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DOE OSTI2020

Achieving 5.9% elastic strain in kilograms of metallic glasses: Nanoscopic strain engineering goes macro

The ideal elastic limit is the upper bound of the achievable strength and elastic strain of solids. However, the elastic strains that bulk materials can sustain are usually below 2%, due to the localization of inelastic deformations at the lattice scale. In this study, we achieved >5% elastic strain in bulk quantity of metallic glass, by exploiting the more uniform and smaller-magnitude atomic-scale lattice strains of martensitic transformation as a loading medium in a bulk metallic nanocomposite. The self-limiting nature of martensitic transformation helps to prevent lattice strain transfer that leads to the localization of deformation and damage. This lattice strain egalitarian strategy enables bulk metallic materials in kilogram-quantity to achieve near-ideal elastic limit. This concept is verified in a model in situ bulk amorphous (TiNiFe)-nanocrystalline (TiNi(Fe)) composite, in which the TiNiFe amorphous matrix exhibits a maximum tensile elastic strain of similar to 5.9%, which approaches its theoretical elastic limit. As a result, the model bulk composite possesses a large recoverable strain of similar to 7%, a maximum tensile strength of above 2 GPa, and a large elastic resilience of similar to 79.4 MJ/m 3 . The recoverable strain and elastic resilience are unmatched by known high strength bulk metallic materials. This design concept opens new opportunities for the development of high-performance bulk materials and elastic strain engineering of the physiochemical properties of glasses.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Elastic-plastic deformation of molybdenum single crystals shocked to 12.5 GPa: Crystal anisotropy effects

Here, to understand crystal anisotropy effects on shock-induced elastic-plastic deformation of molybdenum (Mo), results from high-purity single crystals shocked along [110] and [111] orientations to an elastic impact stress of 12.5 GPa were obtained and compared with the [100] results previously reported [A. Mandal and Y. M Gupta, J. Appl. Phys. 121, 045903 (2017)]. Measured wave profiles showed a time-dependent response, and strong anisotropy was observed in the elastic wave attenuation with the propagation distance, elastic limits, shock speeds, and overall structure of the wave profiles. Resolved shear stresses on {110} $\langle$111$\rangle$ and {112} $\langle$111$\rangle$ slip systems provided insight into the observed anisotropy in elastic wave attenuation and elastic limits and showed that shear stresses, and not longitudinal stresses, are a better measure of strength in shocked single crystals. Under shock compression, resolved shear stresses at elastic limits were comparable to the Peierls stress of screw dislocations in Mo. Elastic wave attenuation was rapid when shear stresses were larger than the Peierls stress. Large differences in the elastic limits under shock and quasi-static loading are likely a consequence of the large Peierls stress value for Mo. Numerically simulated wave profiles, obtained using the dislocation-based plasticity model described in the [100] work, showed good agreement with all measured wave profiles but could not differentiate between the {110} $\langle$111$\rangle$ and {112} $\langle$111$\rangle$ slip systems. Overall, experimental results and corresponding numerical simulations for the three crystal orientations have provided a comprehensive insight into shock-induced elastic-plastic deformation of Mo single crystals, including the development of a continuum material model.

36 MATERIALS SCIENCE↗

DOE OSTI2021

MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials

We report the MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ( C ij ) obtained from any ab-initio density-functional theory (DFT) code. The current version of this package reads the output of VASP, ABINIT, and Quantum Espresso codes (but it can be easily generalized to any other DFT code) and performs the appropriate post-processing of elastic constants as per the requirement of the user. This program can also detect the input structure's crystal symmetry and test the mechanical stability of all crystal classes using the Born-Huang criteria. Various useful material-specific properties such as elastic moduli, longitudinal and transverse elastic wave velocities, Debye temperature, elastic anisotropy, 2D layer modulus, hardness, Pugh's ratio, Cauchy's pressure, Kleinman's parameter, and Lame's coefficients, can be estimated using this program. Another existing feature of this program is to employ the ELATE package (2016) [29] and plot the spatial variation of several elastic properties such as Poisson's ratio, linear compressibility, shear modulus, and Young's modulus in three dimensions. Further, the MechElastic package can plot the equation of state (EOS) curves for energy and pressure for a variety of EOS models such as Murnaghan, Birch, Birch-Murnaghan, and Vinet, by reading the inputted energy/pressure versus volume data obtained via numerical calculations or experiments. This package is particularly useful for the high-throughput analysis of elastic and mechanical properties of materials.

