CN108287191A - A kind of magnetic memory signal properties study method based on FLAPW algorithms - Google Patents
A kind of magnetic memory signal properties study method based on FLAPW algorithms Download PDFInfo
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Abstract
A kind of magnetic memory signal properties study method based on FLAPW algorithms belongs to the magnetic memory signal detection technique field of ferrimagnet more particularly to a kind of magnetic memory signal properties study method based on FLAPW algorithms.The present invention provides a kind of magnetic memory signal properties study method based on FLAPW algorithms.The present invention includes the following steps：Step 1）：Establish magnetomechanics model；Step 2）：The use of FLAPW worldwide earthquake disaster methods.
Description
Technical field
The invention belongs to the magnetic memory signal detection technique fields of ferrimagnet, more particularly to a kind of FLAPW that is based on to calculate
The magnetic memory signal properties study method of method.
Background technology
Pipeline transportation is international oil gas transport one of major way, has that freight volume is big, not climate and ground other factors
The advantages that limiting, can working continuously and is at low cost.
The security maintenance of long oil and gas pipeline is the key problem of pipeline operation.Come from the analysis of pipeline accident in recent years
It sees, newly-built pipeline accident takes place frequently, and is not fully developed the gross imperfection of tube body at this time.The non-destructive testing technology such as magnetic powder of routine,
Leakage field, vortex and infiltration etc. played an important role in the defect inspection of pipeline, accident prevention etc., but can only find
Formed macroscopical volume defect, can not caused by the factors such as construction, welding, settlement of foundation, medium internal pressure, thermal expansion still
The region of stress concentration of unshaped volume defect implements effectively evaluating, to avoid causing prominent due to stress damage
Send out sexual behavior event.Stress concentration is the major reason that sudden accident occurs for long oil and gas pipeline；Especially newly-built pipeline is in tubulation
With there are a large amount of region of stress concentrations, some region of stress concentrations to have reached threshold yield point, lead to pipeline in work progress
The generation of sudden accident after operation.Magnetic memory method can effectively judge the region of stress concentration of ferromagnetic metal component, still
Newtonian mechanics and Maxwell equation are not all elaborated about power is magnetic-coupled, and the power magnetic coupling mechanism of magnetic memory signal is still
It comes to a conclusion without unified, the algorithm for magnetic memory signal is also the bottleneck problem in the field.
Invention content
The present invention addresses the above problem, provides a kind of magnetic memory signal properties study method based on FLAPW algorithms.
To achieve the above object, the present invention adopts the following technical scheme that, the present invention includes the following steps：
Step 1)：Establish magnetomechanics model
The process that ferromagnetic component reaches yield limit under external force is that electron shell is never filled to half and arrives
Electron shell was full of the process of half, and aggregated momentum square quantum number is expressed as during being somebody's turn to do：
Wherein, J is aggregated momentum square quantum number, and L is track aggregated momentum square, and S is resultant spin square, and n is electron number, and N is total grain
Subnumber；The charge density distribution known to formula (1) can characterize the variation of aggregated momentum square；
According to the gyromagnetic effect of ferromagnetic object, the total magnetic moment and aggregated momentum square of object have following relationship：
Wherein, M is the intensity of magnetization of material, and g is that gyromagnetic ratios are constant, e=4.8025 × 10-10C.G.S. electrostatic
Unit, m=9.1066 × 10-28Gram, for electric proton rest mass, c=3 × 1010Cm/s are the light velocity；It is obtained by formula (2),
The aggregated momentum square and total magnetic moment of component are proportional；
The magnetism of ferrimagnet is made of the magnetism of earth's magnetic field magnetic memory signal and material itself, i.e.,：
Wherein, B0=μ0H indicates earth's magnetic field magnetic memory signal intensity, B1=μ0M indicates that material magnetic memory signal itself is strong
Degree, μ0Indicate that space permeability, H are magnetic field intensity, M is the intensity of magnetization of material；
Formula (2) is substituted into formula (3), the magnetic memory signal of ferrimagnet is expressed as：
In conjunction with formula (3)~(4), the relationship of aggregated momentum square and atomic magnetic moment is expressed as：
