原位通孔鼓泡法测试二维材料杨氏模量

二维材料因其独特的晶体结构、新奇的物理特性和优异的力学性能,在光电器件、微纳机电系统等诸多领域有着广阔的应用前景,其中力学性能对于器件的制备、功能性、稳定性以及服役寿命等方面尤为重要。本文提出了一种测量二维材料杨氏模量的普适性实验方法,借助通孔鼓泡技术对材料进行连续可控加载,同时结合原子力探针技术原位表征其力学响应。该技术较好地解决了文献中常用恒定分子数鼓泡技术在测试二维材料杨氏模量中存在的加载周期长、加载不连续等弊端。以单层或双层石墨烯薄膜为例,利用自行搭建的通孔鼓泡实验平台结合原子力显微技术实现了鼓泡高度和直径大小的原位测量,借助Hencky解获得石墨烯杨氏模量,实验数值与文献报道相符。此外,在三角波和正弦波两种动态循环加载方式下,该测试方法均表现出良好的稳定性。本文工作不仅发展了一种普适原位的二维材料杨氏模量实验测试方法,也为大面积二维材料薄膜力学性能的程序化测试与分析、高通量实验数据的力学统计分析打下了可靠的实验基础。     

二维材料力学行为的压痕测试

准确了解二维材料的力学性能对于推动其应用具有重要意义, 无基底压痕技术是目前最广泛采用的二维材料力学性能测试方法之一, 本文综述了二维材料压痕研究的最新进展以及所面临的问题, 并对将来的研究工作进行了展望.无基底压痕技术是将二维材料转移到带有沟槽或柱形孔的基底上, 制备二维材料"梁"和"鼓"模型, 然后利用原子力显微镜测量其在压针作用下的载荷--位移关系, 最后通过基于连续介质薄膜导出的压痕响应分析模型拟合实验结果, 估算出二维材料的弹性模量和本征强度.由于二维材料的厚度远小于连续介质薄膜, 来自于压头以及基底孔侧壁的范德华力对二维材料的压痕响应具有显著影响, 造成二维材料与传统压痕分析模型中的基本假设不符, 导致不能准确预测二维材料的弹性模量; 另外, 由于传统压痕模型无法准确描述二维材料在大变形下的非线性行为, 以及由缺陷等引起的应力集中, 导致由压痕测试表征的二维材料(特别是多晶二维材料)本征强度具有较大的偏差. 因此, 一方面需要正确了解由压痕技术获得的二维材料力学性能, 另一方面还需对目前的研究方法做进一步的改进和完善.      

Indentation tests investigation of mechanical behavior of two-dimensional materials

准确了解二维材料的力学性能对于推动其应用具有重要意义, 无基底压痕技术是目前最广泛采用的二维材料力学性能测试方法之一, 本文综述了二维材料压痕研究的最新进展以及所面临的问题, 并对将来的研究工作进行了展望.无基底压痕技术是将二维材料转移到带有沟槽或柱形孔的基底上, 制备二维材料"梁"和"鼓"模型, 然后利用原子力显微镜测量其在压针作用下的载荷--位移关系, 最后通过基于连续介质薄膜导出的压痕响应分析模型拟合实验结果, 估算出二维材料的弹性模量和本征强度.由于二维材料的厚度远小于连续介质薄膜, 来自于压头以及基底孔侧壁的范德华力对二维材料的压痕响应具有显著影响, 造成二维材料与传统压痕分析模型中的基本假设不符, 导致不能准确预测二维材料的弹性模量; 另外, 由于传统压痕模型无法准确描述二维材料在大变形下的非线性行为, 以及由缺陷等引起的应力集中, 导致由压痕测试表征的二维材料(特别是多晶二维材料)本征强度具有较大的偏差. 因此, 一方面需要正确了解由压痕技术获得的二维材料力学性能, 另一方面还需对目前的研究方法做进一步的改进和完善.     

