E-Journal of Advanced Maintenance Vol. 11 No. 3 (2019) 118-123
Japan Society of Maintenology

Investigating the performances of parameters of magnetic hysteretic loop
on characterizing the residual plastic strain in low carbon steel
Xiaodong ZHANG, Bin WU , Xiucheng LIU*and Cunfu HE
College of Mechanical Engineering and Applied Electronics Technology, Beijing University ofTechnology, Beijing 100124, China
ABSTRACTThe residual plastic strain in ferromagnetic structural components will affect the structural integrity, themechanical properties of materials and even the service life. Therefore, accurately characterizing the degree ofresidual plastic strain is important to predict the service life time of components. The plastic deformation
changes the dislocation density and the magnetic hysteretic properties of ferromagnetic materials. The variationin the shape of magnetic hysteresis curves will be suitable indicators for nondestructive evaluation of theresidual plastic deformation in ferromagnetic steels. The core issue is to find stable magnetic parameters a thatare sensitive to the changes of the residual plastic strain. In this study, the performances of the magneticparameters (including coercive force Hc, maximum magnetic flux density Bmax, hysteresis loss WL and theharmonic amplitudes of magnetic flux density b1, b3) to the residual plastic strain in low carbon steel wereinvestigated by experiments. Especially, the influences of excitation frequency on the performances of magnetic
parameters in characterizing the residual plastic strain were analyzed. The results show that both the parametersof Bmax and b1 demonstrate linear dependency on the residual plastic strain εp even the frequency of the appliedmagnetic field changes. Therefore, the parameters of Bmax and b1 are preferred parameters to characterize theresidual plastic strain in the tested low carbon steel.
KEYWORDS
Magnetic hysteretic loop, residual plastic strain, low carbon steel, magnetizing frequency

1.

Introduction

Plastic deformation occurred in ferromagnetic materials results in residual plastic strains, which
may lead to the generation of micro-cracks and change the mechanical properties of the materials [1].
Accurately characterizing the degree of residual plastic strain is helpful for material evaluation. The
application of the magnetic technique is capable of evaluating the residual strain in a quick andnondestructive way.
The plastic deformation changes both the dislocation density and residual stress inside theferromagnetic materials, affecting the pining effect applied to the domain-wall while the materials issubjected to an external magnetic field. The change of microstructures and the residual stress affects
the macroscopic hysteretic magnetic properties of ferromagnetic materials [2, 3]. The influences ofplastic deformation on the magnetic properties and magnetic parameters has been studied in Ref. [4,5]. To explain the magnetic behavior induced by plastic deformation, J-A model was extended toincorporate the effect of plastic deformation by introducing the dislocation density into the effective
field of the model [6-8]. Therefore, the magnetic method, major hysteresis loop measurement, can beapplied on the characterization of the residual plastic strain of magnetic material [9]. In order tomeasure the major magnetic hysteresis loop, the magnetic measurements should be static and theeffect of eddy current on the magnetization curves can be negligibly. However, in the actual detection,
the exciting frequency is low frequency, such as 5Hz and 10Hz, which can be regarded as
pseudo-static. And the effect of different low exciting frequencies on the parameters extracted fromthe hysteresis loop should be investigated.
In this study, the residual plastic strain is induced in dog bone specimens of low carbon steel bystretching the specimen to its plastic stage and then unloading to free state. The magnetic hysteretic
curves of the specimens are measured. Multiple parameters extracted from the measured hysteretic*Corresponding author, E-mail: xiuchliu@bjut.edu.cn118

X. Zhang, et al./ Magnetic hysteretic characterization of residual plastic strain in low carbon steel

curves are used to characterize the residual plastic strain. Linear curve fitting operation is applied tothe measured data to help find suitable magnetic parameters for nondestructive evaluation of residual
plastic strain. Meanwhile, the influences of excitation frequency on the reliability of magnetic
parameters in characterizing the residual plastic strain were analyzed. Under different excitation
frequencies, the sensitivity of the investigated magnetic parameters to the residual plastic strain isanalyzed. Finally, the suitable magnetic parameters for residual plastic deformation evaluation areselected by conducting comparison studies.

2.

Experiment2.1. Specimen preparation
The chemical composition of the tested low carbon steel is given in Table. 1. The specimens aremachined from the same carbon steel plate along the rolling direction, and the sizes of the dog bone
specimens are shown in Fig.1. The sizes of the middle part of the specimen is selected as about
120mm(length)×30mm(width)×3mm(thickness), according to the Chinese Standard GB/T 228-2002.
Then the specimens were alternatively uniaxially tensioned to plastic deformation stages withdifferent applied tensile stress holding 60s and then unloaded from different stress levels. The stressrate is 20MPa/s. The residual strain at the center of specimen is measured by micrometer, namely thechange of calibration length before and after tensile test. As a results, the residual plastic strains ofeach specimen is different from the rest specimens. The measured residual plastic strains for all thetested specimen are given in Table 2. No.1 specimen is non-deformed to act as a reference.
Table 1 Chemical composition of low carbon steel
Specimenswt (%)

C0.041

Si0.017

Mn0.11

P0.012

Cu0.012

Cr0.014

S0.0082

Fig1. The dimensions of the specimen (non-deformed)
Table 2 Residual plastic strain of the specimens
Specimens
εp (%)
Specimens
εp (%)

10.00
10
3.99

2
0.80
11
4.88

3
1.11
12
5.56

4
1.59
13
6.21

5
1.91
14
6.58

6
2.23
15
9.10

7
2.72
16
9.19

8
3.24
17
10.70

93.69
18
13.29

2.2. Experiments and results
The experimental system as shown in the Fig.2 consists of a signal excitation and acquisition
system, the bipolar power supply, a U-shaped ferrite yoke, a hall sensor and the induction coil. In theexperiments, the signal generator output a sinusoidal wave with the frequency of 2, 6, 10, 14, 18 Hz
respectively. The output signal is amplified by a bipolar power supply and then fed into the excitationcoil wound on the yoke to provide magnetic field for samples magnetization. A Hall sensor wasplaced above the specimen to obtain the surface magnetic field intensity and the induction coil waswound directly around the sample to measure the change of the magnetic flux.

