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4 Magnetic NDE

4 Magnetic NDE. 4.1 Magnetic Properties 4.2 Magnetic Measurements 4.3 Magnetic Materials Characterization 4.4 Magnetic Flaw Detection . 4.1 Magnetic Properties. p m magnetic dipole moment N number of turns I current A encircled vector area. Q charge v velocity R radius vector.

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4 Magnetic NDE

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  1. 4 Magnetic NDE 4.1 Magnetic Properties 4.2 Magnetic Measurements 4.3 Magnetic Materials Characterization 4.4 Magnetic Flaw Detection

  2. 4.1 Magnetic Properties

  3. pmmagnetic dipole moment N number of turns I current A encircled vector area Q charge v velocity R radius vector M magnetization V volume χ magnetic susceptibility H magnetic field B magnetic flux density μ0 permeability of free space μr relative permeability +I -I Magnetization

  4. Diamagnetism: μr < 1 no remanence orbit distortion e.g., copper, mercury, gold, zinc Paramagnetism: μr > 1 no remanence orbit and spin alignment e.g., aluminum, titanium, platinum Ferromagnetism: μr >> 1 remanence, coercivity, hysteresis self-amplifying paramagnetism Curie temperature e.g., iron, nickel, cobalt Classification of Magnetic Materials

  5. pmmagnetic dipole moment pspin electron spin porb electron orbital motion N number of turns I current A encircled area e charge of proton τ orbital period r orbital radius v orbital velocity Ei induced electric field Fe decelerating electric force m mass of electron n dipoles within unit volume χ magnetic susceptibility B Q v Fm B v Q Fe - χ ≈ 1-10 ppm Diamagnetism

  6. B Fm pm -I θ Tm +I Fm pm magnetic dipole moment B magnetic flux density Fm magnetic force Tm twisting moment or torque Um potential energy of the dipole kB Boltzmann constant T absolute temperature n dipoles within unit volume χ magnetic susceptibility Curie Law: χ ≈ 5-50 ppm Weak Paramagnetism, Curie Law

  7. Curie law: M magnetization H exciting magnetic field χ magnetic susceptibility C material constant T absolute temperature Ht total magnetic field Hi interaction field α material factor TC Curie temperature Curie-Weiss law: Strong Paramagnetism, Curie-Weiss Law:

  8. (i) magnetic polarization is produced by collective action of similarly oriented spins within magnetic domains (ii) very high permeability (iii) magnetic hysteresis (v) remnant magnetic polarization (remanence) (vi) coercive magnetic field (coercivity) (iv) depolarization above the (magnetic) Curie temperature B Br first magnetization H Hc Ferromagnetism

  9. N N S N S S S N S S N N S S S N N N S S S N N N [001] Spontaneous Magnetization [111] [010] “easy” magnetic axis [100] [110]

  10. easy magnetic axes 1 demagnetization (spontaneous magnetization) H = 0 domain wall movement B 2 partial magnetization H irreversible rotation 5 2 1 4 3 H 3 “knee” of the magnetization curve H reversible rotation 4 technical saturation H thermal precession not shown 5 full saturation (no precession) Magnetic Domains in Single Crystals

  11. 4.2 Magnetic Measurements

  12. noise threshold 105 Hall 104 103 GMR 102 Flux Density [pT/Hz1/2] SDP 101 100 fluxgate SQUID 10-1 10-2 0 5 10 15 20 25 Frequency [Hz] coil: Magnetic Sensors

  13. B z z y x b I I x x Fe Fm a VH Hall Detector

  14. B1 hard magnetic cores low-frequency or dc external magnetic field high-frequency excitation B B Iexc B2 H sensing voltage (to be low-pass filtered) Vsens B = 0 B≠ 0 B1 B1 t t B2 B2 t t B1 + B2 B1 + B2 t t Fluxgate

  15. vibration (ω) B0 Vsens B0 bias magnetic flux density M magnetization χ magnetic susceptibility µ0 permeability of free space d specimen displacement d0 specimen amplitude ω angular frequency t time κ geometrical coupling factor A coil cross section Φ1,2 flux in coil 1 and 2 N number of turns Vsens sensing voltage Vibrating-Sample Magnetometer