二维材料力学行为的压痕测试

准确了解二维材料的力学性能对于推动其应用具有重要意义,无基底压痕技术是目前最广泛采用的二维材料力学性能测试方法之一,本文综述了二维材料压痕研究的最新进展以及所面临的问题,并对将来的研究工作进行了展望.无基底压痕技术是将二维材料转移到带有沟槽或柱形孔的基底上,制备二维材料"梁"和"鼓"模型,然后利用原子力显微镜测量其在压针作用下的载荷–位移关系,最后通过基于连续介质薄膜导出的压痕响应分析模型拟合实验结果,估算出二维材料的弹性模量和本征强度.由于二维材料的厚度远小于连续介质薄膜,来自于压头以及基底孔侧壁的范德华力对二维材料的压痕响应具有显著影响,造成二维材料与传统压痕分析模型中的基本假设不符,导致不能准确预测二维材料的弹性模量;另外,由于传统压痕模型无法准确描述二维材料在大变形下的非线性行为,以及由缺陷等引起的应力集中,导致由压痕测试表征的二维材料(特别是多晶二维材料)本征强度具有较大的偏差.因此,一方面需要正确了解由压痕技术获得的二维材料力学性能,另一方面还需对目前的研究方法做进一步的改进和完善.     

基于多项式代理模型的薄膜材料力学参数识别

针对鼓泡方法对具有不同本构关系的薄膜材料力学参数识别方法难以统一的问题,提出了一种基于代理模型的薄膜材料力学参数识别方法。首先,运用多项式代理模型将薄膜材料力学参数与薄膜试件在不同测点的挠度仿真值之间的关系显式化,然后采用改进的鼓泡实验装置测量并获得薄膜试件上各测点的扰度实验值,再以相应的测点多项式代理模型值与实验值之间的相对误差的平方和作为目标函数,采用状态转移算法对材料参数进行反解,获得能表征薄膜的真实材料参数。采用这一方法,对304不锈钢薄膜和橡胶材料进行识别实验,证实了这一方法的有效性和可靠性。因此可以利用本文的方法研究鼓泡实验装置的仪器化,从而为进一步实现薄膜材料力学参数识别方法的统一提供新的思路。     

环形薄板二维驻波的研究

在理论上和实验上对环形薄板二维驻波波节图形(克拉尼图形) 进行了研究. 通过在极坐标下对垂直板面方向小振动方程进行分离变量, 求解出环形薄板小振动方程在外边界悬空时分别在两种内边界条件, 即内边界悬空和内边界简支下的解析解的简正模式, 并计算了在第一种边条件下几种共振模式的径向波速近似值, 以及两种边条件下的圆形驻波波节线的半径和薄板的弹性模量. 发现通过调节环形薄板上点振动源的频率, 可精确控制薄板上出现的克拉尼图形. 实验上观察到了仅有圆形波节线, 仅有辐射状波节线, 以及两种波节线同时存在3 种简正模式的情形, 且波节线的数量可严格控制. 理论结果跟实验符合得很好.      

有限厚度模型校准二维MoS2的Bimodal-AFM杨氏模量测量

二维材料因其独特的晶体结构、新奇的物理特性和优异的力学性能, 在微纳机电系统、柔性电子器件等诸多领域有着广阔的应用前景. 弹性模量是二维材料的基本力学特性参量之一, 对其器件应用及应变调控有重要影响. 受限于二维结构和原子级厚度特征, 难以实现二维材料弹性模量的精确测量. 双模原子力显微镜的振幅调制-频率调制模式是一种高效测量二维材料杨氏模量的方法, 但刚性衬底对测量结果的影响不可忽视. 本工作通过双模原子力显微镜直接测得衬底与二维硫化钼的杨氏模量分布图, 并基于有限厚度模型对衬底效应进行修正, 得到了样品的本征杨氏模量值. 利用第一性原理计算得到了二维二硫化钼的弹性系数和杨氏模量, 对比发现实验和计算结果相当. 这说明双模原子力显微镜测量是一种可靠的二维材料杨氏模量直接测试方法, 且该方法无需制备悬空二维材料等繁琐步骤, 避免了常规测试中的不足. 本工作为大面积二维材料薄膜力学性能的程序化测试分析以及高通量力学实验数据的统计分析提供了可靠的实验基础.      

二维材料实验力学综述

以石墨烯为代表的二维材料因其原子级厚度、独特物理性质,成为近年来物理、化学、材料交叉学科的研究热点,在合成制备、结构表征、应用开发等方面的研究工作表明其在微纳机电系统、光电器件与功能复合材料领域有广泛且重要的应用前景。然而,由于二维材料结构与尺度的独特性,在其基本物性的理解方面仍存在许多未解决的问题,尤其是力学性能的表征,面临着诸多挑战。本文综述了二维材料本征力学性质和界面力学行为的微纳测试与表征技术的最新进展,例如纳米压痕技术、微孔鼓泡法等,并详细探讨了影响二维材料力学性能及行为的主要因素,分析了其微观尺度下的作用机制,以期通过物理或化学手段实现力学性能的调控。     

