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At least 91 records · Page 5

Elasticity of some mantle crystal structures. II.

The single-crystal elastic constants are determined as a function of pressure and temperature for rutile structure germanium dioxide (GeO2). The data are qualitatively similar to those of rutile TiO2 measured by Manghnani (1969). The compressibility in the c direction is less than one-half that in the a direction, the pressure derivative of the shear constant is negative, and the pressure derivative of the bulk modulus has a relatively high value of about 6.2. According to an elastic strain energy theory, the negative shear modulus derivative implies that the kinetic barrier to diffusion decreases with increasing pressure.

Wang, H.↗

An investigation of the isotropy of epoxy polymers

Measurements of the engineering constants E, G, and nu are routinely made for polymeric materials. If these materials are isotropic, these measurements should satisfy the relationship G = E/2(1 nu). However, many past measurements have indicated that this relationship is not satisfied. This raises questions about the assumptions of material isotropy and the applicability of Hooke's law. The methods used to measure these engineering constants for a number of different polymers are first described. Then, new results obtained in the current investigation are presented, indicating that the elastic constants do in fact satisfy the isotropic relationship for strains up to 0.5 percent. However, it is shown that at strain levels above this level, the relationship between stress and strain is nonlinear.

Odom, Edwin M.↗

Multiscale Analysis of Thermo-Mechanical Behavior of Boron Nitride-Reinforced Epoxy Nanocomposites

The effect of size, shape, morphology, and arrangement of micro constituents of Boron Nitrite (BN) nanoplatelet/epoxy composites on their properties were investigated using a multi scale approach that includes Molecular Dynamics (MD) and micromechanics. The thermo-mechanical properties of the composites were evaluated using molecular theory and the analysis showed that the elastic constants of BN/epoxy composites were not severely affected by temperature. Also, the micromechanical analysis of Generalized Method of Cells (GMC) was utilized at higher length scale to evaluate elastic properties of the composites, for different geometries and arrangements of micro constituents. The predicted results of the analysis showed that the size, aspect ratios, morphology, and the arrangements of inclusions in BN/epoxy nanocomposites all have remarkable effect on the mechanical performances of the material systems.

nanocomposites↗

A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading

An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.

Norwood, D. S.↗

Aluminum under high pressure: 1 equation of state

A curve of applied pressure P versus lattice constant a is calculated for single crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The method is taken from Fermi surface analysis . This essentially experimental information is used to verify that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the P versus a curve should have reasonable a priori accuracy, which may be improved if experimental data in the intermediate pressure region can be provided to refine the energy dependent pseudo-potential. At 3 megabars the lattice constant is reduced by only 22%; the ion cores at this pressure are still very well separated.

Friedli, C.↗

Aluminum under high pressure. I - Equation of state

A curve of applied pressure versus lattice constant is calculated for single-crystal aluminum. It results from an application of the method of structural expansions for deriving the energies of simple metals, a method known to give reasonable results for the elastic constants even at second order in the effective electron-ion interaction. The latter is taken from Fermi-surface analysis, and it is verified that the extant face-centered cubic structure remains the preferred crystalline phase up to the highest pressures considered. Arguments are given to suggest that the curve should have reasonable a priori accuracy and can admit possible improvement if experimental data in the intermediate-pressure region can be provided to refine the (in principle) energy-dependent pseudopotential. At three megabars, the lattice constant is reduced by only 22 per cent; the ion cores at this pressure are still very well separated.

Friedli, C.↗

A single fracture toughness parameter for fibrous composite laminates

A general fracture toughness parameter Qc was previously derived and verified to be a material constant, independent of layup, for centrally cracked boron aluminum composite specimens. The specimens were made with various proportions of 0 and + or - 45 degree plies. A limited amount of data indicated that the ratio Qc/epsilon tuf' where epsilon tuf is the ultimate tensile strain of the fibers, might be a constant for all composite laminates, regardless of material and layup. In that case, a single value of Qc/epsilon tuf could be used to predict the fracture toughness of all fibrous composite laminates from only the elastic constants and epsilon tuf. Values of Qc/epsilon tuf were calculated for centrally cracked specimens made from graphite/polyimide, graphite/epoxy, E glass/epoxy, boron/epoxy, and S glass graphite/epoxy materials with numerous layups. Within ordinary scatter, the data indicate that Qc/epsilon tuf is a constant for all laminates that did not split extensively at the crack tips or have other deviate failure modes.

