Nonlinear surface acoustic waves: realization of solitary pulses and fracture

A laser-based technique for the contact-free generation and detection of strongly nonlinear surface acoustic wave (SAW) pulses with amplitudes limited by the materials strength has been developed. The effects of nonlinear propagation of short elastic surface pulses with finite strength in isotropic solids, such as fused quartz, anisotropic solids, such as silicon, and dispersive media were investigated. Solitary surface wave propagation was observed in layered structures for normal and anomalous dispersion. In addition, a SAW-based method for evaluating the critical fracture stress of anisotropic brittle solids, such as single crystal silicon, is introduced.     

DC effects,sub-harmonics,stochasticity and "memory" for contact acoustic non-linearity

Acoustic wave interaction with non-bonded contacts was found to be inherently non-linear due to asymmetrical stiffness distribution across the interface. A diode-type non-linearity results in local static elastic fields inside the contact, which are shown to be a source of transient longitudinal and shear DC-acoustic pulses polarized oppositely to a biasing contact stress. A parametric modulation of contact stiffness leads to acoustic instability effects, multiple sub-harmonics, and amplitude "self-modulation", and provides chaotic noise-like non-linear acoustic excitations in solids. For realistic cracked flaws, contact acoustic non-linearity exhibits amplitude hysteresis and storage caused by acoustic wave impact on the defect. Maximum storage time observed comes to several hours for read-in time less than half a minute. A long-term non-linear memory is believed to be due to a slow relaxation of thermally induced micro-strain within the crack area.     

Surface morphological response of crystalline solids to mechanical stresses and electric fields

Surface morphological evolution under the action of external fields is a fascinating topic that has attracted considerable attention within the surface science community over the past two decades. In addition to the interest in a fundamental understanding of field-induced nonlinear response and stability of surface morphology, the problem has been technologically significant in various engineering applications such as microelectronics and nanofabrication. In this report, we review theoretical progress in modeling the surface morphological response of stressed elastic solids under conditions that promote surface diffusion and of electrically conducting solids under surface electromigration conditions. A self-consistent model of surface transport and morphological evolution is presented that has provided the basis for the theoretical and computational work that is reviewed. According to this model, the surface morphological response of electrically conducting elastic solids to the simultaneous action of mechanical stresses and electric fields is analyzed. Emphasis is placed on metallic surfaces, including surfaces of voids in metallic thin films.Surfaces of stressed elastic solids are known to undergo morphological instabilities, such as the Asaro–Tiller or Grinfeld (ATG) instability that leads to emanation of crack-like features from the surface and their fast propagation into the bulk of the solid material. This instability is analyzed theoretically, simulated numerically, and compared with experimental measurements. The surface morphological evolution of electrically conducting, single-crystalline, stressed elastic solids under surface electromigration conditions is also examined. We demonstrate that, through surface electromigration, a properly applied and sufficiently strong electric field can stabilize the surface morphology of the stressed solid against both crack-like ATG instabilities and newly discovered secondary rippling instabilities; the effects of important parameters, such as surface crystallographic orientation, on the surface morphological response to the simultaneous action of an electric field and mechanical stress also are reviewed. In addition, electromigration-driven surface morphological response is analyzed systematically, focusing on the current-driven surface morphological evolution of voids in metallic thin films; this analysis has been motivated largely by the crucial role of void dynamics in determining the reliability of metallic interconnects in integrated circuits and has led to the interpretation of a large body of experimental observations and measurements. The electromigration-driven translational motion of morphologically stable voids, effects of current-driven void dynamics on the evolution of the electrical resistance of metallic thin films, and current-driven void–void interactions also are reviewed. Furthermore, theoretical studies are reviewed that demonstrated very interesting current-driven nonlinear void dynamics in stressed metallic thin films, including the inhibition of electromigration-induced instabilities due to the action of biaxial tensile stress, and stress effects on the electromigration-driven translational motion of morphologically stable voids.Complex, oscillatory surface states under surface electromigration conditions have been observed in numerical studies. In this report, emphasis is placed on void surfaces in metallic thin films, for which stable time-periodic states have been demonstrated. It is shown that increasing parameters such as the electric-field strength or the void size past certain critical values leads to morphological transitions from steady to time-periodic states; the latter states are characterized by wave propagation on the surface of a void that migrates along the metallic film at constant speed. The transition onset corresponds to a Hopf bifurcation that may be either supercritical or subcritical, depending on the symmetry of the surface diffusional anisotropy as determined by the crystallographic orientation of the film plane. It is also shown that, in the case where the Hopf bifurcation is subcritical, the simultaneous action of mechanical stress leads the current-driven void morphological response to the stabilization of chaotic attractors; in such cases, as the applied stress level increases, the void dynamics is set on a route to chaos through a sequence of period-doubling bifurcations. The observation of current-driven chaotic dynamics in homoepitaxial islands also is discussed.     

