Showing papers on "Elastic modulus published in 1991"

Aspects of fracture in particulate reinforced metal matrix composites

Abstract: The tensile deformation and fracture behaviour of the aluminium alloy 6061 reinforced with SiC has been investigated. In the T4 temper plastic deformation occurs throughout the gauge length and the extent of SiC particle cracking increases with increasing strain. In the T6 temper strain becomes localised and particle cracking is more concentrated close to the fracture. The elastic modulus decreases with increasing particle damage and this allows a damage parameter to be identified. The fraction of SiC particles which fracture is less than 5%, and over most of the strain range the damage controlling the tensile ductility can be recovered, indicating that other factors, in addition to particle cracking are important in influencing tensile ductility. It is suggested that macroscopic fracture is initiated by the SiC particle clusters that are present in these composites as a result of the processing. The matrix within the clusters is subjected to high levels of triaxial stress due to elastic misfit and the constraints exerted on the matrix by the surrounding particles. Final fracture is then produced by crack propagation through the matrix between the clusters.

Softening of bulk modulus and negative Poisson's ratio near the volume phase transition of polymer gels

Abstract: The static bulk and shear modulus of poly (N‐isopropylacrylamide)/water gel (NIPA gel) have been obtained as a function of temperature by measuring the change of sample size induced by an applied tension. It is deduced that the method gives the static elastic moduli of gels to a good approximation except just above the discontinuous transition temperature T0, where the stress‐induced shift of T0 made the estimation of elastic strain impossible. Two kinds of NIPA gels with different polymer concentration and crosslinking density were used as samples, of which one undergoes a discontinuous volume phase transition and the other a continuous one. In both gels, the bulk modulus softens drastically towards the transition showing that the soft mode of this transition is a uniform and isotropic volume‐deformation mode. The shear modulus, on the other hand, shows only a small anomaly at the transition. The anomaly exhibited by the Poisson’s ratio σ is quite peculiar, i.e., it becomes negative and approaches −1 towards the critical point. It is shown that the results can be explained fairly well on the basis of the Flory‐type phenomenological theory extended to take into account the concentration dependence of the interaction parameter.

Increase in Mechanical Strength of Al–Y–Ni Amorphous Alloys by Dispersion of Nanoscale fcc-Al Particles

Abstract: Ni-base amorphous alloys with the homogeneous dispersion of nanoscale fcc-Ni particles have been produced in the composition range of 5 to 14 at%Si and 7 to 15%B. The particle size and interparticle spacing are 10 and 20 nm, respectively. The alloys exhibit tensile fracture strength (σ f ), Young's modulus (E) and hardness (H v ) which are higher than those of the corresponding amorphous single phase alloys, accompanying an increase in fracture elongation (∈ f )

Interface stresses and their effects on the elastic moduli of metallic multilayers.

Abstract: The embedded-atom method is used to calculate the surface stresses and the interface stresses for several fcc metals and interfaces between them. While the surface stresses are all positive (i.e., they tend to put the underlying crystal in compression), in several instances (e.g., in the Pt/Ni system) negative interface stresses are found. The effects of the interface stresses on the elastic moduli of metallic multilayers are discussed.

Hardness and elastic modulus of TiN based on continuous indentation technique and new correlation

Abstract: Young’s modulus and hardness of TiN films are reported. The films, deposited on 440C stainless steel, range between 0.25 and 1.0 μm in thickness. They fall to within 3% of stoichiometry and have a 〈111〉 texture. Within experimental resolution, the properties of films with different thickness are indistinguishable: calculated values of Young’s modulus and hardness are 550±50 GPa and 31±4 GPa, respectively. Properties are obtained from a continuous indentation technique. A new correlation is used for identifying whether all films have the same properties, independent of thickness, and for measuring hardness of thin films. The same correlation is utilized for measuring machine compliance and obtaining the profile of the indenter tip. An elasticity analysis aids in obtaining elastic modulus from compliance data.