Poe, C. C., Jr.↗

Through-Thickness Tensile Properties of Triaxial Braided Composites

The through-thickness strength of triaxial braided composites was measured using thin specimens bonded to metallic tabs. Despite providing reasonable engineering estimates of the bulk properties, some test specimen limitations were noted: For strong epoxies, significant shear and tensile stresses occur and induce failure between the first layer and bond-line; the strains over much of the exterior are ~10% lower than interior strains, which are representative of the nominal state; and failure often occurred near or along the adhesive bond line. These interference were partially overcome by adding a large radius to the gage section. Based on the finite element analysis and experimental measurements, the nominal elastic modulus and Poisson's ratio are E(sub 33) = 10.7 GPa and v(sub 31) = 0.08 for the three triaxial braided composites tested. Strengths vary from 14 to 40 MPa depending on the resin. Relative to the in-plane properties, the through thickness modulus, fracture strength, failure strain, and Poisson's ratio are 1/5th, 1/30th, 1/6th, and 1/4th. Interlaminar failure occurred with varying degrees of fiber tear out along with little damage to axial tows, resulting is a smooth undulating fracture surface. Post cure temperature excursions to 177 deg C (350 deg F) had little effect on elastic constants but reduced the strength E862 based composites severely. The strength of PR520 and 5208 based composites increased.

composite↗

Origin of multi-ring basin ridge systems - An upper limit to elastic deformation based on a finite-element model

A finite-element model of a 500-km diameter lunar basin flooded with 10 km of basalt was used to represent the central portion of a multi-ring basin undergoing elastic deformation as a result of basin subsidence. Gravitational forces due to the weight of the basalt were set as the initial forces in the model; elastic constants computed from seismic velocities of lunar samples provided strength specifications. In addition, the crust was constrained by permitting no displacements at a depth of 60 km. Because of the strength of the lithosphere, surface subsidence amounted to only 20 m. This magnitude of elastic deformation does not equal that found on the lunar surface, but the orientation of principal stress and the position of circumferential compressional stress are compatible with the evolution of inner-ring and radial ridge systems by gravitational-induced downdropping.

Maxwell, T. A.↗

A variable-order laminated plate theory based on the variational-asymptotical method

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Lee, Bok W.↗

Uniaxial Tensile Properties of AS4 3D Woven Composites with Four Different Resin Systems: Experimental Results and Analysis: Property Computations

As a part of the NASA Composite Technology for Exploration project, eight different AS4 3D orthogonal woven composite panels were manufactured and were subjected to mechanical testing including uniaxial tension along the weaves' warp direction. Each set, with four different resin systems (KCR-IR6070, EP2400, RTM6, and RS-50), included weave architectures designed using 12K and 6K AS4 carbon fiber yarns. For the tension testing conducted at Room Temperature Ambient (RTA) conditions, the elastic modulus and strength of these eight panels (as-processed and thermally-cycled) were measured and compared while the potential evolution of micro-cracking before and after thermal cycling were monitored via optical microscopy and X-Ray Computed Tomography. The data set also included test results of the as-processed materials at Elevated Temperature Wet (ETW) conditions. In the second part of this study, efforts were made to compute elastic constants for AS4 6K/RTM6 and AS4 12K/RTM6 materials by implementing a finite element approach and the Multiscale Generalized Method of Cells (MSGMC) technique developed at NASA Glenn Research Center. Digimat-FE was used to model the weave architectures, assign properties, calculate yarn properties, create the finite element mesh, and compute the elastic properties by applying periodic boundary conditions to finite element models of each repeating unit cell. The required input data for MSGMC was generated using Matlab® from Digimat exported weave information. Experimental and computational results were compared, and the differences and limitations in correlating to the test data were briefly discussed.

Property Computations↗

Uniaxial Tensile Properties of AS4 3D Woven Composites with Four Different Resin Systems: Experimental Results & Analysis - Property Computations

As a part of the NASA Composite Technology for Exploration project, eight different AS4 3D orthogonal woven composite panels were manufactured and were subjected to mechanical testing including uniaxial tension along the weaves' warp direction. Each set, with four different resin systems (KCR-IR6070, EP2400, RTM6, and RS-50), included weave architectures designed using 12K and 6K AS4 carbon fiber yarns. For the tension testing conducted at Room Temperature Ambient (RTA) conditions, the elastic modulus and strength of these eight panels (as-processed and thermally cycled) were measured and compared while the potential evolution of micro-cracking before and after thermal cycling were monitored via optical microscopy and X-Ray Computed Tomography. The data set also included test results of the as-processed materials at Elevated Temperature Wet (ETW) conditions. In the second part of this study, efforts were made to compute elastic constants for AS4 6K/RTM6 and AS4 12K/RTM6 materials by implementing a finite element approach and the Multiscale Generalized Method of Cells (MSGMC) technique developed at NASA Glenn Research Center. Digimat-FE was used to model the weave architectures, assign properties, calculate yarn properties, create the finite element mesh, and compute the elastic properties by applying periodic boundary conditions to finite element models of each repeating unit cell. The required input data for MSGMC was generated using Matlab® from Digimat exported weave information. Experimental and computational results were compared, and the differences and limitations in correlating to the test data were briefly discussed.

