Search NASA⌕ Search

SEARCH · Search NASA

Results for “effective elastic moduli”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Testing the Predictive Capability of the High-Fidelity Generalized Method of Cells Using an Efficient Reformulation

The High-Fidelity Generalized Method of Cells is a new micromechanics model for unidirectionally reinforced periodic multiphase materials that was developed to overcome the original model's shortcomings. The high-fidelity version predicts the local stress and strain fields with dramatically greater accuracy relative to the original model through the use of a better displacement field representation. Herein, we test the high-fidelity model's predictive capability in estimating the elastic moduli of periodic composites characterized by repeating unit cells obtained by rotation of an infinite square fiber array through an angle about the fiber axis. Such repeating unit cells may contain a few or many fibers, depending on the rotation angle. In order to analyze such multi-inclusion repeating unit cells efficiently, the high-fidelity micromechanics model's framework is reformulated using the local/global stiffness matrix approach. The excellent agreement with the corresponding results obtained from the standard transformation equations confirms the new model's predictive capability for periodic composites characterized by multi-inclusion repeating unit cells lacking planes of material symmetry. Comparison of the effective moduli and local stress fields with the corresponding results obtained from the original Generalized Method of Cells dramatically highlights the original model's shortcomings for certain classes of unidirectional composites.

Arnold, Steven M.↗

A limit to strong shock behavior in the dynamic response of matter at pressure

Solids under high pressures experience a series of regimes, where their microstructure adapts to the applied compression and these key transitions are discussed in this paper. As strain increases, new forces emerge at extreme pressures. A previous study introduced the concept of the weak shock limit (WSL), at which the ambient theoretical shear strength is overcome. Above the WSL, further deformation under strong shock conditions results in electrons occupying higher energy levels as strain increases. As pressure rises further, shock melting occurs in the material and at around three times this melting pressure, the strong shock limit is reached where the driving physics under pressure switches, with electrons forced into higher energy states. This leads to significant reduction in their compressibility due to changes in electronic structure and developing electron degeneracy pressures. A derivation for conditions at this state is presented, which indicates that a dependence of the threshold pressure on the free electron number density defines the limit observed. This correlation suggests that ambient material moduli govern material compression up to nearly 50% strain. These observations show that models should account for different behaviors as dominant physics changes in each regime accessed as shock pressure increases.

36 MATERIALS SCIENCE↗

Fatigue Crack Measurement in Composite Materials by Ultrasonic Methods

The nondestructive detection of intra-ply microcracking in unlined pressure vessels fabricated from composite materials is critical to ensuring mission success. Microcracking in composite structures due to combined fatigue and cryogenic thermal loading can be very troublesome to detect in-service and when it begins to link through the thickness can cause leakage and failure of the structure. These leaks may lead to loss of pressure/propellant, increased risk of explosion and possible cryo-pumping. The work presented herein develops a method and an instrument to locate and measure intraply fatigue cracking through the thickness of laminated composite material by means of correlation with ultrasonic resonance. Resonant ultrasound spectroscopy provides measurements which are, sensitive to both the microscopic and macroscopic properties of an object. Elastic moduli, acoustic attenuation, and geometry can all be probed. The approach is based on the premise of half-wavelength resonance. The method injects a broadband ultrasonic wave into the test structure using a swept frequency technique. This method provides dramatically increased energy input into the test article, as compared to conventional spike pulsed ultrasonics. This relative energy increase improves the ability to measure finer details in the materials character, such as micro-cracking and porosity. As the micro-crack density increases, more interactions occur with the higher frequency (small wavelength) components of the signal train causing the spectrum to shift toward lower frequencies. Preliminary experiments have verified a measurable effect on the resonance spectrum of the ultrasonic data to detect microcracking. Methods involving self organizing neural networks and other clustering algorithms show that the resonance ultrasound signatures from composites vary with the degree of microcracking and can be separated and identified.

Walker, James L.↗

Compositional and phase dependence of elastic modulus of crystalline and amorphous Hf 1- x Zr x O 2 thin films