Obtained by formula (4)~(5), aggregated momentum square, atomic magnetic moment and magnetic memory signal correlation；
Charge density, the relationship of aggregated momentum square and magnetic memory signal are studied, and then studies the magnetomechanics under outer force effect and closes
System, according to Kohn-Sham equations, the single electron Schrodinger equation in the case where there is outer force effect is：
Wherein, p is effective bohr magneton number, reflects electron spin campaign and track motion conditions, and ψ is wave function, and E is
System capacity function；VeffFor external force effective poential, formula (6) characterizes the correspondence of aggregated momentum square outer field action gesture；
External force effective poential V in formula (6)eff(r) it is expressed as：
Wherein, V (r) is outer field action gesture, Vc(r) it is Coulomb potential and exchange correlation potential Vxc(r), Exc[ρ (r)] indicates to exchange
Correlation energy, electron density distribution function ρ (r), r indicate electronic coordinate；Formula (7) can characterize the direct of charge density and outer force effect
Contact；
It is obtained by formula (4)~(7), under external force, as stress increases, electron shell full level influences material
Charge density distribution causes the variation of aggregated momentum square and atomic magnetic moment, and system magnetic characteristic is caused to change；By constructing wave letter
Number ψ solves the variation of the charge density distribution and atomic magnetic moment in formula (6), and research ferrimagnet is under outer force field
Magnetomechanics characteristic；
Step 2)：The use of FLAPW worldwide earthquake disaster methods
Linearly sew plus plane wave basic function is expressed as：
On the basis of linearly sewing plus the wave function of the middle formula (8) of plane wave method, when handling external force gesture and charge density,
The limitation for improving the shape of pair potential adds correction term in gap areaI.e.：
Wherein, MT indicates that ball inner region, i indicate ball exterior domain, and Hamiltonian matrix and overlapping matrix are constructed by formula (9),
Formula (6) is substituted into again and solves wave function, obtains the wave function ψ under different aggregated momentum square J, i.e.,：
Wherein, ciFor expansion coefficient, obtained by Rayleigh-Ritz variation principles, i.e., by ψVThe functional of (k, r) composition
The condition in value is taken, n equation is obtained：
Construct the charge density of ball inner region and ball exterior domain, different aggregated momentum square J respectively by the wave function of formula (10)
Lower different charge density is respectively：
Wherein, ρ (r) is charge density；∫BZFor in the integral of first Brillouin-Zone；Charge density is solved by formula (12)
Afterwards, it substitutes into and solves aggregated momentum square J in formula (6), research atomic magnetic moment variation, and then ferrimagnet is studied under outer force field
Magnetomechanics characteristic.
As a preferred embodiment, the invention also includes the simulation modeling part of the accuracy for verification algorithm, emulation
Modeled segments are established magnetomechanics model, are as follows using the X80 steel in practical engineering application as research object：
It after solving charge density by formula (12), substitutes into and solves aggregated momentum square in formula (6), so as to find out outer in formula (7)
Power gesture Veff, during being somebody's turn to do, charge density characterizes magnetism characteristic, external force gesture VeffMechanical characteristic is characterized, by magnetomechanics association of characteristics
Together, magnetomechanics model is established；
Fe in X80 steel is main component, and foreign atom C, which accounts for 0.06%, Si and accounts for 0.28%, Mn and account for 1.83%, P, to be accounted for
0.01%, according to the element proportioning setting of above-mentioned X80 steel, (the i.e. above-mentioned each atom of element proportioning setting contains each element in model
Amount)；
Model is established using the quantum mechanics module CASTEP crystal library based on density functional theory.
It is of the present invention to utilize the quantum mechanics module CASTEP based on density functional theory as another preferred embodiment
The modeling pattern that model is established in crystal library is：It is extended to obtain 3 × 6 respectively in tri- basic vector directions a, b, c of independent structure cell
× 12 surpass primitive cell structure.
As another preferred embodiment, simulation modeling part of the present invention is during simulation calculation, by Brillouin zone
Sampled point k takes 6 × 3 × 2, and plane wave cut-off takes 330eV, atomic binding energy to be set in 0.01eV, different orbital electron
Between exchange correlation can use generalized gradient approximation (generalized gradient approximation, GGA) function
Handle the exchange correlation energy between electronics.
