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The scatter of elastic waves due to a thin, flat ellipsoidal inhomogeneity, either penny shaped or elliptical is discussed. An average theorem appropriate for dynamic effective mass density and effective moduli was developed via a self-consistent scheme. Effective material properties of two-component media consisting of randomly distributed spheres are given here as a special case.
Abstract The elastic behavior of nanoparticles depends strongly on particle shape, size, and crystallographic orientation. Many prior investigations have characterized the elastic modulus of nanoscale particles using experiments or simulations; however their reported values vary widely depending on the methods for measurement and calculation. To understand these discrepancies, we used classical molecular dynamics simulation to model the compression of platinum nanoparticles with two different polyhedral shapes and a range of sizes from 4 to 20 nm, loaded in two different crystal orientations. Multiple standard methods were used to calculate the elastic modulus from stress-vs-strain data for each nanoparticle. The magnitudes and particle-size dependence of the resulting moduli varied with calculation method and, even for larger nanoparticles where bulk-like behavior may be expected, the effective elastic modulus depended strongly on shape and orientation. Analysis of per-atom stress distributions indicated that the shape- and orientation-dependence arise due to stress triaxiality and inhomogeneity across the particle. When the effective elastic modulus was recalculated using a representative volume element in the center of a large nanoparticle, the elastic modulus had the expected value for each orientation and was shape independent. It is only for single-digit nanoparticles that meaningful differences emerged, where even the very center of the particle had a lower modulus due to the effect of the surface. These findings provide better understanding of the elastic properties of nanoparticles and disentangle geometric contributions (such as stress triaxiality and spatial inhomogeneity) from true changes in elastic properties of the nanoscale material.
The effect of interleaves placed between the fiber-reinforced plies of multilayered composite laminates is investigated analytically, with the composite approximated by linearly elastic isotropic media consisting of half-planes separated from a finite-width layer by thin interleaves of low extensional and shear moduli. Integral equations are derived which describe the effect of interleaves on damage growth. Numerical solutions are then developed which are based on Gaussian integration techniques and Hadamard's concept of differentiation of Cauchy integrals. Critical stresses and displacements are calculated to investigate the influence of relative elastic properties and geometry of the interleafed composite on interface debonding, extent and suppression and delamination, and stress relieving in the undamaged plies.
This study deals with the effect of assumed tow architecture on the elastic material properties and stress distributions of plain weave woven composites. Specifically, the examination of how a cross-section is assumed to sweep-out the tows of the composite is examined in great detail. The two methods studied are extrusion and translation. This effect is also examined to determine how sensitive this assumption is to changes in waviness ratio. 3D finite elements were used to study a T300/Epoxy plain weave composite with symmetrically stacked mats. 1/32nd of the unit cell is shown to be adequate for analysis of this type of configuration with the appropriate set of boundary conditions. At low waviness, results indicate that for prediction of elastic properties, either method is adequate. At high waviness, certain elastic properties become more sensitive to the method used. Stress distributions at high waviness ratio are shown to vary greatly depending on the type of loading applied. At low waviness, both methods produce similar results.
Materials development topics include: development of analysis techniques to adjust heterogeneous data; determination of thermal conductivity for AISI 347 stainless steel and elastic moduli and Poisson's ratio for Inconel 718 and Ti 5Al-2.5Sn; embrittlement effects of 1400 psi gaseous hydrogen for alloy 718 and Ti 5Al-2.5Sn; cryogenic radiation damage of Ti 5Al-2.5Sn; and evaluation of prepreg, impregnation, and fabric materials for optimum fibrous graphite properties. Component support topics include: tensile design allowable development of Ti 5Al-2.5Sn for turbopump applications; evaluation of fatigue, fracture toughness, and stress corrosion properties of AA 7039-T63 for pressure vessel applications; development of AISI 347 sheet tensile and creep properties for nozzle applications; evaluation of orbital weld techniques for aluminum line fabrication; material selection of shield materials; development of high load friction and wear properties of hard chrome/gold plate combinations; and evaluation of weld processes for NASS duct coolant channel fabrication.
