Showing papers on "Young's modulus published in 1999"

Re-configurable fluid circuits by PDMS elastomer micromachining

Abstract: We report on a microfabrication technique for realizing re-configurable micro fluidics devices using polymethylsiloxane material (PDMS). The mechanical characteristics of the material, including the Young's modulus and the adhesion energy have been determined experimentally. The magnitude of Young's modulus ranges from 8.7/spl times/10/sup 5/ Pa to 3.6/spl times/10/sup 5/ Pa. The adhesion energy is a function of the PDMS composition as well as chemical treatment. A method for efficiently developing flow interconnects has been demonstrated.

Compressive and tensile behaviour of aluminum foams

Abstract: The uniaxial compressive and tensile modulus and strength of several aluminum foams are compared with models for cellular solids. The open cell foam is well described by the model. The closed cell foams have moduli and strengths that fall well below the expected values. The reduced values are the result of defects in the cellular microstructure which cause bending rather than stretching of the cell walls. Measurement and modelling of the curvature and corrugations in the cell walls suggests that these two features account for most of the reduction in properties in closed cell foams.

The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded Isotropic Linearly Elastic Materials

Abstract: The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic Lame problem for a pressurized homogeneous isotropic hollow circular cylinder or disk is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. It is shown that the stress response of the inhomogeneous cylinder (or disk) is significantly different from that of the homogeneous body. For example, the maximum hoop stress does not, in general, occur on the inner surface in contrast with the situation for the homogeneous material. The results are illustrated using a specific radially inhomogeneous material model for which explicit exact solutions are obtained.

Finite-element modeling of nanoindentation

Abstract: Procedures have been developed based on finite-element modeling of nanoindentation data to obtain the mechanical properties of thin films and ion-beam-modified layers independently of the properties of the underlying substrates. These procedures accurately deduce the yield strength, Young’s elastic modulus, and layer hardness from indentations as deep as 50% of the layer thickness or more. We have used these procedures to evaluate materials ranging from ion implanted metals to deposited, diamond-like carbon layers. The technique increases the applicability of indentation testing to very thin layers, composite layers, and modulated compositions. This article presents an overview of the procedures involved and illustrates them with selected examples.

Elastic Properties of Single-Wall Nanotubes

Abstract: , BC2N, and C3N4. These studies have been carried out using a total-energy, non-orthogonal, tight-binding parametrisation which is shown to provide results in good agreement both with calculations using higher levels of theory and the available experimental data. Our results predict that of all types of nanotubes considered, carbon nanotubes have the highest Young’s modulus. We have considered tubes of different diameters, ranging from 0.5 to 2 nm, and find that in the limit of large diameters the mechanical properties of nanotubes approach those of the corresponding flat graphene-like sheets.

Tensile tests of ropes of very long aligned multiwall carbon nanotubes

Abstract: We have directly measured the Young’s modulus and tensile strength of multiwall carbon nanotubes by pulling very long (∼2 mm) aligned nanotube ropes with a specially designed stress-strain puller. This puller can apply an axial force to the rope and simultaneously measure the corresponding rope elongation and the change in rope resistance. The average Young’s modulus and tensile strength obtained were 0.45±0.23 TPa and 1.72±0.64 GPa, respectively, which are lower than those calculated and measured previously. The factors that affect the mechanical strengths of nanotubes are discussed.