As another preferred embodiment, the invention also includes the calculated charge density and atomic magnetic moment of verification model accuracy
Part, calculated charge density and atomic magnetic moment part include the following steps：
(1) charge density calculates
On the model for establishing model using the quantum mechanics module CASTEP crystal library based on density functional theory
Z-axis direction apply variation pressure, calculate electron shell in charge density；
Distribution of charges is observed with stress variation collection of illustrative plates, passes through charge density, aggregated momentum square quantum number and the total magnetic moment of atom
Variation judges the variation of magnetic memory signal；
(2) atomic magnetic moment calculates
Atomic magnetic moment, observation stress and atomic magnetic moment relational graph are calculated, judges the situation of change of magnetic memory signal.
As a preferred embodiment, the pressure that z-axis direction on model of the present invention applies variation be high intensity from
The stress of 0GPa to 40GPa, is divided into 10GPa.
As another preferred embodiment, during observation distribution of charges of the present invention is with stress variation collection of illustrative plates, look into first
When seeing stress from 0GPa to 10GPa, the situation of change of distribution of charges, and pass through charge density, aggregated momentum square quantum number and atom
The variation of total magnetic moment judges the variation of magnetic memory signal；Then, when checking stress from 10GPa to 40GPa, the variation of distribution of charges
Situation, and judge by the variation of charge density, aggregated momentum square quantum number and the total magnetic moment of atom the variation of magnetic memory signal.
As another preferred embodiment, atomic magnetic moment and charge density of the present invention, which calculate, passes through MatStudio (full name
Material Studio) software calculating.
As another preferred embodiment, the invention also includes the magnetic memory signal changing rules of verification ferromagnetic metal component
Experiment, the experiment is using rectangle tabular sample, universal testing machine, magnetic memory signal detection device made of X80 proximate matter material
And extensometer；
Sample is connected with the force output end of universal testing machine first, by extensometer and magnetic memory signal detection device
Detection probe is connected with sample；
The detection signal output port of extensometer is connected with the signal input port of universal testing machine sub computers, magnetic note
The detection of the detection signal output port and the host of magnetic memory signal detection device of recalling the detection probe of signal detection apparatus is believed
Number input port is connected；
Sample is monitored by the host of magnetic memory signal detection device and the detection probe of magnetic memory signal detection device to exist
The situation of change of magnetic memory signal in loading process monitors sample in stress by universal testing machine sub computers and extensometer
Ess-strain situation in the process.
As another preferred embodiment, specimen length of the present invention is 450 ± 0.5mm, and width is 50 ± 0.5mm, thick
Degree is 18.8mm, form tolerance 0.2mm.
As another preferred embodiment, universal testing machine of the present invention uses SHT4106 microcomputer controlled electro-hydraulic servos ten thousand
It can testing machine.
As another preferred embodiment, magnetic memory signal detection device of the present invention uses TSC-3M-12 type Magnetic Memories
Signal detection apparatus.
As another preferred embodiment, the length direction both ends of sample of the present invention are applied with universal testing machine up and down respectively
Power output end connects, and one middle side part of width direction in sample, the detection probe of magnetic memory signal detection device is arranged in extensometer
It is bonded with the center of sample.
As another preferred embodiment, it is of the present invention experiment the specific steps are：
Step 1)：Start universal testing machine, carry out first time stretching, stops after being pulled to setting force value, drawing force is returned to
0MPa；
Step 2)：Step 1 is repeated, universal testing machine is started, second is carried out and stretches, stops after being pulled to setting force value, draws
Stretch is returned to 0MPa；
Step 3)：Step 1 is repeated, universal testing machine is started, carries out third time stretching, stops after being pulled to setting force value, draws
Stretch is returned to 0Mpa；
Step 4)：Start universal testing machine, carries out the 4th stretching, be pulled to sample fracture；
Step 5)：After universal testing machine is out of service, sample and magnetic memory signal detection device are removed, read number
According to arrangement curve observes stress-strain diagram and specimen surface magnetic memory signal change curve.
