Theory and Practice Making use of the Barkhausen Effect

Transcription

1 Theory and Practice aking ue of the Barkhauen Effect David C. Jile Anon arton Ditinguihed Profeor Palmer Endowed Chair Department of Electrical & Computer Engineering Iowa State Univerity Workhop on Large Fluctuation and Collective Phenomena in Diordered aterial ay 18, 11

2 Summary Stochatic/determinitic Barkhauen model Equation decribing the phenomenon Comparion of theory and experiment Variation of emiion with other factor uch a tre Variation of Barkhauen ignal amplitude Theoretical prediction invere law Variation of ignal with frequency and ditance Poibilitie for depth profiling of propertie Challenge

3 The variation of magnetization with magnetic field look deceptively imple Yet behind it lie a large number of very complicated interrelated mechanim which are hard to model A further problem i that magnetic behavior i inhomogeneou and doe not cale eaily a dimenion change The reult ha been a number of different model which do not fit together very well

4 Langevin-Wei odel An array of magnetic moment at temperature T and in a magnetic field H will ditribute themelve among the available energy tate according to the probability ditribution P P = P ( mh / k T ) exp µ Integrating over all poible angle and normalizing give = Nm [ coth ( µ mh / k T ) ( k T µ mh )] B B / Wei extended thi to include internal coupling proportional to the magnetization He = a with the reult [ coth( µ m( H + α )/ k T ) ( k T µ m( H + α ))] = Nm B B / which decribe the anhyteretic magnetization curve for ferromagnet B

5 Anhyteretic magnetization curve with different temperature and different aniotropie + Low temperature 1. High temperature H D D H 1D -1. "Superparamagnetic magnetization equation in two dimenion," D.C. Jile, S.J. Lee, J. Kenkel and K. etlov. Applied Phyic Letter, 77, 19,.

6 Energy Diipation and Hyterei Energy i only diipated by irreverible magnetization procee A model with diipation proportional to change in give good reult E pin n ( ) = d = irr µ ok m Energy output (change in magnetotatic energy) mut equal energy input minu energy diipated due to any loe uch a hyterei µ ε π d irr dh = µ dh k irr e an e µ d irr

7 Irreverible Change in agnetization Differentiating the energy equation lead to a differential for the rate of change of magnetization d dh irr e = 1 k ( ) an Thi can be written in the form of a differential with repect to the applied field H d dh irr = k α 1 irr ( ) ( ) an irr an irr

8 Iotropic odel of Hyterei The irreverible component of magnetization varie according to the differential equation dirr 1 = an irr dh k α ( ) ( ) The reverible component of magnetization varie a an d rev d an d irr = c dh dh dh Therefore hyterei can be repreented in term of, a, α, k, and c uing the equation d dh = 1 ( 1+ c) k irr ( an ) c d + α ( ) ( 1+ c) dh an an "Determination of theoretical parameter for modelling bulk magnetic hyterei propertie uing the theory of ferromagnetic hyterei," D.C. Jile, J.B. Thoelke and.k. Devine. IEEE Tran. ag.

9 Comparion of odel and Experimental eaurement Comparion of meaured and modelled hyterei curve of cobalt modified gamma iron oxide material After P. Andrei and A. Stancu, Hyterei in particulate recording media. Experiment and imulation with Preiach and Jile-Atherton model, Journal of agnetim and agnetic aterial, 6, , 1999.

10 Other magnetic propertie - Barkhauen effect Voltage / ax Voltage H V Virr Barkhauen.6 Time () Barkhauen ignal hown a voltage againt time. The time dependence of magnetic field H, voltage in flux coil V, and envelope of irreverible component of voltage in flux coil V irr are alo hown on the ame time cale. Change in Barkhauen emiion in carbon teel a a reult of applied tenile tre.

11 Stochatic Proce Barkhauen model odel aume Barkhauen activity i proportional to the rate of irreverible change in magnetization d dt BE irr ' = χ irr H BE = N < dic > < dic >: Average dicontinuou change in magnetization due to Barkhauen jump Avalanche: Number of Barkhauen event N(t n ) in a given time interval i correlated with number of event in the previou time interval t n-1 N( t n N( t BE ) = N( t n 1 ( t n ) = δ n 1 rand ) =< ) + N( t dic N( t n 1 n 1 ) ) ' > χ ' rr H N ( t n 1 ) + δ rand N ' ( t n 1 ) δ rand : Random number (-1.47 < δ rand < 1.47)

12 Comparion of model with experiment

13 Other Factor Effect of Stre Applied tre can be treated in mot repect like an effective magnetic field which change the aniotropy of the material H = 3 λ µ o T Later thi wa extended to cover the cae of a uniaxial tre at an arbitrary direction to the applied magnetic field H 3 ( θ) = ( co θ νin θ) µ o λ i the tre, θ i the angle between the tre axi and the direction of H, and ν i Poion ratio. T

