·Home ·Table of Contents ·Materials Characterization and testing

Theoretical Analysis of the Influence of Different Microstructure on Barkhausen Noise Li Qiang Liu zhiming Miao longxiu Yuan Zuyi College of Mechanical and electric Engineering, Northern Jiaotong University Beijing 100044 Chain. Contact

ABSTRACT:

In this paper, the characteristic of Barkhausen Noise in different microstructure of metal has been studied. The volt that is generated by Barkhausen Noise is approximately expressed as Gauss pulse. The theory analysis of the influence of different microstructure on Barkhausen Noise is done.

Introduction

Recently, Barkhausen Noise analysis method is one of advanced nondestructive method to measure stress state of ferromagnetic material. The magnetic-elastic instrument was developed by use of the Barkhausen Noise analysis theory and it could be measured and analyzed residual stress[1] and fatigue limit [2]of the ferromagnetic materials. A large number of researches[3][4][5] showed that output volt of the magnetic-elastic instrument ,MP(Magnetic parameter) not only is correlated with local stress state, but also is correlated with metallurgical microstructures of the ferromagnetic material. Until now, the theoretical investigation of the relationship between different microstructure and Barkhausen Noise are not systematic. The main aim of this paper is to analyze theoretically the relationship between the different microstructure and the BN(Barkhausen Noise)
It is well known fact that the ferromagnetic materials are composed of a large number of micro-region with same magnetization orientation. These micro-region are called magnetic domains. Each magnetic domain is divided by magnetic domain walls. Under the action of alternating magnetic field, the Barkhausen Noise is created through discontinuous motion of the magnetic domain walls. And so, a series of elective pulse signals could be produced in a receiver coil located on a specimen surface and the whole elective pulse signals is known as Barkhausen Noise. Recently, currently recognized theory considered that BN is dependent on the discontinuous motion of 180° magnetic domain walls. In this paper, the elective pulse produced through motion of the magnetic domain walls are approximately expressed as Gaussian pulse to analyze influence of different microstructure on the BN. The important conclusion of this paper is that the output of the magnetic-elastic instrument, MP is in proportion to the mean free distance of the domain walls motion, L.

Theoretical model of BN

MP was described as Gaussian pulse
When outer magnetic field is essentially proportion to the time, BN is displayed in the most abrupt portion of magnetic hysteresis curve in magnetization process. And so, there are a series of voltage pulse were produced in detective coil. BN is formed.

(1)

Where H_m is the largest strength of the outer magnetic field, dH/dt is magnetization rate, DF  is the increment of magnetic flux density in the magnetization region, s is variance of duration time. Experiments identify that total voltage value e_total in the detective coil is sum of the voltages of continuous Gauss pulses in a magnetization period T. Suppers that interval time and duration time of each Gauss pulse are constants, i.e. s = constant. And so the sum of the Gauss pulses in a magnetization period T is, N = T/t. When the outer magnetic field condition is given, t is constant. The total voltage value is

(2)

Where is determined by the condition of outer magnetic field and amplitude value of a Gauss pulse is

(3)

The sum of total amplitude value of Gauss pulse in a whole period T is . The number of pulses in T is N. The output of the magnetic-elastic instrument is MP, MP=ku=kG_pt, where u is mean value of voltage output of sensor [7], therefore. We have

(4)

Where coefficient of ratio C_r is , in the given condition of magnetization, B, k is constants. s, t are correlated with microstructure of materials. s, t depend on mean free distance
In view of productive machancoim of the BN, it is produced when a 180° magnetic domain wall has suddenly departed from a place pinned by a inclusion or is nearing another inclusion. At last, the magnetic domain wall is pinned by the new inclusion. When the outer magnetic field strength is coming at critical value, i.e. in this strength the domain wall can be departed from the pinning place and will arrive to the next pinning place without any resistance. When the domain wall departed from a pinning place to the next pinning place, the displacement of the domain wall is L. L is called mean free distance of the domain wall. When the domain wall moved from a inclusion to another inclusion, a Gauss pulse is created and the Barkhausen jump is appeared with duration time t₀. We define the t₀ = L / , where is mean speed of the domain wall movement, L is mean free distance of the domain wall.
The mean speed of the domain wall movement is proportional to the outer magnetic field strength, i. e. = C_vH_p Where H_p is the minimum strength of the outer magnetic field to take domain wall away from the pinning place and to produce unreversible motion. C_v is the proportional constant. The expression of H_p is

(5)

Where m_o is initial permeability, I_s is saturated magnetization strength. Assume that the inclusion led the domain wall to be pinning is spherical, its diameter is d and its arrangement is a regular and simple cubic lattice. Cubic axes of the inclusion lattice are parallel with easily magnetized axes as shown in Fig. 2.
The domain wall is pinned and stopped in the center of the inclusion. This arises mainly because when energy density of the domain wall is not varied, the domain wall is located in the center of the inclusion and the total free energy of the domain wall is the minimum. Therefore, the domain wall is in the most stable condition.
Now we only consider the area of a simple domain wall in the inclusion lattice. Suppose that the displacement of a domain wall is X, after has punched by an inclusion, the area of the domain wall is:. If r is the energy density of the domain wall, then the energy of the domain wall may be expressed as E_r = rS. When the domain wall moves X, then the variation of the domain wall energy per volume is



