DE LA RECHERCHE À L’INDUSTRIE Modelling of Barkhausen … · 2020. 12. 16. · Commissariat à...
Transcript of DE LA RECHERCHE À L’INDUSTRIE Modelling of Barkhausen … · 2020. 12. 16. · Commissariat à...
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
DE LA RECHERCHE À L’INDUSTRIE
Commissariat à l’énergie atomique et aux énergies alternatives - www.cea.fr
Modelling of Barkhausen envelop for the characterization of magnetic materials08 October 2020
Patrick FAGAN
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
Plan
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Introduction: theoretical basis for the Barkhausen Noise Simulation: Jiles-Atherton-Sablik and multi-scale model Experimental setup and results
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
Introduction: the Barkhausen noise
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At micrometric scale, magnetic domains surrounded by domain wallsUnder external magnetizing fields, the domain walls move in such a way to enlarge domains whose internal magnetization M is aligned with the external field H
Faraday Law
M
𝑽𝑽𝑩𝑩𝑩𝑩 𝒕𝒕 ∝ 𝒅𝒅𝒅𝒅𝒅𝒅𝒕𝒕→ 𝑽𝑽𝑩𝑩𝑩𝑩 𝒕𝒕 ∝ 𝒅𝒅𝒅𝒅
𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒕𝒕
(𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅
spatial derivative of M, 0 inside a domain and supposed constant in domain walls)
In this case,𝑽𝑽𝑩𝑩𝑩𝑩 𝒕𝒕 ∝ 𝒅𝒅𝒅𝒅𝒅𝒅𝒕𝒕→ induced voltage is proportional to domain wall speed
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
Introduction: the Barkhausen noise
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Proposed setup: use a coil to detect the induced Barkhausen noise voltage
Sum at macroscopic scale: 𝑽𝑽𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 𝒕𝒕 = ∑𝑽𝑽𝑽𝑽𝑩𝑩𝑩𝑩(𝒕𝒕,𝒅𝒅,𝒚𝒚, 𝒛𝒛)Constructive and destructive superposition between induced noises from all the domain wall movements considered→ RMS, and more recently MBNE:
𝒅𝒅𝑩𝑩𝑴𝑴𝑴𝑴 𝒕𝒕 = �𝟎𝟎
𝒕𝒕𝒔𝒔𝒄𝒄𝒔𝒔𝒔𝒔
𝒅𝒅𝒅𝒅𝒅𝒅𝒕𝒕
𝑽𝑽𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝟐𝟐 𝒕𝒕 𝒅𝒅𝒕𝒕
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
From the Barkhausen noise to the MBNE(H)
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4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
Simulation: the Jiles-Atherton-Sablik model
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Input: external magnetization field H, strain 𝝈𝝈, magnetostriction λ, 5 parameters and an anhysteretic function 𝒅𝒅𝒂𝒂𝒔𝒔 𝒅𝒅Output: differential equation of M in function of H
𝑑𝑑𝑑𝑑𝑑𝑑𝐻𝐻𝑒𝑒
