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In this study, the properties of Rayleigh wave fields scattered at a surface from open vertical cracks with different shapes are investigated. The scattered Rayleigh wave is determined by both the incident Rayleigh wave and its interaction with the crack, and the wave fields are modeled using the Green's function method based on the reciprocity theorem. The reflection coefficient of the Rayleigh wave in two-dimensional coordinates is employed to simplify the area integration over the crack surface for the scattered Rayleigh wave to a line integration over the length of the crack. Numerical simulations are carried out, and the effects of the crack length and depth on the scattered Rayleigh wave fields are discussed. The results indicate that the distribution of a scattered Rayleigh wave field is mainly determined by the crack length, while the amplitude is closely related to the crack depth. Since the reflection coefficient becomes almost stable when the ratio of the crack depth to the Rayleigh wavelength is larger than 1, the variation in the scattered Rayleigh wave field is insignificant for cracks with the same length but varying depths. This work will be helpful for solving the inverse problem of evaluating crack geometry using ultrasonic Rayleigh waves and for further work on Rayleigh waves scattered by cracks with different directions of extension and angles with the surface. [ABSTRACT FROM AUTHOR]

This article investigates the interactions of two-plane waves in weakly nonlinear elastic solids containing quadratic and cubic nonlinearity. The analytical solutions for generated combined harmonic waves are derived using the Green's function approach applied to a generated system of quasi-linear equations of motion. Wave mixing solutions are obtained and include shape functions that permit closed-form solutions for a variety of interaction geometries. An explicit example is highlighted for a spherical interaction volume assuming isotropic elastic constants. Several parameters of the generated field after mixing are analyzed including resonant and nonresonant mixing, the role of interaction angle, and the frequencies of the two incident waves. Wave mixing offers the potential for sensing localized elastic nonlinearity and the present model can be used to help design experimental configurations. [ABSTRACT FROM AUTHOR]

In nonlinear ultrasound testing, the relative nonlinear parameter is conveniently measured as a sensitive means of detecting and imaging overall variation of microstructures and damages. Compared to the quadratic nonlinear parameter ( β ′ ), the cubic nonlinear parameter ( γ ′ ), calculated as the third harmonic amplitude divided by the cube of the fundamental amplitude, has generally a higher value, providing better sensitivity in nonlinear parameter mapping. Since the third harmonic amplitude is about two orders of magnitude lower than the fundamental amplitude, efficient excitation and highly sensitive reception of third harmonic is very important. In this paper, we explore an odd harmonic thickness resonant transducer that meets the requirements for pulse-echo third harmonic generation (THG) measurements. We also address the problem of source nonlinearity that may be present in the measured amplitude of the third harmonic and propose a method to properly correct it. First, we measure γ ′ for a series of aluminum specimens using the through-transmission method to observe the behavior of γ ′ as a function of specimen thickness and input voltage, and examine the effects of various corrections such as attenuation, diffraction and source nonlinearity. Next, we apply the odd harmonic resonant transducer to pulse-echo THG measurements of precipitation heat-treated specimens. It is shown that such transducer is very effective in generation and detection of fundamental and third harmonics under finite amplitude toneburst excitation. The highly sensitive detectability of γ ′ are presented as a function of aging time, and the sensitivity of γ ′ is compared with that of β ′ and β ′ 2 . [ABSTRACT FROM AUTHOR]

Harmonic generation measurement is recognized as a promising tool for inspecting material state or micro-damage and is an ongoing research topic. Second harmonic generation is most frequently employed and provides the quadratic nonlinearity parameter (β) that is calculated by the measurement of fundamental and second harmonic amplitudes. The cubic nonlinearity parameter ( β 2 ), which dominates the third harmonic amplitude and is obtained by third harmonic generation, is often used as a more sensitive parameter in many applications. This paper presents a detailed procedure for determining the correct β 2 of ductile polycrystalline metal samples such as aluminum alloys when there exists source nonlinearity. The procedure includes receiver calibration, diffraction, and attenuation correction and, more importantly, source nonlinearity correction for third harmonic amplitudes. The effect of these corrections on the measurement of   β 2 is presented for aluminum specimens of various thicknesses at various input power levels. By correcting the source nonlinearity of the third harmonic and further verifying the approximate relationship between the cubic nonlinearity parameter and the square of the quadratic nonlinearity parameter ( β ∗ β ), β 2 ≈ β ∗ β , the cubic nonlinearity parameters could be accurately determined even with thinner samples and lower input voltages. [ABSTRACT FROM AUTHOR]

This work presents theoretical and numerical models for the backscattering of two-dimensional Rayleigh waves by an elastic inclusion, with the host material being isotropic and the inclusion having an arbitrary shape and crystallographic symmetry. The theoretical model is developed based on the reciprocity theorem using the far-field Green's function and the Born approximation, assuming a small acoustic impedance difference between the host and inclusion materials. The numerical finite element (FE) model is established to deliver a relatively accurate simulation of the scattering problem and to evaluate the approximations of the theoretical model. Quantitative agreement is observed between the theoretical model and the FE results for arbitrarily shaped surface/subsurface inclusions with isotropic/anisotropic properties. The agreement is excellent when the wavelength of the Rayleigh wave is larger than, or comparable to, the size of the inclusion, but it deteriorates as the wavelength gets smaller. Also, the agreement decreases with the anisotropy index for inclusions of anisotropic symmetry. The results lay the foundation for using Rayleigh waves for quantitative characterization of surface/subsurface inclusions, while also demonstrating its limitations. [ABSTRACT FROM AUTHOR]

Machining of free-form surfaces has an important role in industrial manufacturing, but conventional tool-path generation strategies for free-form surfaces machining have the drawbacks of serious flattening distortion and poor tool-path continuity. Therefore, a novel method is developed to generate a spiral tool path for the machining of free-form surfaces by improving surface-flattening distortion and tool-path continuity. First, physical shell mapping is presented to flatten a free-form surface into a plane, which takes stretching energy, bending energy, and global energy into account. Then, the spatial spiral polyline is rounded to generate a spiral path by proposing reverse-compensation optimisation. Therefore, the free-form surfaces can be quickly flattened with less distortion, remaining free of overlap, and can in addition be machined at high speed along a C2 continuous spiral tool path. Further, the flattening error, tool-path length, mean curvature, mean scallop-height error of the spiral path, machining time and surface roughness are obviously reduced. Finally, simulation results are given to show the effectiveness and feasibility of the presented strategy. [ABSTRACT FROM AUTHOR]