Correlation between Young's modulus and porosity in porous materials

Abstract: where E is the effective Young’s modulus of porous material with porosity p, E0 is Young’s modulus of solid material, pc is the porosity at which the effective Young’s modulus becomes zero and f is the parameter dependent on the grain morphology and pore geometry of porous material [1]. As was noted by Wagh et al. [2], fittings of the experimental data to Equation 1 often give pc= 1 [1, 3] and do not explain the data accurately. In recent experimental works, either pc≡ 1 is preferably used [4–6] or a linearized model ( f ≡ 1) by Lam et al. [7] is used, where pc is considered to be an initial powder porosity. In this letter, it will be shown that the empirical relationship shown in Equation 1 is identical with the percolation theory equation for the behavior of Young’s and shear modulus with porosity. Further, the applicability of the percolation model for Young’s modulus of porous materials will be demonstrated and the results will be discussed. The porous materials are preferably prepared from powders, the particle size and shape of which can vary significantly. During the powder consolidation, various porosities can be achieved by varying the technological parameters such as temperature, external pressure or time. Compacting starts from just touching powder particles and goes to the lower porosity by the creation and growth of the necks between particles. The subsequent closure of the pore channels leads to the elimination of the pores. Three various porosity ranges can be usually identified, e.g., Danninger et al. [8] observed for sintered iron the following porosity ranges: 1. porosity≤3%: fully isolated pores of nearly spherical or elliptical shape 2. porosity ≥20%: fully interconnected pores of complex shape 3. porosity between 3% and 20%: both isolated and interconnected pores are present in various amounts. This indicates that the powder consolidation is in general a connectivity problem, which is studied by the percolation theory [9]. According to the percolation theory, there exists a critical volume fraction nc, called a percolation threshold, at which a solid phase forms a continual network spanning the whole system. At and above the percolation threshold, the geometrical, physical and mechanical properties of the system behave as

Elastic constants of tetrahedral amorphous carbon films by surface Brillouin scattering

Abstract: The elastic constants of tetrahedral amorphous carbon (ta-C) and hydrogenated tetrahedral amorphous carbon (ta-C:H) thin films were determined nondestructively by surface Brillouin scattering. Besides the usual Rayleigh surface mode, we also observe a new pseudosurface acoustic mode of longitudinal polarization, which is a modified version of the longitudinal guided mode usually found in slow-on-fast supported films. The Young’s modulus E of a ta-C with 88% sp3 is 757 GPa, and the shear modulus G is 337 GPa. The moduli of ta-C:H with 70% sp3 and 30 at. % H are lower, E=300 GPa and G=115 GPa.

Elastic and plastic properties of GaN determined by nano-indentation of bulk crystal

Abstract: The major obstacle to the production of a blue laser is posed by difficulties with the preparation of defect-free GaN layers. A considerable amount of empirical work is presently being undertaken to achieve this goal. However, there is a lack of basic research on the reduction of residual stress and defects in these epilayers since the mechanical characteristics of GaN have not been measured yet. This is due to difficulties with experimental examination of thin films. This work addresses the mechanical properties of bulk GaN obtained by a high-pressure method. Young’s modulus (295 GPa), hardness (20 GPa), yield strength (15 GPa), and the stress–strain curve of GaN have been evaluated using nano-indentation. The cause of the sudden depth excursions during indentation of GaN epilayers has been clarified.

Tensile testing of polysilicon

Abstract: Tensile specimens of polysilicon are deposited on a silicon wafer; one end remains affixed to the wafer and the other end has a relatively large paddle that can be gripped by an electrostatic probe. The overall length of the specimen is less than 2 mm, but the smooth tensile portion can be as small as 1.5×2μm in cross section and 50μm long. The specimen is pulled by a computer-controlled translation stage. Force is recorded with a 100-g load cell, whereas displacement is recorded with a capacitance-based transducer. Strain can be measured directly on wider specimens with laser-based interferometry from two small gold markers deposited on the smooth portion of the specimen. The strength of this linear and brittle material is measured with relative ease. Young's modulus measurement is more difficult; it can be determined from either the stress-strain curve, the record of force versus displacement or the comparison of the records of two specimens of different sizes. Specimens of different sizes—thicknesses of 1.5 or 3.5 μm, widths from 2 to 50 μm and lengths from 50 to 500 μm—were tested. The average tensile strength of this polysilicon is 1.45±0.19 GPa (210 ±28 ksi) for the 27 specimens that could be broken with electrostatic gripping. The average Young's modulus from force displacement records of 43 specimens is 162±14 GPa (23.5 ±2.0×103 ksi). This single value is misleading because the modulus values tend to increase with decreasing specimen width; that is not the case for the strength. The three methods for determining the modulus agree in general, although the scatter can be large.

