Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation

The normalized relaxation modulus represents a salient feature of viscoelastic materials and its determination is of great significance for various applications. From the normalized relaxation modulus, for instance, one can derive the loss factor of a viscoelastic polymer and judge whether a material is suitable for damping applications or not. By using dimensional analysis and the elastic–viscoelastic correspondence principle, the normalized relaxation function of a linear viscoelastic material obtained from indentation relaxation tests is shown to depend only on the indentation load but not on the indenter geometry and the shape of the indented solid. The result could enable circumvention of the difficulties encountered in the calibration of the indenter geometry and the preparation of indented samples. Numerical simulations are performed on a number of cases of practical interest, including the spherical indentation test of a soft layer lying on a rigid substrate, a flat punch indenter indenting into a soft layer with a rough surface bonded to a rigid substrate, a rigid indenter with irregular shape indenting into a particle, inclined contact of a cylindrical indenter with a cylinder, and indentation of porous substrates. The numerical examples demonstrate that the conclusion from the theoretical analysis is valid for all these situations.     

FeCrNiCoCu纳米压痕性能的分子动力学研究

纳米压痕是研究金属特性最广泛的方法之一.因此,本文采用分子动力学方法研究了晶粒数、压痕半径和压痕速度对FeCrNiCoCu压痕性能的影响.结果表明,晶粒数从4增加到16,杨氏模量和硬度值逐渐减小,呈现反Hall-Petch现象;随着压头半径的增加,杨氏模量增大,硬度受接触面积的影响较大而减小,较大的压头半径有利于模型内部位错的产生和扩展;压入速度对杨氏模量和硬度的影响微弱,压入速度越快,位错密度越低,位错传播速度越慢.本工作以期为FeCrNiCoCu的研究提供理论指导.     

利用分子动力学方法铁素体-渗碳体相界面效应探究

珠光体是十分重要的组织结构,因此本文构建了含铁素体-渗碳体相界面的模型,并采用分子动力学模拟方法模拟纳米压入的过程。通过对模拟结果的力学性能和组织结构分析,探究了铁素体-渗碳体相界面效应。研究发现,距铁素体-渗碳体晶界不同距离（位置压入）,在压入最初阶段,压头载荷随着压头与晶界距离的增大而增大,当压入深度达到一定深度后,载荷随着距离的增大而减小。杨氏模量和最大剪切模量受压头尖端下方原子结构的直接影响,硬度受到结构完整性和类型的共同影响。铁素体-渗碳体相界面影响了纳米压入过程中位错形核、增殖和扩展,宏观表现为在相同压入深度下,不同压入位置压头载荷的差异。     

Mechanical properties of sol-gel derived lead zirconate titanate thin films by nanoindentation

Lead zirconate titanate (PZT) thin films are deposited on platinized silicon substrate by sol-gel process. The crystal structure and surface morphology of PZT thin films are characterized by X-ray diffraction and atomic force microscopy. Depth-sensing nanoindentation system is used to measure mechanical characteristics of PZT thin films. X-ray diffraction analyses confirm the single-phase perovskite structures of all PZT thin films. Nanoindentation measurements reveal that the indentation modulus and hardness of PZT thin films are related with the grain size and crystalline orientation. The increases of the indentation modulus and hardness with grain size are observed, indicating the reverse Hall-Petch effect. Furthermore, the indentation modulus of (1 1 1)-oriented PZT thin film is higher than those of (1 0 0)- and random-oriented films. The consistency between experimental data and numerical results of the effective indentation moduli for fiber-textured PZT thin films using Voigt-Reuss-Hill model is obtained.     

