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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Effect of High Impact or Non-impact Loading Activity on Bone Bending Stiffness and Mineral Density

Material properties of conical bone, including mineral density (BMD) and its geometry is closely related to its load-carrying capacity. These two primary components determine the strength of conical bone. High impact loading involving acceleration and deceleration movements used in gymnastics induce higher BMD of the affected bone compared to the non-impact acceleration and deceleration movements used in swimming. Study of these two groups of athletes on bone bending stiffness has not been reported. The purpose of this study was to compare differences in bone bending stiffness and BMD between competitive female synchronized swimmers and female gymnasts. Thirteen world class female synchronized swimmers (SYN) and 8 female gymnasts (GYM), mean age 21 +/- 2.9 yr. were recruited for this study. We used a mechanical response tissue analyzer (Gaitscan, NJ) to calculate EI, where E is Young's modulus of elasticity and I is the cross-sectional moment of inertia. EI was obtained from tissue response to a vibration probe placed directly on the skin of the mid-region of tibia and ulna. BMD of the heel and wrist were measured with a probe densitometer (PIXI, Lunor, WI). The SYN were taller than (p < 0.05) the GYM but weighed the same as the GYM. EI obtained from tibia and ulna of the SYN (291 +/- 159 and 41 +/- 19.4, respectively) were not significantly different from thc GYM (285 +/- 140 and 44 +/- 18.3, respectively). BMD of the heel and wrist in GYM were higher than in SYN (p < 0.001). High impact weight-bearing activities promote similar bone strength but greater BMD response than non-impact activities performed in a buoyant environment.

Liang, Michael T. C.↗
NASA NTRS2006

Towards Multifunctional Characteristics of Embedded Structures With Carbon Nanotube Yarns

This paper presents recent results on research of achieving multifunctional structures utilizing Carbon Nanotube (CNT) yarns. The investigation centers on creating composite structures with CNT yarns to simultaneously achieve increases in mechanical strength and the ability to sense strain. The CNT yarns used in our experiments are of the single-ply and two-ply variety with the single-ply yarns having diameters on the order of 10-20 m. The yarns are embedded in silicon rubber and polyurethane test specimens. Mechanical tests show an increase in modulus of elasticity, with an additional weight increase of far less than one-percent. Sensing characteristics of the yarns are investigated on stainless steel test beams in an electrical bridge configuration, and are observed to have a strain sensitivity of 0.7mV/V/1000 micro-strain. Also reported are measurements of the average strain distribution along the direction of the CNT yarns on square silicon rubber membranes.

Hernandez, Corey D.↗
NASA NTRS2006

Multifunctional Characteristics of Carbon Nanotube (CNT) Yarn Composites

By forming composite structures with Carbon Nanotube (CNT) yarns we achieve materials capable of measuring strain and composite structures with increased mechanical strength. The CNT yarns used are of the 2-ply and 4-ply variety with the yarns having diameters of about 15-30 micrometers. The strain sensing characteristics of the yarns are investigated on test beams with the yarns arranged in a bridge configuration. Additionally, the strain sensing properties are also investigated on yarns embedded on the surface of a flexible membrane. Initial mechanical strength tests also show an increase in the modulus of elasticity of the composite materials while incurring a weight penalty of less than one-percent. Also presented are initial temperature characterizations of the yarns.

