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E-raamat: Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach

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  • Ilmumisaeg: 11-Nov-2013
  • Kirjastus: Plenum Publishing Co.,N.Y.
  • Keel: eng
  • ISBN-13: 9781489901422
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Nov-2013
  • Kirjastus: Plenum Publishing Co.,N.Y.
  • Keel: eng
  • ISBN-13: 9781489901422

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Ultrasound is currently used in a wide spectrum of applications ranging from medical imaging to metal cutting. This book is about using ultrasound in nondestructive evaluation (NDE) inspections. Ultrasonic NDE uses high-frequency acoustic/elastic waves to evaluate components without affecting their integrity or performance. This technique is commonly used in industry (particularly in aerospace and nuclear power) to inspect safety-critical parts for flaws during in-service use. Other important uses of ultrasonic NDE involve process control functions during manufacturing and fundamental materials characterization studies. It is not difficult to set up an ultrasonic NDE measurement system to launch waves into a component and monitor the waves received from defects, such as cracks, even when those defects are deep within the component. It is difficult however to interpret quantitatively the signals received in such an ultrasonic NDE measurement process. For example based on the ultrasonic signal received from a crack, what is the size, shape, and orientation of the crack producing the signal? Answering such questions requires evaluation procedures based on a detailed knowledge of the physics of the entire ultrasonic measurement process. One approach to obtaining such knowledge is to couple quantitative experiments closely with detailed models of the entire ultrasonic measurement system itself. We refer to such models here as ultrasonic NDE measurement models. In other areas of engineering, models have revolutionized how engineering is practiced. A classic example is the impact of the finite-element method on elastic stress analysis.
1. An Ultrasonic System
1(14)
1.1. Elements of an Ultrasonic NDE System
1(2)
1.2. Pulser-Receiver
3(2)
1.3. Ultrasonic Transducers
5(4)
1.4. Ultrasonic Digitizers
9(1)
1.5. Ultrasonic Terminology
10(2)
1.6. About the Literature
12(1)
1.7. Problems
12(1)
1.8. References
13(2)
2. Linear Systems and the Fourier Transform
15(14)
2.1. Linear Time-Shift Invariant Systems
15(1)
2.2. Fourier Transform
16(3)
2.3. LTI Systems and the Impulse Response Function
19(2)
2.4. An Ultrasonic NDE Measurement System as an LTI System
21(2)
2.5. About the Literature
23(1)
2.6. Problems
24(4)
2.7. References
28(1)
3. Fundamentals
29(20)
3.1. Governing Equations for a Fluid
29(4)
3.1.1. Equations of Motion
29(1)
3.1.2. Constitutive Equations
30(1)
3.1.3. Wave Equation
31(1)
3.1.4. Interface/Boundary Conditions
32(1)
3.2. Governing Equations for an Elastic Solid
33(12)
3.2.1. Equations of Motion
34(1)
3.2.2. Constitutive Equations
35(1)
3.2.3. Navier's Equations
36(1)
3.2.4. Interface/Boundary Conditions
37(2)
3.2.5. Wave Equations for Potentials
39(1)
3.2.6. Dilatation and Rotation
40(1)
3.2.7. Governing Equations in Cartesian Coordinates