Measurement and interpretation of stress in copper films as a function of thermal history

Abstract: Since copper has some advantages relative to aluminum as an interconnection material, it is appropriate to investigate its mechanical properties in order to be prepared in advance for possible problems, such as the cracks and voids that have plagued aluminum interconnect systems. A model previously used to interpret the behavior of aluminum films proves to be, with minor modification, also applicable to copper. Although the thermal expansion of copper is closer to that of silicon and, consequently, the thermally induced strains are smaller, the much larger elastic modulus of copper results in substantially higher stresses. This has implications for the interaction of copper lines with dielectrics.

The Determination of Surface Plastic and Elastic Properties by Ultra Micro-indentation

Abstract: An ultra micro-indentation system for investigating the elastic and plastic properties of surface coatings and near-surface materials is described. The instrument produces minute indentations by the application of loads to geometrically accurate pointed or spherical diamond indenters. Material properties are derived from records of the load and depth of penetration. Depth of penetration is measured with a resolution less than 1 nm. The force at initial contact can be substantially less than 0,1 mN. The instrument has a wide range of research and quality control applications which include the determination of the depth distribution of hardness and elastic modulus of hard and soft materials – TiN, gold and polymer films and coatings, for example. It also has applications in the determination of the workhardening index, in fracture mechanics and in exploring the material properties of small areas of individual phases in polyphased materials.

Open pore description of mechanical properties of ceramics

Abstract: A dependence of Young's modulus of elasticity on open porosity in ceramics is derived from an open-porosity model, which in the literature, is applied to salinity conductivity and fluid permeability in rocks. A random distribution of grain and pore size is assumed. The relation developed,E(p)=E o(1−"p)m, whereE is the modulus of elasticity of the porous ceramic,E o is the theoretical elastic modulus,p is the porosity andm is an exponent dependent on the tortuosity of the structure of the ceramic, adequately describes the dependence of the modulus of elasticity on porosity. The model is applied to the experimental data from several ceramics such as alumina, silicon nitride, silicon carbide, uranium oxide, rare-earth oxides, and YBa2Cu3O7−δ superconductor, and the value ofm is obtained for each case. We have shown thatm has a value of nearly 2 for sintered ceramics, unless sintering aids or hot pressing have been used during fabrication of the ceramic. Such additional procedures approximately double the magnitude ofm.

Limits of imaging resolution for atomic force microscopy of molecules

Abstract: The imaging resolution of an atomic force microscope operating in contact with a Langmuir–Blodgett (LB) film is predicted as a function of applied force, tip radius, adhesive force, and tip and film properties. The elastic modulus and the hardness of the LB film were measured using a nanoindenter and the imaging resolution is predicted using both a simple Hertzian elastic analysis and one that includes adhesive forces between the tip and the sample. For a small applied force (<1 nN) the resolution improves sharply as the tip radius and the adhesive force decrease. The onset of inelastic deformation, however, limits the resolution of the sharpest tips.

Tensile and Fatigue Behavior of Silicon Carbide Fiber‐Reinforced Aluminosilicate Glass

Abstract: The onset of damage accumulation in ceramic-matrix composites occurs as matrix microcracking and fiber/matrix debonding. Tension tests were used to determine the stress and strain levels to first initiate microcracking in both unidirectional and cross-ply laminates of silicon carbide fiber-reinforced aluminosilicate glass. Tension–tension fatigue tests were then conducted at stress levels below and above the matrix cracking stress level. At stress levels below matrix microcracking, no loss in stiffness occurred. At stresses above matrix cracking, the elastic modulus of the unidirectional specimens exhibited a gradual decrease during the first 10 000 cycles, and then stabilized. However, the cross-ply material sustained most of the damage on the first loading cycle. It is shown that fatigue life can be related to nonlinear stress–strain behavior of the 0° plies, and that the cyclic strain limit was approximately 0.3%.

Temperature Dependence of the Elastic Moduli of Monoclinic Zirconia

Abstract: We have used Brillouin scattering to measure the temperature dependence of the sound velocities of the longitudinal and transverse vibrational modes in various directions in small single crystals of monoclinic ZrO2. Using these velocities and the Christoffel equation, we have calculated the 13 elastic stiffness moduli between room temperature and the monoclinic—tetragonal transformation temperature.