  16. electromagnet specimen W’ = W - Fm spacer h Ummagnetic potential energy pm magnetic dipole moment B magnetic flux density M magnetization V volume Uggravitational potential energy U total potential energy h height W actual weight W’ apparent weight χ magnetic susceptibility H magnetic field µ0 permeability of free space precision scale for a single dipole: for a given magnetized volume: Faraday Balance

  17. 4.3 Magnetic Materials Characterization

  18. 1.5 hardened steel 1 0.5 soft iron Flux Density [Tesla] 0 -0.5 -1 -1.5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Magnetic Field [kA/m] para- and diamagnetic materials: Magnetic Properties ferromagnetic materials:

  19. Flux Density Flux Density Differential Permeability Magnetic Field anhysteretic initial magnetization curve Initial Magnetization B magnetic flux density H magnetic field M magnetization µ0 permeability of free space µd differential permeability M0 saturation magnetization n dipoles per unit volume pm magnetic dipole moment

  20. B technical saturation: Br H H Hc Br remanence [Vs/m2] Mr remnant magnetization µ0 permeability of free space Hc coercive field [A/m] Hci intrinsic coercivity U0 magnetic energy density A hysteresis area [J/m3] Retentivity, Coercivity, Hysteresis

  21. 2 2 2 2 B|| B|| σ = 0 MPa σ = 36 MPa B 1 1 1 1 B Flux Density [T] Flux Density [T] Flux Density [T] Flux Density [T] 0 0 0 0 -1 -1 -1 -1 -2 -2 -2 -2 -300 -300 -300 -300 -200 -200 -200 -200 -100 -100 -100 -100 0 0 0 0 100 100 100 100 200 200 200 200 300 300 300 300 Magnetic Field [A/m] Magnetic Field [A/m] Magnetic Field [A/m] Magnetic Field [A/m] σ = 110 MPa σ = 183 MPa B|| B|| B B mild steel (Langman 1985) Texture, Residual Stress

  22. Spontaneous magnetostriction: easy magnetic axes H = 0 Induced magnetostriction: H Ms spontaneous magnetization M0 saturation magnetization e spontaneous strain within a single domain ε1,2,3 principal strains Magnetostriction

  23. B H = 0 domain wall movement H H magnetic field Barkhausen noise Amplitude •magnetic Barkhausen noise • acoustic Barkhausen noise Time Barkhausen Noise

  24. χ magnetic susceptibility C material constant T temperature TC Curie temperature ferromagnetic materials (T < TC): typical alloy 1.2 typical pure metal Ms / M0 1.0 0.8 0.6 0.4 Curie-Weiss law: T / TC 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 Curie Temperature

  25. 4.4 Magnetic Flaw Detection

  26. exciter coil sensor (small coil, Hall cell, etc.) ferromagnetic test piece Magnetic Flux Leakage Advantages: fast inexpensive large, awkward shaped specimens (particle) Disadvantages: material sensitive poor sensitivity poor penetration depth

  27. Gauss' law: Ampère's law: xn xn medium II medium II qII BII qII HII HII,n HI,t BII,n BI,t xt HII,t boundary xt BII,t BI,n qI qI HI,n BI HI medium I medium I Magnetic Boundary Conditions

  28. BII 90 qII µI/µII = 75 10 30 60 100 medium II (air) Nonmagnetic Angle, θII [deg] 45 30 15 medium I (ferromagnetic) qI BI 0 0 15 30 45 60 75 90 Ferromagnetic Angle, θI [deg] BII qII medium II (air) BI qI medium I (ferromagnetic) Magnetic Refraction

  29. air gap ferromagnetic core electromagnet Exciter Magnets H magnetic field N number of turns I excitation current MMF magnetomotive force Φ magnetic flux ℓ length of flux line µ0µr magnetic permeability A cross section area Rm magnetic reluctance

  30. N I electromagnet magnetometer crack Normal Magnetic Field Tangential Magnetic Field Lateral Position Lateral Position Yoke Excitation Detection Methods:  magnetic particle (gravitation, friction, adhesion, cohesion, magnetization)  magnetic particle with ultraviolet paint  coil  Hall detector, GMR sensor  fluxgate, etc.

  31. B H 1 2 low magnetic field high magnetic field crack crack Subsurface Flaw Detection saturation greatly reduces the differential permeability

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