Ultrasonic wave scattering from rough,imperfect interfaces. Part II. Incoherent and coherent scattered fields

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used quasi-static boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.     

Quantifying moisture damage at mastic–aggregate interface

This study quantifies moisture damage at the asphalt mastic–aggregate interfaces using finite element method modelling technique in ABAQUS. A model aggregate surrounded by a layer of mastic is subjected to static loads of varying magnitudes and patterns. Using dynamic shear and elastic moduli of wet and dry mastic and aggregate as model inputs, moisture-induced damage is quantified through parameters such as contact stresses at interface, load to initiate damage and de-bonding at the interface. Results show that contact stresses are significantly higher in dry samples than wet samples. It is revealed that damage initiates at a smaller magnitude of deformation (0.0508 mm) in the wet sample than that (0.508 mm) in the dry sample. That is, a stiffer dry sample carries more loads and deforms less before damage initiation than a softer wet sample. In addition, approximately 6.8% interface de-bonding occurs in the dry sample, whereas 49.1% de-bonding occurs in the wet sample.     

粗糙表面固态耦合超声检测研究

固态耦合超声检测时两固体粗糙表面接触界面处的超声波不完全耦合,为提升该界面处超声检测的耦合效果,需深入研究其耦合特性。以粗糙表面的弹簧接触模型为基础,结合粗糙表面接触理论推导出固态耦合超声检测的耦合界面理论模型。根据实际情况以及材料参数分析,得到表征界面耦合效果的平均声反射系数与接触载荷以及接触表面当量粗糙度的关系,并与T模型的计算结果进行对比。在不同当量表面粗糙度和不同接触载荷下分别测得接触界面的平均声反射系数,并对比了不同当量表面粗糙度下界面声耦合效果达到最佳时接触载荷的理论值和实验值,计算得最大相对误差为13.04%,表明实验结果与所提出的理论模型结果基本吻合。所建立的固态耦合超声检测界面理论模型形式简洁,实用性强,并可通过针对性地控制相关参数来改善耦合效果。     

Assessment of Adhesive Bond Strength from Ultrasonic Tone-Bursts

A model for the amplitude and phase of ultrasonic tone-bursts incident on adherend–adhesive interfaces is developed for both reflected and transmitted waves. The model parameters include the interfacial stiffness constants, which characterize the elastic properties of idealized adherend–adhesive interfaces having a continuum of bonds. The ultrasonic continuum model is linked to the more realistic physico-chemical model of adhesive bonding via a scaling equation that establishes the relationship between the interfacial stiffness constants of the ultrasonic continuum model and the fraction of actual bonds in the physico-chemical model. The link to the physico-chemical model enables a quantitative assessment of the absolute bond strength. The ultrasonic continuum model and scaling equation are applied to the simulation assessment of the absolute bond strength of two aluminum alloy adherends joined by an epoxy adhesive. Model input is obtained from the calculated phase of tone-bursts reflected from the adherend–adhesive interfaces as a function of the interfacial stiffness constants. The simulation shows that the reflected phase is dominated by the first interface encountered by the incident tone-burst with little contribution from the second interface. The simulation also shows that the accuracy in assessing the adhesive bond strength depends on the sensitivity of the reflected phase to variations in the interfacial stiffness constants, reflecting the nonlinearities in both the phase-stiffness constant relationship and scaling equation.     