The elastic moduli of amorphous and crystalline atomic layer-deposited Hf 1-x Zr x O 2 (HZO, x = 0, 0.31, 0.46, 0.79, 1) films prepared with TaN electrodes on silicon substrates were investigated using picosecond acoustic measurements. The moduli of the amorphous films were observed to increase between 211 ± 6 GPa for pure HfO 2 and 302 ± 9 GPa for pure ZrO 2 . In the crystalline films, it was found that the moduli increased upon increasing the zirconium composition from 248 ± 6 GPa for monoclinic HfO 2 to 267 ± 9 GPa for tetragonal ZrO 2 . Positive deviations from this increase were observed for the Hf 0.69 Zr 0.31 O 2 and Hf 0.54 Zr 0.46 O 2 compositions, which were measured to have moduli of 264 ± 8 GPa and 274 ± 8 GPa, respectively. These two compositions contained the largest fractions of the ferroelectric orthorhombic phase, as assessed from polarization and diffraction data. The biaxial stress states of the crystalline films were characterized through sin 2 (ψ) x-ray diffraction analysis. The in-plane stresses were all found to be tensile and observed to increase with the increasing zirconium composition, between 2.54 ± 0.6 GPa for pure HfO 2 and 5.22 ± 0.5 GPa for pure ZrO 2 . The stresses are consistent with large thermal expansion mismatches between the HZO films and silicon substrates. Furthermore, these results demonstrate a device-scale means to quantify biaxial stress for investigation on its effect on the ferroelectric properties of hafnia-based materials.

36 MATERIALS SCIENCE↗

Beam and Torsion Tests of Aluminum-alloy 61S-T Tubing

Tests were made to determine the effect of length and the effect of ratios of diameter to wall thickness upon the flexural and torsional moduli of failure of 61S-T aluminum-alloy tubing. The moduli of failure in bending, as determined by tests in which the tubing was loaded on the neutral axis at the one-third points of the span, were found to bear an approximately linear relationship with diameter-thickness ratio and were practically independent of span within the limits investigated. Empirical equations are given describing the relations obtained. The moduli of failure in torsion were found to be dependent upon length as well as upon diameter-thickness ratios. Empirical equations are given for predicting strengths within the range of plastic buckling. Within the elastic range, available torsion theories were found to be satisfactory.

Moore, R L↗

Elasticity of two-dimensional ferroelectrics across their paraelectric phase transformation

The mechanical behavior of two-dimensional (2D) materials across 2D phase changes is unknown, and the finite temperature (T) elasticity of paradigmatic SnSe monolayers—ferroelectric 2D materials turning paraelectric as their unit cell turns from a rectangle into a square—is described here in a progressive manner. To begin with, their zero–T total energy landscape gives way to (Boltzmann-like) averages from which the elastic behavior is determined. Furthermore, these estimates are complemented with results from the strain-fluctuation method, which employs the energy landscape or ab initio molecular dynamics data. All approaches capture the coalescence of elastic moduli < C 11 (T) > = < C 22 (T) > due to the structural transformation. The broad evolution and sudden changes of elastic parameters < C 11 (T) >, < C 22 (T) >, and < C 12 (T) > of these atomically thin phase-change membranes establishes a heretofore overlooked connection among 2D materials and soft matter.

2-dimensional systems↗

Evaluating proxies for the drivers of natural gas productivity using machine-learning models

We report the extensive development of unconventional reservoirs using horizontal drilling and multistage hydraulic fracturing has generated large volumes of reservoir characterization and production data. The analysis of this abundant data using statistical methods and advanced machine-learning (ML) techniques can provide data-driven insights into well performance. Most predictive modeling studies have focused on the impact that different well completion and stimulation strategies have on well production but have not fully exploited the available in situ rock property data to determine its role in reservoir productivity. We have used machine-learning techniques to rank rock mechanical properties, microseismic attributes, and stimulation parameters in the order of their significance for predicting natural gas production from an unconventional reservoir. The data for this study came from a hydraulically fractured well in the Marcellus Shale in Monongalia County, West Virginia. The data classes included measurements aggregated by well completion stage that included (1) gas production, (2) well-log-derived measurements including bulk density, elastic moduli, shear impedance, compressional impedance, brittleness, and gamma measurements, (3) microseismic attributes, (4) long-period long-duration (LPLD) event counts, (5) fracture counts, and (6) stimulation parameters that included the fluid injection volume and average pumping pressure. To identify observable proxies for the drivers of gas production, we evaluated five commonly used ML approaches including multivariate adaptive regression spline, Gaussian mixture model, random forest, gradient boosting, and neural network. We selected five variables including LPLD event count, seismogenic b-value, hydraulic diffusivity, cumulative moment, and fluid volume as the features most likely to impact gas productivity at the stage level in the study area. The data-driven selection of these parameters for their importance in determining gas production can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs. Plain language summary: We use machine-learning methods and data-driven selection of reservoir parameters to rank and better understand their importance in determining gas production, which can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs.