鼓泡法试验薄膜力学行为的研究

本文采用弹性理论,研究了鼓泡法试验过程中,外力(P)与薄膜中心挠度(w_0)之间的本构关系,计算出P与w_0的数学表达式.该分析模型考虑了薄膜内延展变形及薄膜中残余拉应力对本构关系的影响,并在较大挠曲区间范围内(挠度为10~(-2)～10~2倍薄膜厚度)分析本构关系特征.分析结果表明,外力与薄膜中心挠度之间本构关系可表示为:P∝w_0~n,n为指数.随着薄膜中心挠度的增加,薄膜的主要力学行为由弯曲过渡到延展,本构关系由线性过渡到立方关系,本构关系方程指数n由1增加到3.利用本构方程进行数值计算结果表明,薄膜挠曲所需外力随着薄膜半径增加而减小,随着残余拉应力的增加而增加.相对于以往不考虑延展变形的小挠度模型,本文所提出的力学模型更适合于大挠度条件下鼓泡法试验.     

石墨烯摩擦学及石墨烯基复合润滑材料的研究进展

本综述详细介绍了二维碳纳米材料-石墨烯的纳米摩擦学性能,以及作为纳米润滑薄膜、润滑添加剂和润滑填料的研究进展.总结了石墨烯的各种纳米摩擦机理,阐述了通过自组装、多层构筑、表面化学改性等技术改善石墨烯与基底的结合性、润滑剂中的分散性,与基体材料的界面结合强度以及石墨烯提高材料减摩抗磨性能的机制,并指出石墨烯作为高性能润滑材料仍需解决的问题及未来的研究趋势.     

用能量法分析层状材料弹性接触问题

利用能量法分析了层状材料（薄膜／基体）弹性接触问题，得到了具有一阶精度的闭合解，给出了求解薄膜弹性模量和泊松比的表达式，并与有限元的数值解进行了比较。二者比较结果表明：在工程材料范围内，理论解与数值解相差在6％以内；同时表明单相材料中剪切模量与弹性模量之间的关系也适用层状材料中的薄膜材料。在数值解的基础上，讨论了薄膜厚度与压头半径的比值对求解精度的影响，发现此比值对精度影响不大。通过对层状材料等效泊松比与等效弹性模量的定义，给出了用压痕实验测定薄膜泊松比与弹性模量的方法。     

Adhesive elastic contact between a symmetric indenter and an elastic film

This paper examines the frictionless adhesive elastic contact problem of a rigid sphere indenting a thin film deposited on a substrate. The result is then used to model the elastic phase of micro-nanoscale indentation tests performed to determine the mechanical properties of coatings and films. We investigate the elastic response including the effects of adhesion, which, as the scale decreases to the nano level, become an important issue. In this paper, we extend the Johnson–Kendall–Roberts, Derjaguin–Muller–Toporov, and Maugis–Dugdale half-space adhesion models to the case of a finite thickness elastic film coated on an elastic substrate. We propose a simplified model based on the assumption that the pressure distribution is that of the corresponding half-space models; in doing so, we investigate the contact radius/film thickness ratio in a range where it is usually assumed the half-space model. We obtain an analytical solution for the elastic response that is useful for evaluating the effects of the film-thickness, the interface film–substrate conditions, and the adhesion forces. This study provides a guideline for selecting the appropriate film thickness and substrate to determine the elastic constants of film in the indentation tests.     

Compression of solid and annular circular discs bonded to rigid surfaces

Although it is noted in the literature that the presence of a central hole in an elastic layer bonded to rigid surfaces can cause significant drop in its compression modulus, not much attention is given for investigating thoroughly and in detail the influence of the hole on the layer behavior. This paper presents analytical solutions to the problem of the uniform compression of bonded hollow circular elastic layers, which includes solid circular layers as a special case as the radius of hollow section vanishes. The closed-form expressions derived in this study are advanced in the sense that three of the commonly used assumptions in the analysis of bonded elastic layers are eliminated: (i) the incompressibility assumption, (ii) the “pressure” assumption and (iii) the assumption that plane sections remain plane after deformation. Through the use of the analytical solutions derived in the study, the compressive behavior of bonded circular discs is studied. Particular emphasis is given to the investigation of the effects of the existence of a central hole on the compression modulus, stress distributions and maximum stresses/strains in view of three key parameters: radius ratio of the hole, aspect ratio of the disc and Poisson’s ratio of the disc material.     