Hernandez, Corey D.↗
NASA NTRS2005

Reactive Additives for Phenylethynyl-Containing Resins

Phenylethynyl-containing reactive additive (PERA) compounds and mixtures have been found to be useful for improving the processability of oligomers, polymers, co-oligomers, and copolymers that contain phenylethynyl groups. The additives can be incorporated in different forms: A solution of an amide acid or an imide of a PERA can be added to a solution of phenylethynyl-containing oligomer, polymer, co-oligomer, or copolymer; or An imide powder of a PERA can be mixed with a dry powder of a phenylethynyl-containing oligomer, polymer, co-oligomer, or copolymer. The effect of a given PERA on the processability and other properties of the resin system depends on whether the PERA is used in the amide acid or an imide form. With proper formulation, the PERA reduces the melt viscosity of the resin and thereby reduces the processing pressures needed to form the adhesive bonds, consolidate filled or unfilled moldings, or fabricate fiber-reinforced composite laminates. During thermal cure, a PERA reacts with itself as well as with the phenylethynyl-containing host resin and thereby becomes chemically incorporated into the resin system. The effects of the PERA on mechanical properties, relative to those of the host resin, depend on the amount of PERA used. Typically, the incorporation of the PERA results in (1) increases in the glass-transition temperature (Tg), modulus of elasticity, and parameters that characterize behavior under compression, and (2) greater retention of the aforementioned mechanical properties at elevated temperatures without (3) significant reduction of toughness or damage tolerance. Of the formulations tested thus far, the ones found to yield the best overall results were those for which the host resin was the amide acid form of a phenylethynyl-terminated imide (PETI) co-oligomer having a molecular weight of 5,000 g/mole [hence, designated PETI-5] and a PERA denoted as PERA-1. PETI-5 was made from 3,3',4'4'-biphenyltetracarboxylic dianhydride, 3,4'-oxydianiline (3,4'-ODA), 1,3-bis(3-aminophenoxy) benzene (1,3-APB), and 4-phenylethynylphthalic anhydride (PEPA). PERA-1 was made from 3,5-diamino- 4.-phenylethynylbenzophenon and equimolar amounts of phthalic anhydride and PEPA. To make PERA-1 in the imide form, the aforementioned ingredients were processed by refluxing in glacial acetic acid. To make the amide form of PERA-1, the ingredients were reacted in N-methyl-2-pyrrolidinone (NMP) under nitrogen at a temperature of 23 C (see figure). On the basis of the processability and other properties, a blend comprising 20 weight percent of PERA-1 and 80 weight percent PETI-5 was selected for further evaluation. Relative to neat PETI-5, the blend exhibited an increase in Tg; improved processability; and comparable values of shear strength in adhesion to titanium panels, open-hole compressive properties, compression properties after impact, and resistance to microcracking.

Connell, John W.↗
NASA NTRS2004

Formulations for Stronger Solid Oxide Fuel-Cell Electrolytes

Tests have shown that modification of chemical compositions can increase the strengths and fracture toughnesses of solid oxide fuel-cell (SOFC) electrolytes. Heretofore, these solid electrolytes have been made of yttria-stabilized zirconia, which is highly conductive for oxygen ions at high temperatures, as needed for operation of fuel cells. Unfortunately yttria-stabilized zirconia has a high coefficient of thermal expansion, low resistance to thermal shock, low fracture toughness, and low mechanical strength. The lack of strength and toughness are especially problematic for fabrication of thin SOFC electrolyte membranes needed for contemplated aeronautical, automotive, and stationary power-generation applications. The modifications of chemical composition that lead to increased strength and fracture toughness consist in addition of alumina to the basic yttria-stabilized zirconia formulations. Techniques for processing of yttria-stabilized zirconia/alumina composites containing as much as 30 mole percent of alumina have been developed. The composite panels fabricated by these techniques have been found to be dense and free of cracks. The only material phases detected in these composites has been cubic zirconia and a alumina: this finding signifies that no undesired chemical reactions between the constituents occurred during processing at elevated temperatures. The flexural strengths and fracture toughnesses of the various zirconia-alumina composites were measured in air at room temperature as well as at a temperature of 1,000 C (a typical SOFC operating temperature). The measurements showed that both flexural strength and fracture toughness increased with increasing alumina content at both temperatures. In addition, the modulus of elasticity and the thermal conductivity were found to increase and the density to decrease with increasing alumina content. The oxygen-ion conductivity at 1,000 C was found to be unchanged by the addition of alumina.

Bansal, Narottam P.↗
NASA NTRS2011

Thermal Energy for Lunar In Situ Resource Utilization: Technical Challenges and Technology Opportunities

Oxygen production from lunar raw materials is critical for sustaining a manned lunar base but is very power intensive. Solar concentrators are a well-developed technology for harnessing the Sun s energy to heat regolith to high temperatures (over 1375 K). The high temperature and potential material incompatibilities present numerous technical challenges. This study compares and contrasts different solar concentrator designs that have been developed, such as Cassegrains, offset parabolas, compound parabolic concentrators, and secondary concentrators. Differences between concentrators made from lenses and mirrors, and between rigid and flexible concentrators are also discussed. Possible substrate elements for a rigid mirror concentrator are selected and then compared, using the following (target) criteria: (low) coefficient of thermal expansion, (high) modulus of elasticity, and (low) density. Several potential lunar locations for solar concentrators are compared; environmental and processing-related challenges related to dust and optical surfaces are addressed. This brief technology survey examines various sources of thermal energy that can be utilized for materials processing on the lunar surface. These include heat from nuclear or electric sources and solar concentrators. Options for collecting and transporting thermal energy to processing reactors for each source are examined. Overall system requirements for each thermal source are compared and system limitations, such as maximum achievable temperature are discussed.