58 GEOSCIENCES↗

Atomistic insight into the ferroelastic post-stishovite transition by high-pressure single-crystal X-ray diffraction

Abstract The post-stishovite transition is a classic pseudo-proper typed ferroelastic transition with a symmetry-breaking spontaneous strain. This transition has been studied using high-pressure spontaneous strains, optic modes, and elastic moduli (Cij) based on the Landau modeling, but its atomistic information and structural distortion remain poorly understood. Here we have conducted synchrotron single-crystal X-ray diffraction measurements on stishovite crystals up to 75.3 GPa in a diamond-anvil cell. Analysis of the data reveals atomic positions, bond lengths, bond angles, and variations of SiO6 octahedra across the transition at high pressure. Our results show that the O coordinates split at ~51.4 GPa, where the apical and equatorial Si-O bond lengths cross over, the SiO6 octahedral distortion vanishes, and the SiO6 octahedra start to rotate about the c axis. Moreover, distortion mode analysis shows that an in-plane stretching distortion (GM1+ mode) occurs in the stishovite structure at high pressure while a rotational distortion (GM2+ mode) becomes dominant in the post-stishovite structure. These results are used to correlate with elastic moduli and Landau parameters (symmetry-breaking strain e1–e2 and order parameter Q) to provide atomistic insight into the ferroelastic transition. When the bond lengths of two Si-O bonds are equal due to the contribution from the GM1+ stretching mode, C11 converges with C12, and the shear wave VS1[110] polarizing along [110] and propagating along [110] vanishes. Values of e1–e2 and Q are proportional to the SiO6 rotation angle from the occurrence of the GM1+ rotational mode in the post-stishovite structure. Our results on the pseudo-proper type transition are also compared with that for the proper type in albite and improper type in CaSiO3 perovskite. The symmetry-breaking strain, in all these types of transitions, arises as the primary effect from the structural angle (such as SiO6 rotation or lattice constant angle) and its relevant distortion mode in the low-symmetry ferroelastic phase.

Geochemistry & Geophysics↗

Evaluation of microcrack thermal shock damage in ceramics: Modeling and experiment

In this paper we present an experimental and theoretical study of the effect of microcrack damage on ceramic properties. For the experimental investigation, ceramic samples of aluminum oxide and reaction bonded silicon nitride (RBSN) are used. Thermal shock treatment from different temperatures up to 1000 C is applied to produce the microcracks. Both surface and bulk ultrasonic wave methods are used to correlate the change of elastic constants to microstructural degradation and to determine the change in elastic anisotropy induced by microcrack damage. For the theoretical investigation, damage mechanics, which relates microstructural damage to material service life and mechanical failure, is used. The change in elastic properties due to microcrack damage calculated from the theoretical model is compared with the experimental results for determination of the applicability of damage theory. It is shown that two independent experimental methods (bulk wave and surface wave) give the same results for shear moduli of damaged ceramics. The experimental results aagree reasonably well with the moduli predicted from the cracked solid model.

Chu, Y. C.↗

Mechanical properties of a biodegradable bone regeneration scaffold

Poly (Propylene Fumarate) (PPF), a novel, bulk erosion, biodegradable polymer, has been shown to have osteoconductive effects in vivo when used as a bone regeneration scaffold (Peter, S. J., Suggs, L. J., Yaszemski, M. J., Engel, P. S., and Mikos, A. J., 1999, J. Biomater. Sci. Polym. Ed., 10, pp. 363-373). The material properties of the polymer allow it to be injected into irregularly shaped voids in vivo and provide mechanical stability as well as function as a bone regeneration scaffold. We fabricated a series of biomaterial composites, comprised of varying quantities of PPF, NaCl and beta-tricalcium phosphate (beta-TCP), into the shape of right circular cylinders and tested the mechanical properties in four-point bending and compression. The mean modulus of elasticity in compression (Ec) was 1204.2 MPa (SD 32.2) and the mean modulus of elasticity in bending (Eb) was 1274.7 MPa (SD 125.7). All of the moduli were on the order of magnitude of trabecular bone. Changing the level of NaCl from 20 to 40 percent, by mass, did not decrease Ec and Eb significantly, but did decrease bending and compressive strength significantly. Increasing the beta-TCP from 0.25 g/g PPF to 0.5 g/g PPF increased all of the measured mechanical properties of PPF/NVP composites. These results indicate that this biodegradable polymer composite is an attractive candidate for use as a replacement scaffold for trabecular bone.

