The modulus of elasticity of steel - is it 200 GPa?

In cold-formed steel construction, the use of a range of thin, high strength steels (0.35 mm thickness and 550 MPa yield stress) has increased significantly in recent times. A good knowledge of the basic mechanical properties of these steels is needed for a satisfactory use of them. In relation to the modulus of elasticity, the current practice is to assume it to be about 200 GPa for all steel grades. However, tensile tests of these steels have consistently shown that the modulus of elasticity varies with grade of steel and thickness. It was found that it increases to values as high as 240 GPa for smaller thicknesses and higher grades of steel. This paper discusses this topic, presents the tensile test results for a number of steel grades and thicknesses, and attempts to develop a relationship between modulus of elasticity, yield stress and thickness for the steel grades considered in this investigation.

Influence of Joint Thickness and Mortar-Block Elastic Properties on the Strength and Stresses Developed in Soil-Cement Block Masonry

Soil-cement blocks are employed for load bearing masonry buildings. This paper deals with the study on the influence of bed joint thickness and elastic properties of the soil-cement blocks, and the mortar on the strength and behavior of soil-cement block masonry prisms. Influence of joint thickness on compressive strength has been examined through an experimental program. The nature of stresses developed and their distribution, in the block and the mortar of the soil-cement block masonry prism under compression, has been analyzed by an elastic analysis using FEM. Influence of various parameters like joint thickness, ratio of block to mortar modulus, and Poisson's ratio of the block and the mortar are considered in FEM analysis. Some of the major conclusions of the study are: (1) masonry compressive strength is sensitive to the ratio of modulus of block to that of the mortar (Eb/Em) and masonry compressive strength decreases as the mortar joint thickness is increased for the case where the ratio of block to mortar modulus is more than 1; (2) the lateral tensile stresses developed in the masonry unit are sensitive to the Eb/Em ratio and the Poisson's ratio of mortar and the masonry unit; and (3) lateral stresses developed in the masonry unit are more sensitive to the Poisson's ratio of the mortar than the Poisson's ratio of the masonry unit.

Elastic Properties of Boron Nitride Nanotubes and Their Comparison with Carbon Nanotubes

Boron Nitride Nanotubes (BNNTs) have alternating boron and nitrogen atoms in graphite like network and are strongly polar in nature due to a large charge on boron and nitrogen atoms. Hence electrostatic interactions are expected to play an important role in determining the elastic properties of BNNTs. In the absence of specific partial atomic charge information for boron and nitrogen, we have studied the elastic properties BNNTs varying the partial atomic charges on boron and nitrogen. We have computed Young modulus (Y) and Shear modulus (G) of BNNT as a function of the tube radius and number of walls using molecular mechanics calculation. Our calculation shows that Young modulus of BNNTs increases with increase in magnitude of the partial atomic charge on B and N and can be larger than the Young modulus of CNTs of same radius. This is in contrast to the earlier finding that CNTs has the largest tensile strength (PRL, 80, 4502, 1998). Shear modulus, on the other hand depends weakly on the magnitude of partial atomic charge and is less than the shear modulus of the CNT. The values obtained for Young modulus and Shear modulus are in excellent agreement with the available experimental results.

Elastic properties of fast ion conducting lithium based borate glasses

Elastic properties of Li2O-PbO-B2O3 glasses have been investigated using sound velocity measurements at 10 MHz. Four series of glasses have been investigated with different concentrations of Li2O, PbO and B2O3. The variations of molar volume have been examined for the influences of Li2O and PbO. The elastic moduli reveal trends in their compositional dependence. The bulk and shear modulus increases monotonically with increase in the concentration of tetrahedral boron which increases network dimensionality. The variation of bulk moduli has also been correlated to the variation in energy densities. The Poisson's ratio found to be insensitive to the concentration of tetrahedral boron in the structure. The experimental Debye temperatures are in good agreement with the expected theoretical values. Experimental observations have been examined in view, the presence of borate network and the possibility of non-negligible participation of lead in network formation. (c) 2005 Elsevier B.V. All rights reserved.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Interaction analysis of strip footing resting on a non-homogeneous elastic medium

In this paper, a plane stress solution for the interaction analysis of strip footing resting on (i) a non-homogeneous elastic half-plane and (ii) a non-homogeneous elastic layer resting on a rigid stratum has been presented. The analysis has been done using a combined analytical and FEM method in which the discretization of the half-plane is not required and thereby minimizes the computational efforts considerably. The contact pressure distribution and the settlement profile for the selected cases of varying modulus half-plane, which has more relevance to foundation engineering, have been given. Experimental verification through a photoelastic method of stress analysis has been carried out for the case of footing on Gibson elastic half-plane, and the contact pressure distribution thus obtained has been compared with the theoretical results. Copyright (C) 1996 Elsevier Science Ltd

Instabilities of soft elastic microtubes filled with viscous fluids: Pearls, wrinkles, and sausage strings

A linear stability analysis is presented to study the self-organized instabilities of a highly compliant elastic cylindrical shell filled with a viscous liquid and submerged in another viscous medium. The prototype closely mimics many components of micro-or nanofluidic devices and biological processes such as the budding of a string of pearls inside cells and sausage-string formation of blood vessels. The cylindrical shell is considered to be a soft linear elastic solid with small storage modulus. When the destabilizing capillary force derived from the cross-sectional curvature overcomes the stabilizing elastic and in-plane capillary forces, the microtube can spontaneously self-organize into one of several possible configurations; namely, pearling, in which the viscous fluid in the core of the elastic shell breaks up into droplets; sausage strings, in which the outer interface of the mircrotube deforms more than the inner interface; and wrinkles, in which both interfaces of the thin-walled mircrotube deform in phase with small amplitudes. This study identifies the conditions for the existence of these modes and demonstrates that the ratios of the interfacial tensions at the interfaces, the viscosities, and the thickness of the microtube play crucial roles in the mode selection and the relative amplitudes of deformations at the two interfaces. The analysis also shows asymptotically that an elastic fiber submerged in a viscous liquid is unstable for Y = gamma/(G(e)R) > 6 and an elastic microchannel filled with a viscous liquid should rupture to form spherical cavities (pearling) for Y > 2, where gamma, G(e), and R are the surface tension, elastic shear modulus, and radius, respectively, of the fiber or microchannel.