119X. Zhang, et al./ Magnetic hysteretic characterization of residual plastic strain in low carbon steel

Fig.2 The Schematic diagram of experimental system

The hysteresis loops of the dog bone samples were measured at room temperature and thespecimens were preliminarily demagnetized via demagnetizer TC-2 before measuring the magnetic
hysteretic curves in order to eliminate the disturbance of different initial remanence introduced bymanufacturing process.
The typical output signals of Hall sensor and pick-up coil and the obtained hysteresis loop areplotted in Fig.3. The variation in the shape of magnetic hysteresis loop may be suitable indicators for
nondestructive evaluation of the residual plastic strain. Several parameters are extracted or estimatedfrom the measured results to characterize the residual plastic strain of the samples. The investigatedparameters includes the coercive force Hc, hysteresis loss WL, maximum magnetic flux density Bmax,
the first and third harmonic amplitudes of measured surface magnetic field b1, b3 and the ratio of third
to first harmonic amplitude b3/b1 .

Fig.3 The typical magnetic signals measured

The results obtained under the condition with an excitation frequency of 2 Hz are taken as
examples to investigated the sensitivity of the magnetic parameters on the characterizing the residualstrain. Simple linear regression fitting operation is applied to the measured data of magnetic
parameters and the residual strain. The analysis results are shown in Fig.4.
Both the parameters of Bmax and b1 demonstrate linear dependency on the residual plastic strain εp,whose regression coefficients R2 are 0.9654 and 0.9607, respectively.
The shape of the measured hysteresis loop depends on the frequency of the applied magnetic
field due to eddy current loss and anomalous loss [10]. Here, the effect of the magnetizing frequency
on the correlation between the magnetic parameters and the residual strain is especially investigatedby experiments. The results obtained under the case with magnetizing frequencies of 6, 10, 14, 18 Hz
are shown in Fig.5.
The effect of the magnetizing frequency on the dependency of individual magnetic parameter on
the residual strain is limited. However, the magnetizing frequency changes both the slope and theintercept of fitted lines.

120

X. Zhang, et al./ Magnetic hysteretic characterization of residual plastic strain in low carbon steel

Fig. 4. The relationship between magnetic parameters and residual plastic strain

As the magnetizing frequency increases, the values of Hc and WL increase while the value of b1,b3, b3/b1 decrease. Among the investigated parameters, the values of Bmax and b1 experiences minorchanges as the magnetizing frequency changes. The linear regression coefficients R2 for all the fittedlines in the Fig.5 are listed in Table. 3.
As compared to the rest parameters, the regression coefficients is higher than 0.9 for the cases ofthe parameters of Bmax and b1, indicating that the parameters of Bmax and b1 demonstrate good linear
dependency on the residual plastic strain εp. In addition, the performance (regression coefficients) of
the parameters of Bmax and b1 on characterizing the residual strain are nearly not affected by the121

X. Zhang, et al./ Magnetic hysteretic characterization of residual plastic strain in low carbon steelmagnetizing frequencies. Therefore, the parameters of Bmax and b1 are preferred parameters tocharacterize the residual plastic strain in the tested low carbon steel.
The eddy current loss and anomalous loss will generated when the magnetizing frequency
increase, which will directly affect the coercive force Hc and hysteresis loss WL. However, themaximum magnetic flux density Bmax is insensitive to the eddy current loss and anomalous. So thevalues of Bmax and b1 experiences changes a little as the magnetizing frequency changes and the valuesof Hc and WL change greatly.

Fig. 5. The relationship between magnetic parameters and residual plastic strain at different frequencies
of applied field122

X. Zhang, et al./ Magnetic hysteretic characterization of residual plastic strain in low carbon steel

Table 3 The linear regression coefficients R2 for the cases with different magnetizing frequencies
2Hz
6Hz
10Hz
14Hz
18Hz

3.

R2(Hc)
0.06820.00000.21840.25790.4672R2(WL)
0.50510.57690.65600.67010.7016R2(Bmax)
0.96540.96550.96730.96620.9652R2(b1)
0.96070.96120.96150.96230.9627R2(b3)
0.88450.88070.86870.86480.8450R2(b3/b1)
0.75810.72010.65760.61000.5056

Conclusion

In this work, the magnetic hysteretic loops measurement technique was employed tocharacterizing the residual plastic strain occurred in low carbon steels. The reliability of magnetic
parameters were studied and the influence of frequency of the applied magnetic field on thesensitivities of magnetic parameters were analyzed. It is found that under the conditions of the tested
different magnetizing frequencies, the parameters of Bmax and b1 demonstrates linear dependency on
the residual plastic strain of εp. The eddy current loss and anomalous loss will generated when themagnetizing frequency increase, which will directly affect the coercive force Hc and hysteresis loss
WL. However, the maximum magnetic flux density Bmax is insensitive to the eddy current loss andanomalous. Furthermore, the magnetic properties is determined by the microstructure of the material,
The change of microstructure with different residual strain need to further study to explain the changeof magnetic parameters.

Acknowledgement
This work was supported by the National Natural Science Foundation of China (Project Nos.
11527801 and 11402008).

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