Researchers at New Mexico Tech, Los Alamos National Laboratory (LANL), Sandia National Laboratory (SNL), and other collaborators are developing a methodology to improve characterization of stress in the subsurface by means of a model-based inversion of reservoir engineering data, time lapse seismic measurements, and microseismicity. Historically, various geophysical techniques have been used in efforts to understand the state of stress in the subsurface through direct and indirect imaging of stress sensitive features (faults and fractures) and observations of transient stress related observations (time variant elastic moduli and microseismicity). Standard direct and indirect techniques for seismic fault and fracture imaging suffer from detectability limits due to reliance on high data quality and multiplicity. Variations in effective elastic properties from inversion of high quality seismic (Vertical Seismic Profile (VSP)) data may be used to infer stress near the wellbore through integration with independent experimental characterization of the stress-velocity relationship. Given a sufficiently robust observation network, microseismic emissions may be inverted to characterize focal mechanisms which, together with supporting assumptions and constraints, inform estimates of in-situ stress. While each of these techniques contributes in part to the characterization of stress within limited spatial and temporal domains, no one method provides an unambiguous stress measurement or a predictive capability over a site scale spatial extent. Challenges associated with solution non-uniqueness, measurement ambiguity, and irregular sampling may be greatly minimized through combination of one or more of independent measurements within a common framework in which realistic geological, hydrodynamic, geomechanical, and seismological constituent process models may act as constraints.
The influence of elevated and cryogenic temperatures on the elastic moduli and fracture strengths of several C6000/PMR-15 and C6000/NR-15082 laminates was measured. Tests were conducted at -157 C, 24 C, and 316 C (-250 F, 75 F, and 600 F). Both notched and unnotched laminates were tested. The average stress failure criterion was used to predict the fracture strength of quasi-isotropic notched laminates.
The influence of elevated and cryogenic temperatures on the elastic moduli and fracture strengths of several C6000/PMR-15 and C6000/NR-15082 laminates was measured. Tests were conducted at -157 C, 24 C, and 316 C (-250 F, 75 F, and 600 F). Both notched and unnotched laminates were tested. The average stress failure criterion was used to predict the fracture strength of quasi-isotropic notched laminates.
In this study, it is demonstrated through a simple example of the Roorda-Koiter frame that the unavoidable dissimilarity in the distribution of elastic moduli may further reduce the load-carrying capacity in addition to the well-recognized effect of initial geometric imperfections.
Plutonium (Pu) has, in theory, well defined crystal structures: its atoms are arranged in regular spatial patterns. But Pu is radioactive, and as its nuclei decay those regular spatial patterns are interrupted. The interruptions are lattice imperfections, which are known to affect how materials respond to their environment. To adequately model Pu, we need to know which lattice imperfections are present, how they interact with each other, and how they affect the material’s response to its environment. The work presented here aims to use density functional theory (DFT) calculations to begin to answer the latter, in particular, how individual lattice imperfections affect measurable effects including thermal expansion (the change in volume in response to a change in temperature), heat capacity (the amount of thermal energy needed to change a material’s temperature), and elastic moduli (a material’s resistance to applied stresses). Pu poses many computational challenges. The $\textit{f}$ electrons require special attention. Of all the elements, Pu has the largest number of electrons that must be included in the calculations. Thermal effects require calculating the phonons (the lattice vibrations), which for systems containing lattice imperfections demand large, complex computational cells - but computational resources limit the size and complexity. With careful restructuring of how the calculations are performed, all these challenges have been met to enable calculations that provide insight into how lattice imperfections affect Pu’s response to its environment. Reported here are the computational challenges and the advances developed to meet them, along with the first results showing the strong effect that one prototype lattice imperfection (an interstitial Pu atom in a delta-phase Pu lattice) has on Pu’s response to its environment.
Torsion tests on specimens of same orthotropic composite material having at least two different thicknesses enable determination of effective in-plane and out-of-plane shear moduli. Moduli are calculated from experimental data with elasticity-theory equations that relate applied torque, torsional twist angle, specimen width/thickness ratio, and ratio of two shear moduli. Tests were developed to yield information on degratation of properties of composite saturated by moisture.
