Methods-A Potential-Dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts
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Wan, Charles Tai-Chieh↗
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Low frequency bulk modulus of partially molten peridotite, KLB-1
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Weidner, Donald J.↗
Elastic Modulus Testing for TriTruss Struts
The TriTruss is a novel structural module developed by researchers at NASA Langley Research Center (LaRC) that can be used in space to assemble large backing structures for a variety of applications. One such application is the metering truss and primary mirror backbone support structure of an in-space assembled telescope(iSAT). For the iSAT application, the TriTruss will be supporting mirror segments, payloads, and instruments, all of which require the TriTruss to have robust structural integrity. An accurate elastic modulus value is crucial to the finite element analysis(FEA) of the structure. Initial testing indicated that the equivalent elastic modulus provided by the manufacturer and used in the analyses did not accurately predict the behavior of the structure. In this paper, the in-house testing method developed at LaRC to accurately measure the equivalent elastic modulus of the composite struts for use in the analyses is described. A tensile and compressive equivalent elastic modulus was computed from the data obtained in this test. The testing resulted in a tensile equivalent elastic modulus of 24.6 Msi (standard deviation of 0.888 Msi) or 169 GPa (standard deviation of 6.20 GPa) and a compressive equivalent elastic modulus of 22.8 Msi (standard deviation of 0.780 Msi) or 157 GPa(standard deviation of 5.38 GPa) for the single wall thickness struts. For double wall thickness struts, the testing resulted in a tensile equivalent elastic modulus of32.1 Msi (standard deviation of 1.003 Msi) or 221 GPa (standard deviation of 6.91GPa) and a compressive equivalent elastic modulus of 31.9 Msi (standard deviation of 1.123) or 220 GPa (standard deviation of 7.74 GPa).1
TriTruss↗
Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials
Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.
42 ENGINEERING↗
The elastic modulus correction term in creep activation energies Applied to oxide dispersion strengthened superalloy
The effect of elastic modulus and the temperature dependence of elastic modulus on creep activation energies for an oxide dispersion strengthened nickel-base superalloy are investigated. This superalloy is commercially known as Inconel Alloy MA 753, strengthened both by gamma-prime precipitates and by yttria particles. It is shown that at intermediate temperatures, say below 1500 F, where elastic modulus is weakly dependent on temperature, the modulus correction term to creep activation energy is small. Accordingly, modulus corrections are insignificant for the superalloy considered, which shows high apparent creep activation energies at this temperature. On the contrary, at very high temperatures, the elastic modulus correction term can be significant, thus reducing the creep activation energy to that of vacancy self-diffusion. In order to obtain high-temperature creep resistance, a high-value elastic modulus with a weak dependence on temperature is required.
Malu, M.↗
Quasistatic vs. Dynamic Modulus Measurements Of Plasma-Sprayed Thermal Barrier Coatings
Plasma-sprayed 8wt% yttria-stabilized zirconia (8YSZ) thermal barrier coatings (TBCs) have been demonstrated to exhibit nonlinear hysteretic elastic behavior by quasistatic cyclic compression and cylindrical punch indentation measurements. In particular, the instantaneous (tangential) elastic modulus increases with applied stress and exhibits significant hysteresis during cycling. Sound velocity (dynamic) measurements also show an increase in TBC modulus with applied compressive stress, but in contrast show no significant hysteresis for the modulus during cycling. The nonlinear elastic behavior of the TBCs evidenced by these tests is attributed to coating compaction and internal sliding. The differences between the quasistatic and dynamic measurements are explained by the relative absence of the effect of internal sliding in the dynamic modulus measurements. By incorporating short load reversals into the larger loading cycle and measuring the instantaneous modulus at the start of each load reversal, the effects of internal sliding can be substantially reduced in the quasistatic measurements, and the resulting modulus values show good agreement with the modulus values determined by dynamic sound velocity measurements.