Design Considerations for Cushion Form Bearings in Artificial Hip Joints

Abstract: Lubrication mechanisms and contact mechanics have been analysed in a new generation of ‘cushion form’ bearings for artificial hip joints, which comprise low elastic modulus layers on the articulating surfaces. Comparisons have been made with ‘ hard’ bearings used in existing prostheses and also with the natural hip joint. Lubricating film thicknesses are enhanced by larger contact areas and lower contact pressures. For a fixed contact area, simultaneous changes in layer thickness and radial clearance have been shown to have a small effect on elastohydrodynamic film thickness. Hard bearings designed with the same contact area as the cushion bearings produced a similar film thickness, but lubricant film thickness is not optimized in current designs. The main advantage of using a cushion bearing with low elastic modulus layers was found to be associated with microelastohydrodynamic lubrication. Careful selection of the elastic modulus is important in order to ensure that this lubrication regime was effective...

The bulk modulus of C60 molecules and crystals: A molecular mechanics approach

Abstract: In this letter, the bulk modulus of an individual C60 molecule is calculated in terms of the C,C bond force constant. A range of values for the bulk modulus is obtained with literature values for the force constant. The values obtained all exceed the bulk modulus (441 GPa) of diamond. With a C,C bond force constant equal to that between adjacent carbon atoms in graphite, 7.08 mdyn/A, a bulk modulus of 903 GPa is obtained. On the basis of a simple composite model it is calculated that single closest‐packed C60 crystals of C60 will have a bulk modulus of roughly 668 GPa under hydrostatic pressures. The calculated bulk modulus for a single C60 ‘‘buckyball’’ therefore suggests the possibility that a C60 crystal could be the most incompressible material known, at a pressure above about 50 GPa.

Matrix cracking in intermetallic composites caused by thermal expansion mismatch

Abstract: Matrix cracking in brittle matrix composites caused by thermal expansion misfit has been addressed by a combination of experiment with calculations. It has been established that a critical reinforcement size exists below which matrix cracking is suppressed. This concept is summarized in terms of a non-dimensional group; R , of the reinforcement size, misfit strain, elastic modulus and matrix toughness. It has also been demonstrated that the interface exerts a major influence on matrix cracking, through relaxation of constraint by debonding. Furthermore, the results imply that a failsafe value of R exists, of order unity, that can be used to select material combinations that suppress matrix cracking.

The elastic and electromechanical properties of tetragonal BaTiO3 single crystals

Abstract: From velocity of sound measurements, obtained using Brillouin scattering and ultrasound techniques, the elastic and piezoelectric constants at room temperature have been determined on high‐quality monodomain tetragonal BaTiO3 single crystals. The elastic constants are in fair agreement with those measured previously by the low‐frequency equivalent circuit method. However, the electromechanical properties are significantly different. It is suggested that high frequency relaxation may have an influence on the measurements of those parameters.

Length vs. active force relationship in single isolated smooth muscle cells.

Abstract: The length vs. active force relationship (L-F) may provide information about changes in smooth muscle contractile protein interactions as muscle length changes. To characterize the L-F in single toad stomach smooth muscle cells, cells were attached to a force measurement system, electrically stimulated, and isometric force and elastic modulus (an estimate of the number of attached cross bridges) determined at different cell lengths. Cells generated maximum stress (Pmax = 152.5 mN/mm2) and elastic modulus (Eact = 0.68 x 10(4) mN/mm2) at their rest length (Lcell = 78.0 microns; distance between cell attachments). At shorter lengths, active force and elastic modulus declined proportionally with active force eliminated at 0.4 Lcell. Stretching the relaxed cells up to 1.4 Lcell shifted the subsequent L-F along the length axis by the amount of the stretch but did not change Pmax or the shape of the L-F. In activated cells, force was a function of cell length rather than of shortening history. We interpret these findings as evidence that 1) Lcell is close to the optimum length for force generation, 2) the decline in force at lengths less than Lcell results from a reduced number of attached cross bridges, and 3) stretching relaxed smooth muscle cells may not move the contractile units to new positions on their L-F.

