Scaling Functions In Conical Indentation Of Elastic-Plastic Solids

The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young's modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young's modulus E and Poisson's ratio nu are known.

Microstructure Observation And Mechanical Behavior Modeling For Limnetic Nacre

In the present research, microstructure of a kind of limnetic shell (Hyriopsis cumingii) is observed and measured by using the scanning electron microscopy, and mechanical behavior experiments of the shell nacre are carried out by using bending and tensile tests. The dependence of mechanical properties of the shell nacre on its microstructure is analyzed by using a modified shear-lag model, and the overall stress-strain relation is obtained. The experimental results reveal that the mechanical properties of shell nacre strongly depend on the water contents of the limnetic shell. Dry nacre shows a brittle behavior, whereas wetting nacre displays a strong ductility. Compared to the tensile test, the bending test overestimates the strength and underestimates the Young's modulus. The modified shear-lag model can characterize the deformation features of nacre effectively.

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.

Effect of a laser pre-quenched steel substrate surface on the crack driving force in a coating-steel substrate system

A mechanical model of a coating/laser pre-quenched steel substrate specimen with a crack oriented perpendicular to the interface between the coating and the hardened layer is developed to quantify the effects of the residual stress and hardness gradient on the crack driving force in terms of the J-integral. It is assumed that the crack tip is in the middle of the hardened layer of the pre-quenched steel substrate. Using a composite double cantilever beam model, analytical solutions can be derived, and these can be used to quantify the effects of the residual stress and the hardness gradient resulting from the pre-quenched steel substrate surface on the crack driving force. A numerical example is presented to investigate how the residual compressive stress, the coefficient linking microhardness and yield strength and the Young's modulus ratio of the hardened layer to the coating influence the crack driving force for a given crack length. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The size-dependent bending elastic properties of nanobeams with surface effects

A theoretical model is presented to investigate the size-dependent bending elastic properties of a nanobeam with the influence of the surface relaxation and the surface tension taken into consideration. The surface layer and its thickness of a nanostructure are defined unambiguously. A three-dimensional (3D) crystal model for a nanofilm with n layers of relaxed atoms is investigated. The four nonzero elastic constants of the nanofilm are derived, and then the Young's modulus for simple tension is obtained. Using the relation of energy equilibrium, the size-dependent effective elastic modulus and effective flexural rigidity of a nanobeam with two kinds of cross sections are derived, and their dependence on the surface relaxation and the surface tension is analysed.

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.

Three-dimensional finite element analysis of composites with coated spherical inclusions

A three-dimensional finite element analysis has been used to determine the internal stresses in a three-phase composite. The stresses have been determined for a variety of interphase properties, the thicknesses of the interphase and the volume fractions of particles. Young's modulus has been calculated from a knowledge of these stresses and the applied deformation. The calculations show that stress distributions in the matrix and the mechanical properties are sensitive to the interphase property in the three-phase composites. The interfacial stresses in the three-dimensional analysis are in agreement with results obtained by an axisymmetric analysis. The predicted bulk modulus in three-dimensional analysis agrees well with the theoretical solution obtained by Qui and Weng, but it presents a great divergence from that in axisymmetric analyses. An investigation indicates that this divergence may be caused by the difference in the unit cell structure between two models. A comparison of the numerically predicted bulk and shear modulus for two-phase composites with the theoretical results indicates that the three-dimensional analysis gives quite satisfactory results.

关于Young-Laplace公式的吉布斯自由能证明

对于为论证球形液滴附加压强的Young-Laplace公式而设计的一个理想实验,有文献试图借助吉布斯自由能函数进行证明,本文给出符合这一条件的证明方法.

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.

Size-dependent elastic properties of Ni nanofilms by molecular dynamics simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

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.

Mechanics of adhesive contact on a power-law graded elastic half-space

We consider adhesive contact between a rigid sphere of radius R and a graded elastic half-space with Young's modulus varying with depth according to a power law E = E-0(z/c(0))(k) (0 < k < 1) while Poisson's ratio v remaining a constant. Closed-form analytical solutions are established for the critical force, the critical radius of contact area and the critical interfacial stress at pull-off. We highlight that the pull-off force has a simple solution of P-cr= -(k+3)pi R Delta gamma/2 where Delta gamma is the work of adhesion and make further discussions with respect to three interesting limits: the classical JKR solution when k = 0, the Gibson solid when k --> 1 and v = 0.5, and the strength limit in which the interfacial stress reaches the theoretical strength of adhesion at pull-off. (C) 2009 Elsevier Ltd. All rights reserved.

Adhesive behavior of two-dimensional power-law graded materials

In this paper, we investigate the adhesive contact between a rigid cylinder of radius R and a graded elastic half-space with a Young's modulus varying with depth according to a power-law, E = E-0(y/c(0))(k) (0 < k < 1), while the Poisson's ratio v remains constant. The results show that, for a given value of ratio R/C-0, a critical value of k exists at which the pull-off force attains a maximum; for a fixed value of k, the larger the ratio R/c(0), the larger the pull-off force is. For Gibson materials (i.e., k = 1 and v = 0.5), closed-form analytical solutions can be obtained for the critical contact half-width at pull-off and pull-off force. We further discuss the perfect stick case with both externally normal and tangential loads.