Electromagnetic NDE

1. Electromagnetic NDE Peter B. Nagy Research Centre for NDE Imperial College London 2009

2. Aims and Goals Aims 1 The main aim of this course is to familiarize the students with Electromagnetic (EM) Nondestructive Evaluation (NDE) and to integrate the obtained specialized knowledge into their broader understanding of NDE principles. 2 To enable the students to judge the applicability, advantages, disadvantages, and technical limitations of EM techniques when faced with NDE challenges. Objectives At the end of the course, students should be able to understand the: 1 fundamental physical principles of EM NDE methods 2 operation of basic EM NDE techniques 3 functions of simple EM NDE instruments 4 main applications of EM NDE

3. Syllabus 1 Fundamentals of electromagnetism. Maxwell's equations. Electromagnetic wave propagation in dielectrics and conductors. Eddy current and skin effect. 2 Electric circuit theory. Impedance measurements, bridge techniques. Impedance diagrams. Test coil impedance functions. Field distributions. 3 Eddy current NDE techniques. Instrumentation. Applications; conductivity, permeability, and thickness measurement, flaw detection. 4 Magnetic measurements. Materials characterization, permeability, remanence, coercivity, Barkhausen noise. Flaw detection, flux leakage testing. 5 Alternating current field measurement. Alternating and direct current potential drop techniques. 6 Microwave techniques. Dielectric measurements. Thermoelectric measurements. 7 Electromagnetic generation and detection of ultrasonic waves, electromagnetic acoustic transducers (EMATs).

4. 1 Electromagnetism 1.1 Fundamentals 1.2 Electric Circuits 1.3 Maxwell's Equations 1.4 Electromagnetic Wave Propagation

5. 1.1 Fundamentals of Electromagnetism

6. Fe y Q1 x z r Q2 Fe Electrostatic Force, Coulomb's Law Fe Coulomb force Q1, Q2 electric charges ( ne, e  1.602  10-19 As) er unit vector directed from the source to the target r distance between the charges ε permittivity (ε0≈ 8.85  10-12 As/Vm) dρ ρ r Q1 x Fe independent of x dQ2 infinite wall of uniform charge density q

7. y infinite wall of uniform charge density q Qt x Fe z charged parallel plane electrodes Q A +Q -Q E l Electric Field, Plane Electrodes

8. +Qs E1 E2 d +Qs -Qs +Qs E1 -Qs Electric Field, Point Sources monopole dipole

9. z E Ez P ER θ r+ r r +Qs R d -Qs Electric Field of Dipole

10. Electric Dipole in an Electric Field E +Q Fe Fe pe -Q pe electric dipole moment Q electric charge d distance vector E electric field Fe Coulomb force Te twisting moment or torque

11. D dS Qenc closed surface S Electric Flux and Gauss’ Law qcharge (volume) density D electric flux density (displacement) E electric field (strength, intensity) ε permittivity  electric flux Qenc enclosed charge

12. dℓ dℓ dℓ Electric Potential E B dℓ Fe A Q W work done by moving the charge Fe Coulomb force ℓ path length E electric field Q charge U electric potential energy of the charge V potential of the electric field

13. +Q +Q +Q A E E -Q dℓ l -Q E -Q dℓ Capacitance C capacitance V voltage difference Q stored charge

14. dA E Current, Current Density, and Conductivity I current Q transferred charge t time J current density A cross section area n number density of free electrons vd mean drift velocity e charge of proton m mass of electron τ collision time Λ free path v thermal velocity k Boltzmann’s constant T absolute temperature σ conductivity

15. I + V _ dℓ dℓ A Resistivity, Resistance, and Ohm’s Law V voltage I current R resistance P power σ conductivity ρ resistivity L length A cross section area

16. +I -I Magnetic Field Q dv B F Lorenz force v velocity B magnetic flux density Q charge Fm B pm pmmagnetic dipole moment (no magnetic monopole) N number of turns I current A encircled vector area

17. B Fm pm -I +I Fm Magnetic Dipole in a Magnetic Field pm magnetic dipole moment Q charge v velocity R radius vector B magnetic flux density Fm magnetic force Tm twisting moment or torque