The thermomechanical fatigue (TMF) behavior of three continuous-fiber ceramic composites (CFCC's) was examined. The three matrices consisted of two different glass-ceramics and silicon carbide, respectively. The matrices of some of the specimens with the silicon carbide matrix were enhanced to improve oxidation resistance. All three were reinforced with Nicalon fibers with various fiber architectures. The thermoelastic properties of the matrix relative to the fibers, the elastic moduli and coefficients of thermal expansion (CTE), were different in each composite, providing a comparison of the effects of these critical properties. The specimens were tested under in-phase (IP) and out-of-phase (OP) cyclic loadings with respect to thermal cycling between 600 C and 1100 C. One of the glass-ceramic composites had greatly increased TMF lives compared to the other glass-ceramic matrix composites. This was probably caused by the reversal of the CTE mismatch between the fibers and the matrices and caused by the different oxidation resistances of the composites. For the same TMF lives a cross-ply reinforced composite had a maximum cyclic stress half as great, as that of unidirectionally reinforced composite. This indicated that the (0 deg) ply fibers had a strong influence of TMF life. Both the glass ceramic matrix composites had shallow-slope stress-life plots that indicated sensitivity to damage and therefore low damage tolerance. The composites with an unenhanced silicon carbide matrix experienced the shortest TMF lives of all the CFCC's tested. However, the enhanced composite had the longest. Also, the enhanced composite demonstrated the best damage tolerance as evidenced by a stress-life curve that curves sharply upward to the left. In all the composites, out-of-phase cyclic loading was worse than in-phase cyclic loadings despite the CTE mismatch between fiber and matrix. A damage investigation and a preliminary analysis of the stresses in the fibers and matrices taking into account their respective thermoelastic properties provided insight into the relative behavior of the glass-ceramic matrix composites under IP and OP TMF.
The third-order elastic (TOE) model has been used to describe the widely observed nonlinear mechanical behaviors of earth materials. In addition to linear elastic constants ( λ , μ ), three nonlinear elastic moduli ( A , B , C ) are required for isotropic rocks. Contrary to previous research on dynamic TOE moduli, this study followed the protocol to measure strain and stress under uniaxial and hydrostatic compressive tests statically, which were later used to invert for the full set of TOE moduli for four standard rock types with differing pore structures of a porous oolitic limestone, quartz-rich sandstones, and a dense crystalline basalt. The applicability of the TOE model to characterize nonlinearity depends on the fulfillment of path-independence and small-strain assumptions. Using the measured static TOE moduli, the finite element model demonstrates that the stress in the vicinity of the wellbore is more amplified than the stress in the linear elastic case, which leads to a wider zone of rock failure around the wellbore. Due to the long-standing discrepancy between static and dynamic moduli, the rarely reported full set of static TOE moduli is necessary and will benefit future research in understanding the effect of rock nonlinearity on geophysical and geomechanical applications, such as long-term safe storage of CO 2 and generating process of geohazards.
Strategically embedding graphite meshes in a compliant cementitious matrix produces a composite material with relatively high tension and compressive properties as compared to steel-reinforced structures fabricated from a standard concrete mix. Although these composite systems are somewhat similar, the methods used to analyze steel-reinforced composites often fail to characterize the behavior of their more advanced graphite-reinforced counterparts. This Technical Memorandum describes some of the analytical methods being developed to determine the deflections and stresses in graphite-reinforced cementitious composites. It is initially demonstrated that the standard transform section method fails to provide accurate results when the elastic moduli ratio exceeds 20. An alternate approach is formulated by using the rule of mixtures to determine a set of effective material properties for the composite. Tensile tests are conducted on composite samples to verify this approach. When the effective material properties are used to characterize the deflections of composite beams subjected to pure bending, an excellent agreement is obtained. Laminated composite plate theory is investigated as a means for analyzing even more complex composites, consisting of multiple graphite layers oriented in different directions. In this case, composite beams are analyzed using the laminated composite plate theory with material properties established from tensile tests. Then, finite element modeling is used to verify the results. Considering the complexity of the samples, a very good agreement is obtained.
