CN111257807A - 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 PDFInfo
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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 the change 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
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 stress-containing two-phase ferromagnetic material magnetic Barkhausen noise signal, 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 by utilizing the spinning plane grid division and the equivalent spinning interaction coefficient grid division of the Ising model on the basis of the existing Ising model, realizes the magnetic Barkhausen noise signal simulation of the two-phase ferromagnetic material, and quantitatively predicts the influence rule of the component proportion and the stress of the two-phase material on the bimodal peak of the magnetic Barkhausen noise signal.
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 Je2The ratio of the components is β -Q/NBy the factor Je1And Je2The expression of (a) is:
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:
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:
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:
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:
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:
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 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, denoted 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, a spinning plane in an 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 a spinning interaction coefficient J is set in a randomly selected Q spinning plane1The 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 ratios β are 4%, 8% and 12%, respectively, the spin plan view is shown in figure 1.
S2: the divided spin planes are substituted into the Ising model, and magnetic Barkhausen noise signals under different component ratios are obtained through calculation and are 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 the coefficients 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 (5)
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: magnetic Barkhausen noise simulation on stress-containing two-phase ferromagnetic materialIn the method, 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 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 Je2The ratio of the components is β -Q/N, and Q is more than or equal to 1 and less than or equal to N;
step 2: and (3) 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.
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: coefficient of equivalent spin interaction Je1And Je2The expression of (a) is:
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:
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:
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:
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: the expression of M is:
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:
where t is the simulation time, i.e., the number of solution steps in the Monte Carlo algorithm.
4. 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.
5. 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 JeAnd introducing the stress sigma into a model, and analyzing the influence rule of the stress on the magnetic Barkhausen noise signal in the two-phase ferromagnetic material.
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