Secondly, the force value of the present invention that sets is 450MPa.
In addition, experiment of the present invention is stretched using the sample of five completely the same X80 types.
Advantageous effect of the present invention.
The present invention uses a kind of FLAPW worldwide earthquake disasters algorithm, establishes magnetomechanics model, provides material electronics
The charge density of shell and the relationship of magnetic memory signal, provide the correspondence between stress and magnetic memory signal, provide magnetic note
Recall signal characteristic.The present invention be it is a kind of it is effective research magnetic memory signal feature algorithm, be magnetic memory detection technology to ferromagnetic
Property component life appraisal reliable research method is provided.
Description of the drawings
The present invention will be further described with reference to the accompanying drawings and detailed description.The scope of the present invention not only limits to
In the statement of the following contents.
Fig. 1 is illustraton of model of the present invention.
Fig. 2~Fig. 6 is charge density distribution figures of the Fe under different stress.
Fig. 2 is the charge density figure under 0GPa.
Fig. 3 is the charge density figure under 10GPa.
Fig. 4 is the charge density figure under 20GPa.
Fig. 5 is the charge density figure under 30GPa.
Fig. 6 is the charge density figure under 40GPa.
Fig. 7 is stress and atomic magnetic moment relational graph.
Fig. 8 is experimental sample schematic diagram of the present invention.
Fig. 9 is the stress-strain curve of experimental sample of the present invention 1..
Figure 10 is the stress-strain curve of experimental sample of the present invention 2..
Figure 11 is experimental sample of the present invention 1. magnetic memory signal distribution map.
Figure 12 is experimental sample of the present invention 2. magnetic memory signal distribution map.
Figure 13 is present invention experiment connection diagram.
Specific implementation mode
The present invention includes the following steps：
Step 1)：Establish magnetomechanics model
According to electron spin theory and big vast moral rule, the process that ferromagnetic component reaches yield limit under external force is
Electron shell is never filled to the process that half was full of half to electron shell, and aggregated momentum square quantum number indicates during being somebody's turn to do
For：
Wherein, J is aggregated momentum square quantum number, and L is track aggregated momentum square, and S is resultant spin square, and n is electron number, and N is total grain
Subnumber；The charge density distribution known to formula (1) can characterize the variation of aggregated momentum square；
According to the gyromagnetic effect of ferromagnetic object, the total magnetic moment and aggregated momentum square of object have following relationship：
Wherein, M is the intensity of magnetization of material, and g is that gyromagnetic ratios are constant, e=4.8025 × 10-10C.G.S. electrostatic
Unit, m=9.1066 × 10-28Gram, for electric proton rest mass, c=3 × 1010Cm/s are the light velocity；It is obtained by formula (2),
The aggregated momentum square and total magnetic moment of component are proportional；
According to Stoner criterions, magnetic magnetic group by earth's magnetic field magnetic memory signal and material itself of ferrimagnet
At that is,：
Wherein, B0=μ0H indicates earth's magnetic field magnetic memory signal intensity, B1=μ0M indicates that material magnetic memory signal itself is strong
Degree, μ0Indicate that space permeability, H are magnetic field intensity, M is the intensity of magnetization of material；
Formula (2) is substituted into formula (3), the magnetic memory signal of ferrimagnet is expressed as：
In conjunction with formula (3)~(4), the relationship of aggregated momentum square and atomic magnetic moment is expressed as：
Obtained by formula (4)~(5), aggregated momentum square, atomic magnetic moment and magnetic memory signal correlation；
Charge density, the relationship of aggregated momentum square and magnetic memory signal are studied, and then studies the magnetomechanics under outer force effect and closes
System, according to Kohn-Sham equations, the single electron Schrodinger equation in the case where there is outer force effect is：
Wherein, p is effective bohr magneton number, reflects electron spin campaign and track motion conditions, and ψ is wave function, and E is
