Eddy-Current Nondestructive Evaluation (eBook)

Preface 8
Contents 12
1 Introduction 17
1.1 Introduction 17
1.2 Historical Background 18
1.2.1 Michael Faraday 18
1.2.2 Joseph Henry 20
1.2.3 David Hughes 20
1.2.4 Friedrich Förster 21
1.3 Electromagnetic Induction 21
1.4 Eddy-Current Nondestructive Evaluation 23
1.5 Air-Cored Coil 23
1.6 Summary 25
1.7 Exercises 25
References 26
2 Fields 27
2.1 Introduction 27
2.2 Current Density 28
2.3 Alternating Current and Phasor Representation 29
2.4 Conductivity and Resistivity 32
2.5 Electric Field 35
2.6 Magnetic Field 36
2.7 Poynting Vector 37
2.8 Permeability and Magnetic Induction 38
2.9 Electromagnetic Skin Effect 39
2.10 Polarization and Electric Displacement 43
2.11 Summary 44
2.12 Exercises 44
References 45
3 Ferromagnetic Materials 46
3.1 Introduction 46
3.2 Fundamental Source of the Magnetic Field 47
3.3 Magnetization 48
3.3.1 Rayleigh Law 50
3.4 Hysteresis 51
3.5 Permeability 52
3.6 Ferromagnetic Domains 54
3.6.1 Why do Domains Form? 54
3.6.2 Domain Walls 55
3.6.3 Domain Processes During Magnetization 56
3.6.4 Hard and Soft Ferromagnets 57
3.6.5 Evidence for the Existence of Domains 57
3.6.6 The Curie Temperature, TC 58
3.7 Demagnetization 59
3.8 Summary 61
3.9 Exercises 61
References 61
4 Circuits 62
4.1 Introduction 62
4.2 Electromotance and Potential Difference 62
4.3 Resistance 63
4.4 Capacitance 64
4.5 Discharge of a Capacitor Through a Resistor 65
4.6 Forced Oscillation of an RC Circuit by Alternating Electromotance 66
4.7 Inductance 67
4.8 Forced Oscillation of an LRC Circuit by Alternating Electromotance 68
4.9 Impedance 69
4.10 Frequency Response of an LRC Circuit 70
4.11 Equivalent Electrical Circuit for an Eddy-Current Probe 71
4.12 Summary 72
4.13 Exercises 72
References 73
5 Maxwell's Equations 74
5.1 Introduction 74
5.2 Faraday's Law 75
5.3 Maxwell–Ampère Law 77
5.3.1 Quasi-static Regime 78
5.4 Gauss' Law 79
5.5 Gauss' Law for Magnetic Fields 79
5.5.1 Magnetic Vector Potential 80
5.6 Interface Conditions on the Electromagnetic Field 80
5.7 Summary 83
5.8 Exercises 84
References 85
6 Signals and Coils 86
6.1 Introduction 86
6.2 Coil Impedance 88
6.2.1 Isolated Coil Impedance, Z0 88
6.2.2 Coil Impedance in the presence of a Conductor, Z, and the Impedance-Plane Plot 89
6.2.3 Coil Impedance Change Due to a Flaw, ?Z 92
6.3 Surface Coil 93
6.3.1 Excitation of a Half-Space Conductor by a Uniform Current Sheet 95
6.3.2 Circular Current Loop in Air 98
6.3.3 Circular Current Loop above a Half-Space Conductor 103
6.3.4 Coil above a Half-Space Conductor 108
6.3.5 Ferrite Core 112
6.3.6 Sources of Uncertainty 114
6.4 Tangent Coil 123
6.5 Encircling Coil 124
6.5.1 Circular Current Loop Encircling a Solid Cylindrical Conductor 127
6.5.2 Coil Encircling a Solid Cylindrical Conductor 131
6.5.3 Sources of Uncertainty 133
6.6 Bobbin Coil 133
6.6.1 Sources of Uncertainty 134
6.7 Summary 135
6.8 Exercises 136
References 138
7 Layered and Truncated Conductors 140
7.1 Introduction 140
7.2 Layered Conductors 141
7.2.1 Planar Conductor with an Arbitrary Number of Layers 141
7.2.2 Coated Half-Space Conductor 143
7.2.3 Plate Conductor 144
7.2.4 Cylindrical Conductor with an Arbitrary Number of Layers 144
7.2.5 Coated Cylindrical Conductor 146
7.2.6 Tube Conductor 148
7.3 Truncated Conductors 149
7.3.1 Truncated Region Eigenfunction Expansion Method 151
7.3.2 Wedge and Plate Edge 151
7.3.3 End Effects and Cylindrical Conductors 152
7.4 Summary 154
7.5 Examples 154
References 154
8 Probes 156
8.1 Introduction 156
8.2 Absolute Probe 157
8.3 Differential Probe 159
8.4 Driver Pick Up Probe 163
8.5 Plus-Point Probe 164
8.6 Array Probes 165
8.7 Flexible Probes 166
8.8 Hall Sensor Probes 167
8.8.1 The Hall Effect 167
8.8.2 Defect Detection with the Hall Sensor 170
8.8.3 Hall Sensors and Transient EC NDE 171
8.8.4 Hall Sensor Arrays 172
8.8.5 Conclusion 173
8.9 Giant Magnetoresistor (GMR) Probes 174
8.9.1 The Giant Magnetoresistive Effect 175
8.9.2 Defect Detection with the GMR Sensor 176
8.9.3 GMR Sensors and Transient EC NDE 177
8.9.4 GMR Arrays 177
8.9.5 Conclusion 178
8.10 Summary 178
8.11 Exercises 178
References 179
9 Flaw Models 182
9.1 Introduction 182
9.2 Reciprocity Theorem and ?Z 183
9.2.1 Coil and Flaw 184
9.2.2 Two Coils 185
9.3 The Dipole 186
9.3.1 Electric Dipole 186
9.3.2 Current Dipole 188
9.3.3 Magnetic Dipole 188
9.4 Small Flaws 188
9.4.1 Subsurface Sphere 190
9.4.2 Surface Defects 197
9.5 High-Frequency ``Thin-Skin'' Treatment of Surface Cracks 198
9.5.1 Poynting Vector and Z 199
9.5.2 Current-Sheet Excitation of an Unflawed Half-Space 199
9.5.3 Definition of an Ideal Crack 200
9.5.4 Long Crack in a Uniform Field 200
9.5.5 Semicircular Crack in a Uniform Field 204
9.5.6 Long Crack in a Coil Field 205
9.5.7 Rectangular Crack in a Coil Field 205
9.5.8 Semielliptical Crack in a Coil Field 208
9.5.9 Epicyclic Crack in a Coil Field 208
9.6 Other Regimes 211
9.7 Summary 211
9.8 Exercises 212
References 213
10 Appendices 214
10.1 Complex Numbers 214
10.2 Trigonometry 215
10.3 Vector Analysis 215
10.3.1 Continuity and Differentiability 216
10.3.2 Differential Operators 216
10.3.3 Circular–Cylindrical Coordinates 218
10.3.4 Spherical-Polar Coordinates 219
10.3.5 Differential Relationships 220
10.3.6 Integral Theorems 220
10.4 Bessel Functions 221
10.4.1 Separation of Variables 222
10.4.2 Higher Order Bessel Functions 224
10.5 Exercises 225
References 227
Index 228