Nonlinear Rayleigh Surface Waves Research Articles

A Power-Law of Two Kernels in Reductive Nonlinear Rayleigh Equation for Isotropic Elastic Materials

We reinvestigate theoretically a propagation of the nonlinear Rayleigh surface waves (NRSW) on isotropic elastic materials to understand nonlinear characteristics of the reductive nonlinear Rayleig...

Soliton for Nonlinear Rayleigh Surface Waves on Homogeneous Isotropic Materials

We reinvestigate the steady propagation of nonlinear Rayleigh surface waves on homogeneous isotropic materials by the method of multiple scales. We find an explicit form for the steady propagation ...

Nonlinear Rayleigh surface waves to characterize microscale damage due to alkali-silica reaction (ASR) in full-scale, nuclear concrete specimens

Nonlinear Rayleigh surface waves are used to monitor the damage state due to alkali-silica reaction (ASR) in full-scale reinforced concrete block specimens created as part of a full-scale testing program for concrete nuclear containment structures. The measurement technique uses a wedge/transducer source to generate and a non-contact, air-coupled receiver to detect nonlinear Rayleigh surface waves to obtain the acoustic nonlinearity parameters for three different reinforced block concrete specimens – a confined and an unconfined ASR specimen, plus a control specimen – at three different time intervals. These results further validate the utility of nonlinear Rayleigh waves to quantify the progress of microscale damage due to ASR in full-scale, concrete structures.

Generation Mechanism of Nonlinear Rayleigh Surface Waves for Randomly Distributed Surface Micro-Cracks.

This paper investigates the propagation of Rayleigh surface waves in structures with randomly distributed surface micro-cracks using numerical simulations. The results revealed a significant ultrasonic nonlinear effect caused by the surface micro-cracks, which is mainly represented by a second harmonic with even more distinct third/quadruple harmonics. Based on statistical analysis from the numerous results of random micro-crack models, it is clearly found that the acoustic nonlinear parameter increases linearly with micro-crack density, the proportion of surface cracks, the size of micro-crack zone, and the excitation frequency. This study theoretically reveals that nonlinear Rayleigh surface waves are feasible for use in quantitatively identifying the physical characteristics of surface micro-cracks in structures.

The role of nonlinear ultrasound in the diagnosis of early-stage damage in heterogeneous materials

Predictable noninvasive evaluation of engineering materials requires a more reliable sensing technique capable of providing quantitative information of early stage damage. Nonlinear ultrasound (NLU) is a promising candidate because it provides a direct measure of the nonlinear elastic behavior of materials. NLU excels in the direction and quantification of damage that originates at or beneath the material’s microscale. This talk will present a procedure for the second harmonic generation (SHG) measurements using nonlinear Rayleigh surface waves. This technique quantifies material nonlinearity through the acoustic nonlinearity parameter, β. Specifically, microscale material characterization of physical/chemical phenomena in heterogeneous materials will be reviewed by means of the acoustic nonlinearity parameter, β. The results reveal how the SHG technique can provide the quantitative relationship between the acoustic nonlinearity parameter and the damage state of these materials. Last, new strategies for the application of the SHG technique will be discussed with an emphasis on bio-engineering materials and rocks.

Measuring Alkali-Silica Reaction (ASR) Microscale Damage in Large-Scale Concrete Slabs Using Nonlinear Rayleigh Surface Waves

The second harmonic generation (SHG) of nonlinear Rayleigh waves is applied to characterize the damage state induced by alkali-silica reaction (ASR) in large-scale plain concrete slabs. A measurement setup that uses a wedge transmitter and a non-contact, air-coupled receiver is implemented to generate and detect nonlinear Rayleigh surface waves and to obtain both the linear and nonlinear acoustic parameters, while complementary measurements track expansion of the concrete slabs. These results demonstrate the potential of SHG using nonlinear Rayleigh waves to assess the evolution of microscale damage induced by ASR in large-scale, in-service concrete components.

