Ultrasonic Nondestructive Testing of Materials : Theoretical Foundations book cover
1st Edition

Ultrasonic Nondestructive Testing of Materials
Theoretical Foundations

ISBN 9781138075962
Published March 29, 2017 by CRC Press
772 Pages 220 B/W Illustrations

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Book Description

Ultrasonic Nondestructive Testing of Materials: Theoretical Foundations explores the mathematical foundations and emerging applications of this testing process, which is based on elastic wave propagation in isotropic and anisotropic solids. In covering ultrasonic nondestructive testing methods, the book emphasizes the engineering point of view, yet it relies on the physics and mathematics aspects involved in elastic wave propagation theory.

As a result, this resource becomes a missing link in the literature by combining coverage of the theoretical aspects of testing and providing intuitive assessments of numerous standard problems to illustrate fundamental assertions. Content includes a brief description of the theory of acoustic and electromagnetic fields to underline the similarities and differences as compared to elastodynamics. It also covers vector algebra and analysis, elastic plane and Rayleigh surface waves, and ultrasonic beams, as well as transducer radiation, inverse scattering, and ultrasonic nondestructive imaging.

Includes numerical computations to explain wave propagation phenomena and compare results of analytical formulations

Although ultrasonic nondestructive testing can often be roughly understood in terms of plane waves and beams, this book addresses the key issues of transducer radiation and defect scattering and imaging, respectively. The authors physically formulate point source synthesis, and, in mathematical terms, they use representation integrals with Green functions, always including intuitive interpretations with mathematical evaluations.

Replacing cumbersome index notation with a coordinate-free version, this reference offers step-by-step documentation of relevant tensorial elastodynamic cases involving isotropic and anisotropic materials. It provides all necessary mathematical tools readers require to understand the mathematical and physical basis for ultrasonic nondestructive testing.

Table of Contents

Contents Flow Chart

Mathematical Foundations
Scalar, Vector and Tensor Fields
Vektor and Tensor Analysis
Time and Spatial Spectral Analysis with Fourier Transforms
Delta Function

Governing Equations of Elastodynamics
Newton-Cauchy Equation of Motion and Deformation Rate Equation in the Time and Frequency Domain
Physical Foundations
Transition and Boundary Conditions

Constitutive Equations; Governing Equations; Elastodynamic Energy Conservation
Linear Non-Dissipative Materials: Cauchy-Hooke Law
Elastodynamic Energy Conservation Theorem for Non-Dissipative Materials in the Time and Frequency Domain
Linear Dissipative Materials
Piezoelectricity and Magnetostriction

Governing Equations of Acoustics
Transition and Boundary Conditions
Wave Equations in the Time and Frequency Domain
Solutions of the Homogeneous Acoustic Wave Equations in Homogeneous Materials: Plane Longitudinal Pressure Waves
Acoustic Source Fields in Homogeneous Materials: Point Source Synthesis with Green Functions
Hygens’ Principle for Acoustic Scattered Fields in Homogeneous Materials

Maxwell Equations; Poynting Vector; Lorentz Force
Transition and Boundary Conditions
Constitutive Equations: Permittivity, Permeability; Dissipation: Susceptibility Kernels, Conductivity
Wave Equations in the Time and Frequency Domain
Solutions of Homogeneous Electromagnetic Wave Equations in Homogeneous Isotropic Materials: Plane Transverse Electromagnetic Waves
Electromagnetic Source Fields in Homogeneous Isotropic Materials; Tensor Electromagnetic Green Functions
Electromagnetic Scattered Fields; Electromagnetic Formulation of Huygens’ Principle
Two-Dimensional Electromagnetism: TM- and TE-Decoupling

Vector Wave Equations
Wave Equations for Anisotropic and Isotropic Non-Dissipative Materials
Helmholtz Decomposition for Homogeneous Isotropic Materials: Pressure and Shear Waves
Decoupling of Scalar SH-Waves for Inhomogeneous Isotropic Two-Dimensional
Frequency Domain Wave Equations for Non-Dissipative and Dissipative Materials

Elastic Plane Waves in Homogeneous Materials
Homogeneous Plane Waves in Isotropic Non-Dissipative Materials
Inhomogeneous Plane Waves in Isotropic Non-Dissipative Materials
Plane Waves in Anisotropic Non-Dissipative Materials
Plane Waves in Isotropic Dissipative Materials

Reflection, Transmission and Mode Conversion of Elastic Plane Waves at Planar Boundaries between Homogeneous Non-Dissipative Materials
Stress-Free Planar Boundary of a Homogeneous Isotropic Non-Dissipative Elastic Half-Space
Planar Boundary between Homogeneous Isotropic Non-Dissipative Elastic HalfSpaces
Planar Boundary between a Homogeneous Isotropic Non-Dissipative and a Homogeneous Transversely Isotropic Non-Dissipative Half-Space and a Homogeneous Transversely Isotropic Non-Dissipative Half Space

Rayleigh Surface Waves
Planar Surfaces
Slightly Curved Surfaces

Plane Wave Spatial Spectrum
Acoustic Plane Wave Spatial Spectrum
Elastic Plane Wave Spatial Spectrum

Ultrasonic Beams and Wave Packets
Gaussian Beams as Paraxial Approximation of a Spatial Plane Wave Spectrum
Pulsed Beams as Exact Solutions of an Approximate Wave Equation
Pulsed Beams as Approximate Solutions of Eikonal and Transport Equations

Point Sources in Homogeneous Isotropic Infinite Space; Elastodynamic Source Fields
Homogeneous Infinite Space Scalar Green Function
Homogeneous Isotropic Infinite Space Green Tensors of Elastodynamics
Two- and Three-Dimensional Elastodynamic Source Fields
Elementary Spherical Waves and Plane Waves

Force Density and Dilatation Rate Sources on Surfaces of Homogeneous Isotropic Half-Spaces; Radiation Fields of Piezoelectric Transducers
Acoustic Half-Spaces with Soft or Rigid Surfaces
Strip-Like Normal and Tangential Force Density Distributions on the StressFree Surface of an elastic Half-Space: Plane Wave Spectral DecomposItion of the Two-Dimensional Second Rank Green Tensor
Force Densities on the Surface of a Stress-Free Half-Space
Circular Normal Force Force Density Distribution on the Stress-Free Surface of an Elastic Half-Space: Point Source Characteristic
Radiation Fields of Piezoelectric Transducers

Scatterers in Homogeneous Isotropic Non-Dissipative Infinite Spaces
Huygens' Principle
Integral Equations for Secondary Surface Deformation Sources on Scatterers with Stress-Free Surfaces: Displacement Field Integral Equation and Stress Field Integral Equation
Integral Equations for the Equivalent Sources of Penetrable Scatterers
Scattering Tensor; Far-Fields

Inverse Scattering: US-NDT Imaging
SAFT: Synthetic Aperture Focusing Technique
FT-SAFT: Fourier Transform Synthetic Aperture Focusing Technique

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Langenberg, Karl-Jörg; Marklein, René; Mayer, Klaus


"... absolutely a must for every scientist who would like to further evaluate theoretically ultrasonic NDT. The studies described by Langenberg et al. have very strongly enhanced the interpretation of propagation of elastic waves also in anisotropic and inhomogeneous media we have in practice, for instance, in welds of austenitic stainless steels or dissimilar metal (Ni-alloys) welds in the nuclear and chemical industries."
-- Gerd Dobmann, Fraunhofer-IZFP, Saarbrücken, Germany