CN111257807B - Simulation method of magnetic Barkhausen noise signal in stress-containing two-phase ferromagnetic material - Google Patents

Simulation method of magnetic Barkhausen noise signal in stress-containing two-phase ferromagnetic material Download PDF

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CN111257807B
CN111257807B CN202010106235.4A CN202010106235A CN111257807B CN 111257807 B CN111257807 B CN 111257807B CN 202010106235 A CN202010106235 A CN 202010106235A CN 111257807 B CN111257807 B CN 111257807B
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stress
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barkhausen noise
magnetic barkhausen
noise signal
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何存富
王志
刘秀成
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Beijing University of Technology
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Abstract

The invention discloses a method for simulating a magnetic Barkhausen noise signal in a stress-containing dual-phase ferromagnetic material, which comprises the steps of carrying out mesh division on a spinning plane in an Ising model, and carrying out assignment on different model parameters in a divided sub-spinning plane mesh so as to simulate different magnetic properties of two components. The ratio of the number of meshes occupied by each of the two components can be adjusted to simulate variations in the ratio of the components. Solving the Ising model by using a Monte Carlo algorithm to obtain a magnetic Barkhausen noise signal of the two-phase material with different component ratios. And describing the relation between the spin interaction coefficient and the stress in the Ising model by using a fourth-order polynomial, substituting the relation into a biphase material magnetic Barkhausen noise signal simulation model, and analyzing the change rule of the characteristics of the magnetic Barkhausen noise signal under the combined action of the component ratio and the stress. The influence rule of the component proportion and the stress change on the magnetic Barkhausen noise predicted by the method disclosed by the invention is consistent with the experimental result.