Contact instabilities of anisotropic and inhomogeneous soft elastic films

Anisotropy plays important roles in various biological phenomena such as adhesion of geckos and grasshoppers enabled by the attachment pods having hierarchical structures like thin longitudinal setae connected with threads mimicked by anisotropic films. We study the contact instability of a transversely isotropic thin elastic film when it comes in contact proximity of another surface. In the present study we investigate the contact stability of a thin incompressible transversely isotropic film by performing linear stability analysis. Based on the linear stability analysis, we show that an approaching contactor renders the film unstable. The critical wavelength of the instability is a function of the total film thickness and the ratio of the Young's modulus in the longitudinal direction and the shear modulus in the plane containing the longitudinal axis. We also analyze the stability of a thin gradient film that is elastically inhomogeneous across its thickness. Compared to a homogeneous elastic film, it becomes unstable with a longer wavelength when the film becomes softer in going from the surface to the substrate.

Model independent bounds on the modulus of the pion form factor on the unitarity cut below the omega pi threshold

We calculate upper and lower bounds on the modulus of the pion electromagnetic form factor on the unitarity cut below the omega pi inelastic threshold, using as input the phase in the elastic region known via the Fermi-Watson theorem from the pi pi P-wave phase shift, and a suitably weighted integral of the modulus squared above the inelastic threshold. The normalization at t = 0, the pion charge radius and experimental values at spacelike momenta are used as additional input information. The bounds are model independent, in the sense that they do not rely on specific parametrizations and do not require assumptions on the phase of the form factor above the inelastic threshold. The results provide nontrivial consistency checks on the recent experimental data on the modulus available below the omega pi threshold from e(+)e(-) annihilation and tau-decay experiments. In particular, at low energies the calculated bounds offer a more precise description of the modulus than the experimental data.

Transmission of elastic waves through a frictional boundary

Incident energy gets transmitted, reflected and absorbed across an interface in jointed rock mass leading to energy dissipation and alteration of waves. Wave velocities get attenuated during their propagation across joints and this behavior is studied using bender/extender element tests. The velocity attenuation and modulus reduction observed in experimental tests are modeled with three dimensional distinct element code and results are validated. Normal propagation of an incident shear wave through a jointed rock mass cause slip of the rock blocks if shear stress of wave exceeds the shear strength of the joint. As the properties of joint determine the transmission of energy across an interface, a parametric study is then conducted with the validated numerical model by varying the parameters that may determine the energy transmission across a joint using modified Miller's method. Results of the parametric study are analyzed and presented in the paper. (C) 2014 Elsevier Ltd. All rights reserved.

STM verification of the reduction of the Young's modulus of CdS nanoparticles at smaller sizes

We demonstrate the first STM evaluation of the Young's modulus (E) of nanoparticles (NPs) of different sizes. The sample deformation induced by tip-sample interaction has been determined using current-distance (I-Z) spectroscopy. As a result of tip-sample interaction, and the induced surface deformations, the I-z curves deviates from pure exponential dependence. Normally, in order to analyze the deformation quantitatively, the tip radius must be known. We show, that this necessity is eliminated by measuring the deformation on a substrate with a known Young's modulus (Au(111)) and estimating the tip radius, and afterwards, using the same tip (with a known radius) to measure the (unknown) Young's modulus of another sample (nanoparticles of CdS). The Young's modulus values found for 3 NP's samples of average diameters of 3.7, 6 and 7.5 nm, were E similar to 73%, 78% and 88% of the bulk value, respectively. These results are in a good agreement with the theoretically predicted reduction of the Young's modulus due to the changes in hydrostatic stresses which resulted from surface tension in nanoparticles with different sizes. Our calculation using third order elastic constants gives a reduction of E which scales linearly with 1/r (r is the NP's radius). This demonstrates the applicability of scanning tunneling spectroscopy for local mechanical characterization of nanoobjects. The method does not include a direct measurement of the tip-sample force but is rather based on the study of the relative elastic response. (C) 2014 Elsevier B.V. All rights reserved.

In-plane effective shear modulus of generalized circular honeycomb structures and bundled tubes in a diamond array structure

Use of circular hexagonal honeycomb structures and tube assemblies in energy absorption systems has attracted a large number of literature on their characterization under crushing and impact loads. Notwithstanding these, effective shear moduli (G*) required for complete transverse elastic characterization and in analyses of hierarchical structures have received scant attention. In an attempt to fill this void, the present study undertakes to evaluate G* of a generalized circular honeycomb structures and tube assemblies in a diamond array structure (DAS) with no restriction on their thickness. These structures present a potential to realize a spectrum of moduli with minimal modifications, a point of relevance for manufactures and designers. To evaluate G* in this paper, models based on technical theories - thin ring theory and curved beam theory - and rigorous theory of elasticity are investigated and corroborated with FEA employing contact elements. Technical theories which give a good match for thin HCS offer compact expressions for moduli which can be harvested to study sensitivity of moduli on topology. On the other hand, elasticity model offers a very good match over a large range of thickness along with exact analysis of stresses by employing computationally efficient expressions. (C) 2015 Elsevier Ltd. All rights reserved.

Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

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.