Nonlinear Rayleigh Waves Research Articles

Fatigue damage evaluation in A36 steel using nonlinear Rayleigh surface waves

This research uses nonlinear Rayleigh waves to characterize the damage due to plastic deformation in A36 steel specimens subjected to quasi-static, monotonic tension, and low cycle fatigue. A36 steel is widely used in the civil infrastructure, such as steel bridges, where fatigue damage can lead to a catastrophic failure. Plastic deformation causes the generation of higher order harmonics in an initially monochromatic Rayleigh wave signal, and this measurable change occurs before macroscopic damage such as cracks appear in a specimen. This increase in the acoustic nonlinearity is produced by plasticity-induced microstructure changes, and thus can be taken as a direct measure of damage. Experiments are conducted using a pair of wedge transducers to generate and detect tone burst ultrasonic Rayleigh surface wave signals. The amplitudes of the first and second order harmonics are measured at different propagation distances to obtain the nonlinearity parameter for a given damage state throughout the fatigue life and monotonic loading process in three specimens. The results of the nonlinear ultrasonic measurements show an increase in the measured acoustic nonlinearity, especially in the early stages of fatigue life. In addition, there is a notably close relationship between the measured acoustic nonlinearity and the cumulative plastic deformation. These results demonstrate the feasibility of using nonlinear Rayleigh waves to characterize damage associated with plastic deformation, and this quantitative information can be a useful input for life prediction models.

Nondestructive Evaluation of Material Damage Using Nonlinear Rayleigh Waves Approach

A nonlinear Rayleigh wave approach is presented for nondestructive evaluation of material damage in this paper. Rayleigh waves are experimentally generated and detected with wedge transducers, and the nonlinear parameters are measured at different stress levels for AZ31 magnesium alloy plate specimen. By experimental way, it is observed that there is a direct correlation between the acoustic nonlinearity measured with nonlinear Rayleigh waves and the level of plasticity. The result shows that there is a significant increase in the nonlinear parameters at monotonic tensile loads above the material’s yield stress, and it demonstrates the effectiveness of the proposed experimental procedure to track the surface damage in alloys.

Fatigue Damage Characterization of Magnesium Thick Plate Using Nonlinear Rayleigh Wave

In order to extend engineering application of nonlinear ultrasonic nondestructive testing technique in wave structure, an experimental technique for excitation and reception directly of Rayleigh wave by fixing piezoelectric sensor on the edge of the specimen is presented. Using the experimental system and procedure, the surface fatigue damage of AZ31 magnesium thick plate is detected by nonlinear Rayleigh waves. Although the experimental results have some dispersion, the ultrasonic nonlinearity parameters overall increase apparently with the fatigue cycles increasing, which demonstrates the Rayleigh wave nonlinearity parameters are sensitive for the changes of microscopic defects in the materials internal, and the experimental system and procedure are reliable. The Rayleigh wave nonlinearity parameters for the thick plate structure fatigue life prediction have potential engineering applications.

Characterization of surface damage of a solid plate under tensile loading using nonlinear Rayleigh waves

This letter reports experimental observation of a direct correlation between the acoustic nonlinearity parameter (NP) measured with nonlinear Rayleigh waves and the accumulation of plasticity damage in an AZ31 magnesium alloy plate specimen. Rayleigh waves are generated and detected with wedge transducers, and the NPs are measured at different stress levels. The results show that there is a significant increase in the NPs with monotonic tensile loads surpassing the material's yielding stress. The research suggests an effective nondestructive evaluation method to track the surface damage in metals.

Linear and Nonlinear Seismic Rayleigh Waves with Damping: A Heuristic Direct Method

In this study, nonlinearity in earthquake is investigated for the propagating seismic waves instead of linear waves. Assuming the presence of nonlinear effects in this earthquake modeling, the Rayleigh waves are formed by incorporating the nonlinear sine-Gordon equation into the linear asymptotic governing equations for finding similarity reduction. The existence of reduction to the modified asymptotic governing equations is demonstrated and is consequently shown to give both the linear and nonlinear Rayleigh waves solutions. The related velocity and amplitude dependent Rayleigh waves are obtained and also the nonlinear form of Rayleigh waves. Multiple nonlinear surface displacements are identified. These nonlinear waves are shown to leave the trails of crucial surface displacements.

Simulation and Experiment of Fatigue Damage Detection in Magnesium Thick Plate Using Nonlinear Rayleigh Wave

In order to extend engineering application of nonlinear ultrasonic nondestructive testing technique in wave structure,an experimental technique for excitation and reception directly of Rayleigh wave by fixing piezoelectric sensor on the edge of the specimen is presented,this method is verified by simulation of the finite element method(FEM).By using the experimental system and procedure,cumulative effect of nonlinear Rayleigh waves is proved,nonlinearity parameters nearly linear increase with Rayleigh wave propagation distance increasing,which demonstrates the Rayleigh wave nonlinearity parameters are sensitive for the changes of microscopic defects in the materials internal,and the experimental system and procedure are reliable.Finally,the surface fatigue damage of AZ31 magnesium thick plate is detected by nonlinear Rayleigh waves.Although the experimental results have some dispersion,the ultrasonic nonlinearity parameters overall increase apparently with the fatigue cycles increasing,which shows the Rayleigh wave nonlinearity parameters for the thick plate structure fatigue life prediction have potential engineering applications.

