magnetic field intensities changed greatly in first several cycles, and they became reversible as the number of bending cycles was increased. The shapes of magnetic signal curves remained relatively unchanged during the fatigue test from 10,000 to 400,000 cycles for Fig. 3a and from 10,000 to 30,000 cycles for Fig. 3b. According to the theory of magnetomechanical effect based on the ‘‘effective field theory’’ and a ‘‘law of approach’’ developed by Jiles, a differential equation to describe the change in magnetism with applied stress under a constant magnetic field is obtained as follows [11]: dM 1 dMan ¼ 2 sð1 cÞðM an M irr Þ þ c ds ds
(1)
where e and c are constants, Mirr and Man present the irreversible and anhysteretic components of magnetization, respectively. The magnetization M can be expressed as the sum of the reversible component Mrev due to domain wall bending and the irreversible component Mirr due to wall displacement M ¼ M rev þ M irr
(2)
in which Mrev is given by Mrev ¼ cðMan M irr Þ
(3)
Using Eqs. (2) and (3), Eq. (1) becomes dM 1 dMan ¼ 2 sðM an MÞ þ c ds ds
3.1. Before and after clamped Fig. 2a and b shows the residual field distributions at different points of the specimens before and after clamped, respectively. It can be seen that both normal components of magnetic field intensities, Hp(y), were weak and behaved random along the top surface before clamped, whereas there was a marked change after clamped, with absolute value of Hp(y) mostly exhibiting an increase, especially in the vicinity of the two clamps. The initial field was asymmetric because of different residual stresses generated by manufacturing process, which was actually related to micro-inhomogeneity of the specimen. After the specimen was clamped, the additional magnetic fields were induced in the two clamps made of ferromagnetic material, since compressive stress was introduced. Consequently, the magnetic field at both clamped ends showed an abrupt increase, and the Hp(y) values of eleven measurement points were disturbed and affected. The position of the maximum variation in Hp(y) occurred near the two clamps. The real magnetic memory signals on the surface of the specimens were concealed completely, and both the curves were insensitive to the stress concentration zones.
(4)
Eq. (4) models the stress dependence of magnetization, which shows the rate of change of magnetization depends on not only stress s but also the anhysteretic magnetization Man. Since the anhysteretic magnetization is in the lowest energy state of the domains [12], the magnetization tends towards the anhysteretic curve on the application of stress. It follows from this that the overall magnetization will either reduce or stay static until the magnetization of the material and the anhysteretic curve converge with some initial magnetization. In this experiment, the specimens exhibited remanences in the range of 166 to 533 A/m and 258 to 619 A/m after loading, respectively, greater than 45-steel’s anhysteretic magnetization under the earth’s magnetic field. The magnetization is reduced with applied stress to overcome the internal friction forces so that it could approach its anhysteretic state, which was an irreversible process. Once most weak domain wall pinning sites were overcome, the magnetization of the specimen reached the anhysteretic magnetization. However, this is mostly a reversible process because domain walls remaining on strong pinning sites do not become unpinned by stress cycles [13], just as shown in Fig. 3, which was also observed in cyclic tensile tests [7]. Table 2 Mechanical properties of specimen material. Steel number
Yield strength ss (MPa)
Ultimate strength sb (MPa)
0.45% C
716
934
Fig. 1. Specimen shape (in mm) and measurement points.
Table 1 Chemical composition (%) of specimen material. Steel number
C
Si
Mn
P
S
Cr
Ni
Cu
0.45% C
0.43–0.46
0.25–0.33
0.64–0.66
0.008–0.020
0.010–0.014
0.04–0.08
o0.02–0.07
0.08–0.14
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J. Leng et al. / NDT&E International 42 (2009) 410–414
Fig. 2. Hp(y) components of the magnetic field intensities along the surface of the specimen before and after clamped: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
Fig. 3. Hp(y) components of the magnetic field intensities along the surface of the specimen during the cyclic procedure: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
Another interesting phenomenon was both the curves at different cycles intersected at the measurement point 6, which rotated counterclockwise around the point 6 with increasing cycles, finally approaching stability. To eliminate the influence of the two clamps, let Hp(y) components at cycle 0 be reference values, and those at other cycles minus the corresponding reference values are shown in Fig. 4. It can be seen from the plots that this characteristic is more apparent, and the point of intersection is approximately crossing zero value, recognizing the most serious stress concentration zones, which has a good agreement with the fact that the point 6 is at the crack centre.