Numerical study of pile-up in bulk metallic glass during spherical indentation

Pile-up around indenter is usually observed during instrumented indentation tests on bulk metallic glass. Neglecting the pile-up effect may lead to errors in evaluating hardness, Young’s modulus, stress-strain response, etc. Finite element analysis was employed to implement numerical simulation of spherical indentation tests on bulk metallic glass. A new model was proposed to describe the pile-up effect. By using this new model, the contact radius and hardness of Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5 bulk metallic glass were obtained under several different indenter loads with pile-up, and the results agree well with the data generated by numerical simulation. Supported by the National Natural Science Foundation of China (Grant Nos 10725211, 10721202 and 10472119) and the Key Project of Chinese Academy of Sciences (Grant Nos KJCX2-YW-M04 and KJCX-SW-L08)     

Experimental and numerical approach on interfacial properties of W/Al bilayer films for electronic devices manufacturing

The aim of this article is to provide a systematic method for performing experimental tests and theoretical evaluations on interfacial adhesion properties of the W/Al bilayer thin films interface. Samples W/Al bilayer thin films assembly is deposited on the quartz glass by using radio frequency magnetron sputtering. Based on the analysis of the experimental indentation data, the elastic modulus and hardness of the sample are investigated. The test results show that both of the values are easily influenced by the indentation depth. At the meantime, a finite element model is built to simulate the interface mechanical properties. The analysis shows that stress is mainly centralized close to the indenter and the maximum stress occurs in the lower layer Al film, not in the upper W film. The comparison between the experiment and the simulation shows the validity of the test and the modeling of each other to a certain extent. The investigation builds a basis for future work such as the fabrication of W/Al bilayer thin films for micro/nano manufacturing.     

带玻璃衬垫的硅泡沫薄膜压痕理论的近似解析与数值研究

基于弹性和多胞/泡沫固体理论,用近似解析和数值方法研究了带玻璃衬垫的硅多胞/泡沫薄膜压痕问题.研究的重点在于考察接触区的压力分布和压痕临界深度ε_c,并将计算得到的理论结果与实验结果进行了对比,两者基本一致.为了对这类薄膜结构系统完整性作合理的评估,分析了多胞/泡沫材料变形和破损机理,由此提出了压痕能概念并给出了相应的解析表达式. 关键词： 薄膜 材料试验 固体的力学性质     

Mechanical properties of thin films of hydrogenated silicon and their relationship with microstructure

Thin films of hydrogenated silicon were deposited on glass and single-crystalline silicon substrates using a capacitively coupled radio-frequency plasma-enhanced vapor-deposition system with the help of direct-current bias stimulation. Micro-Raman scattering was applied to investigate the microstructure of the thin films obtained. The crystalline volume fraction, X _c, was obtained from the Raman spectra. Microscopic mechanical characterization of the thin films was carried out by nanoindentation based on the conventional depth-sensing indentation method. An analytical relation between X _c and the elastic modulus was thereby established. The elastic modulus of the film on a glass substrate was found to be lower than that of the film on a monocrystalline silicon substrate with the same X _c. The grain size of a phosphorus-doped thin film was smaller than that of the intrinsic one, with greater ordering of the grains and X _c was found to be usually above 40%. A film with boron doping was on the opposite side, with X _c usually below 40%. In the phosphorus-doped, intrinsic, and boron-doped films, the elastic moduli were lower when the X _c values were 45%, 30%, and 15%, respectively.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

氢化硅薄膜介观力学行为及其与微结构内禀关联特性

使用等离子体增强化学气相沉积系统，在射频和直流负偏压的双重激励下制备了本征和掺杂后的氢化硅薄膜.利用拉曼谱对薄膜进行了微结构分析，用纳米压痕系统研究了薄膜的介观力学行为.研究表明：制备于玻璃衬底上的氢化硅薄膜，由于存在非晶态的过渡缓冲层，弹性模量小于相应的制备于单晶硅衬底的薄膜.对于掺杂的氢化硅薄膜，由于磷的掺入使得薄膜晶粒细化、有序度提高，薄膜的晶态比一般在40％以上.而硼的掺入，薄膜晶态比减小，一般低于40％.同时发现，掺磷、本征和掺硼的氢化硅薄膜分别在晶态比为45％，30％和15％左右处，弹性模量较 关键词： 氢化硅薄膜 拉曼谱 弹性模量 晶态比     

Predictions of Young's Modulus of Polymer Composites Reinforced with Short Natural Fibers

Polymers reinforced with natural fibers are beneficial to prepare biodegradable composite materials. A new expression for the Young's modulus of short, natural fiber (SNF) reinforced polymer composites was derived based on a micro-mechanical model. The Young's moduli of poly(lactic acid) reinforced with reed fibers and low-density polyethylene (LDPE) reinforced with sisal fibers, from literature data, were estimated in the fiber weight fraction range from 0 to 50% using the equation and both the compounding rule and the Halpin–Tsai equation, and the estimations were compared with the reported measured data. The results showed that the predictions of the Young's moduli by means of the new Young's modulus equation were close to the measured data from the low density polyethylene/sisal fiber composites, as well as the poly(lactic acid)/reed composites at high fiber concentration. Comparing with other Young's modulus equations, the new Young's modulus equation would be more convenient to use owing to the parameters in the equation being easily determined.     

