4.1 Magnetic Properties

4 Magnetic NDE 4.1 Magnetic Properties 4.2 Magnetic Measurements 4.3 Magnetic Materials haracterization 4.4 Magnetic Flaw Detection 4.1 Magnetic Properties

Magnetization +I -I pm = NIA p m N I A magnetic dipole moment number of turns current encircled vector area Q charge p 1 m = 2 Q R v v velocity R radius vector M = pm V M = χ =μ 0( + M) =μ0μr μ r = 1 + χ M V χ μ 0 μ r magnetization volume magnetic susceptibility magnetic field magnetic flux density permeability of free space relative permeability lassification of Magnetic Materials Diamagnetism: μ r < 1 no remanence orbit distortion e.g., copper, mercury, gold, zinc Paramagnetism: μ r > 1 no remanence orbit and spin alignment e.g., aluminum, titanium, platinum Ferromagnetism: μ r >> 1 remanence, coercivity, hysteresis self-amplifying paramagnetism urie temperature e.g., iron, nickel, cobalt

Diamagnetism pm = porb + pspin Fm Fe F e Q Q v F m = ev = eei v QA eπr2 v porb = NI A = = τ 2πr erv p orb = 2 dφ F = 2π re e i = 2πr dt e dφ m dv = 2 π r dt e dt 2 m π r = 2πr Δv e Δ v = er 2m e2r2 μ 2 2 0 e r Δ porb = = 4m 4m μ 2 2 0 e r χ orb = N 4m p m p spin p orb N I A e τ r v E i F e m N χ magnetic dipole moment electron spin electron orbital motion number of turns current encircled area charge of proton orbital period orbital radius orbital velocity induced electric field decelerating electric force mass of electron dipoles within unit volume magnetic susceptibility - χ 1-10 ppm Weak Paramagnetism, urie Law pm = porb + pspin F m p m θ -I +I T m F m Tm = pm T m = p m sin θ θ θ Um = T( θ) θ = pm sinθdθ 90 90 U m = p m cosθ U m = pmi Um pu ( m) = e k T p m F m magnetic dipole moment magnetic flux density magnetic force T m twisting moment or torque urie Law: M Nμ 2 0 m χ= = = 3kT T U m k T N potential energy of the dipole oltzmann constant absolute temperature dipoles within unit volume χ 5-50 ppm χ magnetic susceptibility

Strong Paramagnetism, urie-weiss Law: χ= M urie law: M T χ T M χ magnetization exciting magnetic field magnetic susceptibility t = + i = + αm M = t T M M M χ= = = t i MT α M T t i α T c material constant absolute temperature total magnetic field interaction field material factor urie temperature χ= T α urie-weiss law: χ= T Tc Ferromagnetism (i) (ii) (iii) (v) (vi) (iv) magnetic polarization is produced by collective action of similarly oriented spins within magnetic domains very high permeability magnetic hysteresis remnant magnetic polarization (remanence) coercive magnetic field (coercivity) depolarization above the (magnetic) urie temperature r first magnetization c

Spontaneous Magnetization [001] [111] [010] easy magnetic axis [100] [110] N N N N N N S S N S N S S S S S S S N N S S S S Utotal = Uinternal + Uwall + Uexternal Magnetic Domains in Single rystals easy magnetic axes = 0 1 demagnetization (spontaneous magnetization) domain wall movement 2 partial magnetization 3 4 5 irreversible rotation 1 2 3 knee of the magnetization curve reversible rotation 4 technical saturation thermal precession not shown 5 full saturation (no precession)

4.2 Magnetic Measurements Magnetic Sensors 10 5 noise threshold Flux Density [pt/z 1/2 ] 10 4 10 3 10 2 10 1 10 0 all GMR SDP fluxgate 10-1 SQUID 10-2 0 5 10 15 20 25 Frequency [z] coil: d Φ V = N = ω i N Aaxial dt

all Detector z y x F = Q ( E + v ) z Fy = e( Ey + vxz) = 0 Ix F m F e a b Ix Ix V E y = a = enab vx I V x = aey = avxz = z enb V V = R Ix b z R = 1 en Fluxgate hard magnetic cores 1 high-frequency excitation I exc low-frequency or dc external magnetic field 2 1 sensing voltage (to be low-pass filtered) V sens = 0 0 1 t t 2 t 2 t 1 + 2 1 + 2 t t

Vibrating-Sample Magnetometer vibration (ω) V sens 0 d = d 0 sin( ωt) M =χ 0 μ 0 Φ 1() t = A[ 0+ μ0m κsin( ωt)] Φ 2() t = A[ 0 μ0m κsin( ωt)] V 1 2 sens () t N Φ t N Φ = + t Vsens() t = 2N Aωχ0 κcos( ωt) 0 bias magnetic flux density M magnetization χ magnetic susceptibility µ 0 permeability of free space d specimen displacement d 0 specimen amplitude ω angular frequency t time κ geometrical coupling factor A coil cross section Φ 1,2 flux in coil 1 and 2 N number of turns V sens sensing voltage Faraday alance electromagnet specimen for a single dipole: for a given magnetized volume: spacer W = W - F m h precision scale U m = pmi Um = MV U = Ug + Um U = W h MV du d W' = = W MV dh dh M =χ d μ 2 ' 0V d W W = μ0 χ V = χ dh 2 dh U m magnetic potential energy p m magnetic dipole moment magnetic flux density M magnetization V volume U g gravitational potential energy U total potential energy h height W actual weight W apparent weight χ magnetic susceptibility magnetic field µ 0 permeability of free space