fractured ends exhibited distinct and opposite poles, invariably positive polarity at the left fractured end and negative polarity at the right fractured end of all specimens, though the pole strengths always differed. Comparing with the variation of magnetic fields, it was found that the distribution of Hp(y) after fracture has the form of a switch in field polarity in the crack area, inducing a distinctive signal feature to identify defected zones [4]. Fracture-induced magnetic effect was earlierly reported by Misra [14]. More detailed discussions about its fundamental mechanism and theoretical model have been subsequently completed [15–17]. More recently, the phenomenon of sharp changes in magnetic signals occurring at the instant of fracture under tensile stress was discussed [6]. It should be noted that in addition to the generation of transient magnetic fields during tensile fracture mentioned by the researchers above, this phenomenon also occurs during bending fatigue failure, though specimens do not undergo large necking, which may be omitted before [15–17]. In fact, the differences between the early and late magnetic fields show the cumulative effects of fatigue. Strictly speaking, the large signal was generated not just at the instant of fatigue fracture but a little prior to fatigue fracture, in accordance with the tensile fracture [16]. However, since the terminal failure is a
3.3. Transient fracture Magnetic field intensities induced by stress showed significant differences after fracture compared with those before failure. A high transient magnetic field was radically produced just after fracture, outreaching the range 2000 to 2000 A/m of the magnetic indicator. Two broken parts were taken carefully from the testing machine, respectively, and then connected up. The magnetization of each specimen varied along the length as shown in Fig. 5, with maximum at the fractured ends. Moreover, the
ARTICLE IN PRESS J. Leng et al. / NDT&E International 42 (2009) 410–414
Fig. 4. nHp(y) signal corresponding to Fig. 3: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
stage of relatively rapid change from cycle to cycle, the corresponding instant of evolutionary changes in magnetic fields is difficult to be determined precisely. Further studies will be focused on this to estimate residual lifetime from cumulative changes in magnetic fields.
4. Conclusions In conclusion, our results obtained from bending fatigue experiments increase the knowledge on stress-induced magnetomechanical effect, up to now limited to tensile tests. It was found that surface magnetic fields of 45-steel specimens generated contains reversible and irreversible process before failure, which can be explained by the derived model, while there is a substantial increase just prior to fracture. The variations of the magnetic fields in ferromagnetic materials reflect different damage states, which can be potentially used as a measure to assess stress status, or early fatigue damage and eventual failure. Nevertheless, one cannot expect simple monotonic correlations between the accumulative damage and magnetic field amplitudes. Future work will be devoted to the field distribution vs. number of cycles during fatigue cycling, especially the location of large magnetic excursion for indicating the evolution of fatigue.
413
Fig. 5. Hp(y) components of the magnetic field intensities along the surface of the specimen just after fracture: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant no. 10772061. We thank professor Bo Fang (Harbin Institute of Technology, China) for the critical review of the manuscript. Also, we are grateful to the referees for their helpful comments and suggestions.
References [1] Jiles DC. Review of magnetic methods for nondestructive evaluation (Part 2). NDT&E Int 1990;23(2):83–92. [2] Pasley RL. Barkhausen effect—an indication of stress. Mater Eval 1970;28(7):157–61. [3] Kusanagi H, Kimura H, Sasaki H. Stress effect on the magnitude of acoustic emission during magnetization of ferromagnetic materials. J Appl Phys 1979;50(4):2985–7. [4] Dubov AA. A study of metal properties using the method of magnetic memory. Met Sci Heat Treat 1997;39(9–10):401–5. [5] Wilson JW, Tian GY, Barrans S. Residual magnetic field sensing for stress measurement. Sensor Actuat A-Phys 2007;135(2):381–7. [6] Dong LH, Xu BS, Dong SY, Chen QZ, Wang D. Variation of stress-induced magnetic signals during tensile testing of ferromagnetic steels. NDT&E Int 2008;41(3):184–9. [7] Yang E, Li LM, Chen X. Magnetic field aberration induced by cycle stress. J Magn Magn Mater 2007;312(1):72–7.
