Identifying the viscoelastic properties of soft matter from the indentation response of a hard film-soft substrate system

The indentation technique is widely used in measuring the mechanical properties of soft matter at the microscale or nanoscale,but still faces challenges by these unique properties as well as the consequent strong surface adhesion, including the strong nonlinear effect, unclear judgment of the contact point, difficulties in estimating the contact area, and the risk of the indenter piercing the sample. Here we propose a two-step method to solve these problems: lay a hard film on a soft matter, and obtain the viscoelastic properties of this soft matter through the indentation response of this composite structure. We first establish a theoretical indentation model of the hard film-soft substrate system based on the theory of plates, elastic-viscoelastic correspondence principle and Boltzmann superposition principle. To verify the correctness of this method, we measure the mechanical properties of the methyl vinyl silicone rubber(MVSR) covered by a Cu nanofilm. Finally, we test the effectiveness and error sensitivity of this method with the finite element method(FEM). The results show that our method can accurately measure the mechanical properties of soft matter, while effectively circumventing the problems of the traditional indentation technique.     

固体力学中侵入问题的若干新进展

本文主要介绍了固体力学中侵入问题近10余年来的发展情况。重点综述了侵入断裂实验及理论研究的新成果;讨论了动静态侵入断裂的关系;简述了侵入方法在测定材料断裂韧性方面的应用。      

AFM nanoindentation of viscoelastic materials with large end‐radius probes

We used atomic force microscopy (AFM) nanoindentation to measure mechanical properties of polymers. Although AFM is generally acknowledged as a high‐resolution imaging tool, accurate quantification of AFM nanoindentation results is challenging. Two main challenges are determination of the projected area for objects as small as AFM tips and use of appropriate analysis methods for viscoelastic materials. We report significant accuracy improvements for modulus measurements when large end‐radius tips with appropriate cantilever stiffnesses are used for indentation. Using this approach, the instantaneous elastic modulus of four polymers we studied was measured within 30 to 40% of Dynamic Mechanical Analysis (DMA) results. The probes can, despite their size and very high stiffnesses, be used for imaging of very small domains in heterogeneous materials. For viscoelastic materials, we developed an AFM creep test to determine the instantaneous elastic modulus. The AFM method allows application of a nearly perfect stepload that facilitates data analysis based on hereditary integrals. Results for three polymers suggest that the observed creep in the materials has a strong plastic flow component even at small loads. In this respect, the spherical indenter tips behave like “sharp” indenters used in indentation studies with instrumented indenters. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1573–1587, 2009     

On the determination of the Young’s modulus of thin films using indentation tests

The main difficulty with the characterization of thin coatings using depth-sensing indentation tests is related to the determination of the contributions of the substrate and the film to the measured properties. In this study, three-dimensional numerical simulations of the Vickers hardness test are used in order to examine the influence of the elastic and plastic properties of the substrate and the film on the composite’s Young’s modulus results. The hardness of the film is equal to or higher than the substrate hardness. A study of the stress distributions and the indentation geometry of composites, film/substrate, was performed, taking into account the relative mechanical properties of the film and substrate. In addition, stress evolution during indentation was studied, in order to quantify the critical indentation depth under which the substrate is not elastically deformed. The accurate evaluation of the Young’s modulus of the films using weight functions is also examined: some of these have previously been proposed and one was introduced for this study. Two different fitting procedures were used to compare the results obtained from eight fictive film/substrate combinations using six weight functions. The first procedure, commonly used, considers the substrate’s modulus as a known parameter in the fitting process. In the second, the film and the substrate’s modulus are considered as unknown variables that are calculated simultaneously during the fitting process. The validity of the conclusions obtained using the fictive materials was checked by applying the weight functions to four real composites.     

纳米压痕过程的三维有限元数值试验研究

采用有限元方法模拟了纳米压痕仪的加、卸载过程，三维有限元模型考虑了纳米压痕仪的标准Berkovich压头．介绍了有限元模型的几何参数、边界条件、材料特性与加载方式，讨论了摩擦、滑动机制、试件模型的大小对计算结果的影响，进行了计算结果与标准试样实验结果的比较，证实了模拟的可靠性．在此基础上，重点研究了压头尖端曲率半径对纳米压痕实验数据的影响．对比分析了尖端曲率半径r＝0与r＝100nm两种压头的材料压痕载荷—位移曲线．结果表明，当压头尖端曲率半径r≠0时，基于经典的均匀连续介质力学本构理论、传统的实验手段与数据处理方法，压痕硬度值会随着压痕深度的减小而升高．     

