石墨烯与柔性基底界面载荷传递的拉曼光谱实验

本文研究了CVD制备的大尺寸石墨烯与柔性PET基底在拉伸变形过程中切向界面载荷传递的问题,采用原位拉曼光谱实验给出了加载过程中石墨烯的正应变、正应力以及界面切应力的分布曲线。分析表明,石墨烯与PET基底间的载荷传递存在四个阶段,分别是初始阶段、粘附阶段、滑移阶段和界面脱粘破坏阶段。在此基础上,本文对50μm、140μm、270μm和600μm四种尺寸石墨烯试件的界面力学性能进行测量,得到了不同尺寸石墨烯试件的界面力学性能参数,并初步给出了基底变形引起的石墨烯切向界面粘接能的变化,同时分析了试件尺寸对石墨烯界面力学性能的影响。实验结果表明,石墨烯材料和柔性基底最大切应力与临界脱粘切向界面粘接能等界面强度指标受到尺寸的显著影响,尺寸越小切向界面强度越高,反之,尺寸越大则越低。     

Static wetting on flexible substrates: a finite element formulation

In static wetting on an elastic substrate, force exerted by the liquid–vapour surface tension on a solid surface deforms the substrate, producing a capillary ridge along the contact line. This paper presents a finite element formulation for predicting elastic deformation, close to the static wetting line (with angle of contact=90o and σSV=σSL).The substrate deformation is modelled with the Mooney–Rivlin constitutive law for incompressible rubber‐like solids. At the contact line, a stress singularity is known to arise, due to the surface tension acting on a line of infinitesimal thickness. To relive the stress singularity, either (i) the surface tension is applied over a finite contact region (of macroscopic thickness), or (ii) the solid crease angle is fixed. These two options suggest that normal component of Neumann's triangle law of forces, for the three surface tensions, is not applicable for elastic substrates (as for rigid ones). The vertical displacement of the contact line is a strong function of liquid/vapour surface tension and shear modulus of the solid. Copyright 2004 John Wiley & Sons, Ltd.     

不同固定方式下高压功率模块的抗冲击性能分析

为了提升高压功率模块在高速冲击环境中的结构可靠性,研究了高压功率模块采用不同固定方式的抗冲击特性。基于一维应力波条件,针对模块在自由式霍普金森杆系统中的运动响应以及能量转换形式进行理论分析,完成了模块的变形能与动能结果对比。采用有限元方法模拟了20 m/s冲击速度下模块的运动和变形过程,提取关键结构的应力分布、挠度、位移响应速度和加速度响应曲线,其中应力响应最高位置在陶瓷基板层,达到427 MPa,挠度响应最高位置在金属底板层,达到了773.8 μm,模块整体位移速度最高达到17.68 m/s,加速度最高达到51 110.7g。对比4种固定方式的冲击响应结果,模块冲击后底板变形量由小到大分别为面贴装固定、四角点固定、短边两点固定和长边两点固定,面贴装模块的位移动能和加速度峰值最大。结果表明采用面贴装固定的模块在冲击加速度载荷下发生变形失效的可能性最小,面贴装在四种固定方式中是可靠性最高的安装方式,之后的选择优先度分别是四角点固定、短边两点固定和长边两点固定。研究成果为半导体高压功率模块在实际应用中的安装固定方式选择提供了重要理论依据。     

粗糙面在梯度表面层上滑动接触的应力分布

对粗糙面在梯度表面层上的滑动过程进行应力分布研究,以模拟实际摩擦过程中,考虑塑性变形情况下,梯度覆层体中的应力分布规律,同时与均质体及单覆层体进行比较研究,分析了在表面载荷相同时滑动接触的应力分布。结果表明覆层体出现塑性变形后,在接触表面上的压力分布与弹性变形时有很大变化,在界面处梯度层的应力分布比单层膜更为理想,其应变梯度也较小;受相同表面载荷作用下产生塑性变形时,梯度层膜在基体产生塑性变形较小     

Mechanics of physisorption on elastomer surface

Mechanical aspects of physisorption on elastomeric substrates are studied via a continuum model in combination with the Lennard-Jones potential. In light of the incompressibility of elastomers, it is shown that the presence of a zero-dimensional adsorbate gives rise to a distributed force on the surface of the substrate. The induced surface deformation is determined, and the adsorption force and energy which depend on the substrate stiffness are derived. The results are then used to examine mutual interaction between two like adsorbates with small spacing, showing complicated attraction and repulsion arising from elastic deformation of the substrate. The dipole and quadruple moments of an adsorbate are also calculated, and the multipole approximation is adopted to quantify the interaction when the two adsorbates are separated remotely.     