40(5)
3.3. About the Literature
45(1)
3.4. Problems
45(3)
3.5. References
48(1)
4. Propagation of Bulk Waves
49(20)
4.1. Plane Waves in a Fluid
49(4)
4.1.1. One-Dimensional Waves
49(1)
4.1.2. Fourier Transform Relations
50(1)
4.1.3. Harmonic Waves
51(1)
4.1.4. Three-Dimensional Waves
52(1)
4.2. Plane Waves in an Elastic Solid
53(4)
4.2.1. One-Dimensional Solutions to Navier's Equations
53(1)
4.2.2. Three-Dimensional Solutions to Navier's Equations
53(4)
4.3. Spherical Waves in a Fluid
57(5)
4.3.1. Fundamental Solution
57(2)
4.3.2. Integral Forms of the Fundamental Solution
59(2)
4.3.3. Far-Field Form of G and Its Derivatives
61(1)
4.4. Spherical Waves in an Elastic Solid
62(4)
4.4.1. Fundamental Solution
62(4)
4.4.2. Far-Field Form of G(ji) and Its Derivatives
66(1)
4.5. About the Literature
66(1)
4.6. Problems
67(1)
4.7. References
68(1)
5. Reciprocal Theorem and Other Integral Relations
69(22)
5.1. Reciprocal Theorem for a Fluid
69(8)
5.1.1. Integral Representation Theorem
70(2)
5.1.2. Sommerfeld Radiation Conditions
72(3)
5.1.3. Integral Equations for Scattering Problems
75(2)
5.2. Reciprocal Theorem for an Elastic Solid
77(6)
5.2.1. Integral Representation Theorem
78(1)
5.2.2. Radiation Conditions
79(2)
5.2.3. Integral Equations for Scattering Problems
81(2)
5.3. An Electromechanical Reciprocal Theorem
83(3)
5.3.1. Governing Equations
83(1)
5.3.2. Reciprocal Theorem for a Piezoelectric Medium
84(2)
5.4. About the Literature
86(1)
5.5. Problems
86(2)
5.6. References
88(3)
6. Reflection and Refraction of Bulk Waves
91(50)
6.1. Reflection and Refraction at a Fluid-Fluid Interface (Normal Incidence)
91(6)
6.1.1. Reflection and Transmission Coefficients
91(3)
6.1.2. Acoustic Intensity of a Plane Wave
94(3)
6.2. Reflection and Refraction of a Plane Wave at a Fluid-Fluid Interface (Oblique Incidence)
97(18)
6.2.1. Reflection and Transmission Coefficients
97(1)
6.2.2. Critical Angles and Inhomogeneous Waves
98(2)
6.2.3. Energy Reflection and Transmission below the Critical Angle
100(1)
6.2.4. Energy Reflection and Transmission above the Critical Angle
101(1)
6.2.5. Pulse Distortion
102(4)
6.2.6. Stokes' Relations
106(2)
6.2.7. Reflection and Refraction at a Fluid-Fluid Interface in Three Dimensions
108(4)
6.2.8. Snell's Law and Stationary Phase
112(3)
6.3. Reflection and Refraction at a Fluid-Solid Interface at Oblique Incidence
115(8)
6.3.1. Reflection and Transmission Coefficients
115(4)
6.3.2. Energy Flux and Intensity for Elastic Waves
119(3)
6.3.3. Stokes' Relations (Fluid-Solid Interface)
122(1)
6.4. Reflection and Refraction at a Solid-Solid Interface (Smooth Contact)
123(4)
6.5. Reflection and Refraction at a Solid-Solid Interface (Welded Contact)
127(6)
6.5.1. Incident P- and SV-Waves
127(4)
6.5.2. Incident SH-Waves
131(2)
6.6. Reflection at a Stress-Free Surface
133(1)
6.7. About the Literature
134(1)
6.8. Problems
135(5)
6.9. References
140(1)
7. Propagation of Surface and Plate Waves
141(16)
7.1. Rayleigh Surface Waves
141(4)
7.2. Plate Waves-Horizontal Shearing Motions
145(4)
7.3. Lamb Waves
149(4)
7.3.1. Extensional Waves
149(3)
7.3.2. Flexural Waves
152(1)
7.4. Other Waves in Bounded Media
153(1)
7.5. About the Literature
153(1)
7.6. Problems
154(1)
7.7. References