We report results of systematic molecular-dynamics computations of the elastic properties of single-crystalline tungsten containing structural defects, voids and overpressurized He nanobubbles, related to plasma exposure of tungsten serving as a plasma- facing component (PFC) in nuclear fusion devices. Our computations reveal that the empty voids are centers of dilatation resulting in development of tensile stress in the tungsten matrix, whereas He-filled voids (nanobubbles) introduce compressive stress in the plasma-exposed tungsten. We find that the dependence of the elastic moduli of plasma-exposed tungsten, namely, the bulk, Young, and shear modulus, on its void fraction follows a universal exponential scaling relation. We also find that the elastic moduli of plasma-exposed tungsten soften substantially as a function of He content in the tungsten matrix, following an exponential scaling relation; this He-induced exponential softening is in addition to the softening caused in the matrix with increasing temperature. A systematic characterization of the dependence of the elastic moduli on the He bubble size reveals that He bubble growth affects significantly both the bulk modulus and the Poisson ratio of plasma-exposed tungsten, while its effect on the Young and shear moduli of the plasma-exposed material is weak. Our findings contribute directly to the development of a structure-properties database that is required for the predictive modeling of the dynamical response of PFCs in nuclear fusion devices.
Light element alloying in iron is required to explain density deficit and seismic wave velocities in Earth’s core. However, the light element composition of the Earth’s core seems hard to constrain as nearly all light element alloying would reduce the density and sound velocity (elastic moduli). The alloying light elements include oxidizing elements like oxygen and sulfur and reducing elements like hydrogen and carbon, yet their chemical effects in the alloy system are less discussed. Moreover, Fe-X-ray Absorption Near Edge Structure (Fe-XANES) fingerprints have been studied for silicate materials with ferrous and ferric ions, while not many X-ray absorption spectroscopy (XAS) studies have focused on iron alloys, especially at high pressures. To investigate the bonding nature of iron alloys in planetary interiors, we presented X-ray absorption spectroscopy of iron–nitrogen and iron–carbon alloys at high pressures up to 50 GPa. Together with existing literature on iron–carbon, –hydrogen alloys, we analyzed their edge positions and found no significant difference in the degree of oxidation among these alloys. Pressure effects on edge positions were also found negligible. Our theoretical simulation of the valence state of iron, alloyed with S, C, O, N, and P also showed nearly unchanged behavior under pressures up to 300 GPa. This finding indicates that the high pressure bonding of iron alloyed with light elements closely resembles bonding at the ambient conditions. We suggest that the chemical properties of light elements constrain which ones can coexist within iron alloys.
Study examines effects of boron filament diameter on bonds and joints in boron-aluminum composite. Data include static strength, fatigue, and dynamic moduli of elasticity. Manson-Coffin analyses and metallurgical and fracture surface evaluation were also performed.
Low-enriched-uranium (LEU) reactor systems utilize moderators to improve neutron economy. Solid yttrium hydride is one of the primary moderator candidates for high-temperature (>700 °C) nuclear reactor applications. This is due to its ability to retain hydrogen at elevated temperatures compared to other metal hydrides. For reactor modeling purposes, both neutronic and thermos-mechanical modeling, several high-temperature properties for sub-stoichiometric yttrium hydride (YH2−x) are needed. In this paper, we present an atomistics and a neutron diffraction study of the high-temperature properties of Y and YH2−x. Specifically, we focus on the thermal lattice expansion effects in yttrium metal and yttrium hydride, which also govern bulk thermal expansion. Previously reported physical and mechanical properties for sub-stoichiometric yttrium hydride at ambient conditions are expanded using lattice dynamics to take into account high-temperature effects. Accordingly, an array of newly generated properties is presented that enables high-fidelity neutronics, and thermomechanical modeling. These properties include various elastic moduli, thermal expansion parameters for yttrium and yttrium hydride, and single-phase (YH2−x) and two-phase (Y + YH2−x) density as a function of stoichiometry and density.