Eldridge, J. I.↗
Time and temperature dependent modulus of pyrrone and polyimide moldings
A method is presented by which the modulus obtained from a stress relaxation test can be used to estimate the modulus which would be obtained from a sonic vibration test. The method was applied to stress relaxation, sonic vibration, and high speed stress-strain data which was obtained on a flexible epoxy. The modulus as measured by the three test methods was identical for identical test times, and a change of test temperature was equivalent to a shift in the logarithmic time scale. An estimate was then made of the dynamic modulus of moldings of two Pyrrones and two polyimides, using stress relaxation data and the method of analysis which was developed for the epoxy. Over the common temperature range (350 to 500 K) in which data from both types of tests were available, the estimated dynamic modulus value differed by only a few percent from the measured value. As a result, it is concluded that, over the 500 to 700 K temperature range, the estimated dynamic modulus values are accurate.
Lander, L. L.↗
Non-toxic invert analog glass compositions of high modulus
Glass compositions having a Young's modulus of at least 15 million psi are described. They and a specific modulus of at least 110 million inches consist essentially of, in mols, 15 to 40% SiO2, 6 to 15% Li2O, 24 to 45% of at least two bivalent oxides selected from the group consisting of Ca, NzO, MgO and CuO; 13 to 39% of at least two trivalent oxides selected from the group consisting of Al2O3, Fe2O3, B2O3, La2O3, and Y2O3 and up to 15% of one or more tetravelent oxides selected from the group consisting of ZrO2, TiO2 and CeO2. The high modulus, low density glass compositions contain no toxic elements. The composition, glass density, Young's modulus, and specific modulus for 28 representative glasses are presented. The fiber modulus of five glasses are given.
Bacon, J. F.↗
Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation
The effect of differentiation on the transverse mechanical properties of mammalian myocytes was determined by using atomic force microscopy. The apparent elastic modulus increased from 11.5 +/- 1.3 kPa for undifferentiated myoblasts to 45.3 +/- 4.0 kPa after 8 days of differentiation (P < 0.05). The relative contribution of viscosity, as determined from the normalized hysteresis area, ranged from 0.13 +/- 0.02 to 0.21 +/- 0.03 and did not change throughout differentiation. Myosin expression correlated with the apparent elastic modulus, but neither myosin nor beta-tubulin were associated with hysteresis. Microtubules did not affect mechanical properties because treatment with colchicine did not alter the apparent elastic modulus or hysteresis. Treatment with cytochalasin D or 2,3-butanedione 2-monoxime led to a significant reduction in the apparent elastic modulus but no change in hysteresis. In summary, skeletal muscle cells exhibited viscoelastic behavior that changed during differentiation, yielding an increase in the transverse elastic modulus. Major contributors to changes in the transverse elastic modulus during differentiation were actin and myosin.
NASA Discipline Musculoskeletal↗
Improved Calculation of the Young’s Modulus of Rectangular Prisms from Their Resonant Frequency Overtones by Identifying Appropriate Shear Constants
Young’s modulus is an important parameter for characterizing the strength of, and wave propagation through, a given material. This study improves the estimation of Young’s modulus using the impulse excitation technique based on an experimental analysis of 19 borosilicate glass bars. Analysis of the frequency equations relating Young’s modulus to the out-of-plane and in-plane flexural resonant frequencies of rectangular prisms has been conducted for both the fundamental frequency and its overtones at higher orders of vibration. Furthermore, the Young’s moduli of three novaculite rocks with various porosities were then measured up to the seventh order of vibration to validate the optimum shear constant equation for estimating Young’s modulus. Young’s modulus was found to be nearly frequency independent for these rock samples.