System capacity function；VeffFor external force effective poential, formula (6) characterizes the correspondence of aggregated momentum square outer field action gesture；
External force effective poential V in formula (6)eff(r) it is expressed as：
Wherein, V (r) is outer field action gesture, Vc(r) it is Coulomb potential and exchange correlation potential Vxc(r), Exc[ρ (r)] indicates to exchange
Correlation energy, electron density distribution function ρ (r), r indicate electronic coordinate；Formula (7) can characterize the direct of charge density and outer force effect
Contact；
It is obtained by formula (4)~(7), under external force, as stress increases, electron shell full level influences material
Charge density distribution causes the variation of aggregated momentum square and atomic magnetic moment, and system magnetic characteristic is caused to change；By constructing wave letter
Number ψ solves the variation of the charge density distribution and atomic magnetic moment in formula (6), and research ferrimagnet is under outer force field
Magnetomechanics characteristic；
Step 2)：The use of FLAPW worldwide earthquake disaster methods
Linearly sew plus plane wave basic function is expressed as：
On the basis of linearly sewing plus the wave function of the middle formula (8) of plane wave method, when handling external force gesture and charge density,
The limitation for improving the shape of pair potential adds correction term in gap areaI.e.：
Wherein, MT indicates that ball inner region, i indicate ball exterior domain, and Hamiltonian matrix and overlapping matrix are constructed by formula (9),
Formula (6) is substituted into again and solves wave function, obtains the wave function ψ under different aggregated momentum square J, i.e.,：
Wherein, ciFor expansion coefficient, obtained by Rayleigh-Ritz variation principles, i.e., by ψVThe functional of (k, r) composition
The condition in value is taken, n equation is obtained：
Construct the charge density of ball inner region and ball exterior domain, different aggregated momentum square J respectively by the wave function of formula (10)
Lower different charge density is respectively：
Wherein, ρ (r) is charge density；∫BZFor in the integral of first Brillouin-Zone；Charge density is solved by formula (12)
Afterwards, it substitutes into and solves aggregated momentum square J in formula (6), research atomic magnetic moment variation, and then ferrimagnet is studied under outer force field
Magnetomechanics characteristic.
Further include the simulation modeling part of the accuracy for verification algorithm, simulation modeling part is in practical engineering application
X80 steel be research object, establish magnetomechanics model, be as follows：
It after solving charge density by formula (12), substitutes into and solves aggregated momentum square in formula (6), so as to find out outer in formula (7)
Power gesture Veff, during being somebody's turn to do, charge density characterizes magnetism characteristic, external force gesture VeffMechanical characteristic is characterized, by magnetomechanics association of characteristics
Together, magnetomechanics model is established；
Fe in X80 steel is main component, and foreign atom C, which accounts for 0.06%, Si and accounts for 0.28%, Mn and account for 1.83%, P, to be accounted for
0.01%, according to the element proportioning setting of above-mentioned X80 steel, (the i.e. above-mentioned each atom of element proportioning setting contains each element in model
Amount)；
Model is established using the quantum mechanics module CASTEP crystal library based on density functional theory.
The modeling pattern that model is established using the quantum mechanics module CASTEP crystal library based on density functional theory
For：It is extended to obtain 3 × 6 respectively in tri- basic vector directions a, b, c of independent structure cell × 12 surpasses primitive cell structure, model structure is such as
Shown in Fig. 1.
The simulation modeling part is during simulation calculation, will be in cloth after considering computational accuracy and computing resource
Deep area's sampled point k takes 6 × 3 × 2, and plane wave cut-off takes 330eV, to ensure that computational accuracy, atomic binding energy are set in
In 0.01eV, the exchange correlation between different orbital electron can use generalized gradient approximation (generalized gradient
Approximation, GGA) function processing electronics between exchange correlation energy.