Under the action of the outer magnetic field, when the domain wall is in the equilibrium state, DE = 0 must be satisfied, i. e. When the outer magnetic field varied, the 180°domain wall have

(6)

Where m_o is initial permeability. I_s is saturated magnetization strength.q is the angle measured from the outer magnetic field axis to the saturated magnetization strength axis, then the critical outer magnetic field strength is

(7)

The sign b denotes the volume density of the inclusion , and the static of volume of a inclusion to total volume incorporated the inclusion is defined as

(8)

Substituting Eq10 into Eq9, we get

(9)

Where d is thickness of the domain wall, . K_I is anisotropic coefficient of magnetic grain.
Let the volume of the inclusion is V₁,its weight is W₁ and its density is p₁; the volume except for the inclusion is V₂, its weight is W₂ and mean density is p₂, and so the volume ratio is b, the weight ratio is Z. We get

(10)

Since carbides of material vary with tempered temperature, its distribution density value is varied. But its total weight is a invariable value and b is constant. The space of inclusion, a(as shown in Fig. 2) is identical with L, and then, the duration time of a Gauss pulse ,t_s is

(11)

Owing to the statistical theory, when |X| ³ 3s, the value of a Gauss type function f(x) can be considered as zero, i. e. F(x)=0. Then t_s = 6s, we get

(12)

When magnetization period of the outer magnetic field is a fixed value, and then the time of producing BN also is a fixed value, i. e. t_total is a constant. Total number of Barkhausen Jump in the magnetization process is equal to the total number of inclusion led domain wall to be pinned in the sweeping volume of the domain wall. Let the mean free distance of the domain wall motion is L, then n=1/L³, we have

(13)

Substituting Eq14 and Eq15 into Eq4, we get MP=C_dL. Where the coefficient of ratio. Following from Eq5, we can be known that the output of the magnet-elastic instrument, MP is in proportion to the free distance of the domain wall motion, L.

Example of theoretical analysis

After quenching at 860°C, the 42CrMo steel specimens were carried out tempering treatment at different temperature. The microstructures of specimens may be changed with the increase of the tempering temperature. The relationship curve between the output of the magneto-elastic instrument, MP and the tempering temperature is obtained and is shown in Fig3.

Fig 3: MP and tempreing temperature

Fig 4: Coercivity and tempering temperature


Since MP is in proportion to the mean free distance, L, we can be theoretically analyzed the variation of the curve in Fig3 as following:
1. Low tempering temperature case
   In low temperature tempered mastensite, due to supersaturated solid solution of carbon in -Fe, the strong pinning action in produced to block movement of the domain wall. Therefore, the mean free distance of the domain walls motion is smaller. The low tempering temperature corresponds with low MP value as shown in Fig3.
2. Tempering temperature gradually increasing case
   Following from continuously increasing of tempering temperature, the carbon atoms of supersaturated solution in -Fe is continuously separated out with carbide form. By virtue of separation, spherulitization, growing and accumulation of the carbides, the pinning action of the carbon atoms has gradually weakened. Then the mean free distance of the domain wall's motion is larger and the output of the magneto-elastic instrument, MP is larger as shown in Fig3.
According to the conclusion in this paper and experiment relation curve in Fig3, we can deduce that the coercivity is gradually decreased as increasing of the tempering temperature.
For the sake of to judge this argument, using impact type-measuring instrument, and the coercivity of different specimens tempered at different temperature have been measured. The experiment relation curve between the coercivity and the tempering temperature is obtained. Just as we expected, the coercivity is gradually decreased as increasing of the tempering temperature.

Acknowledgement

This work was supported by the National Natural Science Foundation of Chain.

Reference

1. Richard. L. Pasley. Barkhausen effect - an indication of stress. Material Evaluation. (1970).157~161.
2. L. P.Karjalainen and M. Moilanen. Defection plastic deformation during fatigue of mild steel by the measurement of Barkhausen noise. NDT. International (1979). 4. 51~55
3. S.Tiitto. On the influence of microstructure on magnetization transitions in steel. Acta Pol. Scand. , Ph 119, 19(1977)
4. D. K. Bhatiacharya. T. Jayakumar. V. Moorthy. S. Vaidyanathan and Baldev Raj. Characterization of microstructures in 17-4-PH strainless steel by magnetic Barkhausen noise analysis. NDT&E International Vol.26. No.3 (1993). 141~148
5. K.Tiitoo and R.Fix. Automatical control of camshaft grinding process by Barkhausen noise . Materials Evaluation Vol.48. No.7. (1990). 904~907.
6. H.Sakamoto. M. Okada and M.Homma. Theoretical analysis of Barkhausen noise in carbon steels. IEEE. Transactions on magnetic. Vol.23. No.5. (1987). 2236~2238.
7. S. Saynajakangas, A non-destructive electromagnetic method for structural studies of ferrous alloy. Acta Pol. Scand. E. 33(1973)
8. C. Kittel and K. F. Calt Ferromagnetic domain theory Solid State Physics. 9. New york, Academic Press, (1956) P437

© AIPnD , created by NDT.net

|Home|    |Top|