Showing papers on "Elastic modulus published in 1998"

Measurement of mechanical properties by ultra-low load indentation

Abstract: Ultra-low load indentation, also known as nanoindentation, is a widely used tool for measuring the mechanical properties of thin films and small volumes of material. One of the great advantages of the technique is its ability to probe a surface and map its properties on a spatially resolved basis, sometimes with a resolution of better than 1 μm. In this paper, techniques for measuring mechanical properties by ultra-low load indentation techniques are reviewed and discussed. Emphasis is given to the use of sharp indenters and how they can be used to measure elastic modulus, hardness, and fracture toughness. These fundamental mechanical properties characterize the three primary modes of deformation in solids—elasticity, plasticity, and fracture.

Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques

Abstract: Finite element simulation of conical indentation of a wide variety of elastic-plastic materials has been used to investigate the influences of pileup on the accuracy with which hardness and elastic modulus can be measured by load and depth-sensing indentation techniques. The key parameter in the investigation is the contact area, which can be determined from the finite element results either by applying standard analysis procedures to the simulated indentation load-displacement data, as would be done in an experiment, or more directly, by examination of the contact profiles in the finite element mesh. Depending on the pileup behavior of the material, these two areas may be very different. When pileup is large, the areas deduced from analyses of the load-displacement curves underestimate the true contact areas by as much as 60%. This, in turn, leads to overestimations of the hardness and elastic modulus. The conditions under which the errors are significant are identified, and it is shown how parameters measured from the indentation load-displacement data can be used to identify when pileup is an important factor.

Nano-indentation of polymeric surfaces

Abstract: This paper presents results of normal hardness, plasticity index and elastic modulus for a selection of organic polymers (a poly(methylmethacrylate), PMMA, a poly(styrene), PS, a poly(carbonate), PC, and an ultra-high molecular weight poly(ethylene), UHMWPE) obtained using the contact compliance method. The paper describes in detail the dependence of the imposed penetration depth, the maximum load and the deformation rate upon the hardness and elastic modulus values for these polymeric surfaces; typical penetration depths range from about 10 nm to m where the imposed loads are less than 300 mN. The results show a considerable strain-rate hardening effect for the present systems and possibly a peculiarly harder response of these materials at the near-to-surface (submicron) layers. The paper includes considerations of a practical nature which are drawn in order to overcome some intrinsic limitations of this technique when it is used for polymeric surfaces, especially for a creeping phenomenon which may be observed at the incipient unloading experimental segments. The appropriateness of using a tip calibration constructed upon hard substrates when indenting polymers is reviewed at the conclusion of the paper.

Measuring the Elastic Properties of Thin Polymer Films with the Atomic Force Microscope

Abstract: The elastic properties of thin gelatin films were investigated with the atomic force microscope (AFM). The degree of swelling and thus the softness of the gelatin can be tuned by immersing it in mixtures of propanol and water. Therefore, we have chosen gelatin films as a model system to characterize the measurement of elasticity of thin and soft samples. The major aim of this study was to investigate the influence of the film thickness on the apparent elastic (Young's) modulus. Thus, we prepared wedge-shaped samples with a well-defined thickness of up to 1 μm. The Young's modulus of our samples was between 1 MPa and 20 kPa depending on the degree of swelling. The elasticity was calculated by analyzing the recorded force curves with the help of the Hertz model. We show that the calculated Young's modulus is dependent on the local film thickness and the applied loading force of the AFM tip. Thus, the influence of the hard substrate on the calculated softness of the film can be characterized as a function of...

Relationships between hardness, elastic modulus, and the work of indentation

Abstract: The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

Evaluation of Young's Modulus of Carbon Nanotubes by Micro-Raman Spectroscopy

Abstract: Micro-Raman spectroscopy is used to monitor the cooling-induced compressive deformation of carbon nanotubes embedded in an epoxy matrix. Young’s modulus of single- and multiwall nanotubes may then be derived from a concentric cylinder model for thermal stresses, using the D*-band shift for each tube type. The resulting values of the elastic moduli are in very good agreement with predicted theoretical values, and with the published experimental data set of Treacy et al., Nature (London) 381, 678 (1996).