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.     

The Effect of Elastic Surface Coating on the Finite Deformation and Bifurcation of a Pressurized Circular Annulus

A plane-strain theory of an elastic solid coated with a thin elastic film on part or all of its boundary was developed recently by Steigmann and Ogden (1997a). In this paper the theory is applied to the (plane-strain) problem of a thick-walled circular cylindrical tube which is subject to both internal and external pressure and which has an elastic coating on one or both of its circular cylindrical boundaries. The effect of the coating on the symmetrical response of the annular cross-section of the tube is determined first. It is noted, in particular, that while the pressure may exhibit a maximum followed by a minimum during inflation for an uncoated tube it may be a monotonic increasing function of the radius for a coated tube with coating elastic modulus sufficiently large. Next, the possibility of bifurcation from a symmetrical configuration is examined and again the influence of the coating is analysed. The effect of a coating on the outer boundary is compared with that on the inner boundary. Specifically, during compression, coating on the outer boundary delays bifurcation compared with the uncoated case. On the other hand, when the coating is on the inner boundary, bifurcation is either delayed or advanced relative to the uncoated situation depending on the values of the bending stiffness and tube thickness parameters. Generally, bifurcation is delayed by an increase in the magnitude of the bending stiffness of the coating at fixed values of the other parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mechanics of indentation for piezoelectric thin films on elastic substrate

Frictionless normal indentation problem of rigid flat-ended cylindrical, conical and spherical indenters on piezoelectric film, which is either in frictionless contact with or perfectly bonded to an elastic half-space (substrate), is investigated. Both conducting and insulating indenters are considered. With Hankel transform, the general solutions of the homogeneous governing equations for the piezoelectric layer and the elastic half-space are presented. Using the boundary conditions for a vertical point force or a point electric charge, and the boundary conditions on the film/substrate interface, the Green’s functions can be obtained by solving sets of simultaneous linear algebraic equations. The solution of the indentation problem is obtained by integrating these Green’s functions over the contact area with unknown surface tractions or electric charge distribution, which will be determined from the boundary conditions on the contact surface between the indenter and the film. The solution is expressed in terms of dual integral equations that are converted to a Fredholm integral equation of the second kind and solved numerically. Numerical examples are also presented. The comparison between two film/substrate bonding conditions is made. It shows that the indentation rigidity of the film/substrate system is lower when the film is in frictionless contact with the substrate. The effects of the Young’s modulus and Poisson’s ratio of the elastic substrate, indenter electrical condition and indenter prescribed electric potential on the indentation responses are presented.     

Indentation responses of piezoelectric films ideally bonded to an elastic substrate

The influences of elastic substrate on the indentation force, contact radius, electric potential and electric charge responses of piezoelectric film/substrate systems are investigated by the integral transform method. The film is assumed to be ideally bonded to the substrate and the contact interaction between the indenter and the film is assumed to be frictionless, with three kinds of axisymmetric insulating and conducting indenters (i.e., punch, cone and sphere) considered. Obtained results show that when the ratio of the contact radius to the film thickness is close to zero, the influences of the elastic substrate disappear and the indentation behaviors converge to the piezoelectric half space solutions while the indentation responses approach the corresponding ones of elastic half space as the ratio gets to infinity. The transition between the piezoelectric and the elastic half space indentation solutions for the film/substrate system is quantified in terms of the film thickness and the elasticity of the substrate. Finite element analysis on an insulating sphere indentation is conducted to verify the numerical calculations and good agreement is observed. The obtained results are believed to be useful for developing experimental techniques to extract the material properties of piezoelectric film/substrate systems.     

A continuum model for size-dependent deformation of elastic films of nano-scale thickness

Ultra-thin elastic films of nano-scale thickness with an arbitrary geometry and edge boundary conditions are analyzed. An analytical model is proposed to study the size-dependent mechanical response of the film based on continuum surface elasticity. By using the transfer-matrix method along with an asymptotic expansion technique of small parameter, closed-form solutions for the mechanical field in the film is presented in terms of the displacements on the mid-plane. The asymptotic expansion terminates after a few terms and exact solutions are obtained. The mid-plane displacements are governed by three two-dimensional equations, and the associated edge boundary conditions can be prescribed on average. Solving the two-dimensional boundary value problem yields the three-dimensional response of the film. The solution is exact throughout the interior of the film with the exception of a thin boundary layer having an order of thickness as the film in accordance with the Saint-Venant’s principle.