Description

Simulation method of magnetic Barkhausen noise signal in stress-containing two-phase ferromagnetic material
Technical Field
A simulation method of a magnetic Barkhausen noise signal in a stress-containing dual-phase ferromagnetic material belongs to the cross content of the fields of magnetic physics and nondestructive testing, is not only helpful for revealing physical phenomena, but also can be used as a theoretical basis for component proportion and stress nondestructive testing of the dual-phase material.
Background
The magnetic Barkhausen noise detection method has the characteristic of nondestructive detection and is very sensitive to the change of the internal component proportion and the stress of the material. In the experimental process, the magnetic Barkhausen noise signal detected in the two-phase ferromagnetic material is observed to show a bimodal phenomenon, and the bimodal characteristic shows a regular change trend along with the change of the two-phase volume ratio and the stress.
At present, a macroscopic hysteresis model is mostly combined with a linear superposition method to realize a simulation method of a magnetic Barkhausen noise signal of a stress-containing two-phase ferromagnetic material, but the method cannot consider microscopic characteristic information and cannot consider the relation between two single phases. Therefore, a reasonable simulation method of the magnetic barkhausen noise signal of the stress-containing two-phase ferromagnetic material is not available.
The invention creatively provides a method for setting grids by utilizing Ising model spinning plane grid division and equivalent spinning interaction coefficients on the basis of the existing Ising model, realizes the simulation of magnetic Barkhausen noise signals of a two-phase ferromagnetic material, and quantitatively predicts the influence rule of the component proportion and stress of the two-phase material on the bimodal peak of the magnetic Barkhausen noise signals.
Disclosure of Invention
The invention aims to provide a method for simulating a magnetic Barkhausen noise signal in a stress-containing dual-phase ferromagnetic material, so as to realize the prediction of the magnetic Barkhausen noise signal of the dual-phase ferromagnetic material under the action of stress theoretically.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a simulation method of magnetic Barkhausen noise signals in a stress-containing dual-phase ferromagnetic material is specifically realized by the following steps:
step 1: in the magnetic Barkhausen noise simulation method of the stress-containing two-phase ferromagnetic material, an Ising model is combined with a Monte Carlo algorithm. Firstly, carrying out grid division on spin planes in an Ising model to form N spin sub-planes with equal spin number, wherein each spin sub-plane comprises N spin points, and Q (Q is more than or equal to 1 and less than or equal to N) is selected to set an equivalent spin interaction coefficient to be Je1The spin interaction coefficient in the remaining N-Q sub-spin planes is set to Je2In this case, the component ratio is β ═ Q/N. Equivalent spin interaction coefficient Je1And Je2The expression of (a) is:
Figure BDA0002388529170000011
in the formula J1And J2Is the spin interaction coefficient in the absence of stress; j. the design is a squareσ1And Jσ2Coefficient of spin interaction due to internal stress σ of the bicomponent lattice, Jσ1And Jσ2The relation with stress sigma is four timesThe polynomial form is expressed as follows:
Figure BDA0002388529170000025
in the formula p11、p12、p13、p14、p21、p22、p23、p24Is the polynomial coefficient.
In the magnetic barkhausen noise signal simulation of the stress-containing two-phase ferromagnetic material, the energy E of the total spin system of the Ising model considering the component ratio and the stress is expressed as follows:
Figure BDA0002388529170000021
wherein S represents the two spin states, the value of S is +/-1, the spin-up and the spin-down are represented respectively, and Nxn represents the number of total spin points.
If the influence of the stress (σ ═ 0) is not considered, equation (3) degenerates to a model suitable for the two-phase ferromagnetic material in the unstressed state, and the energy E of the total spin system thus formed is expressed as:
Figure BDA0002388529170000022
step 2: solving the whole spin plane region of the stress-containing two-phase ferromagnetic material magnetic Barkhausen noise signal simulation Ising model expressed by the formula (3) or the formula (4) by using a Monte Carlo algorithm, and expressing the magnetization M by using the arithmetic mean value of a spin system, wherein the expression is as follows:
Figure BDA0002388529170000023
in the simulation of the magnetic Barkhausen noise signal of the stress-containing two-phase ferromagnetic material, the magnetic Barkhausen noise signal is calculated, and the expression is as follows:
Figure BDA0002388529170000024
where t is the simulation time, i.e., the number of solution steps in the Monte Carlo algorithm.
The magnetic Barkhausen noise signal of the two-phase material under the condition of different component volume ratios can be obtained by solving the formula (3). The magnetic Barkhausen noise signal simulation of the two-phase material under the stress action can be obtained by solving the formula (4), and the influence rule of the component ratio and the stress on the magnetic Barkhausen noise signal can be quantitatively predicted.
Drawings
Figure 1Ising model spin-plane plots.
Fig. 2 is a graph of the magnetic barkhausen noise signal of the two-phase material under different component ratios obtained by simulation.
FIG. 3 is a signal envelope diagram of magnetic Barkhausen noise of a two-phase material under different component ratios.
Fig. 4 is a graph of magnetic barkhausen noise signals at a specified stress for a component fraction β of 4%.
In the biphasic material of FIG. 5, represents J1Magnetic Barkhausen noise peaks of the phases are plotted against stress.
In the biphasic material of FIG. 6, representative J2Magnetic Barkhausen noise peaks of the phases are plotted against stress.
Detailed Description
In order to make the objectives, technical solutions and advantages of the present invention more apparent, the present invention will be further described with reference to the accompanying drawings and detailed description of the present invention.
The invention provides a method for simulating a magnetic Barkhausen noise signal in a stress-containing dual-phase ferromagnetic material, which comprises the following steps of:
s1: in the magnetic Barkhausen noise simulation method of the stress-containing two-phase ferromagnetic material, the spinning plane in the Ising model is subjected to equal-size grid division, a two-dimensional 20 multiplied by 20 spinning plane is taken as an example and is divided into 25 4 multiplied by 4 spinning planes, and the spinning interaction coefficients are arranged in Q randomly selected spinning planesIs J1The spin interaction coefficient in the other 25-Q spin sub-planes is J, 0.52Where Q is taken to be 1, 2 and 3, respectively, and the corresponding component proportions β are 4%, 8% and 12%, respectively, the schematic diagram of the spin plan is shown in fig. 1.
S2: and substituting the divided spin planes into the Ising model, and calculating to obtain magnetic Barkhausen noise signals with different component ratios as shown in figure 2. The envelope curve of the magnetic Barkhausen noise signal is extracted by adopting a moving average algorithm, and butterfly curves of the two-phase material under different component ratios are drawn and are shown in figure 3.
S3: the coefficients of the terms in equation (2) are assigned, p11＝p21＝1.5×10-34MPa-4，p12＝p22＝-1.1×10-25MPa-3，p13＝p23＝2.2×10-17MPa-2And p14＝p24＝5.0×10-15MPa-1Fig. 4 shows a magnetic barkhausen noise signal under a specific stress obtained by simulation by substituting each coefficient into equation (3) and taking β as an example of 4%.
S4: solving is carried out at intervals of 20MPa within the range of simulated stress of 0-200 MPa to obtain magnetic Barkhausen noise signals of the two-phase material with different component ratios under each simulated stress, and the variation of the double peak value of the extracted signals along with the stress is shown in figures 5 and 6.