Measurement of elastic modulus, Poisson ratio, and coefficient of thermal expansion of on-wafer submicron films

Abstract: A bending beam method has been developed to measure the elastic modulus E, the coefficient of thermal expansion (CTE) and the Poisson ratio ν for on-wafer dielectric films with thicknesses in the submicron range. The method was demonstrated for 0.5 μm thick silicon dioxide films made from tetraethylorthosilane (TEOS). First, the biaxial elastic modulus E/(1-ν) and CTE were measured on blanket TEOS on Si and GaAs substrates and found to be 77 GPa and 1.0 ppm/°C, respectively. The Poisson ratio ν was determined by combining the finite element calculation and the experimental result of the thermal stresses of TEOS fine lines on the Si substrate. The Poisson ratio of TEOS was determined to be 0.24 and, as a consequence, the Young’s modulus was 59 GPa. Fourier transform infrared spectra were obtained for TEOS films on the Si and GaAs substrates to ensure that the chemical structure of the film is independent of the substrate.

Effective elastic properties for lower limb soft tissues from manual indentation experiment

Abstract: Quantitative assessment of the biomechanical properties of limb soft tissues has become more important during the last decade because of the introduction of computer-aided design and computer-aided manufacturing (CAD/CAM) and finite element analysis to prosthetic socket design. Because of the lack of a clinically easy-to-use apparatus, the site and posture dependences of the material properties of lower limb soft tissues have not been fully reported in the literature. In this study, an ultrasound indentation system with a pen-size handheld probe was used to obtain the indentation responses of lower limb soft tissues. Indentation tests were conducted on normal young subjects with four females and four males at four sites with three body postures. A linear elastic indentation solution was used to extract the effective Young's modulus from the indentation responses. The determined modulus ranged from 10.4 to 89.2 kPa for the soft tissues tested. These results were in a similar range as those reported in the literature. The thickness of the lower limb soft tissues varied slightly with body posture changes. The Young's modulus determined was demonstrated to be significantly dependent on site, posture, subject and gender. The overall mean modulus of male subjects was 40% larger than that of female subjects. No significant correlation was established between the effective Young's modulus and the thickness of entire soft tissue layers.

Mechanical characterization of thick polysilicon films: Young's modulus and fracture strength evaluated with microstructures

Abstract: Young's modulus and the fracture strength of thick polysilicon films were evaluated with surface micromachined test structures. The polysilicon films were deposited in an epitaxial reactor and were ...

Temperature and composition dependence of the elastic constants of Ni3Al

Abstract: The stiffness constants, c ij , of monocrystalline Ni3Al of three different compositions, 23.2, 24.0, and 25.0 at. pct Al, were measured over the temperature range from 300 to 1100 K using the rectangular parallelepiped resonance (RPR) method. The bulk modulus, as well as the shear modulus, Young’s modulus, and Poisson’s ratio for randomly oriented polycrystalline stoichiometric Ni3Al, were derived from the stiffness constants. The data indicate that c 44 is essentially independent of composition, decreasing slightly with increasing temperature for all three alloys. The values of c 11 and c 12, however, decrease with increasing aluminum content, the difference being small at room temperature but becoming larger at higher temperatures. We find that c 11 and c 12 are not as sensitive to aluminum concentration as is implied by previous results. A comparison of different shear moduli of Ni3Al and the saturated Ni-Al solid solution in equilibrium with it indicates that the ordered phase is generally elastically stiffer than the solid solution over the range of temperatures at which coarsening of the Ni3Al precipitate has been heavily investigated.