Stress evaluation of laser cladding coating with critically refracted longitudinal wave based on cross correlation function

Research on stress evaluation of laser cladding coating with critically refracted longitudinal wave was introduced in this paper. Two critically refracted longitudinal wave transducers with 5 MHz frequency, spacing between which was constant, were employed as signal emitter and receiver. Based on acoustoelastic equation deduction, relationship between the difference in time of flight and tensile stress is obtained. Combing with cross correlation theory, the difference in time of flight between stressed and unstressed critically refracted longitudinal signals was calculated. Results show that stress evaluation is affected by layer interface and anisotropic microstructure of laser cladding coating, precision of stress evaluation of laser cladding coating increases as step length increases until it attains one cycle. In addition, influence of waveform distortion caused by microstructure of laser cladding coating on stress evaluation is discussed. At last, verification test is carried out and the experimental result is well consistent with theoretical result.     

Coating thickness affects surface stress measurement of brush electro-plating nickel coating using Rayleigh wave approach

A surface ultrasonic wave approach was presented for measuring surface stress of brush electro-plating nickel coating specimen, and the influence of coating thickness on surface stress measurement was discussed. In this research, two Rayleigh wave transducers with 5 MHz frequency were employed to collect Rayleigh wave signals of coating specimen with different static tensile stresses and different coating thickness. The difference in time of flight between two Rayleigh wave signals was determined based on normalized cross correlation function. The influence of stress on propagation velocity of Rayleigh wave and the relationship between the difference in time of flight and tensile stress that corresponded to different coating thickness were discussed. Results indicate that inhomogeneous deformation of coating affects the relationship between the difference in time of flight and tensile stress, velocity of Rayleigh wave propagating in coating specimen increases with coating thickness increasing, and the variation rate reduces of difference in time of flight with tensile stress increasing as coating thickness increases.     

Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure

Based on the theories of nonlinear continuum mechanics, piezoelectricity and elastic waves in solids, theoretical analysis of Bleustein-Gulyaev surface acoustic wave propagation in a prestressed layered piezoelectric structure are described. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO(3) except that they are polarized in opposite directions. It is found that an almost linear behavior of the relative change in phase velocity versus the initial stress is obtained for both surface electrically free and shorted cases. Potential applications in the design of acoustic wave devices are suggested.     

无缝钢轨中温度对应力非线性超声检测的影响

研究了温度与应力共同作用下的非线性超声响应规律。构建了纵波在无缝钢轨内传播的数学模型,将传统原子间势能引入非线性波动方程,得到了无缝钢轨在自由状态及受约束状态两种情况下超声非线性系数随温度变化的函数关系。在理论分析的基础上,进行了无缝钢轨受约束时内部温度应力变化的实物模拟实验,获得的非线性系数变化趋势与理论预期相一致。研究结果表明:温度和应力都对固体介质非线性影响明显,介质非线性系数随着温度的升高而增大,随着内部压应力的增加而减小。因此,当利用非线性系数检测钢轨纵向应力时,需要对温度的影响进行补偿。     

Oscillation of the refractive index at the focal region of a femtosecond laser pulse inside a glass

The temporal evolution of refractive-index change produced by a tightly focused femtosecond (fs) laser pulse inside a soda-lime glass plate was investigated by use of a transient lens method with subpicosecond time resolution. An oscillating behavior of the light intensity in the central region of the probe beam was observed 0-1500 ps after irradiation of the plate. The oscillation was interpreted in terms of a rapid temperature increase and the ensuing propagation of the pressure wave. This study is to our knowledge the first real-time observation of refractive-index change inside a glass induced by a fs laser pulse.     