Feasibility study of a passive smart self-healing cementitious composite

Abstract: The basic concept of a passive smart-healing cementitious composite has been demonstrated, in the laboratory, to be feasible. The basic elements of this smart material include the sensors and actuators in the form of controlled microcracks and hollow glass fibers carrying air-curing chemicals. Controlled microcracking is offered by a strain-hardening engineered cementitious composite developed previously. The mechanisms of sensing and actuation are revealed through in situ environmental scanning electron microscopy observations. The self-healing effectiveness is confirmed by measurement of the elastic modulus of the composite. The elastic modulus is found to regain its original value in a repeat loading subsequent to damage in a first load cycle.

Dynamic shear modulus of a semiflexible polymer network

Abstract: We construct a model for the dynamic shear modulus $G(\ensuremath{\omega})$ of entangled or crosslinked networks of semiflexible polymer that can account for the high-frequency scaling behavior, $G(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{3/4},$ that has recently been observed in solutions of the biopolymer $F$-actin. As we argue, this behavior should not be unique to F-actin, but rather should be a clear characteristic of semiflexible polymers in general. We also report molecular dynamics simulations that support the single filament response that is the basis of our model for the network shear modulus.

On Viscoelastic, Birefringent, and Swelling Properties of Laponite Clay Suspensions: Revisited Phase Diagram

Abstract: Relations between thermodynamics, structural, and mechanical properties of Laponite suspensions were recently discussed in the literature. One important issue concerning the liquid/gel transition of the Laponite suspensions is to understand why a mechanical gel appears concomitantly with what appears as an incomplete nematic transition. To get some insight, we first give a more extended characterization of the viscoelastic properties of these suspensions near the liquid/gel transition. For this purpose, stress relaxation experiments are compared to direct determinations of the viscoelastic modulus in the frequency domain. This permits the following of viscoelastic properties, in the linear regime, on a very extended scale, from 10-5 to 102 rad/s. The data show that the relaxation mechanisms are very slow and are compatible with the presence of a large scale structural organization compared to the elementary particle size. The elastic modulus follows the power law: G‘ = A(C − C0)α. Only the concentration ...

Mechanical properties of silica aerogels

Abstract: Aerogels are extremely low density solids that are characterized by a high porosity and pore sizes in the order of nanometers The mechanical behavior of silica aerogel was investigated with hardness, compression, tension and shear tests The influences of testing conditions, storage environment and age were examined, with particular attention paid to the effects of processing parameters, including fiber-reinforcement Good correlation was found between hardness and compressive strength over a wide range of processing parameters Increasing fiber reinforcement generally retarded shrinkage during fabrication and yielded smaller matrix densities for a given target density For a given fiber content, hardness, compressive strength and elastic moduli increased and strain at fracture decreased with increasing matrix density In the lower ranges of matrix density, fiber reinforcement increased strain at fracture and elastic moduli The mechanical response was also sensitive to environment and storage history With age, the compressive strength and elastic moduli increased while the strain at fracture decreased Tension and shear results indicate that shear strength of aerogels exceeds tensile strength which is consistent with brittle materials response

Micromechanical Properties of Elastic Polymeric Materials As Probed by Scanning Force Microscopy

Abstract: Scanning force microscopy (SFM) was used for probing micromechanical properties of compliant polymeric materials. Classic models of elastic contacts, Sneddon's, Hertzian, and JKR, were tested for various indentation depths and for a variety of polymeric materials. We selected extremely compliant polyisoprene rubbers (Young's modulus, E = 1−3 MPa), elastic polyurethanes (E = 5−50 MPa), and hard surfaces of polystyrene (PS) and polyvinylchloride (PVC) (E = 1−5 GPa). Both Sneddon's and Hertzian elastic models gave consistent and reliable results in the range of indentation depths up to 200 nm which are close to JKR solution. Close correlation is observed between absolute values of elastic moduli determined by SFM and known values for bulk materials.

