SEARCH · Engineering Papers
Results for “STATISTICAL MECHANICS”
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.
Relaxation mechanisms in a disordered system with Poisson-level statistics
Here we discuss the interplay between many-body localization and spin symmetry. To this end, we study the time evolution of several observables in the anisotropic t- j model. Like the Hubbard chain, the studied model contains charge and spin degrees of freedom, yet it has smaller Hilbert space and thus allows for numerical studies of larger systems. We compare the field disorder that breaks the $\mathbb{Z}_2$ spin symmetry and a potential disorder that preserves the latter symmetry. In the former case, sufficiently strong disorder leads to localization of all studied observables, at least for the studied system sizes. However, in the case of symmetry-preserving disorder, we observe that odd operators under the $\mathbb{Z}_2$ spin transformation relax towards the equilibrium value at relatively short timescales that grow only polynomially with the disorder strength. On the other hand, the dynamics of even operators and the level statistics within each symmetry sector are consistent with localization. Our results indicate that localization exists within each symmetry sector for symmetry-preserving disorder. Odd operators' apparent relaxation is due to their time evolution between distinct symmetry sectors.
A multi-length-scale investigation of the applicability of ductility laws for annealed and work-hardened copper
Small-scale mechanical testing provides unique advantages over conventional testing in investigating the mechanical response of nuclear materials. While small-scale testing enables accelerated materials research, it raises the question of comparability to large-scale properties for engineering design considerations. Among different mechanical properties for structural design considerations such as yield and ultimate tensile stress, ductility is of critical importance with respect to structural component health. The effectiveness of using small-scale mechanical testing for probing these mechanical properties is dictated by understanding how the mechanical responses translate from the microscale to the engineering scale. Therefore, a better understanding of size scaling effects via gathering and analysis of experimental data is required to bridge length-scales. Further, this work builds upon previous reports to provide statistical data on how mechanical response changes as the size of the specimens are reduced from conventional sizes. One hundred twenty mesoscale tensile coupons of oxygen-free high thermal conductivity (OFHC) copper in work-hardened and annealed state have been manufactured using micro-wire electrical discharge machining (EDM) and tested under uniaxial tension. The mesoscale specimens have dimensions dictated by pre-selected geometric ratios (i.e., gauge section length over the square root of the cross-section area) with gauge length dimensions of 3 mm (or less) and sub-millimeter gauge widths and thicknesses. The mesoscale responses were compared to bulkscale properties to reveal the effect of specimen size on the mechanical response as a function of grain size and material state for a single phase face-centered cubic metal.
Statistical summaries of fatigue data for design purposes
Two methods are discussed for constructing a design curve on the safe side of fatigue data. Both the tolerance interval and equivalent prediction interval (EPI) concepts provide such a curve while accounting for both the distribution of the estimators in small samples and the data scatter. The EPI is also useful as a mechanism for providing necessary statistics on S-N data for a full reliability analysis which includes uncertainty in all fatigue design factors. Examples of statistical analyses of the general strain life relationship are presented. The tolerance limit and EPI techniques for defining a design curve are demonstrated. Examples usng WASPALOY B and RQC-100 data demonstrate that a reliability model could be constructed by considering the fatigue strength and fatigue ductility coefficients as two independent random variables. A technique given for establishing the fatigue strength for high cycle lives relies on an extrapolation technique and also accounts for "runners." A reliability model or design value can be specified.
Fresnel zone considerations for reflection and scatter from refractive index irregularities
Several different echoing mechanisms are proposed to explain VHF/UHF scatter from clear air; (1) anisotropic scatter; (2) Fresnel reflection, and (3) Fresnel scatter, in order to account for the spatial (angle and range) and temporal dependence of the echoes. The term diffuse reflection describes the echoing mechanism when both scatter and reflection coexist. A unifying formulation is presented incorporating a statistical approach that embraces all mechanisms the above mechanisms and gives conditions under which reflection or scatter dominates. A distinction between Fraunhofer and Fresnel scatter and a criterion is presented under which Fresnel scatter is important.