具微结构地壳中非线性地震波的演化

非线性地震波在地壳中传播及演化规律的研究具有重要实际意义.利用有限差分方法, 对非线性地震纵波和横波在具微结构地壳中的演化过程进行了详细的数值模拟.结果表明,非线性地震纵波和横波在具微结构地壳中可以逐渐演化成一个孤立波或两个孤立波或孤立波列或消失.地震波的初始幅度、频散系数和体力因子对演化过程和结果都有重要影响.研究结果揭示了非线性地震波在一种微结构地壳中的演化规律,这有助于在理论上解释一些特殊地震波现象.     

非一维应变冲击加载下高纯铜初始层裂行为

提出了一种锥形靶层裂实验新方法,开展非一维应变冲击条件下高纯铜初始层裂行为实验研究,讨论了锥形靶内部损伤分布特征及其与自由面速度典型特征之间的内禀关系.结果显示:1)初始层裂的锥形靶内部出现了连续损伤区,损伤区扩展方向与锥面平行,从锥底到锥顶呈现了不同的损伤状态,从微孔洞独立长大到局部聚集,最后形成宏观裂纹,这种损伤状态分布特征归因于锥形靶内部拉伸应力幅值和持续时间的空间演化;2)通过锥形靶横截面损伤度定量统计分析,揭示损伤演化早期的微孔洞成核与早期长大过程是随机的,而损伤演化后期的微孔洞聚集过程具有显著的局域化特征;3)不同位置处实测的自由面法向粒子速度剖面呈现出典型的层裂Pull-back信号,但是通过与内部损伤分布特征对比,揭示基于Pull-back速度获得高纯铜层裂强度本质是微孔洞成核阈值应力,Pull-back回跳速度斜率反映了损伤演化速率,Pull-back回跳幅值与损伤度引起的应力松弛密切相关.     

Evolution of the reflection and focusing patterns and stress states in two-fluid cylindrical shell systems subjected to an external shock wave

Several most important features of the hydrodynamic field induced inside a circular cylindrical shell filled with and submerged into different fluids when it is subjected to an external shock wave are considered. This investigation is a follow-up of an earlier study of the two-fluid shell-shock interaction [S. Iakovlev, Interaction between an external shock wave and a cylindrical shell filled with and submerged into different fluids, Journal of Sound and Vibration 322 (2009) 401-437], and it addresses a number of practically important issues not covered in that work. The focus of this study is on the evolution of the respective hydrodynamic patterns in response to the continuous change of the parameters of the fluids, in particular the speed of sound. Along with the analysis of the hydrodynamic patterns it is also demonstrated that when one is concerned with the highest pressure attained inside the shell, the most dangerous combination of the parameters occurs when the ratio of the internal and external acoustic speeds is close to 0.48, with the respective pressure exceeding the maximum incident pressure by more than 110 percent. The effect that the hydrodynamic features discussed have on the stress state of the shell is addressed as well, and it is observed that the maximum tensile stress is significantly affected by the evolution of the considered hydrodynamic features, whereas the maximum compressive stress is not. It is also observed that the maximum tensile stress is very sensitive to the change of the ratio of the acoustic speeds in the internal and external fluids, with as little an increase of the latter as 13 percent resulting in more than doubling of the former in some cases.     

固体板中超声驻波场的高阶光弹条纹

利用动态光弹法观测了超声波在固体板内多次反射形成的驻波。通过相干叠加增大声波应力,使得动态光弹实验中偏振光的相位变化大于一个周期,从而观测到固体内超声波由行波转化为驻波的过程,并对高阶干涉条纹反映的驻波场特性进行了讨论。通过对声波应力进行定量测量,评估了固体板中超声驻波的激发效率。本文的工作为利用动态光弹法研究透明固体中的高强度声波提供了一种可行的方法。     

Polarization of plane wave propagating inside elastic hexagonal system solids

Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.     