155(2)
8. Ultrasonic Transducer Radiation
157(126)
8.1. Planar Piston Transducer in a Fluid
157(24)
8.1.1. Rayleigh-Sommerfeld Theory
158(2)
8.1.2. On-Axis Pressure
160(5)
8.1.3. Off-Axis Pressure
165(13)
8.1.4. Angular Spectrum of Plane Waves and Boundary Diffraction Wave Theory
178(3)
8.2. Spherically Focused Piston Transducer in a Fluid
181(18)
8.2.1. O'Neil Model and Others
181(2)
8.2.2. On-Axis Pressure
183(6)
8.2.3. Off-Axis Pressure
189(8)
8.2.4. Focusing by an Acoustic Lens
197(2)
8.3. Beam Propagation through a Planar Interface-Planar Probe
199(16)
8.3.1. Fluid-Fluid Interface-Normal Incidence
199(7)
8.3.2. Fluid-Solid Interface-Normal Incidence
206(3)
8.3.3. Fluid-Fluid Interface-Oblique Incidence
209(5)
8.3.4. Fluid-Solid Interface-Oblique Incidence
214(1)
8.4. Beam Propagation through a Planar Interface-Focused Probe
215(6)
8.4.1. Fluid-Fluid Interface
215(4)
8.4.2. Fluid-Solid Interface
219(2)
8.5. Beam Propagation through a Curved Interface
221(23)
8.5.1. Fluid-Fluid Interface
221(17)
8.5.2. Fluid-Solid Interface
238(6)
8.6. Numerical Evaluation of Beam Models
244(16)
8.6.1. Edge Elements
246(10)
8.6.2. Curved Interface Problems with Edge Elements
256(4)
8.7. Contact Transducer
260(7)
8.8. Angle Beam Shear Wave Transducer
267(9)
8.8.1. Angle Beam Transducer Model
267(5)
8.8.2. Edge Elements
272(4)
8.9. About the Literature
276(1)
8.10. Problems
276(5)
8.11. References
281(2)
9. Material Attenuation and Efficiency Factors
283(22)
9.1. Sources of Attenuation
283(4)
9.2. General Model for Measuring Material Attenuation and the System Efficiency Factor
287(14)
9.2.1. Diffraction Correction Integral
289(6)
9.2.2. Attenuation Measurement by a Deconvolution Model and the Wiener Filter
295(3)
9.2.3. Efficiency Factor Measurement by a Deconvolution Model and the Wiener Filter
298(3)
9.3. About the Literature
301(1)
9.4. Problems
301(3)
9.5. References
304(1)
10. Flaw Scattering
305(80)
10.1. Far-Field Scattering Amplitude in a Fluid
305(2)
10.1.1. Volumetric Flaws
305(2)
10.1.2. Cracklike Flaws
307(1)
10.2. Far-Field Scattering Amplitude in an Elastic Solid
307(4)
10.2.1. Volumetric Flaws
307(3)
10.2.2. Cracklike Flaws
310(1)
10.3. Approximate Scattering Solutions-Fluid Model
311(25)
10.3.1. Kirchhoff Approximation-Volumetric Flaws
312(10)
10.3.2. Kirchhoff Approximation-Cracks
322(6)
10.3.3. Born Approximation
328(8)
10.4. Approximate Scattering Solutions-Elastic Solid Model
336(21)
10.4.1. Kirchhoff Approximation-Volumetric Flaws
336(8)
10.4.2. Kirchhoff Approximation-Cracks
344(8)
10.4.3. Born Approximation
352(5)
10.5. Far-Field Scattering Amplitude and Reciprocity
357(5)
10.5.1. Scattering Amplitude in a Fluid
357(3)
10.5.2. Scattering Amplitude in an Elastic Solid
360(2)
10.6. Scattering by a Sphere-Separation of Variables
362(16)
10.6.1. Sphere in a Fluid
362(9)
10.6.2. Sphere in an Elastic Solid
371(7)
10.7. About the Literature
378(1)
10.8. Problems
379(4)
10.9. References
383(2)
11. Transducer Reception Process
385(14)
11.1. Reception in a Single-Fluid Medium
385(2)
11.2. Reception Across a Plane Fluid-Fluid Interface
387(4)
11.3. Reception Across a Plane Fluid-Solid Interface
391(4)
11.4. About the Literature
395(1)
11.5. Problems
395(1)
11.6. References
396(3)