The invention also includes verification model accuracy calculated charge density and atomic magnetic moment part, calculated charge density and
Atomic magnetic moment part includes the following steps：
(1) charge density calculates
On the model for establishing model using the quantum mechanics module CASTEP crystal library based on density functional theory
Z-axis direction apply variation pressure, calculate electron shell in charge density；Charge density such as Fig. 2 under different stress~
Shown in Fig. 6.By the variation for calculating the charge density analysis system magnetic characteristic under different stress；Data are emulated than engineering reality
Small 3 orders of magnitude of data trampled, ferromagnetic component stress is MPa grades in engineering practice, using above-mentioned charge density calculating side
Formula, convenient for analysis under stress, the changing rule of crystal magnetomechanics characteristic；
Distribution of charges is observed with stress variation collection of illustrative plates, passes through charge density, aggregated momentum square quantum number and the total magnetic moment of atom
Variation judges the variation of magnetic memory signal；
As shown in Fig. 2~Fig. 6, charge density unit is μ C/m2Black is minimum, and grey is maximum, is gradually incremented by；Stress
When from 0GPa to 10GPa, with the increase of stress, distribution of charges concentrates on inside atomic nucleus, i.e., electron shell, which is full of, does not cross one
Half, it is disappeared in original central part to Fig. 3 in Fig. 2, charge density reduces, and causes aggregated momentum square quantum number and the total magnetic of atom
Square reduces, and magnetic memory signal weakens；When stress increases to 40GPa from 10GPa, distribution of charges is spread to outside atomic nucleus, electricity
It is more than half that subshell, which is full of, occurs RED sector in Fig. 4 again, charge density increases, and causes aggregated momentum square quantum number and atom
Total magnetic moment increases, and system magnetic characteristic changes；I.e. as stress increases, charge density generates inflection point, and characterization crystal exists
Magnetomechanics characteristic variations situation before and after yield limit；
(2) atomic magnetic moment calculates
Atomic magnetic moment, observation stress and atomic magnetic moment relational graph are calculated, judges the situation of change of magnetic memory signal.
The atomic magnetic moment of Fe is determined by the spin motion of 3d orbital electron near fermi level and track movement, former
The statistical distribution of sub- magnetic moment embodies the magnetic properties of solid；After being stressed effect, atomic magnetic moment occurs apparent system
Change；With the increase of stress, atomic magnetic moment first reduces, and after reaching yield limit, atomic magnetic moment increases, and system magnetic characteristic occurs
Change, magnetic memory signal becomes increasing from reducing, and reverse speed characterisstic occurs；Average atom magnetic moment such as Fig. 7 under different stress
It is shown.
The pressure that z-axis direction on the model applies variation is the stress of the slave 0GPa to 40GPa of high intensity, is divided into
10GPa；
During the observation distribution of charges is with stress variation collection of illustrative plates, when first looking at stress from 0GPa to 10GPa, charge
The situation of change of distribution, and magnetic memory signal is judged by the variation of charge density, aggregated momentum square quantum number and the total magnetic moment of atom
Variation；Then, when checking stress from 10GPa to 40GPa, the situation of change of distribution of charges, and pass through charge density, aggregated momentum
The variation of square quantum number and the total magnetic moment of atom judges the variation of magnetic memory signal.
The atomic magnetic moment and charge density are calculated to be calculated by MatStudio (full name Material Studio) software
The result of calculation obtained is as shown in Figure 7.
The invention also includes the experiment of the magnetic memory signal changing rule of verification ferromagnetic metal component, which uses
Rectangle tabular sample, universal testing machine, magnetic memory signal detection device and extensometer made of X80 proximate matter material；
Sample is connected with the force output end of universal testing machine first, by extensometer and magnetic memory signal detection device
Detection probe is connected with sample；
The detection signal output port of extensometer is connected with the signal input port of universal testing machine sub computers, magnetic note
The detection of the detection signal output port and the host of magnetic memory signal detection device of recalling the detection probe of signal detection apparatus is believed
Number input port is connected；
Sample is monitored by the host of magnetic memory signal detection device and the detection probe of magnetic memory signal detection device to exist
The situation of change of magnetic memory signal in loading process monitors sample in stress by universal testing machine sub computers and extensometer
Ess-strain situation in the process.
Above-mentioned experimental method through the invention, the influence convenient for research stress to ferromagnetic metal component.
