Ultrasonic assessment of rough surface contact between solids from elastoplastic loading-unloading hysteresis cycle

An ultrasonic method to characterize the elastoplastic contact between two rough surfaces is presented. Ultrasonic experiments are performed on three different interfaces formed by aluminum surfaces with different levels of roughness. The frequency-dependent ultrasonic reflection coefficient from the interface is measured during loading and unloading cycles as a function of pressure, from which the ultrasonic interfacial contact stiffness is reconstructed by the least-squares inversion procedure. It is shown that one should distinguish between the ultrasonic (dynamic) interfacial stiffness and static interfacial stiffness for rough surfaces in elastoplastic contact (they are identical for purely elastic contact). It is shown that ultrasonic stiffness is associated with local unloading stiffness. An elastoplastic micromechanical model is used to describe the plasticity-induced hysteresis in the ultrasonically measured interfacial stiffness during loading-unloading cycles. The topographic parameters of the interface contact are reconstructed by matching the model-predicted results with the experimentally determined ultrasonic stiffness. Using these parameters the real area of contact, which is not directly measurable, is predicted during loading-unloading cycles using the model.     

On the relationship between ultrasonic and micromechanical properties of contacting rough surfaces

In this work, it is suggested that a unique set of the interfacial stiffness constants, K_N and K_T, is sufficient to characterize the macroscopic elastic response of an interface between two rough contacting surfaces regardless of the direction of incidence of the ultrasonic wave. It is also shown that by combining ultrasonic spectroscopy with the theoretical procedures developed for a single imperfect interface, the stiffness constants of a double interface can be successfully recovered. The values of the stiffness constants determined from ultrasonic measurements are related to the micromechanical interaction and topography of the contacting surfaces using a micromechanical model of two rough surfaces in contact.     

介观双粗糙弹塑性流体动力润滑界面法向接触刚度模型

弹性流体动力润滑状态通常出现在机械高副零部件的点/线接触部位,如齿轮、轴承和蜗轮蜗杆等.宏观上点/线接触在介观层面表现为两粗糙表面的接触,在微观层面上则又表现为微凸体间的接触.由于在中/重载荷作用下,粗糙表面上的微凸体发生接触后会产生弹塑性/塑性变形,从而使得两粗糙表面的弹流润滑接触转变为弹塑性流体动力润滑接触.此外,界面的接触刚度决定了机械装备的整机刚度.为了精确获得弹性流体动力润滑状态下界面法向接触刚度及其主要影响因素,基于界面的法向接触刚度由固体接触刚度和润滑油膜刚度两部分构成的思想,根据固体弹塑性理论和流体动力学理论,分别对界面间微凸体侧接触及部分膜流体动力润滑进行分析,从微观入手揭示双粗糙表面弹塑性流体动力润滑接触机理,进而建立考虑微凸体侧接触弹塑性变形的流体动力润滑界面法向接触刚度模型.通过仿真分析,揭示了法向载荷、卷吸速度、表面粗糙度及润滑介质特性等因素对润滑界面法向接触刚度的影响规律.研究表明：在相同速度、粗糙度及润滑油黏度的工况下,固体接触刚度和油膜接触刚度均随着法向接触载荷的增加呈非线性增大;在相同载荷、速度及润滑油黏度的工况下,接触表面粗糙度越大,表面形貌对于润滑...     

Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces

The two-dimensional elastic wave propagation in an infinite layered structure with nonlinear interlayer interfaces is analyzed theoretically to investigate the second-harmonic generation due to interfacial nonlinearity. The structure consists of identical isotropic linear elastic layers that are bonded to each other by spring-type interfaces possessing identical linear normal and shear stiffnesses but different quadratic nonlinearity parameters. Explicit analytical expressions are derived for the second-harmonic amplitudes when a single monochromatic Bloch mode propagates in the structure in arbitrary directions by applying the transfer-matrix approach and the Bloch theorem to the governing equations linearized by a perturbation method. The second-harmonic generation by a single nonlinear interface and by multiple consecutive nonlinear interfaces are shown to be profoundly influenced by the band structure of the layered structure, the fundamental Bloch wave mode, and its propagation direction. In particular, the second harmonics generated at multiple consecutive interfaces are found to grow cumulatively with the propagation distance when the phase matching occurs between the Bloch modes at the fundamental and double frequencies.     

Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces

The second-harmonic generation characteristics in the elastic wave propagation across an infinite layered structure consisting of identical linear elastic layers and nonlinear spring-type interlayer interfaces are analyzed theoretically. The interlayer interfaces are assumed to have identical linear interfacial stiffness but can have different quadratic nonlinearity parameters. Using a perturbation approach and the transfer-matrix method, an explicit analytical expression is derived for the second-harmonic amplitude when the layered structure is impinged by a monochromatic fundamental wave. The analysis shows that the second-harmonic generation behavior depends significantly on the fundamental frequency reflecting the band structure of the layered structure. Two special cases are discussed in order to demonstrate such dependence, i.e., the second-harmonic generation by a single nonlinear interface as well as by multiple consecutive nonlinear interfaces. In particular, when the second-harmonic generation occurs at multiple consecutive nonlinear interfaces, the cumulative growth of the second-harmonic amplitude with distance is only expected in certain frequency ranges where the fundamental as well as the double frequencies belong to the pass bands of the layered structure. Furthermore, a remarkable increase of the second-harmonic amplitude is found near the terminating edge of pass bands. Approximate expressions for the low-frequency range are also obtained, which show the cumulative growth of the second-harmonic amplitude with quadratic frequency dependence.     

固-液结合面法向动态接触刚度及阻尼的理论模型与实验分析

固-液接触状态广泛存在于机床核心单元关键零部件的接触运动副中,精确获得固-液结合面法向接触刚度及阻尼参数是高档数控机床产品在研发阶段就存在的一个关键理论与技术问题,并且仍然尚未根本解决.固-液结合面在介观层面上表现为两个粗糙表面的接触,在微观层面上表现为微凸体之间的接触,并在中/重载荷作用下微凸体可能会发生弹性/弹塑性...     

An exact theory of interfacial debonding in layered elastic composites

An exact theory of interfacial debonding is developed for a layered composite system consisting of distinct linear elastic slabs separated by nonlinear, nonuniform decohesive interfaces. Loading of the top and bottom external surfaces is defined pointwise while loading of the side surfaces is prescribed in the form of resultants. The work is motivated by the desire to develop a general tool to analyze the detailed features of debonding along uniform and nonuniform straight interfaces in slab systems subject to general loading. The methodology allows for the investigation of both solitary defect as well as multiple defect interaction problems. Interfacial integral equations, governing the normal and tangential displacement jump components at an interface of a slab system are developed from the Fourier series solution for the single slab subject to arbitrary loading on its surfaces. Interfaces are characterized by distinct interface force–displacement jump relations with crack-like defects modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which account for rigid body translation and rotation, are sought by eigenfunction expansion of the solution of the governing interfacial integral equations. Applications of the theory to the bilayer problem with a solitary defect or a defect pair, in both peeling and mixed load configurations are presented.     

Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods.     

Response of frictional contact problems in thermo-rheologically complex structures

This paper presents a comprehensive computational model for predicting the nonlinear response of frictional viscoelastic contact systems under thermo-mechanical loading and experience geometrical nonlinearity. The nonlinear viscoelastic constitutive model is expressed by an integral form of a creep function, whose elastic and time-dependent properties change with stresses and temperatures. The thermo-viscoelastic behavior of the contacting bodies is assumed to follow a class of thermo-rheologically complex materials. An incremental-recursive formula for solving the nonlinear viscoelastic integral equation is derived. Such formula necessitates data storage only from the previous time step. The contact problem as a variational inequality constrained model is handled using the Lagrange multiplier method for exact satisfaction of the inequality contact constraints. A local nonlinear friction law is adopted to model friction at the contact interface. The material and geometrical nonlinearities are modeled in the framework of the total Lagrangian formulation. The developed model is verified using available benchmarks. The effectiveness and accuracy of the developed computational model is validated by solving two thermo-mechanical contact problems with different natures. Moreover, obtained results show that the mechanical properties and the class of thermo-rheological behavior of the contacting bodies as well as the coefficient of friction have significant effects on the contact response of nonlinear thermo-viscoelastic materials.     

三层流体中斜入射波作用下半无限板的水弹性响应

解析地研究了在三层流体中斜入射波浪与半无限弹性板的相互作用引起的波散射和板的水弹性响应. 三层流体在界面处的密度发生阶跃, 各层为一常数. 假设流体不可压缩、无黏、流体运动无旋. 在线性势流理论框架下, 使用本征函数展开法和内积式给出波板相互作用的半解析解. 根据色散关系分析, 得到了表面波模态和界面波模态入射时的临界入射角. 随着物理参数的变化, 临界角将随之发生变化. 临界角决定了当由开阔水域向板覆盖水域传播的表面波或界面波的存在性: (1)板覆盖水域入射界面上, 透射波能否存在; (2)入射界面之上界面中, 板覆盖水域中的透射波以及开阔水域中的反射波能否存在. 当下界面波入射时并且入射角足够大时, 开阔水域中的下界面波模态是整个流体域中唯一存在的模态.      