12. Ultrasonic Measurement Models
399(36)
12.1. LTI Model for a Single-Fluid Medium
399(4)
12.2. LTI Model for Immersion Testing
403(4)
12.2.1. Fluid-Fluid Model
404(1)
12.2.2. Fluid-Solid Model
405(2)
12.3. Reciprocity-Based Model for Immersion Testing
407(12)
12.3.1. General Model
407(8)
12.3.2. Reduction to an LTI Model
415(4)
12.4. Reciprocity-Based Model for Angle Beam Shear Wave Testing
419(5)
12.5. Electromechanical Reciprocity-Based Measurement Model
424(3)
12.6. Measurement Models and Their Limitations
427(2)
12.7. About the Literature
429(1)
12.8. Problems
430(3)
12.9. References
433(2)
13. Near-Field Measurement Models
435(22)
13.1. Model for a Single-Fluid Medium
435(11)
13.1.1. On-Axis Response to a Circular Transducer
440(1)
13.1.2. Scattering from a Sphere
441(2)
13.1.3. Scattering from the Flat End of a Cylinder
443(3)
13.1.4. Paraxial Approximation Limit
446(1)
13.2. Other Models for a Single-Fluid Medium
446(5)
13.3. Model for a Fluid-Solid Interface (Normal Incidence)
451(3)
13.4. About the Literature
454(1)
13.5. Problems
454(2)
13.6. References
456(1)
14. Quantitative Ultrasonic NDE with Models
457(34)
14.1. Transducer/System Characterization
458(11)
14.1.1. Effective Radius-Planar Transducer
458(2)
14.1.2. Effective Parameters-Spherically Focused Transducer
460(2)
14.1.3. System Efficiency Factor
462(1)
14.1.4. Experimental Results
463(6)
14.2. Flat-Bottom Hole Models and DGS Diagrams
469(12)
14.2.1. Fluid-Fluid Model
476(1)
14.2.2. Special Cases
477(1)
14.2.3. DGS Diagrams
478(3)
14.3. Deconvolution and Far-Field Scattering Amplitudes
481(3)
14.4. Model-Based Ultrasonic Simulation
484(2)
14.5. About the Literature
486(1)
14.6. Problems
487(1)
14.7. References
488(3)
15. Model-Based Flaw Sizing
491(26)
15.1. Concept of Equivalent Flaw Sizing
491(1)
15.2. Kirchhoff Sizing for Cracks
491(7)
15.2.1. Nonlinear Least Squares Sizing Method
493(1)
15.2.2. Linear Least Squares/Eigenvalue Sizing Method
494(4)
15.3. Born Sizing for Volumetric Flaws
498(7)
15.4. TOFE Flaw Sizing
505(3)
15.5. Other Sizing Methods
508(1)
15.6. About the Literature
509(1)
15.7. Problems
509(5)
15.8. References
514(3)
Appendix A. Fourier Transform
517(10)
A.1. Properties of the Fourier Transform
517(2)
A.2. Some Fourier Transform Pairs
519(1)
A.3. Discrete Fourier Transform
520(4)
A.4. Fast Fourier Transform
524(1)
A.5. Problems
525(1)
A.6. References
525(2)
Appendix B. Dirac Delta Function
527(2)
B.1. Properties of the Delta Function
527(1)
B.2. References
528(1)
Appendix C. Basic Notations and Concepts
529(12)
C.1. Indicial Notation
529(3)
C.2. Integral Theorems
532(1)
C.2.1. Gauss' Theorem
532(1)
C.2.2. Stokes' Theorem
533(1)
C.3. Strain and Deformation
533(3)
C.4. Conservation of Mass
536(1)
C.5. Stress
536(3)
C.5.1. Traction Vector
536(1)
C.5.2. Concept of Stress
537(1)
C.5.3. Tractions and Stresses
538(1)
C.6. References
539(2)
Appendix D. Hilbert Transform
541(2)
D.1. Properties of the Hilbert Transform
541(1)
D.2. References
542(1)
Appendix E. Stationary Phase Method
543(8)
E.1. Single-Integral Forms
543(3)
E.2. Double-Integral Forms
546(1)
E.3. Curved-Surface Integral
547(2)
E.4. References
549(2)
Appendix F. Properties of Ellipsoids
551(4)
F.1. Geometry of an Ellipsoid
551(3)
F.2. References
554(1)
Index 555