The specimen length is 450 ± 0.5mm, and width is 50 ± 0.5mm, thickness 18.8mm, and form tolerance is
0.2mm。
The universal testing machine uses SHT4106 microcomputer controlled electro-hydraulic servo universal testing machines.Universal testing machine maximum system
System test force is 1000kN
The magnetic memory signal detection device uses TSC-3M-12 type magnetic memory signal detection devices.TSC-3M-12 type magnetic
The each channel Hp value measurement ranges of memory signal detection device are ± 2000A/m, and Hp Measurement channel numbers are 12 channels, each channel
The basic relative error of magnetic-field measurement is ± 5%, and it is ± 2A/m, RS-232 interface number that each channel magnetic-field measurement, which adds absolute error,
According to transmission speed 115kbps.It is convenient for the present invention to test using TSC-3M-12 type magnetic memory signal detection devices reliable, efficient
It carries out.
Force output end connects up and down with universal testing machine respectively at the length direction both ends of the sample, and extensometer setting exists
One middle side part of width direction of sample, the detection probe of magnetic memory signal detection device are bonded with the center of sample.
It is described experiment the specific steps are：
Step 1)：Start universal testing machine, carry out first time stretching, stops after being pulled to setting force value, drawing force is returned to
0MPa；
Step 2)：Step 1 is repeated, universal testing machine is started, second is carried out and stretches, stops after being pulled to setting force value, draws
Stretch is returned to 0MPa；
Step 3)：Step 1 is repeated, universal testing machine is started, carries out third time stretching, stops after being pulled to setting force value, draws
Stretch is returned to 0Mpa；
Step 4)：Start universal testing machine, carries out the 4th stretching, be pulled to sample fracture；
Step 5)：After universal testing machine is out of service, sample and magnetic memory signal detection device are removed, read number
According to arrangement curve observes stress-strain diagram and specimen surface magnetic memory signal change curve.
The accuracy of experiment can be improved using above-mentioned experiment specific steps.
The force value that sets is 450MPa.
The experiment is stretched using the sample of five completely the same X80 types.The present invention randomly selects two samples,
Observe stress-strain diagram and specimen surface magnetic memory signal change curve.Stress-strain diagram is as shown in Figure 9 and Figure 10.
It can be seen from Fig. 9 and Figure 10 in preceding drawing process three times, sample is several in strsses within the elastic limit-strain curve
It overlaps, and in the 4th stretch breaking process, the stress in stress-strain curves starts constriction occur when reaching maximum value, answer
There is inflection point in power-strain curve, and deformation is uniform along entire specimen length before constriction, is deformed then mainly after constriction occurs
Regional area is concentrated on, more and more thinner in this zone cross-sectional, local stress is higher and higher, and stress-strain curves is caused to occur
Inflection point, until plus load cannot be born and be broken.
In sample 1. with sample 2. repeatedly in drawing process, specimen surface magnetic memory signal change curve such as Figure 11 and Figure 12
It is shown.Relationship, and magnetic are changed linearly before yield limit by magnetic memory signal it can be seen from Figure 11, Figure 12 and stress
Memory signal curve essentially coincides in elastic range, but what the magnetic memory signal stretched every time was all stretched than the last time
Magnetic memory signal value amplitude slightly reduces, and has repeatability well；After sample reaches yield limit, the magnetic at yield limit
There is reverse speed characterisstic in memory signal curve, and magnetic memory signal trend is substantially change.
Since the work hardening capacity of ferromagnetic metal component reduces, it is insufficient to compensate for the stress caused by section reduces
It increases, leads to constriction, in the case where tensile speed is constant, stress reduces, therefore is also inverted in magnetic memory signal
Characteristic.Experiment obtains through the invention：Inflection point of the reverse speed characterisstic with ferromagnetic component in yield limit in magnetic memory signal has
High identical property.
It is understood that above with respect to the specific descriptions of the present invention, it is merely to illustrate the present invention and is not limited to this
Technical solution described in inventive embodiments, it will be understood by those of ordinary skill in the art that, still the present invention can be carried out
Modification or equivalent replacement, to reach identical technique effect；As long as meet use needs, all protection scope of the present invention it
It is interior.