= 𝑑𝑑𝑑𝑑𝑟𝑟𝑒𝑒𝑟𝑟𝑑𝑑𝐻𝐻𝑒𝑒
+ 𝑑𝑑𝑑𝑑𝑖𝑖𝑟𝑟𝑟𝑟𝑑𝑑𝐻𝐻𝑒𝑒
𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅
=𝟏𝟏
𝟏𝟏 + 𝒄𝒄𝒅𝒅𝒂𝒂𝒔𝒔 −𝒅𝒅𝒄𝒄𝒊𝒊𝒊𝒊
𝜹𝜹𝒌𝒌 − 𝜶𝜶(𝒅𝒅𝒂𝒂𝒔𝒔 −𝒅𝒅𝒄𝒄𝒊𝒊𝒊𝒊)+
𝒄𝒄𝟏𝟏 + 𝒄𝒄
𝒅𝒅𝒅𝒅𝒂𝒂𝒔𝒔
𝒅𝒅𝒅𝒅𝒆𝒆
𝐻𝐻𝑒𝑒 = 𝐻𝐻 + 𝛼𝛼𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖 + 𝐻𝐻𝜎𝜎𝑀𝑀𝑖𝑖𝑒𝑒𝑟𝑟 = 𝑐𝑐 𝑀𝑀𝑎𝑎𝑎𝑎 − 𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖
𝑀𝑀𝑎𝑎𝑎𝑎 = 𝑀𝑀𝑠𝑠 𝑓𝑓𝐻𝐻𝑒𝑒𝑎𝑎
𝑑𝑑𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝐻𝐻𝑒𝑒
=𝑀𝑀𝑎𝑎𝑎𝑎 −𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖
𝛿𝛿𝑘𝑘 − 𝛼𝛼(𝑀𝑀𝑎𝑎𝑎𝑎 −𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖)
𝛿𝛿 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝐻𝐻𝑑𝑑𝑑𝑑
𝐻𝐻𝜎𝜎 =32𝜆𝜆𝜇𝜇0
𝜕𝜕𝜆𝜆𝜕𝜕𝑀𝑀
(cos2 𝜃𝜃 − 𝜈𝜈 sin2 𝜃𝜃) 𝒅𝒅𝒅𝒅𝒅𝒅𝝈𝝈
=𝟏𝟏𝝐𝝐𝟐𝟐𝝈𝝈(𝒅𝒅𝒂𝒂𝒔𝒔 −𝒅𝒅) + 𝒄𝒄
𝒅𝒅𝒅𝒅𝒂𝒂𝒔𝒔
𝒅𝒅𝝈𝝈
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Simulation: the Jiles-Atherton-Sablik model
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Advantages Easy to integrate Parameters linked to material characteristics Separation between reversible and irreversible componentsProblems Unsatisfying reconstruction with narrow hysteresis loops Verification of convergence, given a set of parameters, not available
𝑑𝑑𝑀𝑀𝑑𝑑𝐻𝐻
=1
1 + 𝑐𝑐𝑀𝑀𝑎𝑎𝑎𝑎 −𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖
𝛿𝛿𝑘𝑘 − 𝛼𝛼(𝑀𝑀𝑎𝑎𝑎𝑎 −𝑀𝑀𝑖𝑖𝑖𝑖𝑖𝑖)+
𝑐𝑐1 + 𝑐𝑐
𝑑𝑑𝑀𝑀𝑎𝑎𝑎𝑎
𝑑𝑑𝐻𝐻𝑒𝑒𝑀𝑀𝑎𝑎𝑎𝑎 = 𝑀𝑀𝑠𝑠 𝑓𝑓
𝐻𝐻𝑒𝑒𝑎𝑎
Parameter Name
a (A / m) Domain walls density
𝛼𝛼 Interdomain coupling coefficient
c Reversibility coefficient
k (A / m) Average pinning energy
𝑀𝑀𝑠𝑠 (A / m) Saturation magnetization
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Simulation: the multiscale model
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Idea: find M by simulating the material at different scales: magnetic domain, monocrystal, polycrystal
Magnetic domainUniform strain and magnetization
MonocrystalUniform strain, variable magnetizations
PolycrystalVariable strains and magnetizations
Proportion of each orientation of M found by solving a minimum energy problem
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Simulation: the multiscale model
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PolycrystalHypothesis: 𝒅𝒅 = 𝒅𝒅𝒔𝒔 for each domain, spherical coordinate system
𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑𝑎𝑎𝑖𝑖𝑎𝑎 = 𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑎𝑎𝑎𝑎𝑒𝑒𝑒𝑒 + 𝐸𝐸𝑑𝑑𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒𝑚𝑚𝑑𝑑𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑖𝑖𝑒𝑒 + 𝐸𝐸𝑑𝑑𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒𝑚𝑚𝑑𝑑𝑒𝑒𝑚𝑚𝑎𝑎𝑠𝑠𝑚𝑚𝑖𝑖𝑒𝑒 + 𝐸𝐸𝑑𝑑𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒𝑚𝑚𝑑𝑑𝑒𝑒𝑖𝑖𝑦𝑦𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑚𝑚𝑖𝑖𝑎𝑎𝑒𝑒 𝑎𝑎𝑎𝑎𝑖𝑖𝑠𝑠𝑑𝑑𝑚𝑚𝑖𝑖𝑑𝑑𝑎𝑎𝑦𝑦