Drying shrinkage in concrete assessed by nonlinear ultrasound

This research develops a nonlinear ultrasonic (NLU) technique, second harmonic generation (SHG), to monitor the time-dependent microstructural evolution and shrinkage in concrete over a period from 28 to 55days of age. Drying shrinkage by moisture migration from concrete to its environment causes stress and microcracking and can lead to larger crack formation, which compromises performance. Here, the process of drying is monitored by the SHG method using nonlinear Rayleigh surface waves to obtain the acoustic nonlinearity parameter. The results show large changes in the measured acoustic nonlinearity parameter which is attributed to damage generated during drying shrinkage. Finally, the measured acoustic nonlinearity parameter is used to compare the microstructural condition in hardened concrete as affected by shrinkage mitigation (through the use of shrinkage-reducing admixture) and crack filling (or self-healing) by carbonation.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves**Supported by the National Natural Science Foundation of China under Grant Nos 61271356 and 51575541, the National Research Foundation of Korea under Grant Nos 2013-M2A2A9043241 and 2013-R1A2A2A01016042, and the Hunan Provincial Innovation Foundation For Postgraduate under Grant No CX2016B046.

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

Method and analysis for determining yielding of titanium alloy with nonlinear Rayleigh surface waves

Methods for determining yielding of titanium (Ti) alloy material with second harmonic Rayleigh ultrasonic wave are investigated. Both piezoelectric angle beam transducers and high frequency laser scanning vibrometer (LSV) are used to detect ultrasonic signals in the Ti alloy specimens with different plastic strain levels. Technical features and outcomes with use of piezoelectric transducers and LSV are compared. The method using piezoelectric transducers, with much higher signal-to-noise ratio than LSV, has been further improved by deploying two transducers with central frequencies corresponding to the fundamental and second order harmonic signals respectively to improve the testing reliability and accuracy. Both the techniques using piezoelectric transducer and LSV demonstrate consistently that the acoustic nonlinearity increases with plastic strain, and the second harmonic Rayleigh ultrasonic wave can be utilized for effective determination of yielding in Ti alloy. Our experiments further show that the acoustic nonlinearity increases gradually with plastic strain at small plastic strain level, and there is a more significant increase of acoustic nonlinearity when the plastic strain reaches a higher level. Microscopic investigations using scanning electron microscopy (SEM) and high resolution transmission electron microscopy (HRTEM) are conducted for clarifying the relationship between the observed acoustic nonlinearity and micro-structural changes.

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave is defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.

Air-coupled detection of nonlinear Rayleigh surface waves in concrete—Application to microcracking detection

This paper proposes a new technique for the application of the second harmonic generation (SHG) in Rayleigh surface waves to nondestructively quantify microstructural changes and microcracks in heterogeneous cement-based materials (mortar and concrete). The effect of shrinkage reducing admixture (SRA), as it influences microcrack formation in these materials, is considered as an example. A 50kHz wedge transmitter and a 100kHz air-coupled receiver are implemented for the generation and detection of nonlinear Rayleigh waves; the non-contact receiver has the advantage of eliminating the inconsistencies associated with coupling and can be used for inspections of in-service concrete components. The experimental results show that the SRA plays a crucial role in reducing shrinkage microcracks and the addition of the SRA to cement-based materials influences the material nonlinearity. These results demonstrate that the proposed SHG technique is capable of evaluating the relative nonlinearity parameter, βre and can be a reliable method to characterize microstructural changes in cement-based materials.

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.