18. Coulomb Law: Biot-Savart Law: dℓ H r dℓ dℓ I Magnetic Field Due to Currents H magnetic field μ magnetic permeability

19. Gauss’ Law: dℓ r H ℓ R dℓ s I Ampère’s Law Ampère’s Law: Biot-Savart Law: infinite straight wire Ampère’s Law:

20. B I N V F Induction, Faraday’s Law, Inductance E induced electric field B magnetic flux density t time Є induced electromotive force s boundary element of the loop Φ magnetic flux S surface area of the loop μ magnetic permeability N number of turns I current Λ geometrical constant L (self-) inductance

21. Gauss' law: Faraday's law: xn medium II DII qII DII,n DI,t boundary xt DII,t DI,n qI DI medium I tangential component of the electric field E is continuous normal component of the electric flux density D is continuous Electric Boundary Conditions xn medium II qII EII EII,n EI,t xt EII,t qI EI,n EI medium I

22. Gauss' law: Ampère's law: xn xn medium II medium II qII BII qII HII HII,n HI,t BII,n BI,t xt boundary HII,t xt BII,t BI,n qI qI HI,n BI HI medium I medium I tangential component of the magnetic field H is continuous normal component of the magnetic flux density B is continuous Magnetic Boundary Conditions

23. 1.2 Electric Circuits

24. dℓ _ _ + Є Electric Circuits, Kirchhoff’s Laws Kirchhoff’s loop rule (voltage law): I + Є Є electromotive force Vi potential drop on ith element Kirchhoff’s junction rule (current law): Ii current flowing into a junction from the ith branch

25. _ _ Circuit Analysis Kirchhoff’s Laws: + Є Loop Currents: + Є

26. + _ DC Impedance Matching

27. I I I V V V AC Impedance

28. AC Power complex notation correspondence real notation reminder:

29.  AC Impedance Matching

30. 1.3 Maxwell's Equations

31. Nabla operator: Laplacian operator: Gradient of a scalar: Curl of a vector: dℓ a Divergence of a vector: Laplacian of a scalar: Laplacian of a vector: Vector identity: Vector Operations

32. conductivity permittivity permeability Maxwell's Equations Field Equations: Ampère's law: Faraday's law: Gauss' law: Gauss' law: Constitutive Equations: (ε0 ≈ 8.85  10-12 As/Vm) (µ0 ≈ 4π 10-7 Vs/Am)

33. 1.4 Electromagnetic Wave Propagation

34. Electromagnetic Wave Equation Harmonic time-dependence: Maxwell's equations: Wave equations: Example plane wave solution:

35. Wave Propagation versus Diffusion k wave number Propagating wave in free space: c wave speed Propagating wave in dielectrics: n refractive index Diffusive wave in conductors: δ standard penetration depth

36. Intrinsic Wave Impedance Propagating wave in free space: Propagating wave in dielectrics: Diffusive wave in conductors:

37. z z z E E E Ez y y y Ey linear polarization elliptical polarization circular polarization Plane waves propagating in the x-direction: Polarization

38. y Reflection at Normal Incidence I medium II medium incident x reflected transmitted Boundary conditions:

39. y Reflection from Conductors I dielectric II conductor incident x transmitted “diffuse” wave reflected negligible penetration  almost perfect reflection with phase reversal

40. y propagating wave diffuse wave x δ standard penetration depth dielectric (air) conductor 1 magnitude 0.8 real part 0.6 0.4 Normalized Depth Profile, F 0.2 0 -0.2 0 1 2 3 Normalized Depth, x / δ Axial Skin Effect

41. r current density current, I 2a z conductor rod magnitude, 8 a/δ = 1 7 a/δ = 3 6 a/δ = 10 5 Normalized Current Density, J/JDC 4 3 2 1 0 0 0.2 0.4 0.6 0.8 1 Normalized Radius, r/a Transverse Skin Effect Jnnth-order Bessel function of the first kind

42. r current density current, I 2a z conductor rod 100 10 Normalized Resistance, R/R0 1 0.1 0.01 0.1 1 10 100 Normalized Radius, a/δ Transverse Skin Effect