Nonlinear Acoustic Interaction of Contact Interfaces

Nonlinear acoustic interactions at contact interfaces can be used to characterize defects or imperfect bonds at these interfaces. Most methods used to characterize nonlinear interactions consider only a portion of the nonlinear signature, such as nonlinearities caused by high-order harmonics or sidebands. We describe a signal processing algorithm that can extract three nonlinear indicators related to amplitude attenuation, phase shift, and harmonics. Two aluminum blocks were mounted together to form a contact interface and subjected to normal compressive loading. Experiments were conducted to investigate the nonlinear interactions between the ultrasonic waves and interfaces, with a focus on the influence of excitation levels, applied pressure, and surface roughness. The ultrasonic signals were then processed using the nonlinear feature extraction algorithm. We show that the nonlinear indicators can characterize the contact condition of interfaces, and that their sensitivities to pressure differ for interfaces of different roughness and over different pressure ranges.     

An adhesive wear model of fractal surfaces in normal contact

A generalized adhesive wear analysis that takes into account the effect of interfacial adhesion on the total load was developed for three-dimensional fractal surfaces in normal contact. A wear criterion based on the critical contact area for fully-plastic deformation of the asperity contacts was used to model the removal of material from the contact interface. The fraction of fully-plastic asperity contacts, wear rate, and wear coefficient are expressed in terms of the total normal load (global interference), fractal (topography) parameters, elastic–plastic material properties, surface energy, material compatibility, and interfacial adhesion characteristics controlled by the environment of the interacting surfaces. Numerical results are presented for representative ceramic–ceramic, ceramic–metallic, and metal–metal contact systems to illustrate the dependence of asperity plastic deformation, wear rate, and wear coefficient on global interference, surface roughness, material properties, and work of adhesion (affected by the material compatibility and the environment of the contacting surfaces). The analysis yields insight into the effects of surface material properties and interfacial adhesion on the adhesive wear of rough surfaces in normal contact.     

Interesting effects in harmonic generation by plane elastic waves

The harmonics of plane longitudinal and trans-verse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a pri-mary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.     

The low frequency scatter of SH waves by a rough interface in an elastic plate

The study of the reflection and transmission of low frequency SH waves incident upon a rough interface in an elastic plate is undertaken by employing a theory of acoustic wave scattering from rough surfaces originally due to Biot and subsequently generalised to the case of elastic media. In this theory the interface is replaced by a distribution of voids/asperities whose individual size is small compared to the excitation wavelength. We plot the absolute values of the reflection and transmission coefficients versus frequency when a single symmetric SH plate mode is used as the input excitation. The different types of inclusions are used to simulate the rough surface are the hollow, fluid filled and aluminum spheres. Lastly, the loss of energy due to scattering is also estimated for the different inclusion distributions considered.     

Nonlinear Lamb waves in plate/shell structures

鉴于常规超声检测技术对分布式材料细微损伤和接触类结构损伤的检测效果不佳,近年来非线性超声技术逐渐引起广泛关注.超声波在板壳结构中通常以兰姆波的形式进行传播,然而由于兰姆波的频散及多模特性,使得非线性兰姆波的理论和实验研究进展缓慢.本文从经典非线性理论出发,总结了源于材料固有非线性诱发的非线性兰姆波的理论和实验两个方面的研究进展,并综述了兰姆波的二次谐波发生效应在材料损伤评价方面的若干应用;从接触声非线性理论出发,讨论了目前由于接触类结构损伤诱发的非线性兰姆波的研究现状.最后展望了非线性兰姆波的未来研究重点及发展趋势.     