Property Computations↗

Elasticity of some mantle crystals structures. III - Spessartite-almandine garnet

Measurements of the pressure dependence of the elastic constants of spessartite-almandine garnet are given. The basis for velocity systematics among the available natural and synthetic garnet data is then examined. As for any dense oxide, the natural anion in garnet is dominant in size. The ionic sizes of the cations in the various sites are used to determine the extent to which it might be expected that garnets of different chemical formulas are analogous in elastic properties. The results are used to predict that the elastic velocities in garnet-transformed MgSiO3 are the same as those in pyrope (Mg3Al2Si3O12).

Wang, H.↗

Sandwich beam compressive test method

Tests presented show that the sandwich beam in four-point bending could be used to obtain reliable compressive elastic constants for graphite/polyimide laminates although some difficulties were encountered measuring composite compressive strengths. Data were obtained for ultimate stress, ultimate strain, Young's modulus, and Poisson's ratio values in 117K, room temperature, and 589K test environments for the HTS1/PMR-15 material system. A total of 36 compressive tests on various laminates were performed. Also, 24 tensile tests on the same laminate orientations were performed to obtain input to the analytical portion of this program. A portion of the beam test section was analyzed using a linear elastic finite element computer program to predict the stress state in the graphite/polyimide composite. The influence of the honeycomb core of this stress state was analytically determined.

Shuart, M. J.↗

Mechanical properties of triaxially braided composites - Experimental and analytical results

This paper investigates the unnotched tensile properties of two-dimensional (2D) triaxial braid-reinforced composites both experimentally and analytically. The materials are graphite fibers in an epoxy matrix. Three different reinforcing fiber architectures were considered. There were considerable differences in the observed elastic constants from different size strain gage and extensometer readings. Larger strain gages gave more consistent results and correlated better with the extensometer readings. Experimental strains correlated reasonably well with analytical predictions in the longitudinal, 0 deg, fiber direction but not in the transverse direction. Tensile strength results were not always predictable even in reinforcing directions. Minor changes in braid geometry led to disproportionate strength variations. The unit cell structure of the triaxial braid was discussed with the assistance of computer analysis of the microgeometry. Photomicrographs of braid geometry were used to improve upon the computer graphics representations of unit cells. These unit cells were used to predict the elastic moduli with various degrees of sophistication. The simple and the complex analyses were generally in agreement, but none adequately matched the experimental results for all the braids.

Masters, John E.↗

Mechanical properties of triaxially braided composites: Experimental and analytical results

The unnotched tensile properties of 2-D triaxial braid reinforced composites from both an experimental and an analytical viewpoint are studied. The materials are graphite fibers in an epoxy matrix. Three different reinforcing fiber architectures were considered. Specimens were cut from resin transfer molded (RTM) composite panels made from each braid. There were considerable differences in the observed elastic constants from different size strain gage and extensometer reading. Larger strain gages gave more consistent results and correlated better with the extensometer reading. Experimental strains correlated reasonably well with analytical predictions in the longitudinal, 0 degrees, fiber direction but not in the transverse direction. Tensile strength results were not always predictable even in reinforcing directions. Minor changes in braid geometry led to disproportionate strength variations. The unit cell structure of the triaxial braid was discussed with the assistance of computer analysis of the microgeometry. Photomicrographs of braid geometry were used to improve upon the computer graphics representations of unit cells. These unit cells were used to predict the elastic moduli with various degrees of sophistication. The simple and the complex analyses were generally in agreement but none adequately matched the experimental results for all the braids.

Masters, John E.↗

Mechanical properties of triaxially braided composites: Experimental and analytical results

This paper investigates the unnotched tensile properties of two-dimensional triaxial braid reinforced composites from both an experimental and analytical viewpoint. The materials are graphite fibers in an epoxy matrix. Three different reinforcing fiber architectures were considered. Specimens were cut from resin transfer molded (RTM) composite panels made from each braid. There were considerable differences in the observed elastic constants from different size strain gage and extensometer readings. Larger strain gages gave more consistent results and correlated better with the extensometer readings. Experimental strains correlated reasonably well with analytical predictions in the longitudinal, zero degree, fiber direction but not in the transverse direction. Tensile strength results were not always predictable even in reinforcing directions. Minor changes in braid geometry led to disproportionate strength variations. The unit cell structure of the triaxial braid was discussed with the assistence of computer analysis of the microgeometry. Photomicrographs of the braid geometry were used to improve upon the computer graphics representations of unit cells. These unit cells were used to predict the elastic moduli with various degrees of sophistication. The simple and the complex analyses were generally in agreement but none adequately matched the experimental results for all the braids.

Masters, John E.↗

Investigation of Three-Dimensional Stress Fields and Slip Systems for FCC Single Crystal Superalloy Notched Specimens

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e. plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g. cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing, become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a FCC single crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of 3D stress fields and evolution of slip sector boundaries near notches in FCC single crystal tension test specimens, and demonstrate that a 3D linear elastic finite element model that includes the effect of material anisotropy is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near FCC single crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single crystal notches.

Arakere, Nagaraj K.↗