The role of the surface roughness on the integrity of thermally generated oxide scales. Application to the Al2O3/MA956 system

This work deals with the effect of the metal roughness on the integrity of thermally generated oxide scales. For illustrative purposes, experimental evidence is shown for the alumina forming MA 956 alloy. The experimental results reveal that scale spallation occurs more readily in scales with rough surfaces than in scales with smooth surfaces, preferentially at the crests of the scale profile. In order to explain this feature, the effect of the roughness of both the gas/scale and scale/metal interfaces on the thermal stress distribution was analyzed by the finite element method. This analysis shows that with increasing roughness a gradient of compression stresses develops in the scale, being the maximum value of stresses located near the gas/scale interface. In general, the higher the roughness the higher the difference between the maximum and minimum values of the stresses. However, the average value of the stress distribution through the scale thickness decreases with increasing surface roughness. The effect of a planar gas/scale and a rough scale/metal interfaces was also modelled. In this case, the stress gradient in the scale was found to monotonically increase with increasing roughness although in a lower extension than when a rough gas/scale interface was also considered. On the basis of the experimental results and the stress distribution analyses a sequence of the scale failure during the cooling stage are proposed for both cases. It is concluded that the stress component that is normal to the interface and the shear stress play a key role on the scale integrity.     

法向接触刚度对装配体振动模态影响的研究

在对装配体进行模态分析时,装配体接触面间的法向接触刚度对计算结果具有很大影响,但在实际中由于处理困难却往往被省略。基于有限元建模方法分析了装配体接触面法向接触刚度对装配体振动模态的影响。首先,根据接触力学理论推导了法向接触刚度与接触表面粗糙度和接触应力之间的关系;然后,探讨了通过改变层单元弹性模量来模拟法向接触刚度的有限元建模方法;最后,通过算例分析了考虑与不考虑接触刚度时振动模态的差异。研究结果表明,考虑法向接触刚度的有限元等效模型计算结果与解析解非常接近,不考虑接触刚度的整体模型计算结果与解析解异较大,一般超过了10%以上,且频率越低差异越大,另外振型也有明显差异。本文建立的有限元建模方法可用于研究法向接触刚度对装配体振动模态的影响。     

考虑基体变形的结合面连续光滑接触刚度模型

结合面的接触刚度直接影响着机床整机的静、动态力学性能和精度保持性水平。在弹性、弹塑性以及完全塑性接触变形过程中,延续微凸体接触状态变量具有连续且光滑特性的思想,利用Hermite多项式插值函数,建立单个微凸体法向接触刚度模型。考虑到基体变形的影响,在微凸体的3个变形阶段分别引入了基体的弹性接触变形,通过统计学方法,建立了一种考虑基体变形且连续光滑的结合面刚度模型。对比分析了GW、ZMC、KE、Brake模型与该文模型之间的差异,并揭示了表面粗糙度对接触刚度的影响规律。研究表明:考虑基体变形时所获得的接触刚度和接触载荷比忽略基体变形时的要小,且随着表面粗糙度的减小,基体变形的影响快速增加;接触载荷与表面粗糙度是影响结合面接触刚度的2个主要因素,随着载荷的增大或表面粗糙度的减小,接触刚度随之递增。     

Diffuse reflectance and transmittance spectra of an interference layer: 1. Model formulation and properties

A model for the calculation of the diffuse reflectance and transmittance of a single interference layer with rough interfaces on a transparent substrate is presented. The model is based on electric field calculations and scalar scattering theory, and it assumes that the interfaces of the layer are totally uncorrelated. Examples are given of calculated spectra in which the parameters of the model are varied systematically to show the influence from different interface roughness and refractive index combinations as well as absorption in the film. A wavelength-dependent effective root-mean-square roughness is introduced. This depends on the nature of the roughness, and the bandwidth limits are given by the experimental conditions. Finally, total integrated scattering spectra are calculated and the importance of taking multiple reflections in the substrate into account is shown.     