Rayleigh–Lamb Waves in a Compound Wave Guide. Reflection from and Transmission Through the Vertical Interface between Media with Different Impedances

The method of superposition is used to study the first normal wave reflecting from and transmitting through the interface in a compound waveguide consisting of two rigidly joined elastic half-strips with equal width and different mechanical properties. We study how the impedances of the contacting media influence the transformation of the energy of the incident wave to those of the reflected and transmitted waves. Two cases are considered — propagating waves of higher orders appear in the reflected wavefield earlier than in the transmitted wavefield and propagating waves of higher orders appear in the transmitted wavefield earlier than in the reflected wave field. For both cases, the impedances vary so that the incident wave can propagate in both more rigid and softer media. It is shown that by increasing the impedances of the contacting media, the interface can be made more transparent     

A friction contact stiffness model of fractal geometry in forced response analysis of a shrouded blade

To investigate the nonlinear vibration behavior of a shrouded blade with friction dynamic contact interface, a friction contact stiffness model is proposed to describe the friction force at different rough interfaces and different normal loads. In the proposed model, the friction contact interface is discretized to a series of friction contact pairs and each of them can experience stick, slip, or separate states. Fractal geometry is used to simulate the topography of contact surfaces. The contact stiffness is calculated using the Hertz contact theory and fractal geometry, which is related to contact interfaces parameters including normal load, roughness, Young??s modulus, and Poisson??s ratio. The trajectory tracking method is used to predict the friction force and it is not necessary to judge the transition condition among stick, slip, and separate states. It is suitable for complicated periodic motion of the contact interfaces. The forced response of a real shrouded blade is predicted using the proposed model and the multi-harmonic balance method. The effect of surface roughness, initial normal load, and contact area on the forced response of a shrouded blade is studied. It is shown that contact stiffness increases with normal load and fractal dimension. The resonant amplitude is sensitive to the initial normal load and contact surface roughness. The response can be influenced by the contact area, which is an important parameter for blade designers.     

A Comparison of Contact Stiffness Measurements Obtained by the Digital Image Correlation and Ultrasound Techniques

The digital image correlation (DIC) and ultrasound techniques have both previously been employed to measure the contact stiffness of real engineering interfaces, but a comprehensive comparison of these techniques has not previously been carried out. Such a comparison is addressed in the present paper. The principal novelty in this work is that DIC and ultrasound are used to simultaneously measure contact stiffness in the same tests and on the same contact interface. The results show that ultrasound measures somewhat higher contact stiffness magnitudes than DIC: at an average normal contact pressure of 70 MPa, ultrasound was around three times stiffer. Given that the techniques are vastly different in their measurement approach (DIC measures micron-scale relative displacements from external side-on images of the interface, while ultrasound uses the reflection of an Ångstrom scale ultrasonic perturbation from the interior of the interface itself), this level of agreement is thought to be encouraging. The difference in results can partly be explained by consideration of inherent physical differences between the techniques which have previously received little attention. Ultrasound measurement will always give the local elastic ‘unloading stiffness’ (even at a plastically deforming contact); whereas, a load-deflection technique like DIC, will give the ‘loading stiffness’. The reason for this difference is discussed in the paper and tests carried out under increasing tangential load in the pre-sliding regime illustrate this difference experimentally. Under normal loading, the increase in real contact area obscures the effect to some extent as both DIC and ultrasound stiffnesses increase with normal load. The results suggest that rough interfaces may be satisfactorily modelled as a variable stiffness spring whose stiffness increases with contact pressure as the smooth contact case is approached.     

On the Iwan models for lap-type bolted joints

The paper presents mathematical modeling of the non-linear constitutive relation for bolted joints in the framework of the Kragelsky-Demkin theory of rough contact. It is shown that this approach, which maintains the tribology-related features of bolted joint interfaces, leads to a singular Iwan distribution density. In particular, we show that the Iwan density is expressed in terms of the height distribution density of the surface asperities, whereas its singular exponent is determined by the shape exponent of the surface asperities. Following this, constitutive relations for lap joints and the corresponding backbone (force-deflection) curves are obtained. Finally, Masing's hypothesis is applied and Goodman's relation for energy dissipation is recovered in order to describe the effects of cyclic loading. The two cases of a rough surface in contact with a flat surface and of two contacting rough surfaces are treated separately.     

Unloading an elastic-plastic contact of rough surfaces

A statistical model for the unloading of elastic-plastic contact of rough surfaces is presented for a single load-unload cycle. The hystereses of load-separation and load real contact area behavior are analyzed for a wide range of surface roughness and loading conditions. The residual topography of the unloaded rough surfaces is also analyzed and the new distribution functions of asperity heights and summit radii of curvature along with a corresponding GW residual plasticity index are presented. A new modified plasticity index (MPI) is suggested which considers the energy dissipation due to unrecovered plastic deformations. This MPI varies from zero for purely elastic contacts to unity for purely plastic contacts and hence, can better define the level of plasticity of contacting rough surfaces compared to the original GW plasticity index.