Claims (3)

1. A simulation method of magnetic Barkhausen noise signals in a stress-containing dual-phase ferromagnetic material is characterized by comprising the following steps: the specific implementation process of the method is as follows,
step 1: in the magnetic Barkhausen noise simulation method of the stress-containing two-phase ferromagnetic material, a mode of combining an Ising model with a Monte Carlo algorithm is adopted; firstly, carrying out grid division on spin planes in an Ising model to form N spin sub-planes with equal spin number, wherein each spin sub-plane comprises N spin points, and Q spin sub-planes are selected to set an equivalent spin interaction coefficient to be Je1The spin interaction coefficient in the remaining N-Q sub-spin planes is set to Je2At this timeThe proportion of the components is beta-Q/N, and Q is more than or equal to 1 and less than or equal to N;
step 2: solving the whole spin plane region of the stress-containing two-phase ferromagnetic material magnetic Barkhausen noise signal simulation Ising model expressed by the formula (3) or the formula (4) by using a Monte Carlo algorithm, and expressing the magnetization M by using the arithmetic mean value of a spin system;
coefficient of equivalent spin interaction Je1And Je2The expression of (a) is:
Figure FDA0003533579060000015
in the formula J1And J2Is the spin interaction coefficient in the absence of stress; j. the design is a squareσ1And Jσ2Coefficient of spin interaction due to internal stress σ of the bicomponent lattice, Jσ1And Jσ2The relationship to stress σ is expressed in the form of a fourth order polynomial as follows:
Figure FDA0003533579060000016
in the formula p11、p12、p13、p14、p21、p22、p23、p24Is the coefficient of each polynomial;
in the magnetic barkhausen noise signal simulation of the stress-containing two-phase ferromagnetic material, the energy E of the total spin system of the Ising model considering the component ratio and the stress is expressed as follows:
Figure FDA0003533579060000011
wherein S represents the two spin states, the value of S is +/-1, the spin states represent spin-up and spin-down respectively, and Nxn represents the number of total spin points;
if the influence of the stress σ ═ 0 is not taken into consideration, equation (3) degenerates to a model suitable for the two-phase ferromagnetic material in the stress-free state, and the energy E of the total spin system thus formed is expressed as:
Figure FDA0003533579060000012
the expression of M is:
Figure FDA0003533579060000013
in the simulation of the magnetic Barkhausen noise signal of the stress-containing two-phase ferromagnetic material, the magnetic Barkhausen noise signal is calculated, and the expression is as follows:
Figure FDA0003533579060000014
where t is the simulation time, i.e., the number of solution steps in the Monte Carlo algorithm.
2. The method for simulating the magnetic Barkhausen noise signal in the stress-containing dual-phase ferromagnetic material according to claim 1, wherein the method comprises the following steps: the method comprises the steps of carrying out equal-size grid division on a spinning plane in an Ising model, setting different spinning interaction coefficients for a spinning array in a grid to simulate components or phases with different magnetic characteristics, wherein for a two-phase material, the spinning plane contains two grid types with different spinning interaction coefficient values, the quantity ratio of the two grids represents the volume ratio of the two components in the two-phase material, and solving the whole spinning plane area of the Ising model through a Monte Carlo algorithm to obtain the magnetic Barkhausen noise signals of the two-phase material under the condition of different component volume ratios.
3. The method for simulating the magnetic Barkhausen noise signal in the stress-containing dual-phase ferromagnetic material according to claim 1, wherein the method comprises the following steps: by means of equivalent spin interaction coefficient JeIntroducing the stress sigma into the model, and analyzing the stress-pair biphase ferromagnetic materialInfluence rule of magnetic Barkhausen noise signals in the material.
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