Fracture of particles in a particle/metal matrix composite under plastic straining and its effect on the Young's modulus of the composite

Abstract: Fracture of Al 2 O 3 particle in an Al 2 O 3 particle/aluminium alloy metal matrix composite (MMC) under plastic straining was observed by in-situ tensile testing in a scanning electron microscope. The fracture of larger sized particles was found to be preferred to that of smaller sized ones for a given plastic strain. The Young's modulus (E c ) of plastically strained MMC was reduced with increase in plastic strain (e p )

Mechanical properties of highly aligned YBa2Cu3O7−δ effect of Y2BaCuOx particles

Abstract: The elastic modulus and hardness of highly aligned YBa 2 Cu 3 O 7−δ obtained by melt processing was determined using a highly spatially resolved mechanical properties microprobe. Ultra-low load indentation measurements on the (001) cleavage plane of aligned 123, indicated a Young's modulus of 143 ± 4 GPa and a hardness of 10.0 ± 1.9 GPa. For measurements on a plane perpendicular to the cleavage plane, values of 182 ± 4 GPa for the modulus and 10.8 ± 1.7 GPa for the hardness were obtained. A lower modulus in the c -direction is perhaps a result of the layer-like structure of 123, with weak coupling between the layers. Measurements on the trapped single crystal 211 particles yielded a modulus of 213 ± 5 GPa and a hardness of 14.4 ± 2 GPa. Considerations of the thermal and elastic mismatch effects between the 211 particles and the 123 matrix, the large thermal expansion anisotropy of aligned 123, and microstructural examination of polished and fracture surfaces of the aligned samples indicate that the 211 particles perhaps serve to enhance the fracture resistance behavior of 123 by energy dissipation due to interfacial delamination and crack bridging.

Thermal expansion of gels: a novel method for measuring permeability

Abstract: When a gel is heated, the thermal expansion of the pore liquid causes stretching of the solid network. If the heating rate is very high, the gel expands at the same rate as the liquid; at slower rates, some of the liquid drains out and the gel expands less. By measuring the axial deformation of a gel rod, it is possible to determine the elastic relaxation time, which involves the product of the permeability, D , and the elastic modulus of the gel. Using independently measured elastic properties, one readily obtains D . This method is ideally suited for compliant gels for which more direct methods of measurement of D are difficult. In this paper an analysis of the problem is presented showing the relationship of the dilatation of a gel to its permeability and modulus, allowing for syneresis of the gel network. Experimental data are presented for a 2-step base-catalyzed silica gel, showing that expansion can readily be observed during heating at 0.5°C/min with total temperature changes of ∼ 5°C. The permeability determined from this experiment is in good agreement with that obtained previously by a more difficult method.

Wave processes in media with strong acoustic nonlinearity

Abstract: A class of elastic media is considered in which, due to structural inhomogeneities, the parameter of acoustic nonlinearity Γ proves to be much larger than in ‘‘ordinary,’’ homogeneous solids. As an example, porous ‘‘rubberlike’’ media where the transversal wave velocity ct is much less than the longitudinal one cl are shown to have a value of Γ of the order of (cl/ct)2 at the porosity as small as (ct/cl)2 for spherical and cylindrical pores. Experimental data confirm these predictions. Another model discussed here is a ‘‘bimodular’’ medium having different elastic moduli on compression and on stretch. Equations of longitudinal elastic waves and some of their solutions are obtained provided all ‘‘kinematic’’ nonlinear effects can be neglected in comparison with the structural nonlinearity. It is supposed that the class of strongly nonlinear solids can be wide enough and include rocks, metals and other microinhomogeneous materials.

Elastic modulus, poisson's ratio, and compressive strength relationships at early ages

Abstract: The paper presents the results of an experimental investigation into the relationships between the elastic modulus, Poisson's ratio, and the cylinder compressive strength of concrete, especially at early ages. The applicability to concrete at early ages of some of the existing relations between these properties was also examined. Tests were performed on 4 different concrete mixes using conventional 6 x 12-in.-cylinders. Test results were obtained for ages ranging from 6 hr to 28 days. Analyses of test results show that the compressive strength and the elastic modulus are related, and an increase in one is, in general, similarly reflected in an increase in the other. Poisson's ratio was found to be insensitive to both the age and the richness of concrete mix and did not change appreciably with compressive strength development.