Elastic properties of in-situ processed Ti–TiB composites measured by impulse excitation of vibration

Abstract: The elastic moduli, shear moduli and the Poisson ratios of four different in-situ processed titanium (Ti) composites consisting of titanium monoboride (TiB) whiskers were measured using a dynamic method based on impulse excitation of vibration. For comparison, elastic modulus measurements were also made using tensile specimens with strain gages bonded to the specimen. The Ti–TiB composites consisted of 30, 54, 69, and 83 vol.% of TiB whiskers. The 83 vol.% TiB composite also consisted of 7 vol.% TiB2 phase. The study also included a TiB–TiB2 composite containing 16 vol.% TiB2 phase. The elastic and shear moduli of all the composites were found to increase with an increase in the volume fraction of TiB. The Poisson ratio decreased with increasing vol.% of TiB. The dynamic elastic modulus data were found to be in reasonable agreement with the tensile elastic modulus data. The variations in elastic properties with the vol.% of TiB whiskers are assessed in the light of theories on effective elastic response of two phase composites. The probable values of the elastic modulus, the shear modulus, and the Poisson’s ratio of the TiB phase were also estimated using these theories.

The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks

Abstract: The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may be tailored so that the radial and hoop stress are identical throughout the disk.

Tensile testing of AlCu thin films on polyimide foils

Abstract: Mechanical properties of sputtered AlCu(0.5 wt %) thin films, 0.2–2.0 μm thick, were determined by tensile testing. For comparison, tensile tests were also performed on bulk samples of the same composition. The films were deposited on thin polyimide foils. They were characterized with respect to the surface, microstructure, residual stress, and concentration of copper and oxygen. Stress-strain curves of the films were obtained by separating the force working on the polyimide foil from that working on the metal-polyimide compound. Young’s modulus of the films almost corresponded to the bulk value. Films with a thickness >1.5 μm broke by formation of macrocracks while thinner films showed formation of microcracks. The Hall–Petch model, additional strengthening by small grain size, and the role of grain boundary sliding for crack formation are discussed.

Micromechanical properties of silica aerogels

Abstract: Aerogels are nanostructured highly porous solids that present properties which are very different from other materials, i.e., extremely low densities. In this letter, the mechanical properties of aerogels have been studied with a nondestructive microindentation technique. This technique enables the continuous measurement of load-displacement curves during loading and unloading cycles by using very small indentation loads (∼1 mN), small enough to prevent cracking of the aerogels. The samples studied show two different types of mechanical behaviors; the low-density aerogels are elastic, while the denser aerogels behave as elastoplastic materials. Young’s modulus, hardness, and the elastic parameter have been evaluated for these aerogel samples. Power function relationships have been found between these mechanical parameters and the aerogel densities.

Mechanical properties of diamond-like carbon composite thin films prepared by pulsed laser deposition

Abstract: We have investigated the mechanical properties of diamond-like carbon (DLC) thin films that contain foreign atoms. The DLC films were prepared by pulsed laser deposition. A novel target design was adopted to incorporate foreign atoms into the DLC films during film deposition. Copper, titanium and silicon are chosen as the dopants. The chemical composition of the doped films was determined using Rutherford backscattering spectrometry, X-ray photoelectron spectroscopy and calibrated extrapolation. Experimental results of both visible and UV Raman are presented and discussed in terms of peak shape and position. The effect of dopants on the Raman spectrum is also analyzed. Optical microscopy of the pure DLC of a certain thickness showed severe buckling. A brief review of the theoretical background of adhesion is given and the possible mechanisms of adhesion that may work in DLC coatings are discussed. Qualitative scratch tests on the specimens show that pure DLC has quite poor adhesion due to the large compressive stress, while the doped DLC films exhibit much improved adhesion. Wear tests show improved wear resistance in the doped DLC coatings. Nanoindentation results give an average hardness above 40 GPa and effective Young's modulus above 200 GPa for pure DLC. The copper doped DLC films showed slightly decreased hardness and Young's modulus as compared to pure DLC films. Ti and Si can reduce the hardness and Young's modulus more than Cu. All these can be understood by analyzing the internal stress reduction as derived from Raman G-peak shift to lower wavenumbers. A preliminary model of the stress reduction mechanism is discussed.