Claims (1)
1. a kind of magnetic memory signal properties study method based on FLAPW algorithms, it is characterised in that include the following steps：
Step 1)：Establish magnetomechanics model
The process that ferromagnetic component reaches yield limit under external force is that electron shell is never filled to half to electronics
Shell was full of the process of half, and aggregated momentum square quantum number is expressed as during being somebody's turn to do：
Wherein, J is aggregated momentum square quantum number, and L is track aggregated momentum square, and S is resultant spin square, and n is electron number, and N is total population；
The charge density distribution known to formula (1) can characterize the variation of aggregated momentum square；
According to the gyromagnetic effect of ferromagnetic object, the total magnetic moment and aggregated momentum square of object have following relationship：
Wherein, M is the intensity of magnetization of material, and g is that gyromagnetic ratios are constant, e=4.8025 × 10-10C.G.S. electrostatic unit,
M=9.1066 × 10-28Gram, for electric proton rest mass, c=3 × 1010Cm/s are the light velocity；It is obtained by formula (2), component
Aggregated momentum square and total magnetic moment are proportional；
The magnetism of ferrimagnet is made of the magnetism of earth's magnetic field magnetic memory signal and material itself, i.e.,：
Wherein, B0=μ0H indicates earth's magnetic field magnetic memory signal intensity, B1=μ0M indicates material magnetic memory signal intensity itself, μ0Table
Show that space permeability, H are magnetic field intensity, M is the intensity of magnetization of material；
Formula (2) is substituted into formula (3), the magnetic memory signal of ferrimagnet is expressed as：
In conjunction with formula (3)~(4), the relationship of aggregated momentum square and atomic magnetic moment is expressed as：
Obtained by formula (4)~(5), aggregated momentum square, atomic magnetic moment and magnetic memory signal correlation；
Charge density, the relationship of aggregated momentum square and magnetic memory signal are studied, and then studies the magnetomechanics relationship under outer force effect, root
According to Kohn-Sham equations, the single electron Schrodinger equation in the case where there is outer force effect is：
Wherein, p is effective bohr magneton number, reflects electron spin campaign and track motion conditions, and ψ is wave function, and E is system
Energy function；VeffFor external force effective poential, formula (6) characterizes the correspondence of aggregated momentum square outer field action gesture；
External force effective poential V in formula (6)eff(r) it is expressed as：
Wherein, V (r) is outer field action gesture, Vc(r) it is Coulomb potential and exchange correlation potential Vxc(r), Exc[ρ (r)] indicates exchange correlation
Can, electron density distribution function ρ (r), r indicate electronic coordinate；Formula (7) can characterize the direct of charge density and outer force effect
System；
It is obtained by formula (4)~(7), under external force, as stress increases, electron shell full level influences material charge
Density Distribution causes the variation of aggregated momentum square and atomic magnetic moment, and system magnetic characteristic is caused to change；By constructing wave function ψ,
The variation of charge density distribution and atomic magnetic moment in solution formula (6), magnetic of the research ferrimagnet under outer force field
Mechanical characteristic；
Step 2)：The use of FLAPW worldwide earthquake disaster methods
Linearly sew plus plane wave basic function is expressed as：
On the basis of linearly sewing plus the wave function of the middle formula (8) of plane wave method, when handling external force gesture and charge density, improve
The limitation of the shape of pair potential adds correction term in gap areaI.e.：
Wherein, MT indicates that ball inner region, i indicate ball exterior domain, and Hamiltonian matrix and overlapping matrix, then generation are constructed by formula (9)
Enter formula (6) and solve wave function, obtains the wave function ψ under different aggregated momentum square J, i.e.,：
Wherein, ciFor expansion coefficient, obtained by Rayleigh-Ritz variation principles, i.e., by ψVThe functional of (k, r) composition, which takes, stays
The condition of value obtains n equation：
Construct the charge density of ball inner region and ball exterior domain respectively by the wave function of formula (10), under different aggregated momentum square J not
With charge density be respectively：
Wherein, ρ (r) is charge density；∫BZFor in the integral of first Brillouin-Zone；After charge density being solved by formula (12), generation
Enter and solves aggregated momentum square J in formula (6), research atomic magnetic moment variation, and then study magnetic of the ferrimagnet under outer force field
Mechanical characteristic.
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