The impact of infill percentage and layer height in small-scale material extrusion on porosity and tensile properties
We report material extrusion additive manufacturing is prone to introducing porosity within the structure due to the layer-by-layer construction using elliptical beads of material. This open porosity ultimately plays a role in determining the mechanical properties of printed parts. The shape, size, and amount of porosity within a printed part is influenced by a variety of factors, including nozzle diameter, infill percentage, layer height, raster orientation, and print speed. While several studies have investigated these and other parameters’ effects on mechanical performance and porosity, better understanding the interconnected relationships is crucial in balancing the various input parameters to achieve maximum strength. This work initially examined the influence of key print parameters (infill percentage and layer height) on the internal porosity of a printed Acrylonitrile Butadiene Styrene (ABS) part. Then, the print parameters and internal porosity were statistically correlated to final mechanical properties. Porosity was further classified as either open or closed to differentiate between connected voids in the mesostructure from isolated voids within the material itself. Mechanical performance increased with an increasing density and infill percentage, displaying a 224 % increase in elastic modulus and a 150 % increase in ultimate tensile strength. The contribution of layer height was found to be conditional upon the infill percentage.
Indirectly probing the structural change in ion-irradiated Zr-Based metallic glasses from small scale mechanical tests
Ion irradiation was applied to tailor the structural heterogeneities in Zr-based metallic glasses at room temperature. Experimental methods of X-ray diffraction, nanoindentation, and micropillar compression were conducted to examine the irradiation effects on their structural and mechanical property changes. It is found that the irradiated materials retained amorphous structure after room-temperature Ni ion irradiation. The reduction of elastic modulus and hardness measured by nanoindentation indicated the irradiation-induced mechanical degradation. A unified statistic model was employed to quantitatively predict the density and strength of irradiation defects, although their specific structural and physical nature is not explicitly included in this model. The transition of non-intersecting shear bands to multiple intersecting shear bands was observed on compression tests of irradiated micropillars with the increase of irradiation dose. Furthermore, the analysis of the displacement excursion of micropillar compression tests indicated a different deformation mode from the unirradiated state. These results from nanoindentation pop-in and micro-pillar compression tests suggested that irradiation eventually leads to a new state with different types and characteristics of structural heterogeneities from violent displacement cascades and non-equilibrium energy deposition/dissipation processes, which also proves ion irradiation as an effective method to tune the structure and mechanical properties of metallic glasses.
Statistical methods for design and testing of 3D-printed polymers
Different statistical methods are used in various fields to qualify processes and products, especially in emerging technologies like Additive Manufacturing (AM) or 3D printing. Since several statistical methods are being employed to ensure quality production of the 3D-printed parts, an overview of these methods used in 3D printing for different purposes is presented in this paper. The advantages and challenges, to understanding the importance it brings for design and testing optimization of 3D-printed parts are also discussed. The application of different metrology methods is also summarized to guide future researchers in producing dimensionally-accurate and good-quality 3D-printed parts. Here, this review paper shows that the Taguchi Methodology is the commonly-used statistical tool in optimizing mechanical properties of the 3D-printed parts, followed by Weibull Analysis and Factorial Design. In addition, key areas such as Artificial Intelligence (AI), Machine Learning (ML), Finite Element Analysis (FEA), and Simulation require more research for improved 3D-printed part qualities for specific purposes. Future perspectives are also discussed, including other methods that can help further improve the overall quality of the 3D printing process from designing to manufacturing.
Fast strength model characterization using Bayesian statistics
A variety of flow stress models exist with new models constantly being developed. These models aim to approximate the strength of materials in a variety of regimes from quasistatic loading through shock scenarios. All models contain an array of parameters which need to be tuned to the material under study. Some models perform well under limited conditions, requiring adjustment of the parameters when venturing outside of those predefined ranges. Other models perform well over a wide range of conditions with a set of parameters, but may be outperformed by other models optimized on a tighter range of conditions. Recent research by Los Alamos demonstrated the ability to optimize the Johnson Cook (JC) model using a set of 3 plate-impact experiments on Aluminum. They utilized Bayesian statistics and emulation to determine optimal parameters for the model with a quantification of parameter uncertainty. We present an extension of this capability to incorporate velocimetry from plate-impact tests, stress-strain data from split Hopkinson pressure bar and quasistatic compression tests, plus profiles from Taylor cylinders in a unified fashion. Statistically robust comparisons of the performance and uncertainty of different realizations of the JC flow stress model were carried out based on calibration to several possible combinations of these three different experiment types.
Quantitative assessment of fitting errors associated with streak camera noise in Thomson scattering data analysis
Thomson scattering measurements in high energy density experiments are often recorded using optical streak cameras. In the low-signal regime, noise introduced by the streak camera can become an important and sometimes the dominant source of measurement uncertainty. In this paper, we present a formal method of accounting for the presence of streak camera noise in our measurements. We present a phenomenological description of the noise generation mechanisms and present a statistical model that may be used to construct the covariance matrix associated with a given measurement. This model is benchmarked against simulations of streak camera images. We demonstrate how this covariance may then be used to weight fitting of the data and provide quantitative assessments of the uncertainty in the fitting parameters determined by the best fit to the data and build confidence in the ability to make statistically significant measurements in the low-signal regime, where spatial correlations in the noise become apparent. These methods will have general applicability to other measurements made using optical streak cameras.