14 odelled Effect of Stre on agnetic oment Orientation Poitive magnetotriction tre applied along the y axi

15 Detection of Stre Specimen calibration teted under load in Intron Tenile Tet machine BN enor in the middle of gauge length of ample Typical agnetiing and Analyi Condition : agnetiing frequency : f = 3 Hz agnetiing voltage : V = 1 volt No of burt : Analying bandwidth frequency : fa = -15 KHz (about nearet 1 µm) Smoothing parameter: p = 1 Sampling frequency: f =.5 Hz 15

16 eaured Barkhauen Reult Core Surface Strip #36 #- - Depth = =.9mm.mm 11.mm RS RS = = volt volt Barkhauen effect ignal (V) Time (ec) Time (ec) 16

17 Applied tre caue a change in aniotropy energy of magnetic moment 3 E = λ( co θ v in θ ) Thi can be expreed a an equivalent field H 1 E = µ = 3 µ λ The total field i then the um of magnetic field, exchange field and tre-equivalent field H 3λ He = H + H + α = H + + µ o The magnetization i then an aniotropic function of thi total field an Effect of Stre on Barkhauen Emiion H + H + α a ( H, ) = coth a H + H + α α

18 18 Effect of Stre on Barkhauen Emiion ( ) ( ) ( ) + = + = o an a a H dh d α µ λ α α χ , Thi predict how the rate of change of magnetization with field depend on tre and o can be ued to calculate tre. However there i a much eaier way... ( ) 3 () 1 ) ( ) ( 1 o o a a µ λ χ χ µ λ α α α χ = + = + = which predict a traight line graph of 1/χ againt

19 Detection of Tenile Stre - tet reult Applying tenile tre with monotonically increaing load BN peak amplitude (mp) P a 5 P a 1 P a 1 5 P a P a 5 P a 3 P a 3 5 P a 4 P a 4 5 P a 5 P a 5 5 P a 6 P a 6 5 P a 7 P a 7 5 P a 8 P a 8 5 P a 9 P a 9 5 P a Y ie ld tre n g th = P a a g n e tic F ie ld S tre n g th H (in % ) 19

20 Dependence of Barkhauen emiion on tre Fig. 1. Envelope curve of the rectified BN burt for carburized SAE 931 pecimen for different amplitude of applied tre uing a tenile tet machine (reidual tre value from XRD meaured before tre application wa -85Pa). Fig.. BN Peak Amplitude for carburized SAE 931 pecimen a a function of applied tre.

21 Effect of Stre on Differential Suceptibility and Barkhauen Emiion Barkhauen voltage V BE i known from previou work* to be proportional to the differential uceptibility Therefore, a imilar linear expreion hould hold for reciprocal Barkhauen voltage a a function of tre a for the reciprocal differential uceptibility 1 1 3b = V ( ) V () µ BE BE Thi ugget that the mot ueful calibration curve for Barkhauen effect a a function of tre i the reciprocal plot o

22 Comparion of odel equation with eaurement

23 Concluion agnetic propertie, including permeability and Barkhauen effect depend on other external factor uch a tre. A phenomenological/tochatic model ha been developed to decribe Barkhauen and thee effect Development of model i eential for undertanding and interpretation of meaurement reult and for predicting change, uch a with tre. eaurement of thee propertie can be ued for determination of tre and even it variation with depth. 3

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25 Depth Profiling uing Barkhauen Effect There are three key equation The change in flux denity that propagate to the urface i B mea (, x max, ω, ω ) 1 ω = B ω1 xmax origin x ( x, ω) exp δ dxdω The voltage meaured in an induction coil on the urface i V mea (, x max, ω, ω ) 1 ω = NA ω x max 1 db origin ( x, ω, ) dh dh ( x) x exp dt δ dx dω The component of the meaured ignal coming from a particular depth i 4 d V ( x, ω = 1, ω ) V 3 mea max 1, ω x µ oµ r dω (, x, ω )

26 Comparion with X-ray reult BN PEAK VALUE BN PEAK POSITION Ground ide urface 939,9 59,15 Unground initial urface 16, 48,6 Envelope curve of the rectified burt for ample 17A1 TOP 1416,6 45,4 BOTTO 135,4 46, Tenione Reidua - Reidual Stre (Pa) SAE 931 CEENTATO (CARBURIZED),7 mm SN 17 A1,,4,6,8,1,1,14,16,18, profondità - depth (mm) 15 BN RS v ditance (ide urface) B N P E A K V A L U E [m p ] magnetiing current I[%] bottom urface ide urface initial urface top urface BN RS [m p] ditance