Impulse excitation↗
Experimental evaluation of shear modulus scaling of dynamic strength at extreme pressures
Recent progress in the development of dynamic strength experimental platforms is allowing for unprecedented insight into the assumptions used to construct constitutive models operating in extreme conditions. In this work, we make a quantitative assessment of how tantalum strength scales with its shear modulus to pressures of hundreds of gigapascals through a cross-platform examination of three dynamic strength experiments. Specifically, we make use of Split–Hopkinson pressure bar and Richtmyer–Meshkov instability experiments to assess the low-pressure strain and strain rate dependence. Concurrent examination of magnetically driven ramp-release experiments up to pressures of 350GPa allows us to examine the pressure dependence. In this work, using a modern description of the shear modulus, validated against both ab initio theory and experimental measurements, we then assess how the experimentally measured pressure dependence scales with shear modulus. Furthermore, we find that the common assumption of scaling strength linearly with the shear modulus is too soft at high pressures and offer discussion as to how descriptions of slip mediated plasticity could result in an alternative scaling that is consistent with the data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Achieving ultrahigh modulus of resilience and enhanced thermal stability in ZnO x /SU-8 interpenetrating network polymer nanocomposite nanopillars
The modulus of resilience, a mechanical property that quantifies the maximum strain energy density a material can store during elastic deformation, is a crucial parameter for materials used in flexible displays, micro/nano-electro-mechanical system (M/NEMS) actuators, and ultra-sensitive pressure sensors. In this study, ZnO x /SU-8 nanocomposite nanopillars with a diameter of 300 nm, fully infiltrated with a uniformly distributed, interpenetrating amorphous ZnO x filler network, were synthesized via vapor-phase infiltration (VPI). In-situ uniaxial nano-compression tests revealed that the modulus of resilience of ZnO x /SU-8 reaches ∼ 12 MJ/m 3 , which is an ultrahigh value among all engineering materials with comparable strength. In addition, the synthesis fidelity, inorganic infiltration depth, and mechanical performance were all significantly improved compared to VPI-synthesized AlO x nanocomposites. Thermal stability, another key requirement for M/NEMS device materials operating under extreme environments, was also notably enhanced. Furthermore, partial crystallization of the amorphous ZnO x fillers during annealing contributed to an additional increase in modulus of resilience, reaching up to ∼ 13.9 MJ/m 3 . This work presents an effective fabrication strategy for producing nanostructured organic–inorganic hybrid nanocomposites with ultrahigh modulus of resilience and superior thermal stability, paving the way for their integration into next-generation flexible displays and high-performance M/NEMS devices working under harsh environments.
36 MATERIALS SCIENCE↗
Direct measurement and calculation of rubber bulk modulus by piston-cylinder method using conventional mechanical testing equipment
This article describes a method to directly measure the bulk modulus of rubber using a piston-cylinder type apparatus. The function of the testing apparatus is to reliably transfer load to the water inside the vessel and allow for the accurate and continuous measurement of volumetric displacement as the contents are compressed. During the test, load is applied to a piston-cylinder containing the rubber test sample and water using a conventional mechanical testing load frame. Load and the travel of the piston are recorded by a load cell and extensometer, respectfully. A brass or stainless steel plug of the same dimensions as the test sample is tested as a control sample to isolate the compliance of the system, including the compressibility of water and compliance of the piston-cylinder. The results from this control test are used to disincorporate the compliance of the system from the sample test results. Load-linear displacement data are mathematically converted to pressure-volumetric displacement data, from which bulk modulus is calculated. The test apparatus and method are validated using the known bulk modulus of water. Finally, the bulk modulus for two similar rubbers is evaluated. The validity of the results and limitations of the device are discussed.
36 MATERIALS SCIENCE↗
Interfacial Strength in Hierarchical Carbon Fiber Composites: Interplay of Interphase Modulus and Roughness
A facile, direct deposition approach that exploits van der Waals interactions between carbonaceous materials is utilized to create unidirectional hybrid carbon fiber composites. Two small molecule crosslinkers, a trifunctional aromatic (TL) and a difunctional aliphatic (DL) acyl chloride, are first utilized to create a crosslinked interphase with a softer and stiffer modulus respectively. TL crosslinked interphase with a higher modulus improved the tensile strength by 50%, despite non-covalent linking between fiber and matrix, elucidating the critical role of the interphase in alleviating modulus mismatch between the high modulus carbon fiber and the rubbery matrix. Fractional quantities of carbon nanotubes are additionally dispersed in the small molecule crosslinkers which behaved as a dispersant, helping introduce nanoasperities on the carbon fiber surface. Strong “pi-pi” interactions between CNTs and CF contributed to tensile properties, which are increased by 66% compared to the control. A cohesive zone model suggests that a stiffer interphase is better able to exploit surface heterogeneities and roughness on the fiber, synergistically enhancing interfacial strength.