Gordon, Pierce E. C.↗
NASA NTRS2009

Properties of Refractory Concrete in Tension and Compression

Refractory concrete on the LC-39A Flame Deflector has been damaged during multiple Space Shuttle launches (e.g. STS-124, STS-126, STS-119, and STS-125, STS-127). These events have prompted a better understanding of the system via an analytical model of the Flame Deflector assembly to include the Fondu Fyre refractory concrete. This model requires test data inputs of the refractory concrete's mechanical properties, which include stress versus strain curves in tension and compression, modulus of elasticity, and Poisson's ratio. Sections of Fondu Fyre refractory concrete removed from the LC-39A Flame Deflector were provided for this testing.

Sampson, Jeffrey↗
NASA NTRS2014

Mechanical Behavior of Microelectromechanical Microshutters

A custom micro-mechanical test system was constructed using off-the-shelf components to characterize the mechanical properties of microshutters. Microshutters are rectangular microelectromechanical apertures which open and close about a narrow torsion bar hinge. Displacement measurements were verified using both capacitive and digital image correlation techniques. Repeatable experiments on Si3N4 cantilever beams verified that the test system operates consistently. Using beam theory, the modulus of elasticity of the low stress Si3N4 was approximately 150 GPa, though significant uncertainty exists for this measurement due primarily to imprecise knowledge of the cantilever thickness. Tests conducted on microshutter arrays concluded that reducing the Si3N4 thickness from 250 nm to 500 nm reduces the torsional stiffness by a factor of approximately four. This is in good agreement with analytical and finite element models of the microshutters.

silicon nitride↗
NASA NTRS2015

Characterization of Machine Variability and Progressive Heat Treatment in Selective Laser Melting of Inconel 718

The absence of an economy of scale in spaceflight hardware makes additive manufacturing an immensely attractive option for propulsion components. As additive manufacturing techniques are increasingly adopted by government and industry to produce propulsion hardware in human-rated systems, significant development efforts are needed to establish these methods as reliable alternatives to conventional subtractive manufacturing. One of the critical challenges facing powder bed fusion techniques in this application is variability between machines used to perform builds. Even with implementation of robust process controls, it is possible for two machines operating at identical parameters with equivalent base materials to produce specimens with slightly different material properties. The machine variability study presented here evaluates 60 specimens of identical geometry built using the same parameters. 30 samples were produced on machine 1 (M1) and the other 30 samples were built on machine 2 (M2). Each of the 30-sample sets were further subdivided into three subsets (with 10 specimens in each subset) to assess the effect of progressive heat treatment on machine variability. The three categories for post-processing were: stress relief, stress relief followed by hot isostatic press (HIP), and stress relief followed by HIP followed by heat treatment per AMS 5664. Each specimen (a round, smooth tensile) was mechanically tested per ASTM E8. Two formal statistical techniques, hypothesis testing for equivalency of means and one-way analysis of variance (ANOVA), were applied to characterize the impact of machine variability and heat treatment on six material properties: tensile stress, yield stress, modulus of elasticity, fracture elongation, and reduction of area. This work represents the type of development effort that is critical as NASA, academia, and the industrial base work collaboratively to establish a path to certification for additively manufactured parts. For future flight programs, NASA and its commercial partners will procure parts from vendors who will use a diverse range of machines to produce parts and, as such, it is essential that the AM community develop a sound understanding of the degree to which machine variability impacts material properties.

Prater, T.↗
NASA NTRS2015

Characterization of Machine Variability and Progressive Heat Treatment in Selective Laser Melting of Inconel 718