𝐻𝐻 = 𝐻𝐻𝑠𝑠𝑥𝑥𝐻𝐻𝑦𝑦𝐻𝐻𝑧𝑧𝐻𝐻
,𝑀𝑀 = 𝑀𝑀𝑠𝑠
𝑥𝑥𝑑𝑑𝑦𝑦𝑑𝑑𝑧𝑧𝑑𝑑
, 𝑥𝑥2+𝑦𝑦2 + 𝑧𝑧2 = 1
𝐸𝐸𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑎𝑎𝑎𝑎𝑒𝑒𝑒𝑒 = 𝐴𝐴 𝑠𝑠𝑔𝑔𝑎𝑎𝑑𝑑 𝑀𝑀2
(0 inside a magnetic domain)
𝐸𝐸𝑑𝑑𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒𝑚𝑚𝑑𝑑𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑖𝑖𝑒𝑒 = −𝜇𝜇0𝐻𝐻 ⋅ 𝑀𝑀𝐸𝐸𝑑𝑑𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒𝑚𝑚𝑑𝑑𝑒𝑒𝑚𝑚𝑎𝑎𝑠𝑠𝑚𝑚𝑖𝑖𝑒𝑒 = −𝜎𝜎0 ∶ 𝜖𝜖 + 1
2𝜖𝜖 ∶ ℂ ∶ 𝜖𝜖
𝐸𝐸𝑑𝑑𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒𝑚𝑚𝑑𝑑𝑒𝑒𝑖𝑖𝑦𝑦𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑚𝑚𝑖𝑖𝑎𝑎𝑒𝑒 𝑎𝑎𝑎𝑎𝑖𝑖𝑠𝑠𝑑𝑑𝑚𝑚𝑖𝑖𝑑𝑑𝑎𝑎𝑦𝑦 = 𝐾𝐾1 𝑥𝑥2𝑦𝑦2 + 𝑦𝑦2𝑧𝑧2 + 𝑥𝑥2𝑧𝑧2 + 𝐾𝐾2 𝑥𝑥2𝑦𝑦2𝑧𝑧2 (cubic crystal material)
𝛼𝛼 𝜃𝜃,𝜙𝜙 =𝑒𝑒−𝐴𝐴𝑠𝑠 𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖𝑑𝑑 (𝜃𝜃,𝜙𝜙)
∑𝑎𝑎𝑚𝑚𝑚𝑚 𝑑𝑑𝑖𝑖𝑖𝑖𝑒𝑒𝑒𝑒𝑚𝑚𝑖𝑖𝑑𝑑𝑎𝑎𝑠𝑠 𝑒𝑒−𝐴𝐴𝑠𝑠 𝐸𝐸𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑖𝑖𝑑𝑑𝑀𝑀 = ∑𝑎𝑎𝑚𝑚𝑚𝑚 𝑑𝑑𝑖𝑖𝑖𝑖𝑒𝑒𝑒𝑒𝑚𝑚𝑖𝑖𝑑𝑑𝑎𝑎𝑠𝑠 𝛼𝛼 𝜃𝜃,𝜙𝜙 𝑀𝑀 𝜃𝜃,𝜙𝜙
𝑀𝑀 𝜃𝜃,𝜙𝜙 =𝑠𝑠𝑠𝑠𝑠𝑠𝜃𝜃𝑐𝑐𝑠𝑠𝑠𝑠𝜙𝜙𝑠𝑠𝑠𝑠𝑠𝑠𝜃𝜃𝑠𝑠𝑠𝑠𝑠𝑠𝜙𝜙𝑐𝑐𝑠𝑠𝑠𝑠𝜃𝜃
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
Experimental Setup
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Sampling at 500 kHz (current, Hall signal, Barkhausen noise, analogical square and MBNE, dB/dt)Barkhausen signal filtered with a 4th order band-pass filter (between 1 and 10 kHz)
Physical experiment
Signal treatment and acquisitionSimulation
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Experimental results
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Comparison B(H) - MBNE
MBNE renormalized to have the same value at saturation as the inflexion elbow of B(H) (begin of saturation)
Strong anisotropy materials (FeSi) -> rotation negligible comparing to domain wall movements -> strong similarity between B(H) and MBNE almost equals
Weak anisotropy materials (FeCo) -> rotation not negligible, even at saturation -> B(H) et MBNE different, especially after saturation
Strong similarity B(H) – MBNE around Hc
4 novembre 2020Commissariat à l’énergie atomique et aux énergies alternatives Auteur
Experimental results
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B(H) simulation with Jiles-Atherton-Sablik
Same Jiles-Atherton parameter for bothB(H) and MBNE, anhysteretic functionobtained thanks to the multiscale model
Similar results -> inverse reconstructionfeasible? (from MBNE to B(H))
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