Experimental study of nonlinear Rayleigh wave propagation in shot-peened aluminum plates—Feasibility of measuring residual stress

Shot-peening is widely used in the aerospace industry to enhance the resistance of structural components to fatigue damage and stress corrosion by putting the outside layer of a component under an initial, residual compressive stress. The ability to measure these near-surface residual stresses is useful from a quality control and certification perspective, and can help predict the fatigue life of shot-peened components. This paper presents experimental results to examine the feasibility of measuring near-surface residual stresses using nonlinear Rayleigh surface waves. Experiments are conducted on aluminum alloy (AA 7075) samples shot-peened at different peening intensities and thus with different levels of residual stresses. The surface roughness of these samples is also measured. The nonlinear ultrasonic results show a large increase in the acoustic nonlinearity parameter, indicating the potential of nonlinear ultrasonics for the in situ measurement of near-surface residual stresses. The effects of surface roughness and the driving frequency on the measured acoustic nonlinearity parameter are briefly discussed. Finally, a preliminary model is used to interpret some experimental results. Future work to evaluate the separate contributions of cold work, residual stress and surface roughness to the total measured nonlinearity is also discussed.

Variations of the nonlinear equation for diffracting beams in fluids to study different modes of propagation in elastic media.

Four variations of the equation for nonlinear acoustic beam propagation derived originally for a fluid will be reviewed. These variations describe finite amplitude beam propagation in isotropic elastic solids and in crystals, influence of diffraction on nonlinear Rayleigh waves, and nonlinear shear wave beams. The distinguishing features of each case will be discussed. The equation for nonlinear longitudinal wave beams in isotropic solids is based on nonlinear theory of elasticity and is close to the original equation for fluids. The equation for sound beams in crystals takes into account that the direction of energy propagation does not coincide with the direction normal to wavefronts. Nevertheless, the general form of the equation is similar to that of the original equation for fluids. Distinguishing features of Rayleigh waves are that they are two-dimensional and their nonlinearity is nonlocal. Because of the nonlocal nonlinearity, the evolution equation for this case was derived in the frequency domain using Hamiltonian formalism. The equation for nonlinear shear wave beams was derived in the cubic approximation in terms of particle displacement and it accounts for any polarization. Solutions of these evolution equations will be presented to illustrate phenomena specific to each case.

SHORT-TIME EXISTENCE FOR SCALE-INVARIANT HAMILTONIAN WAVES

We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.

Nonlinear Rayleigh waves in soft tissue

Linear and nonlinear Rayleigh waves in soft elastic, tissuelike media are investigated theoretically. When the shear modulus is much smaller than the bulk modulus, as it is for soft tissue, the medium can be modeled as being incompressible provided shear stress alone is sufficient to support a particular mode of propagation. Such is the case for Rayleigh waves. Propagation speeds and penetration depths of the transverse and longitudinal components of Rayleigh waves are evaluated under these conditions. Differences between Rayleigh waves in ordinary solids and in soft elastic media are discussed. In tissuelike media, the transverse component obeys a wave equation, and the longitudinal counterpart obeys the Laplace equation. It is also shown that Rayleigh waves in soft elastic media are degenerate in the sense that the potential and solenoidal components cannot be separated. The analysis is based on Hamiltonian mechanics, following an approach developed by the authors for modeling nonlinear surface acoustic waves in both isotropic and anisotropic solids. Nonlinearity coefficients are estimated that characterize the rate of waveform distortion and harmonic generation. Numerical simulations of nonlinear propagation effects in soft elastic incompressible media are simulated in the quadratic approximation. [Work supported by NIH Grant EB004336.]

Evolution of nonlinear Rayleigh waves in a coated substrate

Nonlinear Rayleigh waves propagating in a substrate coated with a thin elastic film are studied numerically. The evolution model consists of the nonlinear spectral equations of Zabolotskaya [J. Acoust. Soc. Am. 91, 2569–2575 (1992)] augmented ad hoc to include film dispersion. The dispersion relation is obtained from linear theory but is otherwise exact. Both loading and stiffening films are considered. Computations are performed for nonlinear evolution of an initially sinusoidal Rayleigh wave under three distinct dispersion regimes corresponding to different film thicknesses. The validity of the evolution model is also examined.

Sizing of Closed Crack Depth by Nonlinear Leaky Rayleigh Wave

Sizing of Closed Crack Depth by Nonlinear Leaky Rayleigh Wave

Nonlinear Rayleigh waves in a medium with a monatomic nonlinear coating

The nonlinear dynamics of surface acoustic waves at the surface of a linear elastic half-space coated with a monolayer of a nonlinear material is investigated. A one-dimensional nonlinear integrodifferential equation describing the dynamics of such a system is derived. The model proposed is used to study Rayleigh solitons with a stationary profile. The possible phenomenological generalizations of the equations derived and their exact soliton solutions are discussed.