The absence of an economy of scale in spaceflight hardware makes additive manufacturing an immensely attractive option for propulsion components. As additive manufacturing techniques are increasingly adopted by government and industry to produce propulsion hardware in human‐rated systems, significant development efforts are needed to establish these methods as reliable alternatives to conventional subtractive manufacturing. One of the critical challenges facing powder bed fusion techniques in this application is variability between machines used to perform builds. Even with implementation of robust process controls, it is possible for two machines operating at identical parameters with equivalent base materials to produce specimens with slightly different material properties. The machine variability study presented here evaluates 60 specimens of identical geometry built using the same parameters. 30 samples were produced on machine 1 (M1) and the other 30 samples were built on machine 2 (M2). Each of the 30‐sample sets were further subdivided into three subsets (with 10 specimens in each subset) to assess the effect of progressive heat treatment on machine variability. The three categories for post‐processing were: stress relief, stress relief followed by hot isostatic press (HIP), and stress relief followed by HIP followed by heat treatment per AMS 5664. Each specimen (a round, smooth tensile) was mechanically tested per ASTM E8. Two formal statistical techniques, hypothesis testing for equivalency of means and one‐way analysis of variance (ANOVA), were applied to characterize the impact of machine variability and heat treatment on six material properties: tensile stress, yield stress, modulus of elasticity, fracture elongation, and reduction of area. This work represents the type of development effort that is critical as NASA, academia, and the industrial base work collaboratively to establish a path to certification for additively manufactured parts. For future flight programs, NASA and its commercial partners will procure parts from vendors who will use a diverse range of machines to produce parts and, as such, it is essential that the AM community develop a sound understanding of the degree to which machine variability impacts material properties.

Prater, Tracie↗
NASA NTRS2015

Body of Knowledge (BOK) for Copper Wire Bonds

Copper wire bonds have replaced gold wire bonds in the majority of commercial semiconductor devices for the latest technology nodes. Although economics has been the driving mechanism to lower semiconductor packaging costs for a savings of about 20% by replacing gold wire bonds with copper, copper also has materials property advantages over gold. When compared to gold, copper has approximately: 25% lower electrical resistivity, 30% higher thermal conductivity, 75% higher tensile strength and 45% higher modulus of elasticity. Copper wire bonds on aluminum bond pads are also more mechanically robust over time and elevated temperature due to the slower intermetallic formation rate - approximately 1/100th that of the gold to aluminum intermetallic formation rate. However, there are significant tradeoffs with copper wire bonding - copper has twice the hardness of gold which results in a narrower bonding manufacturing process window and requires that the semiconductor companies design more mechanically rigid bonding pads to prevent cratering to both the bond pad and underlying chip structure. Furthermore, copper is significantly more prone to corrosion issues. The semiconductor packaging industry has responded to this corrosion concern by creating a palladium coated copper bonding wire, which is more corrosion resistant than pure copper bonding wire. Also, the selection of the device molding compound is critical because use of environmentally friendly green compounds can result in internal CTE (Coefficient of Thermal Expansion) mismatches with the copper wire bonds that can eventually lead to device failures during thermal cycling. Despite the difficult problems associated with the changeover to copper bonding wire, there are billions of copper wire bonded devices delivered annually to customers. It is noteworthy that Texas Instruments announced in October of 2014 that they are shipping microcircuits containing copper wire bonds for safety critical automotive applications. An evaluation of copper wire bond technology for applicability to spaceflight hardware may be warranted along with concurrently compiling a comprehensive understanding of the failure mechanisms involved with copper wire bonded semiconductor devices.

Body of Knowledge (BOK)↗
NASA NTRS2015

Use of a Tantalum Liner to Reduce Bore Erosion and Increase Muzzle Velocity in Two-Stage Light Gas Guns

Muzzle velocities and gun erosion predicted by earlier numerical simulations of two stage light gas guns with steel gun tubes were in good agreement with experimental values. In a subsequent study, simulations of high performance shots were repeated with rhenium (Re) gun tubes. Large increases in muzzle velocity (2 - 4 km/sec) were predicted for Re tubes. In addition, the hydrogen-produced gun tube erosion was, in general, predicted to be zero with Re tubes. Tantalum (Ta) has some mechanical properties superior to those of Re. Tantalum has a lower modulus of elasticity than Re for better force transmission from the refractory metal liner to an underlying thick wall steel tube. Tantalum also has greater ductility than Re for better survivability during severe stress/strain cycles. Also, tantalum has been used as a coating or liner in military powder guns with encouraging results. Tantalum has, however, somewhat inferior thermal properties to those of rhenium, with a lower melting point and lower density and thermal conductivity. The present study was undertaken to see to what degree the muzzle velocity gains of rhenium gun tubes (over steel tubes) could be achieved with tantalum gun tubes. Nine high performance shots were modeled with a new version of our CFD gun code for steel, rhenium and tantalum gun tubes. For all except the highest velocity shot, the results with Ta tubes were nearly identical with those for Re tubes. Even for the highest velocity shot, the muzzle velocity gain over a steel tube using Ta was 82% of the gain obtained using Re. Thus, the somewhat inferior thermal properties of Ta (when compared to those of Re) translate into only very slightly poorer overall muzzle velocity performance. When this fact is combined with the superior mechanical properties of Ta and the encouraging performance of Ta liners/coatings in military powder guns, tantalum is to be preferred over Re as a liner/coating material for two stage light gas guns to increase muzzle velocity and reduce bore erosion.