36 MATERIALS SCIENCE↗
Atom-in-jellium predictions of the shear modulus at high pressure
Atom-in-jellium calculations of the Einstein frequency in condensed matter and of the equation of state were used to predict the variation of shear modulus from zero pressure to ~10 7 g/cm 3 , for several elements relevant to white dwarf stars and other self-gravitating systems. This is by far the widest range reported electronic structure calculation of shear modulus, spanning from ambient through the one-component plasma to extreme relativistic conditions. The predictions were based on a relationship between the Debye temperature and shear modulus, which we assess to be accurate at the o(10%) level, and is the first known use of atom-in-jellium theory to calculate a shear modulus. Finally, we assessed the overall accuracy of the method by comparing with experimental measurements and more detailed electronic structure calculations at lower pressures.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Analytic fits to atom-in-jellium shear modulus predictions
Fits to AJ shear modulus calculations from ρ0 to the limit of the corresponding AJ EOS table (usually 1000 ρ0), adjusted to reproduce STP shear modulus where possible. Fitting minimized the fractional difference, so low-pressure points would be reproduced accurately despite the wide-ranging tabulation. AJ calculations were at T=0. Isochoric variation G(T) has been small for all cases spot-tested so far, and may have either sign. The fitted equation usually matches the AJ data to within a few percent. Between numerical noise in the AJ calculation and probably-physical structure not captured by the equation, the deviation could be up to 20% in some places in most models, and 30% in a few. AJ does not capture structural phase transitions or phases stabilized by directional bonds, where the shear modulus may vary by a greater amount. Where possible, STP ρ,G were used as parameters, and low pressure AJ points were de-weighted or removed if necessary. Otherwise, such as where AJ fails to capture solid phases with a significantly different shear modulus, the AJ data were fitted as far down in pressure as possible, G0 was also fitted if necessary, and ρ0 was also adjusted if needed to keep G0>0. The resulting models are not intended for use at low pressure, though some are probably adequate for practical purposes
36 MATERIALS SCIENCE↗
The kinetics of crystallization of molten binary and ternary oxide systems and their application to the origination of high modulus glass fibers
Emphasis on the consideration of glass formation on a kinetic process made it possible to think of glass compositions different from those normally employed in the manufacture of glass fibers. Approximately 450 new glass compositions were prepared and three dozen of these compositions have values for Young's modulus measured on bulk specimens greater than nineteen million pounds per square inch. Of the new glasses about a hundred could be drawn into fibers by mechanical methods at high speeds. The fiber which has a Young's modulus measured on the fiber of 18.6 million pounds per square inch and has been prepared in quantity as a monofilament (to date more than 150 million lineal feet of 0.2 to 0.4 mil fiber have been produced). This fiber has also been successfully incorporated both in epoxy and polyimide matrices. The epoxy resin composite has shown a modulus forty percent better than that achievable using the most common grade of competitive glass fiber, and twenty percent better than that obtainable with the best available grade of competitive glass fiber. Other glass fibers of even higher modulus have been developed.
Bacon, J. F.↗
Composite wall concept for high temperature turbine shrouds: Survey of low modulus strain isolator materials
Plasma sprayed yttria stabilized zirconium oxide turbine seal specimens, incorporating various low modulus porous metal strain isolator pads between the zirconium oxide and a dense metal substrate, were subjected to cyclic thermal shock testing. Specimens that had a low modulus pad composed of sintered FeNiCrAlY fibermetal survived 1000 thermal shock cycles without spalling of the ceramic. A figure of merit for the low modulus pad materials taking into consideration the elastic modulus, thermal conductivity, strength, and oxidation resistance of the pad was proposed, and showed reasonable agreement with the thermal shock results. A potential surface distress problem on the zirconium oxide, associated with nonuniform temperature distribution and rapid stress relaxation was identified. One approach to solving the surface distress problem through application of laser surface fusion of the zirconium oxide layer showed some promise, but improvements in the laser surface fusion process are necessary to prevent process associated damage to the ceramic.
Bill, R. C.↗