Effects of harmonic phase on nonlinear surface acoustic waves in the (111) plane of cubic crystals.

Spectral evolution equations are used to perform numerical studies of nonlinear surface acoustic waves in the (111) plane of several nonpiezoelectric cubic crystals. Nonlinearity matrix elements which describe the coupling of harmonic interactions are used to characterize velocity waveform distortion. In contrast to isotropic solids and the (001) plane of cubic crystals, the nonlinearity matrix elements usually cannot be written in a real-valued form. As a result, the harmonic components are not necessarily in phase, and dramatic variations in waveforms and propagation curves can be observed. Simulations are performed for initially monofrequency surface waves. In some directions the waveforms distort in a manner similar to nonlinear Rayleigh waves, while in other directions the velocity waveforms distort asymmetrically and the formation of shocks and cusped peaks is less distinct. In some cases, oscillations occur near the shocks and peaks because of phase differences between harmonics. A mathematical transformation based on the phase of the matrix elements is shown to provide a reasonable approximation of asymmetric waveform distortion in cases where the matrix elements have similar phase.

Nonlinear surface waves on a tangential discontinuity in magnetohydrodynamics

We derive an asymptotic equation that describes the propagation of weakly nonlinear surface waves on a tangential discontinuity in incompressible magnetohydrodynamics. The equation is similar to, but simpler than, previously derived asymptotic equations for weakly nonlinear Rayleigh waves in elasticity, and is identical to a model equation for nonlinear Rayleigh waves proposed by Hamilton et al. The most interesting feature of the surface waves is that their nonlinear self-interaction is nonlocal. As a result of this nonlocal nonlinearity, smooth solutions break down in finite time, and appear to form cusps.

An expansion method for non-linear Rayleigh waves

We use ideas from analytic bifurcation theory to develop expansions for periodic small amplitude traveling surface elastic waves of permanent form in the half-plane (Rayleigh waves). We focus on the case of hyperelastic materials where the traveling wave problem has a variational structure, and solve numerically the equations describing the lowest order approximation to the traveling wave solutions. For the materials considered, there is evidence for solutions describing elastic displacements that have discontinuous derivative at the boundary of the domain.

Amplitude equations for non-linear Rayleigh waves

Abstract We investigate asymptotic equations describing small amplitude surface elastic waves in the half-plane (Rayleigh waves). For hyperelastic materials such model equations are Hamiltonian systems, and are seen to lead to the formation of singularities in the surface elastic displacement. At the time of singularity formation the Fourier spectra of the solutions exhibit power law decay, and the observed exponents suggest the existence of both differentiable and non-differentiable singular profiles.

Laser-generated nonlinear Rayleigh waves with shocks

Intense laser radiation was used to generate a Rayleigh wave pulse of finite amplitude in fused quartz. Measurements of the pulse at two locations along the propagation path reveal the formation of well-defined shocks in the horizontal (in-plane) velocity waveform. As the pulse propagates, the different propagation speeds of the head and tail shocks lead to a considerable increase in the duration of the pulse. Theoretical predictions based on nonlinear spectral evolution equations are in close agreement with the observed waveform distortion and shock formation.

Do Surface Acoustic Solitons Exist?

Nonlinear Rayleigh waves are considered that propagate along the surface of a homogeneous solid medium covered by a thin film. Their dynamics is described by an evolution equation containing dispersion of the Benjamin-Ono type and a nonlocal nonlinearity. Periodic nonlinear wave solutions are found which become solitary waves in the limit of infinite periodicity. It is shown that these solitary solutions are stable, but unlike the Korteweg--de Vries solitons, they do not survive collisions with each other and therefore are no real solitons.

Pulsed nonlinear surface acoustic waves in crystals

A theoretical model developed recently for the propagation of nonlinear surface acoustic waves in crystals [Hamilton et al., Nonlinear Acoustics in Perspective, edited by R. J. Wei (Nanjing U.P., Nanjing, 1996), pp. 64–69] is used to investigate transient effects associated with pulses. The present work extends an earlier theoretical investigation of pulsed nonlinear Rayleigh waves in isotropic solids [Knight et al., J. Acoust. Soc. Am. 96, 3322(A) (1994)]. The latter was verified via comparison with measurements of laser-generated nonlinear Rayleigh waves with shocks in fused quartz [Lomonosov et al., J. Acoust. Soc. Am. 101, 3080(A) (1997)]. Here simulations of waveform distortion and shock formation are presented for pulses in real crystals, including Si, KCl, and Ni, and for a variety of surface cuts and propagation directions. The second- and third-order elastic moduli in the nonlinearity matrix are taken from measurements reported in the literature. Attention is focused on waveforms corresponding to recent measurements of laser-generated nonlinear surface waves propagating in Si along the 〈112〉 direction in the (111) plane [Lomonosov and Hess, Nonlinear Acoustics in Perspective (Nanjing U.P., Nanjing, 1996), pp. 106–111]. Preliminary comparisons of theory with measurements obtained in related experiments are in good agreement. [Work supported by ONR and the RFBR Foundation.]