2D materials↗

DOE OSTI2018

Effects of enzymes on elastic modulus of low-density lipoproteins were investigated using atomic force microscopy

Highlights: • The elastic modulus of the enzymatically digested LDL was evaluated using AFM. • The LDL elastic modulus was decreased not by proteases but by phospholipase A{sub 2}. • The LDL size was unaffected by proteases or PLA{sub 2}. Oxidation of low-density lipoproteins (LDLs) induces development of cardiovascular disease. Recently, reports of studies using atomic force microscopy (AFM) have described that the elastic modulus of metal-induced oxidized LDLs is lower than the modulus before oxidation. However, the mechanisms of change of the elastic modulus have not been well investigated. We postulated that disorder of the LDL structure might decrease the elastic modulus. This study measured the elastic modulus of LDLs before and after enzyme treatment with V8 protease, α-chymotrypsin, and phospholipase A{sub 2}. After LDLs were obtained from serum by ultracentrifugation, LDLs or enzyme-treated LDLs were physically absorbed. They were crowded on a mica surface. Although V8 protease and α-chymotrypsin did not induce the elastic modulus change, treatment with PLA{sub 2} decreased the elastic modulus. The LDL particle size did not change during the enzyme treatment. Results suggest that disordering of the lipid structure of the LDL might contribute to the elastic modulus change. Results show that AFM might be a useful tool to evaluate disorders of complex nanoscale particle structures from lipids and proteins such as lipoproteins.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Establishing temperature upper limits for the ASME Section III, Division 5 design by elastic analysis methods

ection III, Division 5 of the ASME Boiler and Pressure Vessel Code provides two broad paths for the design of high temperature, safety-critical nuclear components: design by elastic analysis and design by inelastic analysis. The design by elastic analysis approach, as the name suggests, uses a linear elastic stress analysis of the component and applies design rules designed to bound response of the actual structure, which will undergo both creep and plasticity. Currently, the Code allows the use of the elastic approach for all operating temperatures up to the maximum use temperatures in the Code. The bounds used in the elastic approach assume an uncoupled material response combining rate dependent creep with rate independent plasticity. However, at elevated temperatures creep and plasticity are coupled, rate dependent mechanisms and so the elastic analysis rules may become non-conservative. We present several examples of potential non-conservatism in the elastic analysis rules at high operating temperatures. Then we describe a systematic method for determining a temperature cutoff describing the transition from non-unified, rate independent plasticity material response to a rate dependent, unified plastic response. Logically, this transition temperature sets the upper bound for the allowable, conservative use of the design by elastic analysis approach and so we propose these temperatures, determined for all the Section III, Division 5 Class A materials, as Code limits for the applicability of the elastic approach.

Messner, M. C.↗

DOE OSTI2015

Estimating Price Elasticity using Market-Level Appliance Data

This report provides and update to and expansion upon our 2008 LBNL report “An Analysis of the Price Elasticity of Demand for Appliances,” in which we estimated an average relative price elasticity of -0.34 for major household appliances (Dale and Fujita 2008). Consumer responsiveness to price change is a key component of energy efficiency policy analysis; these policies influence consumer purchases through price both explicitly and implicitly. However, few studies address appliance demand elasticity in the U.S. market and public data sources are generally insufficient for rigorous estimation. Therefore, analysts have relied on a small set of outdated papers focused on limited appliance types, assuming long-term elasticities estimated for other durables (e.g., vehicles) decades ago are applicable to current and future appliance purchasing behavior. We aim to partially rectify this problem in the context of appliance efficiency standards by revisiting our previous analysis, utilizing data released over the last ten years and identifying additional estimates of durable goods price elasticities in the literature. Reviewing the literature, we find the following ranges of market-level price elasticities: -0.14 to -0.42 for appliances; -0.30 to -1.28 for automobiles; -0.47 to -2.55 for other durable goods. Brand price elasticities are substantially higher for these product groups, with most estimates -2.0 or more elastic. Using market-level shipments, sales value, and efficiency level data for 1989-2009, we run various iterations of a log-log regression model, arriving at a recommended range of short run appliance price elasticity between -0.4 and -0.5, with a default value of -0.45.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