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J. Leng et al. / NDT&E International 42 (2009) 410–414
[8] Dong LH, Xu BS, Dong SY, Chen QZ, Wang YY, Zhang L, et al. Metal magnetic memory testing for early damage assessment in ferromagnetic materials. J Cent South Univ Technol 2005;12(S2):102–6. [9] Wang X, Chen M, Xu BS. Change of magnetic memory signals during the tension–compression fatigue of 48 MnV steel. China Mech Eng 2007;18(15):1862–4. [10] Devine MK, Jiles DC. Magnetomechanical effect in nickel and cobalt. J Appl Phys 1997;81(8):5603–5. [11] Jiles DC. Theory of the magnetomechanical effect. J Phys D: Appl Phys 1995;28(8):1537–46. [12] Jiles DC, Atherton DL. Theory of ferromagnetic hysteresis. J Magn Magn Mater 1986;61(1–2):48–60.
[13] Chen Y, Kriegermeier-Sutton BK, Snyder JE, Dennis KW, Mccallum RW, Jiles DC. Magnetomechanical effects under torsional strain in iron, cobalt and nickel. J Magn Magn Mater 2001;236(1–2):131–8. [14] Misra A. Electromagnetic effects at metallic fracture. Nature (London) 1975;254:133–4. [15] Misra A. Theoretical study of the fracture-induced magnetic effect in ferromagnetic materials. Phys Lett A 1977;62(4):234–6. [16] Misra A, Varshney BG. Can a stress alone applied to a demagnetized ferromagnetic specimen produce any magnetization. J Magn Magn Mater 1990;89(1–2):159–66. [17] Kumar A, Misra A. Shape anisotropy of magnetic field generation during tensile fracture in steel. J Magn Magn Mater 2005;285(1–2):71–8.
Contents lists available at ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Magnetic field variation induced by cyclic bending stress Jiancheng Leng a,b,, Minqiang Xu a, Mingxiu Xu a, Jiazhong Zhang a a b
School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China Department of Mechanical Science and Engineering, Daqing Petroleum Institute, Daqing 163318, PR China
a r t i c l e in f o
a b s t r a c t
Article history: Received 8 October 2008 Received in revised form 18 January 2009 Accepted 22 January 2009 Available online 6 February 2009
Metal magnetic memory technique has provided a new arena for assessing stress status, especially for detecting early damage in ferromagnetic materials. To investigate the magnetomechanical effect of metal magnetic memory phenomenon, the rotary bending fatigue experiments under different stress levels were conducted. The normal components of magnetic field intensities induced by cyclic bending stresses on the surfaces of 45-steel specimens were measured throughout the fatigue process. The results show that surface magnetic fields generated contains reversible and irreversible process prior to failure, while there is a substantial increase just before fracture. Possible reasons for the variations of magnetic fields and corresponding signal characteristics to identify damage zones were discussed. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Magnetic field variation Cyclic bending stress Magnetomechanical effect Metal magnetic memory Transient fracture
1. Introduction More accurate inspection capability is required to evaluate stress status, in particular to detect stress concentration zones due to today’s heightened safety expectations in engineering structures. Most traditional magnetic methods such as magnetic particle inspection, magnetic flux leakage, and eddy current inspection [1] are oriented toward detection developed defects, thus providing little information on the early damage. In view of the limitations, a few studies using magnetic Barkhausen effect [2] and magnetoacoustic emission [3] to probe changes in magnetic properties with applied stress have emerged, but they require an externally applied magnetic field besides the earth’s magnetic field. Perhaps the recent advance in magnetic methods for nondestructive evaluation, already started but still in its infancy, is metal magnetic memory (MMM) technique pioneered by Russian researcher Dubov [4]. MMM phenomenon of ferromagnetic structures relies on self-magnetic leakage field, which is caused by magnetoelastic and magnetomechanical effects. Recently, this idea has attracted much attention [5–10] because special magnetizing devices are not required as compared to the known magnetic methods. Research on MMM technique is conducted by performing numerous static and fatigue experiments. The magnetic field distributions under both applied and residual stresses were measured, respectively [5], and a good correlation was Corresponding author at: School of Astronautics, Harbin Institute of Technol-
ogy, Harbin 150001, PR China. Tel.: +86 45186418020; fax: +86 45186402608. E-mail address: [email protected] (J. Leng). 0963-8695/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ndteint.2009.01.008
shown. Dong et al. reported the variation of stress-induced magnetic signals during static tensile test to investigate the coupling relationship between the stray field signals and stress [6]. Furthermore, the magnetomechanical effect induced by cyclic tensile stress within the elastic region was also discussed and a simple model was derived [7]. On the other hand, tension–tension fatigue [8] and tension–compression fatigue [9] are the most favorable fatigue experiments. However, physical fundamentals of MMM technique have appeared to be very complex. Previous work on the development of magnetomechanical effect concentrated on the magnetization changes under tensile stresses [10], nevertheless experimental research under cyclic loading is scarce, especially under bending moment. Indeed, many industrial components experience bending loads during service. Accordingly, bending fatigue experiments can yield a lot of useful information. The objective of the current work is to explore the change of magnetization induced by cyclic bending stress and to understand the magnetomechanical effect better. The magnetic field distributions at different stress levels throughout the fatigue process are given, and the possible reasons underlying the magnetic trends are discussed.