The contact mechanics of fractal surfaces

The role of surface roughness in contact mechanics is relevant to processes ranging from adhesion to friction, wear and lubrication. It also promises to have a deep impact on applied science, including coatings technology and design of microelectromechanical systems. Despite the considerable results achieved by indentation experiments, particularly in the measurement of bulk hardness on nanometre scales, the contact behaviour of realistic surfaces, showing random multiscale roughness, remains largely unknown. Here we report experimental results concerning the mechanical response of self-affine thin films indented by a micrometric flat probe. The specimens, made of cluster-assembled carbon or of sexithienyl, an organic molecular material, were chosen as prototype systems for the broad class of self-affine fractal interfaces, today including surfaces grown under non-equilibrium conditions, fractures, manufactured metal surfaces and solidified liquid fronts. We observe that a regime exists in which roughness drives the contact mechanics: in this range surface stiffness varies by a few orders of magnitude on small but significant changes of fractal parameters. As a consequence, we demonstrate that soft solid interfaces can be appreciably strengthened by reducing both fractal dimension and surface roughness. This indicates a general route for tailoring the mechanical properties of solid bodies.     

Experimental investigation of the contact mechanics of rough fractal surfaces

The nonstationary character of roughness is a widely recognized property of surface morphology and suggests modeling several solid surfaces by fractal geometry. In the field of contact mechanics, this demands novel investigations attempting to clarify the role of multiscale roughness during physical contact. Here we review the results we recently obtained in the characterization of the contact mechanics of fractal surfaces by depth-sensing indentation. One class of experiments was conducted on organic thin films, load-displacement curves being acquired by atomic force microscopy using custom-designed tips. Another class of experiments focused on well-defined crystalline and mechanically polished ceramic substrates probed by a traditional nanoindenter. We observed the first-loading cycle to be considerably affected by surface roughness. Plastic failure was found to dominate incipient contact while contact stiffness increased on decreasing fractal dimension and roughness. Our findings suggest fractal parameters to drive contact mechanics whenever the penetration depth is kept below the interface width.     

一种非连续介质中热传导过程的数值模拟方法

传统热传导的分析基于连续模型,无法刻画热量在两个接触体之间的传递。该文提出了一种非连续介质中热传导过程的数值计算方法,并编制了相应的C++计算程序。该方法首先将计算域离散为一系列的块体,块体内部划分若干连续介质单元,块体边界设定为潜在接触界面,并利用半弹簧-半棱联合接触模型进行接触对的快速检索及标记。每个块体内部的热传导采用传统连续模型进行计算(该文采用有限体积法),每个接触界面采用点面接触型及棱棱接触型热传导模型进行描述。通过调整接触界面热传导系数中的刚度因子,可以实现接触界面对热传导过程不同的抵抗效应。数值算例表明,该文所述方法可以较为准确地模拟热量在非连续介质中的传递过程;接触界面上的刚度因子越大,界面对热传导过程的抵抗效应越小;当刚度因子大于100,界面抵抗效应基本消失,非连续介质的计算结果与连续介质的计算结果完全一致;此外,接触界面上的刚度因子仅影响热传导的瞬态过程,而不影响其稳态解。     

On the effective conductivity and the apparent viscosity of a thin rough polymer interface using PGD-based separated representations

Composite manufacturing processes usually proceed from preimpregnated preforms that are consolidated by simultaneously applying heat and pressure, so as to ensure a perfect contact compulsory for making molecular diffusion possible. However, in practice, the contact is rarely perfect. This results in a rough interface where air could remain entrapped, thus affecting the effective thermal conductivity. Moreover, the interfacial melted polymer is squeezed flowing in the rough gap created by the fibers located on the prepreg surfaces. Because of the typical dimensions of a composite prepreg, with thickness orders of magnitude smaller than its other in-plane dimensions, and its surface roughness having a characteristic size orders of magnitude smaller than the prepreg thickness, high-fidelity numerical simulations for elucidating the impact of surface and interface roughness remain today, despite the impressive advances in computational availabilities, unattainable. This work aims at elucidating roughness impact on heat conduction and the effective viscosity of the interfacial polymer squeeze flow by using an advanced numerical strategy able to reach resolutions never attained until now, a sort of numerical microscope able to attain the scale of the smallest geometrical detail.     