Investigation of material properties of thin copper films through finite element modelling of microindentation test

Technology processes of thin metal films deposition are entailed with changes in material’s microstructure. As a result, deposited films often are characterized with material properties, which are different from these of the original bulk material. Determination of these material characteristics is of big importance for practice. In the present work the material properties of thin bright copper film with known depth were investigated. The film was deposited electrochemically over substratum composed of metallurgic brass alloy (CuZn36). Based on the results from microindentation test the load-displacement curve is obtained after the indenter is unloaded and the imprint diameter is measured. Consequently the process of indentation was modelled numerically. The numerical simulation is based on the finite element model of the indentation process. As a result of the simulation the load-displacement curve was obtained numerically for a certain set of material parameters. The trial-error approach is applied to find most appropriate set which fit the experimental load-displacement curve. At the end results, which were obtained through numerical simulation give good coincidence with the experiment. Therefore the proposed method can be successfully applied for identification of material parameters of the accepted model. The proposed trial-error approach is appropriate for investigation of thin films with known thickness, deposited on a substrate with known material characteristics.     

Young's Modulus Characterization of Nano-Level Silicon Nanomembrane

Silicon nanomembrane (SiNM) has drawn great attention for the application in nanoelectrical devices as it shows excellent flexibility and is compatible with the integrated circuit process. The mechanical property measurement of the SiNM with nanoscale thickness is critical. A suspended SiNM (40 nm thick) for mechanical measurements is fabricated by transferring a chemically etched ultrathin monocrystalline silicon film from silicon on insulator wafer to a substrate with a multi-hole array. And then, the atomic force probe is utilized to load force on the free-standing SiNM to obtain a force deflection curve, and then the Young's modulus of such floating SiNM can be directly calculated based on the large deflection plane model. It shows that the Young's modulus of such SiNM is basically consistent with that of the bulk silicon. However, the SiNMs’ floating area significantly affects the results, i.e., the Young's modulus varies with the ratio of the suspended area diameter (i.e., hole diameter) to the film thickness. The Young's modulus is independent of hole diameter when the ratio is greater than 425. According to this relationship, the variation of Young's modulus can be predicted for arbitrary thick SiNMs and any transferable nanofilms.     

Quantitative assessment and prediction of contact area development during spherical tip indentation of glassy polymers

This paper describes the development of the contact area during indentation of polycarbonate. The contact area was measured in situ using an instrumented indentation microscope and compared with numerical simulations using an elasto-plastic constitutive model. The parameters in the model were obtained using macroscopic tests. Indentations were performed on samples with different thermal histories and at different speeds. For all cases, the numerical model correctly predicted the development of the contact area during indentation. For increasing strain rates, the contact area decreased at equal indentation depths. Annealing the samples resulted in a smaller contact area at equal indentation depth. Using only numerical simulation, it was also shown that pile-up around the indenter resulted from localization effects and was, thus, promoted by strain-softening properties of the indented material. Strain hardening, on the other hand, will tend to promote sink-in. Finally, we performed simulations of load relaxation during indentation. The results indicate that about 40% of the total observed relaxation may be assigned to plastic effects.     

Surface waves and mode conversion at a surface coated with an elastic heavy layer

A surface wave of frequency lying within bulk band of transverse waves is found in an elastic medium coated with a thin layer endowed with a surface mass density, surface Young's modulus and surface bending modulus. The wave is a particular case of surface resonance with infinite lifetime. In materials with negative Poisson's ratio (auxetics) the wave exists even for coating material with zero bending modulus, whereas with positive Poisson's ratio it requires the surface bending modulus to be larger than the surface Young's modulus. The manifestation of this wave in the reflection coefficient seems promising for fabrication of devices showing monochromator properties.     