NASA Discipline Cell Biology↗

Effects of spaceflight on rat humerus geometry, biomechanics, and biochemistry

The effects of a 12.5-day spaceflight (Cosmos 1887 biosatellite) on the geometric, biomechanical, and biochemical characteristics of humeri of male specific pathogen-free rats were examined. Humeri of age-matched basal control, synchronous control, and vivarium control rats were contrasted with the flight bones to examine the influence of growth and space environment on bone development. Lack of humerus longitudinal growth occurred during the 12.5 days in spaceflight. In addition, the normal mid-diaphysial periosteal appositional growth was affected; compared with their controls, the spaceflight humeri had less cortical cross-sectional area, smaller periosteal circumferences, smaller anterior-posterior periosteal diameters, and smaller second moments of area with respect to the bending and nonbending axes. The flexural rigidity of the flight humeri was comparable to that of the younger basal control rats and significantly less than that of the synchronous and vivarium controls; the elastic moduli of all four groups, nonetheless, were not significantly different. Generally, the matrix biochemistry of the mid-diaphysial cross sections showed no differences among groups. Thus, the spaceflight differences in humeral mechanical strength and flexural rigidity were probably a result of the differences in humeral geometry rather than material properties.

NASA Discipline Number 26-10↗

Slow dynamics in a single bead with mechanical conditioning and transient heating

The contact stiffness of an aluminum bead confined between two slabs diminishes upon mechanical conditioning, and then recovers like log(t) after the conditioning ceases. Here that structure is evaluated for its response to transient heating and cooling, with and without accompanying conditioning vibrations. It is found that, under heating or cooling alone, stiffness changes are mostly consistent with temperature dependent material moduli; there is little or no slow dynamics. Hybrid tests in which vibration conditioning is followed by heating or cooling lead to recoveries that begin like log(t) and then become more complex. On subtracting the known response to heating or cooling alone we discern the influence of higher or lower temperatures on slow dynamic recovery from vibrations. It is found that heating accelerates the initial log(t) recovery, but by an amount more than predicted by an Arrhenius model of thermally activated barrier penetrations. Furthermore, transient cooling has no discernable effect, in contrast to the Arrhenius prediction that it slows recovery.

36 MATERIALS SCIENCE↗

Ultrasonic wave velocity measurement in small polymeric and cortical bone specimens

A system was refined for the determination of the bulk ultrasonic wave propagation velocity in small cortical bone specimens. Longitudinal and shear wave propagations were measured using ceramic, piezoelectric 20 and 5 MHz transducers, respectively. Results of the pulse transmission technique were refined via the measurement of the system delay time. The precision and accuracy of the system were quantified using small specimens of polyoxymethylene, polystyrene-butadiene, and high-density polyethylene. These polymeric materials had known acoustic properties, similarity of propagation velocities to cortical bone, and minimal sample inhomogeneity. Dependence of longitudinal and transverse specimen dimensions upon propagation times was quantified. To confirm the consistency of longitudinal wave propagation in small cortical bone specimens (< 1.0 mm), cut-down specimens were prepared from a normal rat femur. Finally, cortical samples were prepared from each of ten normal rat femora, and Young's moduli (Eii), shear moduli (Gij), and Poisson ratios (Vij) were measured. For all specimens (bone, polyoxymethylene, polystyrene-butadiene, and high-density polyethylene), strong linear correlations (R2 > 0.997) were maintained between propagation time and distance throughout the size ranges down to less than 0.4 mm. Results for polyoxymethylene, polystyrene-butadiene, and high-density polyethylene were accurate to within 5 percent of reported literature values. Measurement repeatability (precision) improved with an increase in the wave transmission distance (propagating dimension). No statistically significant effect due to the transverse dimension was detected.

Non-NASA Center↗

Endothelial, cardiac muscle and skeletal muscle exhibit different viscous and elastic properties as determined by atomic force microscopy

This study evaluated the hypothesis that, due to functional and structural differences, the apparent elastic modulus and viscous behavior of cardiac and skeletal muscle and vascular endothelium would differ. To accurately determine the elastic modulus, the contribution of probe velocity, indentation depth, and the assumed shape of the probe were examined. Hysteresis was observed at high indentation velocities arising from viscous effects. Irreversible deformation was not observed for endothelial cells and hysteresis was negligible below 1 microm/s. For skeletal muscle and cardiac muscle cells, hysteresis was negligible below 0.25 microm/s. Viscous dissipation for endothelial and cardiac muscle cells was higher than for skeletal muscle cells. The calculated elastic modulus was most sensitive to the assumed probe geometry for the first 60 nm of indentation for the three cell types. Modeling the probe as a blunt cone-spherical cap resulted in variation in elastic modulus with indentation depth that was less than that calculated by treating the probe as a conical tip. Substrate contributions were negligible since the elastic modulus reached a steady value for indentations above 60 nm and the probe never indented more than 10% of the cell thickness. Cardiac cells were the stiffest (100.3+/-10.7 kPa), the skeletal muscle cells were intermediate (24.7+/-3.5 kPa), and the endothelial cells were the softest with a range of elastic moduli (1.4+/-0.1 to 6.8+/-0.4 kPa) depending on the location of the cell surface tested. Cardiac and skeletal muscle exhibited nonlinear elastic behavior. These passive mechanical properties are generally consistent with the function of these different cell types.