2. Experimental The material studied was tempered medium carbon 45-steel, which was first water quenched at 840 1C and then tempered at 510 1C. As-received material was in the form of 7.52 mm diameter rods with an annular groove of depth 0.1 mm and width 0.2 mm in
ARTICLE IN PRESS J. Leng et al. / NDT&E International 42 (2009) 410–414
the center to ensure fracture at a prefixed region, as shown in Fig. 1. The specified chemical composition and mechanical properties are shown in Tables 1 and 2, respectively. Due to its high strength and good cutting performance, there are wide applications in gears, main shafts, crankshafts, etc. The rotary bending fatigue experiments were conducted on a PQ1-6-type fatigue pure bending machine at a frequency of 47.5 Hz according to the Chinese Standard GB4337-84. Each specimen was clamped horizontally at both ends between the two clamps, and applied bending moments were 17.4 and 20.4 Nm, respectively. When the specimen under test rotated a predetermined number of cycles continuously, the testing machine was manually shut off and the normal components of the surface magnetic field intensities, Hp(y), of eleven points on top of specimens were immediately measured by a magnetic indicator TSC-1M-4, as shown in Fig. 1. Note that the sensor probe was always perpendicular to the specimen surface with a liftoff of 2 mm during testing.
3. Results and discussion The typical fatigue experiments under bending moments of 17.4 and 20.4 Nm are analyzed below, and the corresponding failure occured at 474,500 and 35,300 cycles, usually the cases in high-cycle and low-cycle fatigue. The whole process can be roughly divided into the following three stages.
411
3.2. Cyclic procedure The magnetic signal curves with counterclockwise rotation during the fatigue process are shown in Fig. 3. The magnetic field intensities changed greatly in first several cycles, and they became reversible as the number of bending cycles was increased. The shapes of magnetic signal curves remained relatively unchanged during the fatigue test from 10,000 to 400,000 cycles for Fig. 3a and from 10,000 to 30,000 cycles for Fig. 3b. According to the theory of magnetomechanical effect based on the ‘‘effective field theory’’ and a ‘‘law of approach’’ developed by Jiles, a differential equation to describe the change in magnetism with applied stress under a constant magnetic field is obtained as follows [11]: dM 1 dMan ¼ 2 sð1 cÞðM an M irr Þ þ c ds ds
(1)
where e and c are constants, Mirr and Man present the irreversible and anhysteretic components of magnetization, respectively. The magnetization M can be expressed as the sum of the reversible component Mrev due to domain wall bending and the irreversible component Mirr due to wall displacement M ¼ M rev þ M irr
(2)
in which Mrev is given by Mrev ¼ cðMan M irr Þ
(3)
Using Eqs. (2) and (3), Eq. (1) becomes dM 1 dMan ¼ 2 sðM an MÞ þ c ds ds
3.1. Before and after clamped Fig. 2a and b shows the residual field distributions at different points of the specimens before and after clamped, respectively. It can be seen that both normal components of magnetic field intensities, Hp(y), were weak and behaved random along the top surface before clamped, whereas there was a marked change after clamped, with absolute value of Hp(y) mostly exhibiting an increase, especially in the vicinity of the two clamps. The initial field was asymmetric because of different residual stresses generated by manufacturing process, which was actually related to micro-inhomogeneity of the specimen. After the specimen was clamped, the additional magnetic fields were induced in the two clamps made of ferromagnetic material, since compressive stress was introduced. Consequently, the magnetic field at both clamped ends showed an abrupt increase, and the Hp(y) values of eleven measurement points were disturbed and affected. The position of the maximum variation in Hp(y) occurred near the two clamps. The real magnetic memory signals on the surface of the specimens were concealed completely, and both the curves were insensitive to the stress concentration zones.