4.3 Magnetic Materials haracterization Magnetic Properties para- and diamagnetic materials: = μ 0 ( + M) M =χ =μ0μr μ r = 1 + χ ferromagnetic materials: = (, Mp) =μ 0 +μ0m(, Mp) 1.5 1 hardened steel Flux Density [Tesla] 0.5 0-0.5-1 soft iron -1.5-5 -4-3 -2-1 0 1 2 3 4 5 Magnetic Field [ka/m]

Initial Magnetization anhysteretic initial magnetization curve Flux Density Flux Density Differential Permeability Magnetic Field μ d = lim M d d =μ 0 ( + M) = M0 M0 npm magnetic flux density magnetic field M magnetization µ 0 permeability of free space µ d differential permeability M 0 saturation magnetization n dipoles per unit volume p m magnetic dipole moment Retentivity, oercivity, ysteresis =μ 0 ( + M) M = M(, Mp) technical magnetization: r c r = μ0mr c+ M( c) = 0 M( ci) = 0 c du0 ci = d Δ U0 = A r remanence [Vs/m 2 ] M r remanent magnetization µ 0 permeability of free space c coercive field [A/m] ci intrinsic coercivity U 0 magnetic energy density A hysteresis area [J/m 3 ]

Texture, Residual Stress mild steel (Langman 1985) 2 2 σ = 0 MPa σ = 36 MPa Flux Density [T] 1 0-1 Flux Density [T] 1 0-1 -2-300 -200-100 0 100 200 300 Magnetic Field [A/m] -2-300 -200-100 0 100 200 300 Magnetic Field [A/m] Flux Density [T] 2 1 0-1 σ = 110 MPa Flux Density [T] 2 1 0-1 σ = 183 MPa -2-300 -200-100 0 100 200 300 Magnetic Field [A/m] -2-300 -200-100 0 100 200 300 Magnetic Field [A/m] Magnetostriction Spontaneous magnetostriction: easy magnetic axes M domain = Ms M0 M volume 0 = 0 ε domain domain 1 = e, ε 2,3 = 0 ε volume 1,2,3 = e 3 Induced magnetostriction: ε 1 = 2e 3 ε1 e ε 2,3 = = 2 3 ε1 ε 2 = e M s M 0 e ε 1,2,3 spontaneous magnetization saturation magnetization spontaneous strain within a single domain principal strains

arkhausen Noise = 0 domain wall movement magnetic field arkhausen noise magnetic arkhausen noise acoustic arkhausen noise Amplitude Time urie Temperature χ magnetic susceptibility urie-weiss law: χ= T Tc T material constant temperature T c urie temperature ferromagnetic materials (T < T c ): M s / M 0 1.2 1.0 0.8 0.6 0.4 0.2 typical pure metal typical alloy 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 T / T c

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

Magnetic oundary onditions Gauss' law: Ampère's law: i = 0 = J medium II x n medium II x n θ ΙΙ II θ ΙΙ boundary I,n I,t II,t II,n x t I,t II,t II II,n x t I θ Ι I,n θ Ι I medium I medium I I,n = II,n I,t = II,t μ I I,n = μii II,n tan θ I I,n = tan θii II,n tan θi μi = tan θii μii Magnetic Refraction II tan θi μi = tan θii μii θ ΙΙ Nonmagnetic Angle, θ II [deg] 90 75 60 45 30 15 µ I /µ II = 10 30 100 0 0 15 30 45 60 75 90 Ferromagnetic Angle, θ I [deg] medium II (air) I II θ Ι θ ΙΙ medium I (ferromagnetic) medium II (air) I medium I (ferromagnetic) θ Ι

Exciter Magnets air gap ferromagnetic core electromagnet Rm d = NI = MMF Φ=μ 0 μ r A Φ MMF = d μ 0 μ r A MMF R m = Φ 1 d 1 = i μ0 μr A μ0 i μri Ai magnetic field N number of turns I excitation current MMF magnetomotive force Φ magnetic flux l length of flux line µ 0 µ r magnetic permeability A cross section area R m magnetic reluctance Yoke Excitation N I electromagnet magnetometer crack Detection Methods: magnetic particle (gravitation, friction, adhesion, cohesion, magnetization) magnetic particle with ultraviolet paint coil all detector, GMR sensor fluxgate, etc. Tangential Magnetic Field Normal Magnetic Field Lateral Position Lateral Position

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