Probing colloid-substratum contact stiffness by acoustic sensing in a liquid phase

In a quartz crystal microbalance, particles adhering to a sensor crystal are perturbed around their equilibrium positions via thickness-shear vibrations at the crystal's fundamental frequency and overtones. The amount of adsorbed molecular mass is measured as a shift in resonance frequency. In inertial loading, frequency shifts are negative and proportional to the adsorbed mass, in contrast with "elastic loading", where particles adhere via small contact points. Elastic loading in air yields positive frequency shifts according to a coupled resonance model. We explore here the novel application of a coupled resonance model for colloidal particle adhesion in a liquid phase theoretically and demonstrate its applicability experimentally. Particles with different radii and in the absence and presence of ligand-receptor binding showed evidence of coupled resonance. By plotting the frequency shifts versus the quartz crystal microbalance with dissipation overtone number, frequencies of zero-crossing could be inferred, indicative of adhesive bond stiffness. As a novelty of the model, it points to a circular relation between bandwidth versus frequency shift, with radii indicative of bond stiffness. The model indicates that bond stiffness for bare silica particles adhering on a crystal surface is determined by attractive Lifshitz-van der Waals and ionic-strength-dependent, repulsive electrostatic forces. In the presence of ligand-receptor interactions, softer interfaces develop that yield stiffer bonds due to increased contact areas. In analogy with molecular vibrations, the radii of adhering particles strongly affect the resonance frequencies, while bond stiffness depends on environmental parameters to a larger degree than for molecular adsorption.     

涂层界面刚度的超声数值仿真检测

针对涂层结合界面刚度在非破坏条件下难以精确测量的问题,提出了一种超声检测特征参量表征刚度系数的方法。利用声波在n层各向同性介质中的反射、透射原理,结合界面的弹簧模型,建立了多层介质界面刚度系数的超声检测数学模型。基体选用钢、铸铁、铝合金,表面选用不同喷涂工艺得到的Al2O3陶瓷涂层,获得了不同界面刚度系数的超声反射频谱。仿真结果表明:分离界面和理想界面时,谐振频率都具有周期性,但周期大小不同;弱结合界面时,随着界面的刚度系数逐渐增加,谐振频率逐渐增多,这些谐振频率均向高频方向移动。与频率较高处相比,频率较低处的谐振频率随着刚度系数的增加向高频移动的速度更快。因此建立了第一个谐振频率与刚度系数之间的关系。在同一刚度系数下,由谐振频率与材料的特性阻抗关系获得如下规律:当涂层材料不变时,谐振频率随着基体特性阻抗的增大而增大;当基体材料不变时,谐振频率随着涂层特性阻抗的增大而减小。给出了以指数函数形式拟合的刚度系数与谐振频率的变化曲线。通过对该指数函数参数与材料特性阻抗之间关系的分析,获得了弱界面时谐振频率与刚度系数和材料特性阻抗三者之间的函数表达式。该方法为涂层复合材料弱界面的超声检测提供了理论支持。     

Detection of chemical interfaces in coherent anti-Stokes Raman scattering microscopy: Dk-CARS. I. Axial interfaces

We develop a full vectorial theoretical investigation of the chemical interface detection in conventional coherent anti-Stokes Raman scattering (CARS) microscopy. In Part I, we focus on the detection of axial interfaces (i.e., parallel to the optical axis) following a recent experimental demonstration of the concept [Phys. Rev. Lett. 104, 213905 (2010)]. By revisiting the Young's double slit experiment, we show that background-free microscopy and spectroscopy is achievable through the angular analysis of the CARS far-field radiation pattern. This differential CARS in k space (Dk-CARS) technique is interesting for fast detection of interfaces between molecularly different media. It may be adapted to other coherent and resonant scattering processes.     