Characterization of stress corrosion cracking in carbon steel using nonlinear Rayleigh surface waves

This research uses nonlinear Rayleigh surface waves to characterize stress corrosion cracking (SCC) damage in carbon steel. Cold rolled carbon steel is widely used for buried fuel pipelines; the environment surrounding these pipelines creates a mildly corrosive environment, which, in combination with an applied stress, can cause SCC. To ensure the safe operation of these structures, it is crucial that damage due to SCC be detected before their structural integrity is reduced by large cracks. In the early stages of SCC, microstructural changes such as dislocation formation and microcrack initiation occur, which have shown to considerably increase the acoustic nonlinearity of a material. These microstructural changes distort and generate higher harmonics in an initially monochromatic ultrasonic wave. This research considers four different levels of SCC induced in four separate 1018 steel specimens, a material which has a similar susceptibility to SCC as steel used for buried fuel pipelines. Then nonlinear ultrasonic measurements are performed before and after the SCC damage is induced. Nonlinear Rayleigh surface waves are utilized to detect the SCC damage that is concentrated near the material surface. The amplitudes of the fundamental and second harmonic waves are measured with contact wedge transducers at varying propagation distances to obtain the acoustic nonlinearity of the specimens as a function of SCC damage. The results show an increase in the measured acoustic nonlinearity in the early stages of SCC, indicating the feasibility of using this nonlinear ultrasonic method to detect the initiation of SCC in carbon steels.

Effect of surface scratches on the characteristics of nonlinear Rayleigh surface waves in glass

Using nonlinear Rayleigh waves, the effect of surface scratches on the propagation of nonlinear ultrasonic waves in a glass plate was investigated. The results showed that the amplitudes of the fundamental and second harmonics of the nonlinear Rayleigh waves decreased with increasing average width of surface scratches due to the interaction between scratch-induced cracks and wave propagation. The increase of the nonlinearity with the average scratch width suggests that the surface scratches caused the decrease of apparent Young's modulus near the glass surface. Nonlinear Rayleigh surface waves could be a potential method for the quantitative and rapid measurement of surface and subsurface damage in brittle materials.

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.

A new technique for measuring the acoustic nonlinearity of materials using Rayleigh waves

This note presents a procedure to generate nonlinear Rayleigh surface waves without having to drive the transmitting piezoelectric transducer at high voltages; driving at low voltages limits the excitation of the intrinsic nonlinearity of the piezoelectric transducer element, and enables an efficient measurement procedure to isolate inherent material nonlinearity. The capabilities of this proposed technique are demonstrated by measuring the material nonlinearity of aluminum alloy 2024 and 6061 plates with Rayleigh surface waves.

Nonlinear surface waves and solitons

First a general introduction on the notion of surface waves on solids (types of different waves), a reminder on the simplest familiar nonlinear dispersive model equations, and another on the basic equations of nonlinear elasticity are given. Then attention is focused on the linear surface wave problem. The main properties of nonlinear surface waves in the absence of dispersion are studied next by use of several asymptotic techniques. The additional effects of dispersion are then considered and combined with those of nonlinearity with an emphasis on the case of so-called shear-horizontal surface waves and solitary-wave solutions for envelope signals. Finally, typical nonlocality is introduced for nonlinear Rayleigh surface waves, and general comments on more general two-dimensional (in propagation space) nonlinear strain waves on structures are evoked by way of conclusion.

Assessment of material damage in a nickel-base superalloy using nonlinear Rayleigh surface waves

A reliable laser-based ultrasonic technique is developed to measure the second order harmonic amplitude of a Rayleigh surface wave propagating in metallic specimens. Rayleigh waves are experimentally generated with a wedge transducer and detected with a heterodyne laser interferometer. The capability of this system to measure the nonlinear contribution present in Rayleigh surface waves is demonstrated, and these results are interpreted in terms of a parameter developed for Rayleigh surface waves which corresponds to the nonlinear parameter of a longitudinal wave, β. The proposed measurement technique is used to assess damage in nickel-base high temperature alloy specimens, and the evolution of material nonlinearity under various loading conditions is quantitatively measured in terms of the increasing amplitude of the second order harmonic. These results show that there is a significant increase in the second order harmonic amplitude at monotonic tensile loads above the material’s yield stress, and that during low cycle fatigue tests, the increase in the second order harmonic amplitude is considerable, although less significant than that in the monotonic loading case. The results from this study show the major role that accumulated plasticity plays in the increase in material nonlinearity, and demonstrate the effectiveness of the proposed experimental procedure to track damage in high temperature alloys.