Size-dependent sharp indentation—I: a closed-form expression of the indentation loading curve

In this paper, a closed-form expression of the size-dependent sharp indentation loading curve has been proposed based on dimensional analysis and the finite deformation Taylor-based nonlocal theory (TNT) of plasticity (Int. J. Plasticity 20 (2004) 831). The key issue is to link the results of FEM based on TNT plasticity with those obtained using conventional FEM by taking as the effective strain gradient, η, that presented in the work of Nix and Gao (J. Mech. Phys. Solids 46 (1998) 411), thus avoiding large-scale finite element computations using strain gradient plasticity theories. Two experiments carried out on 316 stainless-steel and pure titanium have been used to verify the effectiveness of the present analytical model; the results demonstrate that the present analytical expression of the size-dependent indentation loading curve corresponds very well to the experimental indentation loading curve. The empirical constant, α, in the Taylor model estimated from the experimental data has the correct order of magnitude. Also, the results presented in this part can be further applied to establish an analytical framework to extract the plastic properties of metallic materials with sharp indentation on a small scale where the size effect caused by geometrically necessary dislocations is significant. This will be discussed in detail in the second part of the paper.     

Effects of static electric field on the fracture behavior of piezoelectric ceramics

The paper gives an overview on experimental observations of the failure behavior of electrically insulating and conducting cracks in piezoelectric ceramics. The experiments include the indentation fracture test, the bending test on smooth samples, and the fracture test on pre-notched (or pre-cracked) compact tension samples. For electrically insulating cracks, the experimental results show a complicated fracture behavior under electrical and mechanical loading. Fracture data are much scattered when a static electric field is applied. A statistically based fracture criterion is required. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate ceramics and that the concepts of fracture mechanics can be used to measure the electrical fracture toughness. Furthermore, the electrical fracture toughness is much higher than the mechanical fracture toughness. The highly electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under purely electric loading, which is impossible under mechanical loading in the brittle ceramics. The project supported by an RGC grant from the Research Grant Council of the Hong Kong Special Administrative Region, China     

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.     

Structure-property relationships in a reactively coupled ductile matrix/brittle dispersed phase blend

Blends of t-butylaminoethyl methacrylate grafted polyethylene (PE-g-tBAEMA) with methyl methacrylate-methacrylic acid copolymer (PMMA-MAA) and polymethyl methacrylate (PMMA) were prepared in a Banbury type batch mixer. The effects of component proportions and processing conditions on the melt flow index, morphology, impact, and tensile properties of the resulting polymer blends were investigated. The interfacial chemical reaction was studied using Fourier transform infrared (FTIR) technique. It was observed that the melt index of the blends was reduced with increasing melt processing temperature and mixing time, indicating the formation of PE-g-PMMA block copolymer. New IR bands at 1554, 1628, 1800, and 1019 cm^?1 were observed only for PE-g-tBAEMA/PMMA-MAA, the reactive blends, but not for PE-g-tBAEMA/PMMA, the nonreactive blend. These IR bands were attributed to the amide, carboxylate anion and methacrylimide formation resulting from the chemical reaction between the secondary amine on the PE-g-tBAEMA/PMMA moiety and the carboxylic acid on PMMA-MAA segment. The morphology of the blends in various compositions was examined using scanning electron microscopy (SEM) and related to their mechanical properties. All of the blends have a domain structure whose morphology is strongly dependent on the concentration of the dispersed phase. Furthermore, the PE-g-tBAEMA/PMMA-MAA reactive blends were shown to have much finer morphology than the corresponding nonreactive blends. For the reactive polymer blends consisting of brittle particles dispersed in the ductile matrices, the PE-g-tBAEMA/PMMA-MAA, impact and tensile result higher than predicted by the additivity rule were observed. The toughening of polyethylene by PMMA was explained by a “cold-drawing” mechanism. The Young's modulus of the blends and the extent of interfacial adhesion were analyzed with Takayanagi and Sato-Furukawa's theories. © 1993 John Wiley & Sons, Inc.     

Indentation studies of alkali halides at elevated temperatures

The hardness of NaCl and KCl crystals has been estimated from the lengths of dislocation rosette formed around indentation at various temperatures up to 400°C. The hardness decreases with increasing temperature. This is due to the softening of the crystals at elevated temperatures which results in the easy movement of dislocations. The results are discussed using a few available relations which connect hardness to temperature. Arms of indentation dislocation rosette are well defined up to 300°C but around 400°C the rosette pattern is spread over a circular region. A possible mechanism is discussed.