Axisymmetric adhesion tests of soft materials

Abstract: We describe a general, linearized fracture mechanics analysis for studying the adhesive properties of elastic, low modulus materials Several adhesion tests are described, but all involve an elastic material which is brought into contact with a rigid surface along an axis of radial symmetry Relationships between the load, displacement, and radius of the circular contact area between the two materials are described These relationships involve the elastic modulus of the compliant material, the energy release rate (or adhesion energy) and various parameters which characterize the geometry of interest The ratio of the contact radius to the thickness of the elastic material is shown to be a particularly important parameter After reviewing some general concepts relevant to the adhesion of soft polymeric materials, we describe the fracture mechanics analysis, and provide examples from our own work on the adhesion of elastomers, thermoreversible gels and pressure sensitive adhesives

Biomorphic cellular silicon carbide ceramics from wood : II. Mechanical properties

Abstract: Silicon carbide ceramics with anisotropic pore microstructures pseudomorphous to wood were obtained by liquid Si infiltration of porous carbonized wood templates. Depending on the initial cellular microstructure of the various kinds of wood (ebony, beech, oak, maple, pine, balsa) ceramic materials of different density, pore structure and degree of anisotropy were obtained. Strength and elastic modulus of the pyrolyzed carbon preform and of the final silicon carbide ceramic were measured in different loading directions with respect to the initial cell orientation, e.g. axial, radial and tangential. Generally, the mechanical properties increase with fractional density. Strength and strain-to-failure in axial direction exhibit significantly higher values compared to loading in radial and tangential directions. The orientation dependence of microstructure-property relations may become important for the development of advanced anisotropic light weight structural materials.

Modelling drying shrinkage in reconstructed porous materials: application to porous Vycor glass

Abstract: A three-dimensional representation of the microstructure of porous Vycor glass was generated from a transmission electron micrograph, and was analysed to compute the locations of all capillary-condensed water as a function of relative humidity. On solid surfaces where capillary-condensed water was not present, an adsorbed water layer, whose thickness is a function of relative humidity, was placed. As a function of relative humidity, fixed pressures were specified in all capillary-condensed water, and the change in specific surface free energy with relative humidity was taken into account for the adsorbed water layers. New finite-element codes were developed to determine the drying shrinkage, in response to the changes in the specific surface free energy of the adsorbed water layers and to the fixed pressures in the capillary condensed water. Existing finite-element and finite-difference codes were used to evaluate the elastic moduli, the electrical and thermal conductivity, and the fluid permeability of the material. Bulk properties such as fluid permeability and electrical and thermal conductivity agreed well with experiment. By adjusting the elastic moduli of the solid backbone, which are not experimentally determined quantities, the computed porous glass elastic moduli, and computed low and high relative humidity shrinkage all agreed well with experimental values. At intermediate relative humidities, the agreement for shrinkage was worse, partly due to inaccuracies in the simulated water desorption curve, and partly due to the fact that water-induced swelling of the solid backbone, an effect that is probably present in the real material, was not taken into account in the model computations.

Estimation of single-crystal elastic moduli from polycrystalline x-ray diffraction at high pressure: application to FeO and Iron

Abstract: X-ray diffraction data obtained under nonhydrostatic compression of a polycrystalline sample yield an estimate of the single-crystal elasticity tensor of the material when analyzed using appropriate equations. The analysis requires as input the aggregate shear modulus from independent measurements. The high-pressure elastic moduli of face-centered-cubic FeO, body-centered-cubic iron (a-Fe), and the pressure-induced hexagonal close-packed iron (e-Fe) are obtained. This analysis currently provides the only method of determining single-crystal elasticity tensors in the megabar pressure range and of studying elasticity of very high-pressure phases. [S0031-9007(98)05436-2]

Viscoelastic properties of demineralized human dentin measured in water with atomic force microscope (AFM)-based indentation.

