Experimental Verification And Theoretical Analysis Of The Relationships Between Hardness, Elastic Modulus, And The Work Of Indentation

The relationship between hardness (H), reduced modulus (E-r), unloading work (W-u), and total work (W-t) of indentation is examined in detail experimentally and theoretically. Experimental study verifies the approximate linear relationship. Theoretical analysis confirms it. Furthermore, the solutions to the conical indentation in elastic-perfectly plastic solid, including elastic work (W-e), H, W-t, and W-u are obtained using Johnson's expanding cavity model and Lame solution. Consequently, it is found that the W-e should be distinguished from W-u, rather than their equivalence as suggested in ISO14577, and (H/E-r)/(W-u/W-t) depends mainly on the conical angle, which are also verified with numerical simulations. (C) 2008 American Institute of Physics.

Nanoindentation of thin-film-substrate system: Determination of film hardness and Young's modulus

In the present paper, the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates; i.e. glass and silicon, are studied. Nanoindentation XP II and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young's modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, phi, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

Effective elastic modulus of bone-like hierarchical materials

A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.

Simple phenomenological determination of contact stiffness and elastic modulus of Ce-based bulk metallic glasses through nanoindentation

The viscoelastic deformation of Ce-based bulk metallic glasses (BMGs) with low glass transition temperature is investigated at room temperature. Contact stiffness and elastic modulus of Ce-based BMGs cannot be derived using the conventional Oliver-Pharr method [W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992)]. The present work shows that the time dependent displacement of unloading segments can be described well by a generalized Kelvin model. Thus, a modified Oliver-Pharr method is proposed to evaluate the contact stiffness and elastic modulus, which does, in fact, reproduce the values obtained via uniaxial compression tests. (c) 2007 American Institute of Physics.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

Intrinsic correlation between fragility and bulk modulus in metallic glasses

A systematic study on the available data of 26 metallic glasses shows that there is an intrinsic correlation between fragility of a liquid and bulk modulus of its glass. The underlying physics can be rationalized within the formalism of potential energy landscape thermodynamics. It is surprising to find that the linear correlation between the fragility and the bulk-shear modulus ratio exists strictly at either absolute zero temperature or very high frequency. Further analyses indicate that a real flow event in bulk metallic glasses is shear dominant, and fragility is in inverse proportion to shear-induced bulk dilatation. Finally, extension of these findings to nonmetallic glasses is discussed.

A comparative study of Young's modulus of single-walled carbon nanotube by CPMD, MD, and first principle simulations

Carbon nanotubes (CNTs), due to their exceptional magnetic, electrical and mechanical properties, are promising candidates for several technical applications ranging from nanoelectronic devices to composites. Young's modulus holds the special status in material properties and micro/nano-electromechanical systems (MEMS/NEMS) design. The excellently regular structures of CNTs facilitate accurate simulation of CNTs' behavior by applying a variety of theoretical methods. Here, three representative numerical methods, i.e., Car-Parrinello molecular dynamics (CPMD), density functional theory (DFT) and molecular dynamics (MD), were applied to calculate Young's modulus of single-walled carbon nanotube (SWCNT) with chirality (3,3). The comparative studies showed that the most accurate result is offered by time consuming DFT simulation. MID simulation produced a less accurate result due to neglecting electronic motions. Compared to the two preceding methods the best performance, with a balance between efficiency and precision, was deduced by CPMD.

An Instrumented Indentation Method for Young's Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young's modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young's modulus H (n) /E (r) and the ratio of elastic work/total work W (e)/W can be derived. Consequently, a method for Young's modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.

Distribution characteristics of (CS)-C-137 in wind-eroded soil profile and its use in estimating wind erosion modulus

Due to its inert reaction in soil system and distinctive vertical distribution in soil profile, caesium-137 (Cs-137) has been used as a tracer to assess wind erosion. In this study, 62 soil samples were collected from 4 sampling sites in Taipusi County, Inner Mongolia; Caesium-137 activities for those soil samples were measured using a gamma-ray spectrometry in Sichuan University, Chengdu. Distribution pattern of Cs-137 in vertical soil profile was different for different land use and land cover types. Caesium-137 was distributed homogeneously in plow layer of cropland, and negatively exponential in low to medium cover grassland. Distribution pattern in high covered grassland was represented by a peak at 2-4 cm soil depth followed by a negative exponential curve. Based on those findings, simplified mass balance model was chosen to estimate the rate of wind erosion for cropland, while profile distribution model was used for grassland. Estimated wind erosion rates were 7990, 4270 and 1808 Mg(.)km(-2.)a(-1) for cropland, low cover grassland and medium cover grassland, respectively. Wind erosion intensity correlated negatively with plant cover.

Calculation of bulk modulus on carbon nitrides with chemical bond method

The bulk moduli of some superhard materials were calculated by using the chemical bond method. For simple crystals, such as diamonds, c-BN, SiC, Si, BP, and Ge, the calculated results agree with experimental and theoretical values. For crystals of complex structure, such as beta-BC2N crystal and various structural C3N4 crystals, the results indicate that their bulk moduli are large, but do not exceed that of diamond.

Calculation of the bulk modulus of simple and complex crystals with the chemical bond method

The relation between the lattice energies and the bulk moduli on binary inorganic crystals was studied, and the concept of lattice energy density is introduced. We find that the lattice energy densities are in good linear relation with the bulk moduli in the same type of crystals, the slopes of fitting lines for various types of crystals are related to the valence and coordination number of cations of crystals, and the empirical expression of calculated slope is obtained. From crystal structure, the calculated results are in very good agreement with the experimental values. At the same time, by means of the dielectric theory of the chemical bond and the calculating method of the lattice energy of complex crystals, the estimative method of the bulk modulus of complex crystals was established reasonably, and the calculated results are in very good agreement with the experimental values.