Plane strain dynamics of elastic solids with intrinsic boundary elasticity, with application to surface wave propagation

In this paper, in a development of the static theory derived by Steigmann and Ogden (Proc. Roy. Soc. London A 453 (1997) 853), we establish the equations of motion for a non-linearly elastic body in plane strain with an elastic surface coating on part or all of its boundary. The equations of (linearized) incremental motions superposed on a finite static deformation are then obtained and applied to the problem of (time-harmonic) surface wave propagation on a pre-stressed incompressible isotropic elastic half-space with a thin coating on its plane boundary. The secular equation for (dispersive) wave speeds is then obtained in respect of a general form of incompressible isotropic elastic strain-energy function for the bulk material and a general energy function for the coating material. Specialization of the form of strain-energy function enables the secular equation to be cast as a quartic equation and we therefore focus on this for illustrative purposes. An explicit form for the secular equation is thereby obtained. This involves a number of material parameters, including residual stress and moment in the properties of the coating. It is shown how this equation relates to previous work on waves in a half-space with an overlying thin layer set in the classical theory of isotropic elasticity and, in particular, the significant effect of omission of the rotatory inertia term, even at small wave numbers, is emphasized. Corresponding results for a membrane-type coating, for which the bending moment, inertia and residual moment terms are absent, are also obtained. Asymptotic formulas for the wave speed at large wave number (high frequency) are derived and it is shown how these results influence the character of the wave speed throughout the range of wave number values. A bifurcation criterion is obtained from the secular equation by setting the wave speed to zero, thereby generalizing the bifurcation results of Steigmann and Ogden (Proc. Roy. Soc. London A 453 (1997) 853) to the situation in which residual stress and moment are present in the coating. Numerical results which show the dependence of the wave speed on the various material parameters and the finite deformation are then described graphically. In particular, features which differ from those arising in the classical theory are highlighted.     

Residual-stress measurement using surface displacements around an indentation

An experimental method is described which can measure the direction and magnitude of residual and applied stress in metals. The method uses optical interference to measure the permanent surface deformation around a shallow spherical indentation in a polished area on the metal specimen. The deviation from circularly symmetrical surface deformations is measured at known values of applied stress in calibration specimens. This deviation from symmetry can then be used to determine the direction and magnitude of tensile residual stress in specimens of the same material. Determination of compressive residual stress is more limited. A model of the indentation process is offered which qualitatively describes experimental results in 4340 steel for both tensile and compressive stress. The model assumes that the deformation around an indentation os controlled by stresses analogous to those around a hole in an elastic plate. Various conditions are discussed which affect the indentation process and its use to measure stress, including (a) the rigidity of support of the indentor and specimen, (b) the size and depth of the indentation, (c) the uniaxial stress-strain behavior of the specimen material.     

Deformation, stress state and thermodynamic force for a growing void in an elastic–plastic material

The growth of a spherical void in an elastic–plastic body, subjected to external pressure or tension and a gas pressure as well as a surface stress at the void surface, is investigated. The deformation, strain and stress state in the full body is presented. In addition, the local and global energy terms are calculated. Finally the total thermodynamic force on the void surface as well as the total dissipation are evaluated and compared allowing the calculation of the mechanical contribution to void growth due to diffusion of vacancies generated by plastification or irradiation.     

Multiple axial cracks in a coated hollow cylinder due to thermal shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing.     

Nanoindentation modeling of a nanodot-patterned surface on a deformable substrate

A numerical model was developed to simulate the nanoindentation of a Ni nanodot-patterned surface (NDPS) on a deformable Si substrate. Each contacting nanodot on the Si substrate was treated individually in this model and the interaction among the nanodots was considered through the elastic deformation of the Si substrate. The load–deformation relationship for the single-asperity contact between the indenter tip and a nanodot was determined using finite element analysis. A nanoindentation experiment on a Ni NDPS was performed to test the developed model. The simulation and experimental results were found to be in good agreement. The experimentally verified model was used to explore the effects of substrate deformation and surface roughness caused by the Ni nanodots on the nanoindentation behavior. It was found that the effect of the substrate and the effect of roughness must be considered. A detailed study of the substrate deformation shows that the interaction among nanodots, through the substrate, can contribute a considerable portion of the total deformation under a nanodot. The yield strength of the nanodot was found to have a significant effect on the contact deformation, while the elastic modulus was found to have little effect.     