Launchers↗
NASA NTRS2024

3D Printing and Surface Engineering of Ti6Al4V Scaffolds for Enhanced Osseointegration in an In Vitro Study

Ti6Al4V superalloy is recognized as a good candidate for bone implants owing to its biocompatibility, corrosion resistance, and high strength-to-weight ratio. While dense metal implants are associated with stress shielding issues due to the difference in densities, stiffness, and modulus of elasticity compared to bone tissues, the surface of the implant/scaffold should mimic the properties of the bone of interest to assure a good integration with a strong interface. In this study, we investigated the additive manufacturing of porous Ti6Al4V scaffolds and coating modification for enhanced osteoconduction using osteoblast cells. The results showed the successful fabrication of porous Ti6Al4V scaffolds with adequate strength. Additionally, the surface treatment with NaOH and Dopamine Hydrochloride (DOPA) promoted the formation of Dopamine Hydrochloride (DOPA) coating with an optimized coating process, providing an environment that supports higher cell viability and growth compared to the uncoated Ti6Al4V scaffolds, as demonstrated by the higher proliferation ratios observed from day 1 to day 29. These findings bring valuable insights into the surface modification of 3D-printed scaffolds for improved osteoconduction through the coating process in solutions.

metal additive manufacturing↗
NASA NTRSDate not supplied

Investigation of Lunar-Inspired Geopolymer Concrete Formulations Mixed and Cured in Microgravity on the International Space Station (ISS)

The research outlined in this presentation investigates the use of various lunar regolith simulants in geopolymer lunar concrete mixes mixed and cured on the International Space Station (ISS). The motivation for this work is to study the effects of gravity on the microstructure of alkali-activated materials cured with heat, and to develop materials for the construction of long-term infrastructure on the lunar surface with in-situ resource utilization (ISRU). ISRU for construction materials reduces the cost and mass of payloads related to lunar construction. The advantage of geopolymer concrete as opposed to traditional portland cement concrete is that water acts as a medium for the polymerization reaction and leaves the system throughout the process, reducing its demand. Twelve samples of lunar regolith simulant and a solution composed of sodium hydroxide and sodium silicate were sent to the ISS. The three simulants were OPRH2N, OPRL2N, and JSC-1AF, using only particles less than 53 µm in diameter to increase reactivity of the simulant. Simulant to solution ratios were determined by workability while mixing. The simulant and solution were sealed Burst Pouches® along with 2 other sealed bags to prevent material from leaking. Crew member F-14 conducted testing on the ISS by introducing the solution to the simulant in the Burst Pouch®, mixing the sample with a spatula, and then clamping the specimen in the fresh state to prevent flow inside the Burst Pouch®. These specimens were then put in a thermos heated to 80C via sealed drinking water bags to cure for 24 hours with a temperature logger. The cured specimens remained in microgravity for at least 28 days and were returned from the ISS in February 2025. The specimens were then brought to the NASA Marshall Space Flight Center (MSFC) to analyze. Material characterization consisted of conducting Micro-CT tests of entire samples in their sealed apparatus to a resolution of 25µm. 2D image slices were saved in each orthogonal direction of each specimen at a 0.03 mm step size from the 3D model to conduct analytical porosity calculations. Representative samples from each specimen were sampled to perform helium gas pycnometery and were then mounted in resin for SEM imaging, EDS, and nanoindentation. Porosity was analyzed analytically using micromechanics modelling with the assistance of the NASA Multiscale Analysis Tool (NASMAT), as well as the NASA Advanced Supercomputing (NAS) servers (V. Saseendran & N. Yamamoto, 2024). Density was measured using helium gas pycnometery and was then compared to the theoretical density for experimental porosity calculation. Due to the samples’ non-uniform shape being cured in a pouch, traditional compression and tensile strength testing could not be performed. Nanoindentation was conducted at Clarkson University to determine the microhardness and reduced modulus of elasticity. Results from flight samples can be compared to ground samples currently in DLR’s possession to determine the effect on microstructure from being mixed and cured in microgravity. This study gives further insight and understanding of geopolymer lunar concrete and its viability as a lunar construction material with ISRU.