(4)
Eq. (4) models the stress dependence of magnetization, which shows the rate of change of magnetization depends on not only stress s but also the anhysteretic magnetization Man. Since the anhysteretic magnetization is in the lowest energy state of the domains [12], the magnetization tends towards the anhysteretic curve on the application of stress. It follows from this that the overall magnetization will either reduce or stay static until the magnetization of the material and the anhysteretic curve converge with some initial magnetization. In this experiment, the specimens exhibited remanences in the range of 166 to 533 A/m and 258 to 619 A/m after loading, respectively, greater than 45-steel’s anhysteretic magnetization under the earth’s magnetic field. The magnetization is reduced with applied stress to overcome the internal friction forces so that it could approach its anhysteretic state, which was an irreversible process. Once most weak domain wall pinning sites were overcome, the magnetization of the specimen reached the anhysteretic magnetization. However, this is mostly a reversible process because domain walls remaining on strong pinning sites do not become unpinned by stress cycles [13], just as shown in Fig. 3, which was also observed in cyclic tensile tests [7]. Table 2 Mechanical properties of specimen material. Steel number
Yield strength ss (MPa)
Ultimate strength sb (MPa)
0.45% C
716
934
Fig. 1. Specimen shape (in mm) and measurement points.
Table 1 Chemical composition (%) of specimen material. Steel number
C
Si
Mn
P
S
Cr
Ni
Cu
0.45% C
0.43–0.46
0.25–0.33
0.64–0.66
0.008–0.020
0.010–0.014
0.04–0.08
o0.02–0.07
0.08–0.14
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J. Leng et al. / NDT&E International 42 (2009) 410–414
Fig. 2. Hp(y) components of the magnetic field intensities along the surface of the specimen before and after clamped: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
Fig. 3. Hp(y) components of the magnetic field intensities along the surface of the specimen during the cyclic procedure: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
Another interesting phenomenon was both the curves at different cycles intersected at the measurement point 6, which rotated counterclockwise around the point 6 with increasing cycles, finally approaching stability. To eliminate the influence of the two clamps, let Hp(y) components at cycle 0 be reference values, and those at other cycles minus the corresponding reference values are shown in Fig. 4. It can be seen from the plots that this characteristic is more apparent, and the point of intersection is approximately crossing zero value, recognizing the most serious stress concentration zones, which has a good agreement with the fact that the point 6 is at the crack centre.
fractured ends exhibited distinct and opposite poles, invariably positive polarity at the left fractured end and negative polarity at the right fractured end of all specimens, though the pole strengths always differed. Comparing with the variation of magnetic fields, it was found that the distribution of Hp(y) after fracture has the form of a switch in field polarity in the crack area, inducing a distinctive signal feature to identify defected zones [4]. Fracture-induced magnetic effect was earlierly reported by Misra [14]. More detailed discussions about its fundamental mechanism and theoretical model have been subsequently completed [15–17]. More recently, the phenomenon of sharp changes in magnetic signals occurring at the instant of fracture under tensile stress was discussed [6]. It should be noted that in addition to the generation of transient magnetic fields during tensile fracture mentioned by the researchers above, this phenomenon also occurs during bending fatigue failure, though specimens do not undergo large necking, which may be omitted before [15–17]. In fact, the differences between the early and late magnetic fields show the cumulative effects of fatigue. Strictly speaking, the large signal was generated not just at the instant of fatigue fracture but a little prior to fatigue fracture, in accordance with the tensile fracture [16]. However, since the terminal failure is a
3.3. Transient fracture Magnetic field intensities induced by stress showed significant differences after fracture compared with those before failure. A high transient magnetic field was radically produced just after fracture, outreaching the range 2000 to 2000 A/m of the magnetic indicator. Two broken parts were taken carefully from the testing machine, respectively, and then connected up. The magnetization of each specimen varied along the length as shown in Fig. 5, with maximum at the fractured ends. Moreover, the
ARTICLE IN PRESS J. Leng et al. / NDT&E International 42 (2009) 410–414
Fig. 4. nHp(y) signal corresponding to Fig. 3: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
stage of relatively rapid change from cycle to cycle, the corresponding instant of evolutionary changes in magnetic fields is difficult to be determined precisely. Further studies will be focused on this to estimate residual lifetime from cumulative changes in magnetic fields.