绕径旋转横观各向同性圆球壳的变形和应力分析

本文用三维弹性力学理论研究绕径旋转横观各向同性圆球壳的变形和应力分布，给出任意厚度圆球壳的位移和应务的封闭形式解以及数值结果。研究表明球壳上的位移和应力大小与旋转角速度的平方成正比，球面内的正应力远大于径向正应力和剪应力。     

Mechanics of deformation of single- and multi-wall carbon nanotubes

An effective continuum/finite element (FE) approach for modeling the structure and the deformation of single- and multi-wall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The incorporation and role of an initial internal distributed stress through the thickness of the wall, due to the cylindrical nature of the tube, are discussed. The effects of van der Waals forces, crucial in multi-wall nanotubes and in tube/tube or tube/substrate interactions, are simulated by the construction of special interaction elements.The success of this new CNT modeling approach is verified by first comparing simulations of deformation of single-wall nanotubes with molecular dynamics results available in the literature. Simulations of final deformed configurations, as well strain energy histories, are in excellent agreement with the atomistic models for various deformations. The approach was then applied to the bending of multi-wall carbon nanotubes (MWNTs), and the deformed configurations were compared to corresponding high-resolution images from experiments. The proposed approach successfully predicts the experimentally observed wavelengths and shapes of the wrinkles that develop in bent MWNTs, a complex phenomenon dominated by inter-layer interactions. Presented results demonstrate that the proposed FE technique could provide a valuable tool for studying the mechanical behavior of MWNTs as single entities, as well as their effectiveness as load-bearing entities in nanocomposite materials.     

超弹性薄膜与可压缩基底双层结构表面失稳分析

当上层超弹性硬质薄膜和下层可膨胀基底构成的双层结构受压时,薄膜的自由表面可通过形成褶皱降低系统能量.研究表明,上下两层的模量比不同时,上层弹性硬质薄膜将表现出不同的表面失稳模式.本文提出了一种新颖的方法可有效抑制双层软材料的表面失稳,即改变基底材料的泊松比,这种方法同时适用于不具有应变硬化的软材料.首先基于Neo-Hookean模型发展了小变形条件下双层结构表面失稳的理论模型,通过半解析的方法得到了表面失稳的临界应变;然后通过有限元计算与模拟,进一步验证了负泊松比基底可延缓表面失稳.结果表明:(1)当双层结构基底泊松比为正且趋于0.5(不可压缩)时,双层结构在较小的压缩应变下出现表面失稳;(2)当基底的泊松比为负且趋于-1时,可被压缩至46%而不出现表面失稳,即可膨胀基底能有效抑制薄膜的表面失稳.本文发展的方法及主要结果可为延展性电子器件的设计提供指导.     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

Thermo-mechanical solution of film/substrate systems under local thermal load and application to laser lift-off of GaN/sapphire structures

Film/substrate structures may undergo a localized thermal load, which can induce stresses, deformation and defects. In this paper, we present the solutions of temperature and stresses in a film/substrate structure under a local thermal load on the film surface. Then, the generalized Stoney formula, which connects the curvature of deformation and the stress field is obtained. The present solution takes into account the non-uniformity of the temperature field both in the width and thickness directions of the film. The thermo-mechanical solution is applied to the analysis of the temperature distribution, stresses, and damage of a GaN/sapphire system during the laser lift-off (LLO) process. It is shown that the laser with the Gaussian distribution of energy density causes much smaller tensile stresses at the edge of the heated area in the film than the laser with the uniform distribution of energy density, and thus can avoid damage to the GaN films separated from the substrate.     

Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

Indentation of a hard film on a soft substrate: Strain gradient hardening effects

The strain gradient work hardening is important in micro-indentation of bulk metals and thin metallic films, though the indentation of thin films may display very different behavior from that of bulk metals. We use the conventional theory of mechanism-based strain gradient plasticity (CMSG) to study the indentation of a hard tungsten film on soft aluminum substrate, and find good agreement with experiments. The effect of friction stress (intrinsic lattice resistance), which is important in body-center-cubic tungsten, is accounted for. We also extend CMSG to a finite deformation theory since the indentation depth in experiments can be as large as the film thickness. Contrary to indentation of bulk metals or soft metallic films on hard substrate, the micro-indentation hardness of a hard tungsten film on soft aluminum substrate decreases monotonically with the increasing depth of indentation, and it never approaches a constant (macroscopic hardness). It is also shown that the strain gradient effect in the soft aluminum substrate is insignificant, but that in the hard tungsten thin film is important in shallow indentation. The strain gradient effect in tungsten, however, disappears rapidly as the indentation depth increases because the intrinsic material length in tungsten is rather small.     

Patterned bilayer plate microstructures subjected to thermal loading: Deformation and stresses

We studied the deformation of a series of gold/polysilicon patterned plate microstructures fabricated by surface micromachining. The patterned plate microstructures were subjected to a uniform temperature change from 100 °C to room temperature that was intended to induce linear and geometrically nonlinear deformation. We used interferometry to measure full-field deformed shapes of the microstructures. From these measurements we determined the spatially-averaged curvature of the deformed microstructures within individual lines and across the entire plate. The deformation response of the patterned plates can be broadly characterized in terms of the average curvature as a function of temperature change and exhibits linear and geometrically nonlinear behavior. We modeled the deformation response of the patterned plates using geometrically nonlinear plate theory with the finite element method. Good agreement was obtained between predictions and measurements for both local curvature variations across lines and for the evolution of curvature of the entire plate with temperature change. Using a generalized plane strain approach with the finite element method we also modeled the spatial dependence of the stress distribution in the lines and substrate. For thick plates, our results agree with those of previous studies, showing a decrease in the von Mises stress in the metal lines with decreasing linewidth. For thinner substrates, though, we find the behavior with linewidth is opposite and there is a critical substrate thickness (about 10 μm for the system in our study) where the behavior with linewidth changes. These results have important implications in the design of patterned structures for micro-electro-mechanical systems (MEMS) applications where films are of comparable thickness to the underlying substrate.     

An automatic and interactive large-deformation measurement system based on image processing

This paper describes an image-processing-based measurement system by which an automatic large deformation characterization and interactive force control can be realized. The system is provided by a servo-controlled CCD camera and a PC-based frame grabber. A tracking procedure based on the location of a target point is employed for guiding the camera movement. It is intended to monitor the local deformation in a relatively small moving area containing small globules. The globule positions are then used to determine the surface deformation characteristics. In this system, the momentary principal strains being computed online are immediately used to control the applied force. As an illustration, the present system is applied for observing a long-term homogeneous large deformation in SI-rubber specimens being subjected to a constant uniaxial true stress. Four solid, minuscule, relatively undeformable polystyrene globules are used as markers. A true stress control algorithm is developed based on the isotropy assumption in which the transverse area normal to the loading direction becomes determinable from the surface deformation data. It can be stated that the maximum speed of the true stress control is mainly related to the speed of image processing and analysis, which in turn is related to the chosen number of globules and the performance of the PC used. By using four globules, the true stress readjustment could be accomplished for roughly every 4 s. For a large-strain deformation of SI-rubber, it appears that the isotropy assumption is acceptable, since the resulting mean difference between out-of-plane contraction and in-plane contraction is restricted to about±8 percent.     

Laser heating of multilayer assembly and stress levels: elasto-plastic consideration

Laser heating of multilayer assembly results in temperature profiles, which differ in each layer. Depending upon the material and laser pulse properties, high temperature gradients can occur. This, in turn, results in excessive stress levels in the region irradiated by a laser beam. When the magnitude of stress level exceeds the yield stress of the material, plastic deformation is resulted. In this case, elasto-plastic analysis should be applied when modeling the thermal stresses due to a laser heating pulse. In the present study, time exponentially varying pulse laser heating of four and two layer assemblies is considered. The four layer assembly composes of gold, chromium, gold and silicon while two layer assembly is formed from gold and silicon. The resulting temperature field is obtained numerically using a control volume approach. The elasto-plastic analysis employed to compute the stress levels in the substrate material. It is found that stress levels higher than the yield stress of the substrate material occurs in the surface region. This, in turn, results in plastic zone in this region. The size of the plastic region extends towards the solid bulk as the heating progresses.