Adam Johnson↗
NASA NTRS2019

The Influence of Redox Conditions on the Seismic Properties of Polycrystalline Olivine

Eight olivine specimens were fabricated by use of a solgel method and hot-pressing at 1200 degrees Centigrade and 300 megapascals (MPa) inside of welded Pt capsules. Each hot-pressed specimen was then recovered, precision ground, and wrapped in Pt, Ni or NiFe foil to vary oxygen fugacity (fO2) during the subsequent forced torsional oscillation measurements. Mechanical testing was conducted at 10 oscillation periods between 1 and 1000 seconds, at a confining pressure of 200 MPa, during a slow staged-cooling from a maximum temperature of 1200 degrees Centigrade down to room temperature. After mechanical testing, each specimen was axially sectioned and EBSD (Electron BackScatter Diffraction) was used for the determination of the representative grain size, and grain size distribution of each sample. In addition, each longitudinal section was mapped via FTIR (Fourier Transform Infrared Spectroscopy) to determine the spatial distribution and concentrations of chemically bound and molecular water. Amongst these eight specimens, chemically bound ‘water’ contents were observed to vary between 0 and 1150 atom parts per million (ppm) H/Si, and molecular water concentrations varied between 0 and 245 atom ppm H/Si. Our forced-oscillation results demonstrate that the measured magnitude of anelastic relaxation within the experimental ‘window’ of oscillation periods is unrelated to the water content. Rather, a relationship was observed between the magnitude of anelastic relaxation and the prevailing redox conditions, which is influenced by the choice of metal sleeving used during the mechanical test. Further, regardless of water content or metal sleeving, each specimen exhibits coupled variations in shear modulus and dissipation within the observational window, indicative of ‘high-temperature background’ behavior, that can be described by a Burgers-type model. During initial fitting of the Burgers models, the unrelaxed shear modulus at a reference temperature of 900°C (elastic unloading/reloading shear modulus G (sub UR)) and the temperature derivative of the unrelaxed shear modulus (dGU/dT), were treated as adjustable parameters. For all Fe-bearing olivine samples we observe deficits of G (sub UR) and increased values of dGU/dT, relative to the expected elastic (anharmonic) behavior for Fo (Forsterite content percentage) (sub 90) olivine. This behavior is indicative of anelastic relaxation occurring at shorter periods than observable within the ‘window’ of oscillation periods used in the mechanical test. Moving towards a comprehensive and seismologically applicable Burgers model, which includes this newly observed effect of redox conditions on anelastic relaxation, we will present our progress on reconciling truly anharmonic and elastic behavior of Fo (sub 90) olivine with our observed forced-oscillation data.

Cline, C. J., II↗
NASA NTRS1991

An overview of self-consistent methods for fiber-reinforced composites

The Walker et al. (1989) self-consistent method to predict both the elastic and the inelastic effective material properties of composites is examined and compared with the results of other self-consistent and elastically based solutions. The elastic part of their method is shown to be identical to other self-consistent methods for non-dilute reinforced composite materials; they are the Hill (1965), Budiansky (1965), and Nemat-Nasser et al. (1982) derivations. A simplified form of the non-dilute self-consistent method is also derived. The predicted, elastic, effective material properties for fiber reinforced material using the Walker method was found to deviate from the elasticity solution for the v sub 31, K sub 12, and mu sub 31 material properties (fiber is in the 3 direction) especially at the larger volume fractions. Also, the prediction for the transverse shear modulus, mu sub 12, exceeds one of the accepted Hashin bounds. Only the longitudinal elastic modulus E sub 33 agrees with the elasticity solution. The differences between the Walker and the elasticity solutions are primarily due to the assumption used in the derivation of the self-consistent method, i.e., the strain fields in the inclusions and the matrix are assumed to remain constant, which is not a correct assumption for a high concentration of inclusions.

Gramoll, Kurt C.↗
NASA NTRS1985

Elastic constant versus temperature behavior of three hardened maraging steels

Elastic constants of three maraging steels were determined by measuring ultrasonic velocities. Annealed steels show slightly lower bulk moduli and considerably lower shear moduli than hardened steels. All the elastic constants (Young's modulus, shear modulus, bulk modulus and Poisson's ratio) show regular temperature behavior between 76 and 400 K. Young's modulus and the shear modulus increase with increasing yield strength, but the bulk modulus and Poisson's ratio are relatively unchanged. Elastic anisotropy is quite small.

Ledbetter, H. M.↗