4. Conclusions In conclusion, our results obtained from bending fatigue experiments increase the knowledge on stress-induced magnetomechanical effect, up to now limited to tensile tests. It was found that surface magnetic fields of 45-steel specimens generated contains reversible and irreversible process before failure, which can be explained by the derived model, while there is a substantial increase just prior to fracture. The variations of the magnetic fields in ferromagnetic materials reflect different damage states, which can be potentially used as a measure to assess stress status, or early fatigue damage and eventual failure. Nevertheless, one cannot expect simple monotonic correlations between the accumulative damage and magnetic field amplitudes. Future work will be devoted to the field distribution vs. number of cycles during fatigue cycling, especially the location of large magnetic excursion for indicating the evolution of fatigue.
413
Fig. 5. Hp(y) components of the magnetic field intensities along the surface of the specimen just after fracture: (a) under a bending moment of 17.4 Nm and (b) under a bending moment of 20.4 Nm.
Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant no. 10772061. We thank professor Bo Fang (Harbin Institute of Technology, China) for the critical review of the manuscript. Also, we are grateful to the referees for their helpful comments and suggestions.
References [1] Jiles DC. Review of magnetic methods for nondestructive evaluation (Part 2). NDT&E Int 1990;23(2):83–92. [2] Pasley RL. Barkhausen effect—an indication of stress. Mater Eval 1970;28(7):157–61. [3] Kusanagi H, Kimura H, Sasaki H. Stress effect on the magnitude of acoustic emission during magnetization of ferromagnetic materials. J Appl Phys 1979;50(4):2985–7. [4] Dubov AA. A study of metal properties using the method of magnetic memory. Met Sci Heat Treat 1997;39(9–10):401–5. [5] Wilson JW, Tian GY, Barrans S. Residual magnetic field sensing for stress measurement. Sensor Actuat A-Phys 2007;135(2):381–7. [6] Dong LH, Xu BS, Dong SY, Chen QZ, Wang D. Variation of stress-induced magnetic signals during tensile testing of ferromagnetic steels. NDT&E Int 2008;41(3):184–9. [7] Yang E, Li LM, Chen X. Magnetic field aberration induced by cycle stress. J Magn Magn Mater 2007;312(1):72–7.
ARTICLE IN PRESS 414
J. Leng et al. / NDT&E International 42 (2009) 410–414
[8] Dong LH, Xu BS, Dong SY, Chen QZ, Wang YY, Zhang L, et al. Metal magnetic memory testing for early damage assessment in ferromagnetic materials. J Cent South Univ Technol 2005;12(S2):102–6. [9] Wang X, Chen M, Xu BS. Change of magnetic memory signals during the tension–compression fatigue of 48 MnV steel. China Mech Eng 2007;18(15):1862–4. [10] Devine MK, Jiles DC. Magnetomechanical effect in nickel and cobalt. J Appl Phys 1997;81(8):5603–5. [11] Jiles DC. Theory of the magnetomechanical effect. J Phys D: Appl Phys 1995;28(8):1537–46. [12] Jiles DC, Atherton DL. Theory of ferromagnetic hysteresis. J Magn Magn Mater 1986;61(1–2):48–60.
[13] Chen Y, Kriegermeier-Sutton BK, Snyder JE, Dennis KW, Mccallum RW, Jiles DC. Magnetomechanical effects under torsional strain in iron, cobalt and nickel. J Magn Magn Mater 2001;236(1–2):131–8. [14] Misra A. Electromagnetic effects at metallic fracture. Nature (London) 1975;254:133–4. [15] Misra A. Theoretical study of the fracture-induced magnetic effect in ferromagnetic materials. Phys Lett A 1977;62(4):234–6. [16] Misra A, Varshney BG. Can a stress alone applied to a demagnetized ferromagnetic specimen produce any magnetization. J Magn Magn Mater 1990;89(1–2):159–66. [17] Kumar A, Misra A. Shape anisotropy of magnetic field generation during tensile fracture in steel. J Magn Magn Mater 2005;285(1–2):71–8.