What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for 'piling-up' and 'sinking-in' of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and 'indentation size effect' is established.

纳米孪晶铜力学性能和尺度效应的研究

采用基于机制的应变梯度塑性的传统理论(CMSG),对具有不同尺寸的铜纳米晶粒及孪晶的应力-应变关系进行了有限元模拟.在分析中提出了孪晶薄层强化带的概念并用粘聚力模型模拟晶界的滑移和分离现象,给出了在单向拉伸条件下不同厚度孪晶薄层和不同材料参数对孪晶铜总体应力-应变关系的影响,同时也给出了晶粒中孪晶薄层取向分布对孪晶铜应力-应变关系的影响.数值模拟结果显示:随着晶粒尺寸和孪晶薄层间距的减小,应变梯度效应逐渐增强,材料强化效果越明显;孪晶薄层的取向分布对材料整体的力学性能有较大影响,并且随着晶粒及孪晶薄层间距的减小,孪晶薄层取向的影响也越来越小.最后,有限元计算结果与实验数据进行了对比分析.

Equivalent Model Of Expansion Of Cement Mortar Under Sulphate Erosion

The expansion property of cement mortar under the attack of sulfate ions is studied by experimental and theoretical methods. First, cement mortars are fabricated with the ratio of water to cement of 0.4, 0.6, and 0.8. Secondly, the expansion of specimen immerged in sulphate solution is measured at different times. Thirdly, a theoretical model of expansion of cement mortar under sulphate erosion is suggested by virtue of represent volume element method. In this model, the damage evolution due to the interaction between delayed ettringite and cement mortar is taken into account. Finally, the numerical calculation is performed. The numerical and experimental results indicate that the model perfectly describes the expansion of the cement mortar.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Surface-induced melting of metal nanoclusters

We investigate the size effect on melting of metal nanoclusters by molecular dynamics simulation and thermo dynamic theory based on Kofman's melt model. By the minimization of the free energy of metal nanoclusters with respect to the thickness of the surface liquid layer, it has been found that the nanoclusters of the same metal have the same premelting temperature T-pre = T-0 - T-0(gamma(su) - gamma(lv) - gamma(sl))/(rhoLxi) (T-0 is the melting point of bulk metal, gamma(sv) the solid-vapour interfacial free energy, gamma(sl) the liquid-vapour interfacial free energy, gamma(sl),l the solid-liquid interfacial free energy, p the density of metal, L the latent heat of bulk metal, and xi the characteristic length of surface-interface interaction) to be independent of the size of nanoclusters, so that the characteristic length of a metal can be obtained easily by T-pre, which can be obtained by experiments or molecular dynamics (MD) simulations. The premelting temperature T-pre of Cu is obtained by AID simulations, then xi is obtained. The melting point T-cm is further predicted by free energy analysis and is in good agreement with the result of our MD simulations. We also predict the maximum premelting-liquid width of Cu nanoclusters with various sizes and the critical size, below which there is no premelting.

冲击剪切载荷下SiC_P/6151Al复合材料变形局部化及增强颗粒尺寸效应

利用特殊设计的“hat shape”试样，在分离式Hopkinson压杆和MTS通用材料试验机上实验研究了颗粒尺寸和应变率对颗粒增强金属基复合材料（SiC_P/6151Al）变形局部化行为的影响。结果表明：颗粒尺寸对复合材料的变形强化与变形局部化行为有显著影响。具体表现为：颗粒越小，复合材料流动应力越高，即强化效果越好；另一方面，对受载试样的微观检测发现，颗粒越小，复合材料剪切变形局部分越明显。同时发现，冲击载荷（高应变率）下复合材料更容易发生变形局部化。

颗粒增强复合材料的界面开裂与尺度效应

采用基于Huang等提出的塑性应变梯度传统理论发展的有限元方法，模拟了颗粒增强金属基复合材料的界面开裂与颗粒尺度效应．分别针对考虑颗粒与基体间界面开裂和不开裂两种情况进行分析，并将考虑界面开裂的模拟结果与实验结果进行比较，证明了模型的有效性，同时也获得应变梯度理论中所包含的材料特征尺度参量的取值．

EQUIVALENT MODEL OF EXPANSION OF CEMENT MORTAR UNDER SULPHATE EROSION

The expansion property of cement mortar under the attack of sulfate ions is studied by experimental and theoretical methods. First, cement mortars are fabricated with the ratio of water to cement of 0.4, 0.6, and 0.8. Secondly, the expansion of specimen immerged in sulphate solution is measured at different times. Thirdly, a theoretical model of expansion of cement mortar under sulphate erosion is suggested by virtue of represent volume element method. In this model, the damage evolution due to the interaction between delayed ettringite and cement mortar is taken into account. Finally, the numerical calculation is performed. The numerical and experimental results indicate that the model perfectly describes the expansion of the cement mortar.