The Wall Stresses and Insert Load in a Two‐Dimensional Flat‐bottomed Bin with an Equilateral Triangle Insert

The wall stresses and insert load in a two‐dimensional flat‐bottomed bin with a flow corrective insert were investigated. The static wall stress distributions produced by the granular solids were measured and compared with the theoretical prediction using the differential slice method. The variations in the dynamic wall stresses and the dynamic response of the insert load with time were obtained. The comparison of the experimental insert load to the theoretical prediction was demonstrated. In addition, the effect of the flow corrective insert upon the wall stress and insert load was investigated. As the insert half‐angle increases, the effect of disrupting the contact force network above the insert decreases, and the insert load produced by the granular solids increases. Employing the results obtained using stress measurements, the pulsation phenomena of wall stress and insert load in a bin with a triangle flow corrective insert may be further understood.     

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.     

Nonlinear wave propagation in constrained solids subjected to thermal loads

The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.     

Longitudinal waves in carbon nanotubes in the presence of transverse magnetic field and elastic medium

In the present paper, the coupling effect of transverse magnetic field and elastic medium on the longitudinal wave propagation along a carbon nanotube (CNT) is studied. Based on the nonlocal elasticity theory and Hamilton's principle, a unified nonlocal rod theory which takes into account the effects of small size scale, lateral inertia and radial deformation is proposed. The existing rod theories including the classic rod theory, the Rayleigh-Love theory and Rayleigh-Bishop theory for macro solids can be treated as the special cases of the present model. A two-parameter foundation model (Pasternak-type model) is used to represent the elastic medium. The influence of transverse magnetic field, Pasternak-type elastic medium and small size scale on the longitudinal wave propagation behavior of the CNT is investigated in detail. It is shown that the influences of lateral inertia and radial deformation cannot be neglected in analyzing the longitudinal wave propagation characteristics of the CNT. The results also show that the elastic medium and the transverse magnetic field will also affect the longitudinal wave dispersion behavior of the CNT significantly. The results obtained in this paper are helpful for understanding the mechanical behaviors of nanostructures embedded in an elastic medium.     

A mechanistic analysis of stone fracture in lithotripsy

In vitro experiments and an elastic wave model were used to analyze how stress is induced in kidney stones by lithotripsy and to test the roles of individual mechanisms-spallation, squeezing, and cavitation. Cylindrical U30 cement stones were treated in an HM-3-style lithotripter. Baffles were used to block specific waves responsible for spallation or squeezing. Stones with and without surface cracks added to simulate cavitation damage were tested in glycerol (a cavitation suppressive medium). Each case was simulated using the elasticity equations for an isotropic medium. The calculated location of maximum stress compared well with the experimental observations of where stones fractured in two pieces. Higher calculated maximum tensile stress correlated with fewer shock waves required for fracture. The highest calculated tensile stresses resulted from shear waves initiated at the proximal corners and strengthened along the side surfaces of the stone by the liquid-borne lithotripter shock wave. Peak tensile stress was in the distal end of the stone where fracture occurred. Reflection of the longitudinal wave from the distal face of the stone--spallation-produced lower stresses. Surface cracks accelerated fragmentation when created near the location where the maximum stress was predicted.     

Molecular dynamic simulation of stress evolution analysis in Cu nanowire under ultra-high strain-rate simple tension

This study analyses the behaviour of atoms associated with the propagation of stress waves in Cu nanowires (NWs) during uniaxial tensile deformation using molecular dynamic simulation. Maximum local stress (MLS) and virial stress (VS) methods are adopted to express dynamic stress in ?100? Cu NWs under tension. Simulation results indicated that the VS method enhances the averaging effect at ultra-high strain rates (above 10¹⁰ s^?1), leading to serious undervaluation of yield stress. However, the MLS method provides superior prediction results for the dynamic mechanical responses of NWs under tension at the ultra-high strain rate than does the VS. At a strain rate of 7 × 10¹⁰ s^?1, the double-peak stress phenomenon was observed in the stress–strain curve using the MLS method. The response time (T_rs) to wave propagation, observed at an ultra-high strain rate, is responsible for the accumulation of the elastic stress that is applied at the beginning of tensile loading in a short period, producing the first stress peak. Following plastic deformation, the encounter of the wavefronts with the reduced tensile stress causes the fully constructive interference effect in the middle of the tensile NWs, producing the second stress peak. The results explain the dynamic mechanical behaviour of NWs, contributing to future applications of subsonic manufacturing.