Using Meta-Analysis to Estimate World Oil Demand Elasticity

Oil demand elasticities are important behavioral parameters for assessing the effectiveness of many energy policy proposals and the economic impact of oil market shocks. Most of the literature on petroleum demand computes elasticities for one particular petroleum product in a country or group of countries. There are fewer published values for world oil demand elasticity because the reduced-form single equation approach used in much of the petroleum product demand literature leads to endogeneity bias when applied to global demand. This study uses meta-analysis techniques to compute world oil demand elasticity. Metaregressions are first conducted to identify sources of variation in elasticity estimates for transportation and non-transportation sectors collected from 75 studies published from 2000 to 2015. The estimated coefficients from the metaregressions are then summarized into elasticity baseline values for several combinations of moderator variable values. Finally, a global oil demand elasticity is computed as the consumption-weighted average of the two sectoral elasticities. Resulting mean values for the short-run oil demand elasticities with respect to price range from -0.7 to -0.14 depending on the attributes selected for the price variable. The long-run range of mean values is much wider (-0.26, -0.83).

Uria Martinez, Rocio↗

DOE OSTI2023

High temperature elastic properties of sub-stoichiometric yttrium dihydrides

Yttrium hydrides are considered as candidate materials for neutron moderation applied in microreactors (akin transportable tiny nuclear reactors) owing to their superior thermal stability and hydrogen retention. The evolution of elastic properties of these materials at elevated temperatures, needed for predicting the thermomechanical response and performance of the moderator during in-service reactor conditions, however, is lacking. Here, we report the Young’s and shear elastic moduli of three stoichiometries of bulk yttrium hydride (YH x , x = 1.61, 1.82, and 1.84) from room temperature to 1000°C. In situ temperature-dependent measurements of the longitudinal and shear wave velocities were performed using a laser ultrasonic technique while heating the sample in a vacuum-pumped heating stage. The elastic moduli increased linearly with increasing hydrogen content and decreased by ~10% during heating from room temperature to 1000°C in the three YH x compositions. The linear relationship between the elastic moduli and the hydrogen content in yttrium hydride was verified by atomistic calculations based on density functional theory (DFT). The absence of abrupt changes in the temperature-dependent measurements of elastic modulus of the YH x samples suggested negligible loss of hydrogen at elevated temperatures. Excellent agreement was found between the measured and calculated dependence of the elastic moduli on the stoichiometry, thereby providing a new approach for investigating the effects of fabrication-induced parameters (such as porosity) on the elastic moduli. Furthermore, this study demonstrates the utility of the combined approach involving DFT-based atomistic calculations and measurements of the elastic moduli for the informative development of metal hydrides and can be used as a metric for novel moderator materials investigations for emerging microreactors and beyond.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Elastic and thermodynamic properties of cerium-doped yttrium aluminum garnets

Cerium-doped yttrium aluminum garnets (Y 3-x Ce x Al 5 O 12 , Ce:YAGs) are promising yellow light-emitting components of solid-state white light-emitting diodes. Although there have been numerous studies examining the effects of Ce concentrations on the luminescent properties of Y 3-x Ce x Al 5 O 12 , the impacts of Ce dopant on the elastic and thermodynamic properties are not well understood. In this work, we used resonant ultrasound spectroscopy (RUS) to determine the effects of Ce doping (0.025, 0.1, 1 at. %) on the elastic and thermodynamic properties of Y 3-x Ce x Al 5 O 12 . The elastic moduli calculated via the Voigt–Reuss–Hill (VRH) method demonstrated that low Ce dopant concentrations (≤0.1 at. %) induced negligible effects on the elasticity of the YAG host matrix, while a high Ce concentration (1 at. %) yielded significant softening. RUS spectral analysis and SEM images suggested that the elastic softening originated from microstructural differences induced at higher Ce dopant concentrations. Additionally, we demonstrated an increase in elastic anisotropy at higher Ce concentrations, which further elucidated the correlations between structure and elasticity of Y 3-x Ce x Al 5 O 12 . Debye temperatures ($θ_D$), heat capacities ($C_p$), and thermal conductivities ($\mathit{κ}$) were calculated for Ce:YAGs through the relations of RUS-derived parameters (sound velocities, elastic moduli) and previously determined thermal expansion coefficients. Ce:YAG was found to have a significant reduction in $θ_D$, Cp, and $\mathit{κ}$ at Ce concentrations ≥1 at. %. Lastly, extrapolation of $C_p$ and $\mathit{κ}$ to higher temperatures allowed the modeling of thermal stress experienced by Y 3-x Ce x Al 5 O 12 disks up to 1073.15 K.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Atomistic Simulations of the Elastic Compression of Platinum Nanoparticles

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.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Effect of Cr and Al on Elastic Constants of FeCrAl Alloys Investigated by Molecular Dynamics Method

