Nonlinear elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing

Dynamic acoustoelastic testing provides a more complete insight into the acoustic nonlinearity exhibited by micro-inhomogeneous media like granular and cracked materials. This method consists of measuring time of flight and energy modulations of pulsed ultrasonic waves induced by a low-frequency standing wave. Here pulsed ultrasonic head waves were employed to assess elastic and dissipative nonlinearities in a region near the surface of a solid. Synchronization of the ultrasound pulse sequence with the low-frequency excitation provided instantaneous variations in the elastic modulus and the attenuation as functions of the instantaneous low-frequency strain. Weak quadratic elastic nonlinearity and no dissipative nonlinearity were detected in duralumin. In limestone, distinction between tensile and compressive behaviors revealed an asymmetry in the acoustic nonlinearity and hysteresis in both the elastic modulus and the attenuation variations. Measured nonlinear acoustical parameters are in good agreement with values obtained by different techniques. Reversible acoustically induced conditioning modified the acoustic nonlinearity both quantitatively and qualitatively. It reduced tension-compression asymmetry, suggesting a nonequilibrium modification of the sources of acoustic nonlinearity. Additionally to the metrology of the acoustic nonlinearity, head wave based dynamic acoustoelastic testing may be a useful tool to monitor changes in the microstructure or the accumulation of damage in solids.     

A model for the propagation of nonlinear dispersive strain waves in a solid with defect clusters

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is developed with taking into account the interaction with atomic defect clusters. The governing nonlinear dispersive-dissipative equation describing the evolution of longitudinal strain waves is derived. An approximate solution of the model equation was derived which describes asymmetrical distortion of geometry of the solitary strain wave due to the interaction between the strain field and the field of clusters. The contributions of the finiteness of the relaxation times of cluster-induced atomic defects to the linear elastic modulus and the lattice dissipation and dispersion parameters are determined. The amplitudes and width of the nonlinear waves depend on the elastic constants and on the properties of the defect subsystem (atomic defects, clusters) in the medium. The explicit expression is received for the sound velocity dependence upon the fractional cluster volume, which is in good agreement with experiment. The critical value of cluster volume fraction for the influence on the strain wave propagation is determined.     

35CrMoA钢塑性损伤非线性超声响应有限元模拟

基于混合位错超声非线性模型,使用有限元法模拟了非线性超声纵波在35CrMoA钢中的传播过程,并开展了实验验证.结果表明,超声非线性系数与塑性变形具有显著的相关性.金属材料塑性变形引起的超声非线性响应主要来自于位错,文中使用的有限元模型可以较好地模拟不同塑性变形下35CrMoA钢的超声非线性响应.在塑性变形的早期阶段,超...     

Nonlinear wave processes in media containing cracks partially filled with a viscous liquid

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.     

Experimental investigations of nonlinear acoustic phenomena in polycrystalline zinc

The results of experimental and theoretical investigations of nonlinear acoustic phenomena (nonlinear losses, shift of resonance frequency, generation of the third harmonic, and nonlinear sound-by-sound damping) in polycrystalline zinc nonannealed and annealed resonating rods are presented. The measurements were carried out in the 10(-7)-10(-5) strain range at a frequency of about 3 kHz; the frequency of the weak ultrasonic pulse was about 270 kHz. The experimentally observed phenomena are described in frames of phenomenological equations of state containing elastic hysteresis and dissipative nonlinearity. The nonlinear acoustic parameters of these equations are determined by comparison between theoretical dependencies and experimental results. The influence of structural changes in zinc due to annealing on the nonlinear acoustic phenomena is shown.     

Generation of higher acoustic harmonics at a flat rough interface between two solids

The results of experimental studies of the influence of a static pressure applied to a flat rough interface between two solids on its nonlinear elastic properties are presented. The studies were performed by the spectral method on the basis of an analysis of the efficiency of generation of higher acoustic harmonics, which arise upon the reflection of a longitudinal elastic wave of finite amplitude from the boundary and the passage through it. A nonmonotonic dependence of the amplitudes of acoustic harmonics on the value of the external reversible static pressure applied to the interface was revealed: pronounced amplitude maxima for the amplitudes of the second and third harmonics were observed with a decrease in the external static pressure. It was also found that the amplitudes of the second, third, and fourth acoustic harmonics increase with a decrease in the external static pressure (in comparison with their values at the same pressure values during its increase). The experimentally determined power dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic significantly differed from the classical indices for these harmonics. The influence of the external pressure on the values of the nonlinear second- and third-order elastic parameters was analyzed. The experimental results were analyzed on the basis of nonclassical acoustic nonlinearity.     

All-optical probing of the nonlinear acoustics of a crack

Experiments with an all-optical method for the study of the nonlinear acoustics of cracks in solids are reported. Nonlinear acoustic waves are initiated by the absorption of radiation from a pair of laser beams intensity modulated at two different frequencies. The detection of acoustic waves at mixed frequencies, absent in the frequency spectrum of the heating lasers, by optical interferometry or deflectometry provides unambiguous evidence of the elastic nonlinearity of the crack. The high contrast in crack imaging achieved by remote optical monitoring of the nonlinear acoustic processes is due to the strong dependence of the efficiency of optoacoustic conversion on the state of the crack. The highest acoustic nonlinearity is observed in the transitional state of the crack, which is intermediate between the open and the closed ones.     