Universal construction of black hole microstates
We refine and extend a recent construction of sets of black hole microstates with semiclassical interiors that span a Hilbert space of dimension e S , where S is the black hole entropy. We elaborate on the definition and properties of microstates in statistical and black hole mechanics. The gravitational description of microstates employs matter shells in the interior of the black hole, and we argue that in the limit where the shells are very heavy, the construction acquires universal validity. To this end, we show it for very wide classes of black holes; we first extend the construction to rotating and charged black holes, including extremal and near-extremal solutions, with or without supersymmetry, and we sketch how the construction of microstates can be embedded in string theory. We then describe how the approach can include general quantum corrections, near or far from extremality. For supersymmetric black holes, the microstates we construct differ from other recent constructions in that the interior excitations are not confined within the near-extremal throat. Published by the American Physical Society 2024
Investigation of vibrations of working elements of a two coordinate scanner
Radial and axial vibration measurements on the scanning disk and the data storage board of an optical-mechanical scanner are evaluated. Statistical processing of the observational data establishes the excitation source and determines the effect of disk torsional vibrations on the data storage board.
Monolithic ceramic analysis using the SCARE program
The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.
Designing ceramic components with the CARES computer program
NASA-Lewis has developed a public-domain computer program, designated 'Ceramic Analysis and Reliability Evaluation of Structures' (CARES) for calculating the fast-fracture reliability of macroscopically isotropic ceramic components subjected to the complex thermomechanical loadings typical of heat engines. The design methodology employed by CARES encompasses linear elastic fracture mechanics theory, extreme value statistics, and material microstructures; component integrity is conceived as a function of the entire field solution of the stresses, rather than being based solely on the most highly stressed point.
Algorithmic information theory and the hidden variable question
The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive function which may be used to transform l sub n into r sub n for any n. This note demonstrates that such a theory cannot reproduce all the statistical predictions of quantum mechanics. Specifically, consider an ensemble of outcome pairs (l,r). From the associated probability measure, the Shannon entropies H sub n and H bar sub n for strings l sub n and pairs (l sub n, r sub n) may be formed. It is shown that such a theory requires that the absolute value of H bar sub n - H sub n be bounded - contrasting the quantum mechanical prediction that it grow with n.
N III line emission in planetary nebulae - Not Bowen fluorescence
A direct comparison of photometrically observed line ratios in the N III 4640 and 4100 A multiplets emitted by planetary nebulae with theoretically predicted ratios expected from the postulated Bowen process of selective photoexcitation by an O III resonance line shows that the N III lines are not produced by the Bowen process as has been commonly accepted. This will have consequences for the interpretation of these lines in other astrophysical sources. A further, unexpected result is that the N III level populations involved are found to be essentially in statistical equilibrium. Possible populating mechanisms are briefly discussed.
Quantum Mechanical Enhancement of the Random Dopant Induced Threshold Voltage Fluctuations and Lowering in Sub 0.1 Micron MOSFETs
A detailed study of the influence of quantum effects in the inversion layer on the random dopant induced threshold voltage fluctuations and lowering in sub 0.1 micron MOSFETs has been performed. This has been achieved using a full 3D implementation of the density gradient (DG) formalism incorporated in our previously published 3D 'atomistic' simulation approach. This results in a consistent, fully 3D, quantum mechanical picture which implies not only the vertical inversion layer quantisation but also the lateral confinement effects manifested by current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical fluctuations, is an increase in both threshold voltage fluctuations and lowering.
Subscale Test Methods for Combustion Devices
Stated goals for long-life LRE s have been between 100 and 500 cycles: 1) Inherent technical difficulty of accurately defining the transient and steady state thermochemical environments and structural response (strain); 2) Limited statistical basis on failure mechanisms and effects of design and operational variability; and 3) Very high test costs and budget-driven need to protect test hardware (aversion to test-to-failure). Ambitious goals will require development of new databases: a) Advanced materials, e.g., tailored composites with virtually unlimited property variations; b) Innovative functional designs to exploit full capabilities of advanced materials; and c) Different cycles/operations. Subscale testing is one way to address technical and budget challenges: 1) Prototype subscale combustors exposed to controlled simulated conditions; 2) Complementary to conventional laboratory specimen database development; 3) Instrumented with sensors to measure thermostructural response; and 4) Coupled with analysis