The FeCrAl alloy system is recognized as one of the candidate materials for accident-tolerant fuel (ATF) cladding in the nuclear power industry due to its high oxidation resistance under irradiation and high-temperature environments. The concentrations of Cr and Al have a significant effect on elastic properties of the FeCrAl alloy. In this work, elastic constants C 11 , C 12 , C 44 , bulk modulus and shear modulus of FeCrAl alloy were calculated with molecular dynamics methods. We explored compositions with 1–15 wt.% Cr and 1–5 wt.% Al at temperatures from 0 K to 750 K. The results show that the concentrations of Al and Cr have different effects on the elastic constants. When the concentration of Al was fixed, a decrease in bulk modulus and shear modulus with increasing Cr content was observed, consistent with previous experimental results. The dependence of elastic constants on temperature was also the same as in the experiments. Investigations into elastic properties of defect-containing alloys have shown that vacancies, voids, interstitials and Cr-rich precipitations have different effects on elastic properties of FeCrAl alloys. Investigations of elastic properties of defect-containing alloys have shown that vacancies, void, interstitials and Cr-rich precipitations have different effects on elastic properties of FeCrAl alloys. Therefore, the present results indicate that both the Cr and Al concentrations and radiation defects should be considered to develop and apply the FeCrAl alloy in ATF design.

36 MATERIALS SCIENCE↗

NASA NTRS2023

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↗

DOE OSTI2023

Beyond the Stokes approximation: shallow visco-elastic ice-sheet models

Abstract The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects.

58 GEOSCIENCES↗

DOE OSTI2019

The Effects of Shear Strain, Fabric, and Porosity Evolution on Elastic and Mechanical Properties of Clay-Rich Fault Gouge

The elastic and mechanical properties of fault gouge are key controls on fault zone stiffness, strength, damage, healing, and sliding stability. Clay minerals are prevalent in fault zones and have significant effects on friction, porosity, elastic properties, and shear fabric development. Although clay-rich gouges are well studied, the roles of porosity evolution and fabric formation in modulating elastic and mechanical properties are unclear. We have found that with progressive shear, the role of strain localization and fabric development may compete with densification to control the evolution of friction and elastic moduli. We report on a suite of double-direct shear experiments on synthetic gouge composed of 50% Ca-montmorillonite and 50% granular quartz at a normal stress of 25 MPa. We measure the coefficient of friction, porosity, P and S wave speeds, and bulk and shear moduli, and their evolution with shearing, to shear strains up to ~25. We find that the evolution of Vp, Vs, and elastic moduli are controlled by the interplay of porosity loss, shear fabric development, and particle contact stiffness. In general, V p , V s , and elastic moduli increase with shear strain and are accompanied by gradual densification and porosity loss. However, at intermediate shear strains (~2–8) a decrease in V p , V s , and elastic moduli is superimposed on this overall trend. Based on previous microstructural studies, we hypothesize that fabrics develop parallel to shear direction (perpendicular to wave propagation) over this range of strains, leading to reduced fault stiffness and competing with porosity loss as the dominant control on elastic properties.

58 GEOSCIENCES↗

DOE OSTI2020

Evolution of Elastic and Mechanical Properties During Fault Shear: The Roles of Clay Content, Fabric Development, and Porosity

Phyllosilicates weaken faults due to the formation of shear fabrics. Although the impacts of clay abundance and fabric on frictional strength, sliding stability, and porosity of faults are well studied, their influence on elastic properties is less known, though they are key factors for fault stiffness. We document the role that fabric and consolidation play in elastic properties and show that smectite content is the most important factor determining whether fabric or porosity controls the elastic response of faults. We conducted a suite of shear experiments on synthetic smectite-quartz fault gouges (10–100 wt% smectite) and sediment incoming to the Sumatra subduction zone. We monitored Vp, Vs, friction, porosity, shear and bulk moduli. We find that mechanical and elastic properties for gouges with abundant smectite are almost entirely controlled by fabric formation (decreasing mechanical and elastic properties with shear). Though fabrics control the elastic response of smectite-poor gouges over intermediate shear strains, porosity is the primary control throughout the majority of shearing. Elastic properties vary systematically with smectite content: High smectite gouges have values of Vp ~ 1,300–1,800 m/s, Vs ~ 900–1,100 m/s, K ~ 1–4 GPa, and G ~ 1–2 GPa, and low smectite gouges have values of Vp ~ 2,300–2,500 m/s, Vs ~ 1,200–1,300 m/s, K ~ 5–8 GPa, and G ~ 2.5–3 GPa. We find that, even in smectite-poor gouges, shear fabric also affects stiffness and elastic moduli, implying that while smectite abundance plays a clear role in controlling gouge properties, other fine-grained and platy clay minerals may produce similar behavior through their control on the development of fabrics and thin shear surfaces.