界面分形参数对法向接触刚度影响的研究

基于最小二乘法将分形表面简化为三角函数的叠加,采用弹塑性有限元方法计算界面的接触刚度,定量表征了法向接触压力、法向接触变形及法向接触刚度的关系,研究结果揭示了粗糙面分形维数和特征尺度参数对法向接触刚度的影响机制。结果表明:存在基体最优建模厚度,可有效提高粗糙面接触刚度的计算效率;法向接触刚度随法向接触变形及法向接触压力的增加呈现非线性增加趋势;表面分形维数和特征尺度参数对法向接触刚度影响显著,法向接触刚度随分形维数增加而增加,但随特征尺度参数增加而减小。     

Effects of self-affine surface roughness on the adhesion of metal-polymer interfaces

This paper concentrates on a theoretical examination of the influence of roughness on the adhesive properties along metal-polymer interfaces. An algorithm has been designed to generate a self-affine surface roughness. It has been used to examine influence of the Hurst exponent on the interface strength during a pull-off test of metal-polymer laminates. The generated surfaces are implemented in a cohesive zone model representing the interface between a coated steel and polyethylene terephthalate (PET). From the model it can be concluded that a small increase in surface area is linear with the interface strength. This relation does not hold when the increase in surface area becomes larger than 150%. The deviation from the linear relationship increases with smaller Young’s moduli. This is caused by the reduced elastic energy storage in the polymer when local surface characteristics become more important.     

考虑接触刚度的燃气轮机拉杆转子动力特性研究

基于弹塑性理论对具有粗糙表面的长方微元体进行有限元接触分析,根据受力和变形关系得到了不同载荷作用下的法向和切向界面接触刚度。将微元体界面接触刚度与宏观结构应力分析结果相结合,给出了考虑接触刚度的组合结构动力特性研究方法,分析了压气段轮盘接触刚度对某重型燃气轮机拉杆转子固有振动频率的影响。结果表明,界面接触刚度导致转子固有频率降低,随着接触刚度的增加,其对固有频率的影响逐渐减小。接触刚度对转子各阶固有频率的影响不同,法向刚度对第一阶弯曲频率影响较大,切向刚度对第二阶弯曲频率影响较大。     

圆柱滚子轴承混合润滑状态下的超声法膜厚测量

圆柱滚子轴承由于其线接触特点被广泛应用于各类低速重载工况下的大型设备中,其运行性能和稳定性与滚子和内外圈间的接触润滑状态密切相关;基于等效刚度的超声法可用于实际工况的滚子轴承弹流润滑油膜厚度测量,但无法直接适用于低速重载工况下流体润滑和粗糙峰接触共存的混合润滑状态膜厚测量。为此,提出了一种混合润滑状态下的超声测量方法,建立了界面油膜刚度和粗糙体接触刚度的并联模型,通过引入接触系数并结合经验公式对超声法所测界面总刚度进行分解,获取混合润滑状态下的油膜刚度,进而得到更加准确的油膜厚度。将实验结果和理论结果的对比分析,验证了该模型的可行性和有效性。     

燃气轮机拉杆转子考虑接触效应的扭转振动模态分析

燃气轮机转子一般是由多个层叠的轮盘通过拉杆组合而成,各轮盘接触面由磨削加工形成。粗糙度测试结果表明磨削加工的实验拉杆转子轮盘面具有两个不同分形结构的区域。利用结构函数法计算了这种双重分形面的轮廓曲线的分形维数D1、D2和分形粗糙度参数G1、G2 。采用双重分形几何描述接触表面的拓扑结构,并根据赫兹接触理论导出接触微凸体的切向接触刚度。弹塑性双重分形面的切向接触刚度等于所有微观弹性接触点的切向接触刚度的总和。粗糙层是由相接触的微凸体所构成的,其抗扭刚度模化为接触转子轮盘间的一个抗扭弹簧。通过三维有限元模态分析和实验模态分析得到了拉杆转子在不同预紧力下的扭振模态频率。通过上述计算和实验结果识别了粗糙层的抗扭刚度,实验测试结果和理论计算结果相一致,这表明上述接触层抗扭刚度的双重分形模型实合理的,可以有效地考虑接触效应对拉杆转子扭转振动模态频率的影响。