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method (EMM) is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd (Gaunaurd GC and \"{U}berall H, {\em J. Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximation by comparing the dynamic (i.e. frequency-dependent) effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail. The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave. Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system's resonance induced by the existence of bubbles.     

Mechanical and nonlinear elastic characteristics of polycrystalline AMg6 aluminum alloy and <Emphasis Type="Italic">n</Emphasis>-AMg6/C<Subscript>60</Subscript> nanocomposite

The influence of nanostructuring on the mechanical and nonlinear elastic characteristics of polycrystalline AMg6 aluminum alloy and n-AMg6/C₆₀ nanocomposite has been experimentally studied. The independent second- and third-order elastic coefficients are measured via the ultrasonic method. The thir-dorder elastic coefficients have been evaluated via the Tearstone–Bragger approach from the experimentally established velocities of shear and longitudinal bulk acoustic waves as the functions of the uniaxial compression in the studied samples. The nonlinear elastic properties are examined via the spectral acoustic technique in AMg6 aluminum alloy and n-AMg6/C₆₀ nanocomposite, and the nonlinear acoustic parameters are determined.     

Propagation of nonlinear longitudinal waves in a solid with regard to the interaction between the strain field and the field of defects

A model of nonlinear longitudinal wave propagation in a solid with quadratic nonlinearity of an elastic continuum exposed to laser impulses is developed in view of the interaction between the strain field and the field of point defects. The influence of the generation and recombination of laser-induced defects on the propagation of an elastic strain wave is analyzed. The existence of a nonlinear elastic shock wave of low intensity is revealed in the system and its structure is studied. The estimations of the depth and velocity of the wave front are performed. The contributions due to the interaction of the strain field and the field of defects to both a linear elastic modulus and the dispersion parameters of a lattice are found.     

Observation of the "Luxemburg-Gorky effect" for elastic waves

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg-Gorky (L-G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L-G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10(-7) and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed.     

Torsional waves excited by electromagnetic–acoustic transducers during guided-wave acoustic inspection of pipelines

A theory of propagation of torsional waves excited by an electromagnetic–acoustic transducer in a pipe is proposed. This theory takes into account the excitation parameters, geometry, viscosity, and the elastic characteristics of an object. The main testing parameters (the frequency and geometry of the transducer) that determine the possibilities of guided-wave testing of pipelines of various dimensions using torsional waves are theoretically substantiated.     

Second-order and third-order elastic constants of B4C ceramics

The linear and nonlinear elastic properties of B₄C boron carbide ceramics have been studied. The second-order elastic constants and other parameters of the theory of elasticity in the linear approximation have been calculated based on the experimentally measured density and velocity values of longitudinal and shear bulk acoustic waves in the samples. The Thurston-Brugger method has been used to determine the third-order elastic constants of B₄C. To achieve this, we have measured the relative changes of the longitudinal and shear bulk acoustic wave velocities depending on the uniaxial compression applied to the sample.     

Diagnostics of elastic properties of a planar interface between two rough media using surface acoustic waves

The results of experimental studies on the nonlinear elastic properties of a planar interface between two media are presented—an optically polished glass substrate and flat samples with different degrees of roughness. The nonlinear elastic properties of the interfaces between two media were investigated by the spectral method using surface acoustic waves (SAWs). The effect of external pressure applied to the interface on the efficiency of the generation of the second SAW harmonic was studied. Using the measured amplitudes of the first and second harmonics of the SAW that passes along the interface, the second-order nonlinear acoustic parameter was calculated as a function of the external pressure applied to the sample at a fixed amplitude of a probing wave. It was revealed that the nonlinear parameter of the SAW is a nonmonotonic function of the pressure at the boundary. The results were analyzed on the basis of an elastic contact nonlinearity, and it is concluded that these results can be used in nondestructive testing for roughness and waviness of surfaces of flat solids.     

非线性电磁超声对铝合金拉伸变形评价研究

非线性系数是描述材料中微纳尺度损伤的特征参量,非线性系数常通过接触式压电超声进行检测,但耦合剂引起的非线性一般是未知的,针对这一问题,提出了一种非接触式电磁超声非线性纵波检测方法。该方法基于洛伦兹力机理在试件表面产生的振动弹性波,利用不同拉伸载荷下所制备的损伤试件,分别利用压电超声、电磁超声进行非线性超声系数测量。实验结果表明:利用两种非线性超声检测的相对非线性系数与铝合金的拉伸形变呈单调关系,同时也论证了电磁超声纵波基于非线性理论对塑性变形评估的可行性。      

Nonlinear strain waves and densities of defects induced in metal plates by external energy fluxes

A model of nonlinear periodic traveling strain waves induced in laser-irradiated metal plates with quadratic nonlinearity is proposed. Interaction between the elastic strain fields and the concentration of point defects is taken into account. The effect of generation-recombination processes on the evolution of nonlinear localized waves is considered. An equation for the amplitudes of the nonlinear waves is derived. It is employed to analyze the attenuation of the waves with allowance for low-and high-frequency losses.     

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.