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

Work of adhesion is the crucial material parameter for application of theories of adhesive contact. It is usually determined by experimental techniques based on the direct measurements of pull-off force of a sphere. These measurements are unstable due to instability of the load-displacement diagrams at tension, and they can be greatly affected by roughness of contacting solids. We show how the values of work of adhesion and elastic contact modulus of materials may be quantified using a new indirect approach (the Borodich?CGalanov (BG) method) based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Using numerical simulations it is shown that the BG method is simple and robust. The crucial difference between the proposed method and the standard direct experimental techniques is that the BG method may be applied only to compressive parts of the force-displacements curves. Finally, the work of adhesion and the elastic modulus of soft polymer (polyvinylsiloxane) samples are extracted from experimental load-displacement diagrams.     

Nanoindentation of hydrogenated amorphous silicon

Nanoindentation was carried out on thin films of hydrogenated amorphous silicon (a-Si:H) prepared by plasma-enhanced chemical vapor deposition. The composite values of elastic (Young's) modulus, E _c, and hardness, H _c, of the film/substrate system were evaluated from the load–displacement curves using the Oliver–Pharr approach. The film-only parameters were obtained employing the extrapolation of the depth profiles of E _c and H _c. Scanning probe microscopy was employed to image the nanoindenter impressions and to estimate the effect of film roughness and material pile-up on the testing results. It was established that the elastic modulus of thin a-Si:H films is in the range 117–131 GPa, which is lower than for crystalline silicon. In contrast, the values of hardness are in the range 12.2–12.7 GPa, which is comparable to crystalline silicon and higher than for hydrogen-free amorphous silicon. It is suggested that the plastic deformation of a-Si:H proceeds through plastic flow and it is the presence of hydrogen in the amorphous matrix that leads to a higher hardness.     

Mechanical Characterization of Protein Crystals

The mechanical properties (critical stress intensity factor, hardness and Young's modulus) of 4 crystalline materials (two proteins, lysozyme and glucose isomerase and two non‐proteins, glutamic acid and potassium sulphate) were measured with an indentation technique. It was found that the mechanical properties of lysozyme crystals depend on their state – dried, partly dried and moisture saturated – and their surroundings. The hardness, Young's modulus and the critical stress intensity factor of lysozyme crystals were observed to be much lower than those for the tested non‐proteins, leading to the conclusion that crystalline lysozyme is comparatively more fragile and softer. In combination the mechanical properties of lysozyme and the non‐proteins indicated that these materials were fairly brittle. Mechanical properties for crystals of the other protein, glucose isomerase, could not be quantified by indentation. However, qualitatively crystalline glucose isomerase was found to be more ductile and less fragile than crystalline lysozyme. The experimental findings were interpreted in terms of relative susceptibility to attrition and secondary nucleation in stirred industrial crystallizers.     

Analysis of the substrate effects of strain-hardening thin films on silicon under nanoindentation

Mechanical properties of thin films on substrates can be evaluated directly through nanoindentation. For a comprehensive study, thin films should be characterized via Young’s modulus, yield stress and strain-hardening exponent at constant temperature. In this paper, we evaluate these effects of thin films on silicon substrate through finite element analysis. Thin films, from soft to hard relative to the silicon substrate, are investigated in three categories: soft films on hard substrates, soft to hard films on no elastic mismatch substrates, and hard films on soft substrates. In addition to examining the load-displacement curve, the normalized hardness versus normalized indentation depth is checked as well to characterize its substrate effect. We found that the intrinsic film hardness can be acquired with indentation depths of less than 12% and 20% of their film thickness for soft films on hard substrates and for soft to hard films on no elastic mismatch substrates, respectively. Nevertheless, nanoindentation of hard films on soft substrates cannot determine the intrinsic film hardness due to the fact that a soft substrate cannot support a hard film. By examining the von Mises stresses, we discovered a significant bending phenomenon in the hard film on the soft substrate. PACS 61.43.Bn; 62.20.-x; 68.03.Hj; 68.05.Cf; 68.08.De