58 GEOSCIENCES↗

DOE OSTI2020

Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

Westerly granite (WG) has been generally accepted as an isotropic homogeneous rock. Here, we return to WG and observe significant elastic anisotropy using multidirectional ultrasonic sounding on spherical samples at pressures up to 400 MPa. Thermal treatment of WG leads to formation of microcracks that reduce elastic wave velocities and increase its elastic anisotropy. The 3D distribution of P-wave velocities at low pressure is close to orthorhombic symmetry. Application of hydrostatic pressure closes most of thermally induced microcracks and decreases elastic anisotropy of WG, but at high pressure the anisotropy is practically reversed compared to low pressure: maximum P-wave velocity direction at low pressures is near minimum velocity direction at high pressure and vice versa. To understand this effect, microstructures of the rock were investigated by optical and scanning electron microscopy. Preferred orientations of four major rock-forming minerals—quartz, orthoclase, plagioclase, and biotite—were measured by time-of-flight neutron diffraction, which confirms significant crystal alignment. All these data were used to numerically model anisotropic elastic properties of WG. It is shown that WG possesses weak intrinsic elastic anisotropy related mainly to the preferred orientation of feldspars formed during igneous crystallization. Observed microcracks are mostly related to the cleavage planes of feldspars and biotite, and thus also demonstrate preferred orientation. Higher preheating temperatures produce larger quantity of longer microcracks. A numerical model shows that these microcracks act against the weak intrinsic elastic anisotropy of WG, and define the elastic anisotropy at low pressures.

58 GEOSCIENCES↗

DOE OSTI2017

Elastic-plastic deformation of molybdenum single crystals shocked along [100]

To understand the elastic-plastic deformation response of shock-compressed molybdenum (Mo) – a body-centered cubic (BCC) metal, single crystal samples were shocked along the [100] crystallographic orientation to an elastic impact stress of 12.5 GPa. Elastic-plastic wave profiles, measured at different propagation distances ranging between ~0.23 to 2.31 mm using laser interferometry, showed a time-dependent material response. Within experimental scatter, the measured elastic wave amplitudes were nearly constant over the propagation distances examined. These data point to a large and rapid elastic wave attenuation near the impact surface, before reaching a threshold value (elastic limit) of ~3.6 GPa. Numerical simulations of the measured wave profiles, performed using a dislocation-based continuum model, suggested that {110}<111> and/or {112}<111> slip systems are operative under shock loading. In contrast to shocked metal single crystals with close-packed structures, the measured wave profiles in Mo single crystals could not be explained in terms of dislocation multiplication alone. A dislocation generation mechanism, operative for shear stresses larger than that at the elastic limit, was required to model the rapid elastic wave attenuation and to provide a good overall match to the measured wave profiles. However, the physical basis for this mechanism was not established for the high-purity single crystal samples used in this study. As a result, the numerical simulations also suggested that Mo single crystals do not work harden significantly under shock loading in contrast to the behavior observed under quasi-static loading.

36 MATERIALS SCIENCE↗

NASA NTRS1989

Simulation and control problems in elastic robots

Computational issues associated with modeling and control of robots with revolute joints and elastic arms are considered. A manipulator with one arm and pinned at one end is considered to investigate various aspects of the modeling procedure and the model, and the effect of coupling between the rigid-body and the elastic motions. The rigid-body motion of a manipulator arm is described by means of a reference frame attached to the shadow beam, and the linear elastic operator denoting flexibility is defined with respect to this reference frame. The small elastic motion assumption coupled with the method of assumed modes is used to model the elasticity in the arm. It is shown that only terms up to quadratic in these model amplitudes need to be retained. An important aspect of the coupling between the rigid-body and the elastic motion is the centrifugal stiffening effect. This effect stiffens the elastic structure, as to be expected on physical grounds, gives rise to a time-varying inertia term for the rigid-body motion, and, in general, results in an effective inertia term smaller than the rigid-body inertia term. Simulation results are presented for an elastic beam pinned at one end and free at the other, and rotating in a horizontal plane, and control issues such as the order of the model, number of sensors, and modal extraction are examined within this context.

Tadikonda, S. S. K.↗