![Page 1: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/1.jpg)
Electromagnetic NDT
Veera Sundararaghavan
![Page 2: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/2.jpg)
Research at IIT-madras
1. Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field and pulsed eddy current NDT methods.
2. Two dimensional Scalar Potential based Non Linear FEM for Magnetostatic leakage field Problem
3. Study of the effect of continuous wave laser irradiation on pulsed eddy current signal output.
4. Three dimensional eddy current solver module has been written for the World federation of NDE Centers’ Benchmark problem. The solver can be plugged inside standard FEM preprocessors.
5. FEM based eddy current (absolute probe) inversion for flat geometries. Inversion process is used to find the conductivity profiles along the depth of the specimen.
![Page 3: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/3.jpg)
Electromagnetic Quantities
E – Electric Field Intensity Volts/m
H – Magnetic Field Intensity Amperes/m
D – Electric Flux density Coulombs/m2
B – Magnetic Flux density Webers/m2
J – Current density Amperes/m2
Charge density Coulombs/m3
Permeability - B/HPermittivity - D/EConductivity - J/E
![Page 4: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/4.jpg)
Maxwell's equations x H = J + D / t Ampere’s law x E = - t Faraday’s law.B = 0 Magnetostatic
law.D = Gauss’ lawConstitutive relations=D = J =
Classical Electromagnetics
![Page 5: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/5.jpg)
Interface Conditions
1 2
Boundary conditions
•Absorption Boundary Condition - Reflections are eliminated by dissipating energy
•Radiation Boundary Condition – Avoids Reflection by radiating energy outwards
•E1t = E2t
•D1n-D2n = i
•H1t-H2t = Ji
•B1n = B2n
![Page 6: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/6.jpg)
Material Properties
Material Classification
1. Dielectrics
2. Magnetic Materials - 3 groups
• Diamagnetic (
• Paramagnetic (
• Ferromagnetic (
•Field Dependence: eg. B = (H)* H•Temperature Dependence:
Eg. Conductivity
![Page 7: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/7.jpg)
Potential Functions
If the curl of a vector quantity is zero, the quantity can be represented by the gradient of a scalar potential.
Examples:
x E = 0 => E = - V
Scalar:
Vector:
If the field is solenoidal or divergence free, then the field can be represented by the curl of a vector potential.
Examples: Primarily used in time varying field computations
.B = 0 => B = x A
![Page 8: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/8.jpg)
Derivation of Eddy Current Equation
Magnetic Vector Potential : B = xA
x E = - t => Faraday’s Law
x E = - x t => E = - t - V
J = J = - t + JS
Ampere’s Law:
x H = J + Dt
Assumption 1: => at low frequencies (f < 5MHz) displacement current (Dt) = 0
H = B/xA/
Assumption 2 : => Continuity criteria)
Final Expression: (1/A) = -JS + t
![Page 9: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/9.jpg)
Electromagnetic NDT Methods
• Leakage Fields 1/A = -JS
•Absolute/Differential Coil EC & Remote Field EC
1/A = -JS + j• Pulsed EC& Pulsed Remote Field EC
1/A = -JS + t
![Page 10: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/10.jpg)
Principles of EC TestingOpposition between the primary (coil) & secondary (eddy current) fields . In the presence of a defect, Resistance decreases and Inductance increases.
![Page 11: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/11.jpg)
Differential Coil Probe in Nuclear steam generator tubes
![Page 12: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/12.jpg)
Pulsed EC
![Page 13: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/13.jpg)
FEM Forward Model (Axisymmetric)
Governing Equation:
Permeability (Tesla-m/A), Conductivity (S), A magnetic potential (Tesla-m), the frequency of excitation (Hz), Js – current density (A/m2)
Energy Functional:
F(A)/Ai = 0
------ Final Matrix Equation
2 221
.2 2
[ { } ]s
R
A A A jF A J A
z r rrdrdz
2 2
s2 2 2
1 A 1 A A A A ( + + - ) = -J +
r r z r dt
{ } { }e e e eS jR A Q
m
l n
Triangular element
rm
zm
z
r
![Page 14: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/14.jpg)
FEM Formulation(3D)
1
8 7
65
4 3
2
Governing Equation : (1/A) = -JS + j
Solid Elements: Magnetic Potential, A = NiAi
Energy Functional
F(A) = (0.5ii2 – JiAi + 0.5ji
2)dV, i = 1,2,3
No. of Unknowns at each node : Ax,Ay,Az No. of Unknowns per element : 8 x 3 = 24
Energy minimization
F(A)/Aik = 0,k = x,y,z
For a Hex element yields 24 equations, each with 24 unknowns.
Final Equation after assembly of element matrices
[K][A] = [Q] where [K] is the complex stiffness matrix and [Q] is the source matrix
1
3
4
2
![Page 15: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/15.jpg)
Derivation of the Matrix Equation(transient eddy current)
Interpolation function:
A(r,z,t) = [N(r,z)][A(t)]e
[S][A] + [C][A’] = [Q] where,
[S]e = (1/NTNv
[C]e = NTNv
[Q]e = JsNTv
![Page 16: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/16.jpg)
Time Discretisation
Crank-Nicholson method
A’(n+1/2) = ( A(n+1)-A(n) ) / t
A(1/2) = (A(n+1)+A(n) ) / substituting in the matrix equation
[C] + [S] [A]n+1 = [Q] + [C] - [S] [A]n
t 2 t 2
![Page 17: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/17.jpg)
2D-MFL (Non-linear) Program
Flux leakage Pattern
Parameter Input
![Page 18: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/18.jpg)
![Page 19: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/19.jpg)
![Page 20: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/20.jpg)
Differential ProbeAbsolute Probe (DiffPack)
![Page 21: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/21.jpg)
![Page 22: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/22.jpg)
Reluctance = 1
Reluctance = 20Reluctance = 40
Reluctance = 200
![Page 23: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/23.jpg)
Increasing lift off
L = 1 mmL = 2 mm
L = 3 mm
L = 4 mm
![Page 24: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/24.jpg)
![Page 25: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/25.jpg)
![Page 26: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/26.jpg)
Pulsed Eddy Current : Diffusion Process
Input : square pulse (0.5 ms time period)
Total time : 2 ms
![Page 27: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/27.jpg)
Input current density v/s time step
Gaussian InputOutput voltage of the coil
Results : Transient Equation
![Page 28: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/28.jpg)
L (3D model) = 2.08796 x 10-4 HL (Axi-symmetric model) = 2.09670 x 10-4 HError = 0.42 %
Axisymmetric mesh (left) and the 3D meshed model(right)
Validation – 3D ECT problem
![Page 29: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/29.jpg)
Eddy Current WFNDEC Benchmark Problem
![Page 30: Electromagnetic NDT Veera Sundararaghavan. Research at IIT-madras 1.Axisymmetric Vector Potential based Finite Element Model for Conventional,Remote field](https://reader035.vdocument.in/reader035/viewer/2022062717/56649e175503460f94b029f4/html5/thumbnails/30.jpg)
Benchmark Problem