Abstract: Using an atomic force microscope (AFM) with an attachment specifically designed for indentation, we measured the mechanical properties of demineralized human dentin under three conditions: in water, in air after desiccation, and in water after rehydration. The static elastic modulus (E(h)r = 134 kPa) and viscoelastic responses (tau(epsilon) = 5.1 s and tau(sigma) = 6.6 s) of the hydrated, demineralized collagen scaffolding were determined from the standard linear solid model of viscoelasticity. No significant variation of these properties was observed with location. On desiccation, the samples showed considerably larger elastic moduli (2 GPa), and a hardness value of 0.2 GPa was measured. Upon rehydration the elastic modulus decreased but did not fully recover to the value prior to dehydration (381 kPa).

An interface model for the prediction of Young's modulus of layered silicate‐elastomer nanocomposites

Abstract: Recent experiments on layered silicate-elastomer nancomposites by Burnside and Giannelis have shown that there is a discrepancy between theoretical modulus predictions and experimental modulus measurements. A theory is proposed to explain this discrepancy. We hypothesize that the discrepancy is due to imperfect bonding between the matrix/inclusion interface which effectively reduces the aspect ratio and the volume fraction of the inclusion. We use a simple interface model to quantify the imperfect interfacial bonding. From this model, we introduce the concept of the effective aspect ratio and effective volume fraction of the inclusions. These effective quantities depends on a single material parameter, namely, the constant interfacial shear stress, τ. The interfacial shear stress for the elastomer-silicate nanocomposites is found by fitting the theory to the experimentally measured modulus of Burnside and Giannelis. The interfacial shear stress is in the range of thousands of Pascals. For the elastomer-silicate nanocomposite systems considered here, the interfacial shear stress can be decomposed into two parts; intrinsic shear stress τ i and frictional shear stress τ f . The intrinsic interfacial shear stress τ i depends only on the volume fraction of inclusions and decreases with increasing volume fraction of inclusions. On the other hand, the frictional shear stress τ f is found to increase linearly with the applied strain. Since the mean stress is also proportional to the applied strain, this gives rise to an effective coefficient of friction, which is found to be 0.0932 for the nanocomposite system considered here.

Morphological study on poly-p-phenylenebenzobisoxazole (PBO) fiber

Abstract: Morphological survey on new PBO fiber (Zylon®) was conducted by X-ray and transmission electron microscopic studies. Crystal size, orientation of the crystal, fibrils, microvoids, and fine structure were discussed. It was found that the molecule in the fiber showed high orientation (more than 0.99 in Hermann's orientation function for heat-treated fiber) and relatively small crystal sizes in the longitudinal (160 A) and the transverse (110 A) directions. Crystal modulus estimated by extrapolation to perfect orientation on the plot of the fiber modulus as a function of fiber orientation (Northolt's method) shows discrepancy from the crystal modulus directly obtained by X-ray scattering. This discrepancy means that the Northolt's model is insufficient to describe the Young's modulus of PBO fiber. Microvoids elongated to the fiber direction were examined by small-angle X-ray scattering and transmission electron microscopic methods. The diameter of the microvoids was 20 A to 30 A and the fiber had a very thin microvoids-free layer (0.2 μm). Preferential orientation of the a-axis of crystal in the fiber was also confirmed. Summarizing these results, a structure model of the PBO fiber was proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 39–48, 1998

Effective stiffness tensor of composite media : II. Applications to isotropic dispersions

Abstract: Accurate approximate relations for the effective elastic moduli of two- and three-dimensional isotropic dispersions are obtained by truncating, after third-order terms, an exact series expansion for the effective stiffness tensor of d-dimensional two-phase composites (obtained in the first paper) that perturbs about certain optimal dispersions. Our third-order approximations of the effective bulk modulus Ke and shear modulus Ge are compared to benchmark data, rigorous bounds and popular self-consistent approximations for a variety of macroscopically isotropic dispersions in both two and three dimensions, for a wide range of phase moduli and volume fractions. Generally, for the cases considered, the third-order approximations are in very good agreement with benchmark data, always lie within rigorous bounds, and are superior to popular self-consistent approximations.