Non-NASA Center↗

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗

Elastic moduli of transversely isotropic graphite fibers and their composites

The paper demonstrates that it is possible to calculate the complete set of elastic mechanical properties for graphite-epoxy fiber-reinforced materials at any fiber-volume fraction by modifying equations previously developed to include transversely isotropic graphite-fiber properties. Experimental verification of the modified equations is demonstrated by using these equations to curve fit elastic-property data obtained ultrasonically over a range of fiber-volume fractions. Material systems under consideration are T300/5208, AS-3501 and Modomor II/LY558 graphite epoxy. Using the modified equations it is possible to extrapolate for fiber properties. From Modomor II/LY558 ultrasonic data, it is shown that five out of seven extrapolated graphite-fiber properties are consistent with the assumption that graphite fibers are transversely isotropic. Elastic properties for T300/5208 and AS-3501 are ultrasonically evaluated by propagating stress waves through six individual specimens cut at various angles from a block of unidirectional material. Particular attention is devoted to specimen dimensions. To demonstrate the need for accurately calculating or experimentally measuring all lamina elastic properties, a brief discussion is included on the effect that variations in lamina elastic properties have on calculating interlaminar stresses.

Kriz, R. D.↗

Molecular Dynamics Modeling of Carbon Nanotube Composite Fracture Using ReaxFF

Carbon nanotube (CNT) fiber reinforced composites with specific tensile strengths and moduli approaching those of aerospace grade carbon fiber composites have recently been reported. This achievement was enabled by the emerging availability of high N/tex yarns in kilometer-scale quantities. While the production of this yarn is an impressive advance, its strength is still much lower than that of the individual CNTs comprising the yarn. Closing this gap requires understanding load transfer between CNTs at the nanometer dimensional scale. This work uses reactive molecular dynamics simulations to gain an understanding at the nanometer scale of the key factors that determine CNT nanocomposite mechanical performance, and to place more realistic upper bounds on the target properties. While molecular dynamics simulations using conventional force fields can predict elastic properties, the ReaxFF reactive forcefield can also model fracture behavior because of its ability to accurately describe bond breaking and formation during a simulation. The upper and lower bounds of CNT composite properties are investigated by comparing systems composed of CNTs continuously connected across the periodic boundary with systems composed of finite length CNTs. These lengths, effectively infinite for the continuous tubes and an aspect ratio of 13 for the finite length case, result from practical limitations on the number of atoms that can be included in a simulation. Experimentally measured aspect ratios are typically on the order of 100,000, so the calculated results should represent upper and lower limits on experimental mechanical properties. Finally, the effect of various degrees of covalent crosslinking between the CNTs and amorphous carbon matrix is considered to identify the amount of CNT-matrix covalent bonding that maximizes overall composite properties.

Jensen, Benjamin D.↗

Structural deformation and mechanical response of CrS 2 , CrSe 2 and Janus CrSSe

In the framework of density functional theory (DFT), we investigate the structural deformation, and mechanical behavior of the Janus CrSSe, which has out-of-plane structural asymmetry, with conventional transition metal dichalcogenides (TMDs) CrS 2 and CrSe 2 . The Janus CrSSe could be a potential candidate for machinable optoelectronic and piezoelectric applications. Here, we predict that these compounds are chemically, mechanically, and dynamically stable with the covalent bond between the TM(Cr) and chalcogen(X=S, Se) atoms. Due to the influence of tensile strain, the Cr–X bond length of each monolayers increases and the thickness decreases. Interestingly, the in-plane stiffness, shear and layer moduli, Poisson’s ratio, ultimate bi/uni-axial stress of Janus CrSSe are in between the values of CrS 2 and CrSe 2 monolayers. Similar to TMDs, the orientation-dependent in-plane stiffness and Poisson’s ratio demonstrates the isotropic behavior in Janus CrSSe. Furthermore, it can sustain a larger value of uni/bi-axial tensile strain with the critical strain equivalent to CrX 2 monolayers. By applying higher-order strain, we have also found average elastic–plastic behavior as expected. These findings demonstrate that the Janus CrSSe monolayer is a mechanically stable and ductile compound that maintains the hybrid behavior.

36 MATERIALS SCIENCE↗