This paper presents a comprehensive review of the current state of knowledge of second harmonic generation (SHG) measurements, a subset of nonlinear ultrasonic nondestructive evaluation techniques. These SHG techniques exploit the material nonlinearity of metals in order to measure the acoustic nonlinearity parameter, $$\beta $$
 . In these measurements, a second harmonic wave is generated from a propagating monochromatic elastic wave, due to the anharmonicity of the crystal lattice, as well as the presence of microstructural features such as dislocations and precipitates. This article provides a summary of models that relate the different microstructural contributions to $$\beta $$
 , and provides details of the different SHG measurement and analysis techniques available, focusing on longitudinal and Rayleigh wave methods. The main focus of this paper is a critical review of the literature that utilizes these SHG methods for the nondestructive evaluation of plasticity, fatigue, thermal aging, creep, and radiation damage in metals.

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Review of Second Harmonic Generation Measurement Techniques for Material State Determination in Metals

[45] C. S. Tsai, Le T. Nguyen. M. A. Alhaider, “Wideband Acoustotwo Tilting Surface Acoustic Waves,” Appl. Phys. Lett. 26, optic Guided-Light  Beam  Deflector  Using Tilting  Surface 140-143, February 15,1975. Acoustic  Waves,” 1974 Ultrasonics  Symposium  Proceedings, [47] C. S. Tsai, M. A. Alhaider, Le T. Nguyen and B. Kim, “WideIEEE Cat.. # 74. C H 0 896-1SU. 768-772. band Guided-Wave Acoustooptic Bragg Devices Using Multiple [46] C. S. Tsai, Le T: Nguyen, 8. K.’Yao and M. A. Alhaider, “HighTilting Surface Acoustic Waves,” Talk-36, Conference on Laier performance  Acousto-optic  Guided-light  Beam  Device  Using Engineering and Applications, Washington, D. C., May 1975

III. Optical Probing of Surface Waves and Surface Wave Devices

Nonlinear surface acoustic waves on an isotropic solid

The nonlinear interaction of surface acoustic waves propagating in the same direction has been treated from the rigorous theory of thermoelasticity. Exact expressions were derived for the nonlinear volume forces and surface stresses, and the nonlinear cross sections were calculated under two separate assumptions. First, the work done by the nonlinear forces and surface stresses on a normal‐mode surface wave was evaluated and assumed to be totally converted into surface‐wave energy. In the second approach, a linear analytic solution was formulated which simultaneously satisfies the nonlinear wave equation and maintains a stress‐free boundary condition. Numerical values for the strength of second‐harmonic generation were calculated for 24 materials. The characteristics of nonlinear surface‐wave generation were compared with those of nonlinear bulk‐wave generation and significant differences were found. Coupled amplitude equations were derived to treat the case of multiharmonic generation. Finally, a charact...

Nonlinear surface‐wave interactions: Parametric mixing and harmonic generation

Nonlinear electroelastic equations, quadratic in the small field variables, are applied in the analysis of second harmonic generation of surface waves in piezoelectric solids. Preliminary to the treatment of the anisotropic piezoelectric case, the more tractable problems of the second harmonic generation and parametric excitation of surface waves in isotropic elastic solids are treated. In all instances the solutions asymptotically satisfy the nonlinear differential equations and boundary conditions on the surface of the semi‐infinite solid to a specified order in a small parameter. Since the equations are quadratic rather than cubic in the small field variables, only initial spatial rates of growth of the harmonically generated and parametrically excited waves are determined. Nevertheless, an extension of the analysis to enable the calculation of more than the aforementioned initial slopes is indicated. In the isotropic elastic case the solution for the second harmonic reveals, among other things, that t...

Second harmonic generation and parametric excitation of surface waves in elastic and piezoelectric solids

Harmonic generation of acoustic surface waves has been observed experimentally in different laboratories on quartz, lithium niobate, and bismuth germanium oxide sub- strates and a phenomenological model containing one non- linear elastic constant has been proposed to explain the spatial variation of each observed harmonic on a LiNb03 delay line. In this paper we describe how the surface wave nonlinearities of different materials can be quantitatively compared. Using laser light deflection the growth with distance of the second harmonic was measured in LiNb03 and Bi12GeOzo for fun- damental frequencies of 50 and 100 MHz and of the second, third, and fourth harmonics in LiNb03 for a fundamental of 150 MHz. A one-dimensional, single-parameter model is used from which is obtained a system of coupled differential equa- tions describing the harmonic growth. This system is solved numerically as an initial value problem and a value of the single-parameter found for each material which gave good agreement between the measured data and the model pre- dictions. The parameter values found differ by an order of magnitude in the two materials, LiNb03 being the more strongly nonlinear.

G. Coussot

Papers

Harmonic Generation of Acoustic Surface Waves in Bi 12 GeO 20 and LiNbO 3