Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

Ultrasonic Guided Waves in Solid Media

Publisher Summary This chapter discusses the elastic constants of crystals. The elastic properties of solid matter hold interest for both technology and basic research. In the first field applied elasticity is an important discipline for those fundamental considerations of engineering design which are usually included under the designation “strength of materials.” The treatment of structural materials requires semiempirical methods, because their compositions are complex and prior treatment has a pronounced effect. On the other hand, basic research into elastic properties is usually concerned with work on specimens in the simplest state which can be obtained reproducibly—for example, annealed single crystals. The complete tabulation of elastic constants for such specimens is valuable, not only for itself, but also because the data can be correlated with other physical measurements and thereby provide possible insight into the nature of the atomic forces in solid matter. The research aspect of elastic studies is of primary interest for this chapter. The case of the isotropic medium is important both for the chronological development of the subject of elasticity and also for its applicability to polycrystals and glasses.

The Elastic Constants of Crystals

The nondestructive assessment of the damage that occurs in components during service plays a key role for condition monitoring and residual life estimation of in-service components/structures. Ultrasound has been widely utilized for this; however most of these conventional methods using ultrasonic characteristics in the linear elastic region are only sensitive to gross defects but much less sensitive to micro-damage. Recently, the nonlinear ultrasonic technique, which uses nonlinear ultrasonic behavior such as higher-harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response, has been studied as a positive method for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.

Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: A review

Fatigue damage assessment by nonlinear ultrasonic materials characterization

Nonlinear ultrasonic characterization of fatigue microstructures

Ultrasonic Methods in Solid State Physics

The experimental evidence and the associated theory are presented for the dislocation contribution to the generation of the second harmonic of an ultrasonic wave in solids. The contribution is measured through the changes, as a function of static bias stress, in the amplitude of the second harmonic of a fundamental wave (10 Mc/sec compressional wave) propagating in the specimen.In aluminum single crystals the amplitude of the second harmonic, for a given amplitude of the fundamental, changes markedly with static bias stresses ranging from 0 to 106 dyn/cm2. In alloys, there are essentially no changes of the amplitude of the second harmonic even for bias stresses up to 107 dyn/cm2. These observations are consistent with the predicted dependence of the amplitude on dislocation loop length and on the static stress. The effects of small amounts of plastic deformation were consistent with the proposed model.

Dislocation Contribution to the Second Harmonic Generation of Ultrasonic Waves

An instrument for measurement of ultrasonic attenuation and velocity in the frequency range from 5–200 mc/sec is described. The unit incorporates pulsed rf oscillator, superheterodyne receiver, exponential wave‐form generator, precision time delay generator (useful in velocity measurements), CRT display circuits, and appropriate synchronization circuits. Ultrasonic attenuation measurements made in single crystals of NaCl and KCl during deformation and recovery at several temperatures are reported here.

Ultrasonic Attenuation Unit and Its Use in Measuring Attenuation in Alkali Halides

Measurements of changes in ultrasonic attenuation together with changes in ultrasonic velocity have been made concurrently with load strain measurements in tensile tests on the same specimen of aluminum. The results of such measurements taken during loading of the specimen, during relaxation or recovery at constant strain, and during unloading show a number of interesting effects. These observed effects are interpreted in terms of dislocation behavior for the various stages of the experiment. The experimental results for attenuation α and velocity change Δv/v permit the calculation of changes in dislocation density and loop length based on a dislocation damping theory developed in this laboratory to include both megacycle and kilocycle frequencies. The strain due to dislocation motion was calculated with a simple model and with dislocation loop lengths and densities obtained from the data and the theory just mentioned. The comparison of the calculated strain and the measured strain lends support to the use of this model, and while this dislocation damping model may not be entirely correct it does seem to be possible to obtain information about stress‐strain behavior at low strains from sound propagation data alone.

Bruce B. Chick

Papers

Ultrasonic Methods in Solid State Physics

Dislocation Contribution to the Second Harmonic Generation of Ultrasonic Waves

Ultrasonic Attenuation Unit and Its Use in Measuring Attenuation in Alkali Halides

Sensitivity of Ultrasonic Attenuation and Velocity Changes to Plastic Deformation and Recovery in Aluminum

Attenuation of Sound in a Germanium Crystal at Ultra-High Frequencies and Low Temperatures