The effects of capillary force in micro or nano-indentation

Models describing wet adhesion between indenters and substrates joined by liquid bridges are investigated. The influences of indenter shapes and various parameters of structures on capillary force are focused. In the former, we consider several shapes, such as conical, spherical and truncated conical indenter with a spherical end. In the latter, the effects of the contact angle, the environmental humidity, the gap between the indenter and the substrate, etc. are included. Different dependences of the capillary force on the indenter shapes and the geometric parameters are observed. Most interesting finding is that applying the present results to micro- and nano-indentation experiments shows the size effect in indentation hardness not produced but underestimated by the effects of capillary force.(4 refs)

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.

Mechanics of metallic foams: A fractal approach

A fractal approach was proposed to investigate the meso structures and size effect of metallic foams: For a series At foams of different relative densities, the information dimension method was applied to measure meso structures. The generalized sierpinski carpet was introduced to map the meso structures of the foam according to specific dimension. The results show that the fractal-based model can not only reveal the variation of yield strength with specimen size, but also bridge the meso structures and mechanical proper-ties of Al foams directly. Key words: metallic foams; fractal; size effect; meso structures

Prevalence Of Shear Banding In Compression Of Zr41Ti14Cu12.5Ni10Be22.5 Pillars As Small As 150 Nm In Diameter

Recently, the size dependence of mechanical behaviors, particularly the yield strength and plastic deformation mode, of bulk metallic glasses (BMG) has created a great deal of interest. Contradicting conclusions have been drawn by different research groups, based on various experiments on different BMG systems. Based on in situ compression transmission electron microscopy (TEM) experiments on Zr41Ti14Cu12.5Ni10Be22.5 (Vit 1) nanopillars, this paper provides strong evidence that shear banding still prevails at specimen length scales as small as 150 nm in diameter. This is supported by in situ and ex situ images of shear bands, and by the carefully recorded displacement bursts under load control its well as load drops under displacement control. Finite element modeling of the stress state within the pillar shows that the unavoidable geometry constraints accompanying such experiments impart a strong effect on the experimental results, including non-uniform stress distributions and high level hydrostatic pressures. The seemingly improved compressive ductility is believed to be due to such geometry constraints. Observations underscore the notion that the mechanical behavior of metallic glasses, including strength and plastic deformation mode, is size independent at least in Vit 1. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

New Strain Gradient Theory And Analysis

A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments.

A surface energy model and application to mechanical behavior analysis of single crystals at sub-micron scale

Size effects of mechanical behaviors of materials are referred to the variation of the mechanical behavior due to the sample sizes changing from macroscale to micro-/nanoscales. At the micro-/nanoscale, since sample has a relatively high specific surface area (SSA) (ratio of surface area to volume), the surface although it is often neglected at the macroscale, becomes prominent in governing the energy effect, although it is often neglected at the macroscale, becomes prominent in governing the mechanical behavior. In the present research, a continuum model considering the surface energy effect is developed through introducing the surface energy to total potential energy. Simultaneously, a corresponding finite element method is developed. The model is used to analyze the axial equilibrium strain problem for a Cu nanowire at the external loading-free state. As another application of the model, from dimensional analysis, the size effects of uniform compression tests on the microscale cylinder specimens for Ni and Au single crystals are analyzed and compared with experiments in literatures. (C) 2009 Elsevier B.V. All rights reserved.

基于分形的泡沫金属细观结构与尺寸效应研究

提出采用分形理论对泡沫金属的细现结构及尺寸效应进行研究的方法.针对一系列具有不同相对密度和细观结构的泡沫铝,证明了其细观结构在一定尺度内符合分形特征,比较了小岛分维、计盒分维和信息分维等算法对泡沫金属分形表征的适用性,分析了细观结构特征对分维的影响.结合推广的sierpinski垫片模型研究了泡沫铝的屈服强度与分维的联系,建立了泡沫铝屈服强度的尺寸效应模型.研究结果表明,由于引入了表征细现结构特征的分形维数,该模型除能表征屈服强度随试样尺寸的变化规律外,还在一定程度上直接反映了泡沫金属细观结构特征对力学性能的影响.