Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix”

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

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

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Scattering matrix pole expansions for complex wave numbers in R -matrix theory

In this followup article to Ducru et al., we establish new results on scattering matrix pole expansions for complex wave numbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wave numbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift S and penetration P functions: the legacy Lane and Thomas's “force closure” approach versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. Here, in this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and discover new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii a c . We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix—canceling spurious poles and guaranteeing generalized unitarity—while still being able to close channels below thresholds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Residual stresses in Cu matrix composite surface deposits after laser melt injection

Abstract Tungsten carbide particles reinforced metal matrix composite (MMC) coatings can significantly improve surface wear resistance owing to their increased surface hardness. However, the presence of macro‐ and micro‐residual stresses in MMC coatings can have detrimental effects, such as reducing service life. In this study, neutron diffraction was used to determine the residual stresses in spherical fused tungsten carbide (sFTC) reinforced Cu matrix composite surface deposits after laser melt injection. We also developed a thermo‐mechanical coupled finite element model to predict residual stresses. Our findings reveal that sFTC/Cu composite deposits produced with a preheating temperature of 400°C have low residual stresses, with a maximum tensile residual stress of 98 MPa in the Cu matrix on the top surface. In contrast, the sFTC/bronze (CuAl10Ni5Fe4) composite deposit exhibits very high residual stresses, with a maximum tensile residual stress in the Cu matrix on the top surface reaching 651 MPa. These results provide a better understanding of the magnitudes and distributions of residual stresses in sFTC‐reinforced Cu matrix composite surface deposits manufactured via laser melt injection.

Zhang, Xingxing↗
NASA NTRS1992

Effectiveness of metal matrix and ceramic matrix composites as orbital debris shield materials

The effectiveness of two metal matrix composites and one ceramic matrix material in defeating hypervelocity impacts at about 3.8 km/s are evaluated to determine the potential of these composites as spacecraft shield materials. The metal matrix composites investigated consist of SiC particles (70 percent by volume) in an aluminum matrix and Al2O3 particles (50 percent by volume) in an Al matrix. The ceramic composite consists of ZrB2 platelets in a ZrC matrix. Both the metal matrix and ceramic matrix composites are found to perform as well or better than 6061-T6 aluminum, which is presently used in the Whipple type bumper shield of Space Station Freedom. Test results indicate that the composites tested may have applications as micrometeoroid/orbital debris shield materials.

Mcgill, Preston B.↗
NASA NTRS2003

Stress-Dependent Matrix Cracking in 2D Woven SiC-Fiber Reinforced Melt-Infiltrated SiC Matrix Composites

The matrix cracking of a variety of SiC/SiC composites has been characterized for a wide range of constituent variation. These composites were fabricated by the 2-dimensional lay-up of 0/90 five-harness satin fabric consisting of Sylramic fiber tows that were then chemical vapor infiltrated (CVI) with BN, CVI with SiC, slurry infiltrated with SiC particles followed by molten infiltration of Si. The composites varied in number of plies, the number of tows per length, thickness, and the size of the tows. This resulted in composites with a fiber volume fraction in the loading direction that ranged from 0.12 to 0.20. Matrix cracking was monitored with modal acoustic emission in order to estimate the stress-dependent distribution of matrix cracks. It was found that the general matrix crack properties of this system could be fairly well characterized by assuming that no matrix cracks originated in the load-bearing fiber, interphase, chemical vapor infiltrated Sic tow-minicomposites, i.e., all matrix cracks originate in the 90 degree tow-minicomposites or the large unreinforced Sic-Si matrix regions. Also, it was determined that the larger tow size composites had a much narrower stress range for matrix cracking compared to the standard tow size composites.

Morscher, Gregory N.↗
NASA NTRS1994

Implementation of thermal residual stresses in the analysis of fiber bridged matrix crack growth in titanium matrix composites

In this research, thermal residual stresses were incorporated in an analysis of fiber-bridged matrix cracks in unidirectional and cross-ply titanium matrix composites (TMC) containing center holes or center notches. Two TMC were investigated, namely, SCS-6/Timelal-21S laminates. Experimentally, matrix crack initiation and growth were monitored during tension-tension fatigue tests conducted at room temperature and at an elevated temperature of 200 C. Analytically, thermal residual stresses were included in a fiber bridging (FB) model. The local R-ratio and stress-intensity factor in the matrix due to thermal and mechanical loadings were calculated and used to evaluate the matrix crack growth behavior in the two materials studied. The frictional shear stress term, tau, assumed in this model was used as a curve-fitting parameter to matrix crack growth data. The scatter band in the values of tau used to fit the matrix crack growth data was significantly reduced when thermal residual stresses were included in the fiber bridging analysis. For a given material system, lay-up and temperature, a single value of tau was sufficient to analyze the crack growth data. It was revealed in this study that thermal residual stresses are an important factor overlooked in the original FB models.

Bakuckas, John G., Jr.↗
DOE OSTI2024

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S –1 . This factorization of S –1 , written as ZZT = S –1 , is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix–matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Mechanical behaviors of ceramic matrix composites with matrix cracking and fiber debonding

The purpose of this paper is to summarize the current research of the authors on the mechanical behaviors of ceramic matrix composites, including (1) the stress distributions in a composite with matrix cracking and interfacial debonding, (2) the critical strain for matrix cracking, and (3) the effects of fiber/matrix debonding and thermal residual stresses on the critical strain. The stress fields in both bonded and debonded regions are evaluated by taking into account thermal effects. An energy balance approach is followed to determine the critical strain for matrix cracking. From the general equation of the critical strain for matrix cracking, close form solutions have been obtained for two limiting cases: perfect bonding and complete debonding. Numerical solutions are given for the cases of partial fiber debonding and nonzero debonding energy. It is found that thermal residual stresses and the debonding energy have significant effects on the critical strain.

Kuo, Wen-Shyong↗
NASA NTRS1998

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Goldberg, Robert K.↗
DOE OSTI2025

Baryon number violation: from nuclear matrix elements to BSM physics

Processes that violate baryon number, most notably proton decay and $n\bar{n}$ transitions, are promising probes of physics beyond the Standard Model (BSM) needed to understand the lack of antimatter in the Universe. To interpret current and forthcoming experimental limits, theory input from nuclear matrix elements to UV complete models enters. Thus, an interplay of experiment, effective field theory, lattice QCD, and BSM model building is required to develop strategies to accurately extract information from current and future data and maximize the impact and sensitivity of next-generation experiments. Here, we briefly summarize the main results and discussions from the workshop ‘INT-25-91W: Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics,’ held at the Institute for Nuclear Theory, University of Washington, Seattle, WA, 13–17 January 2025.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Texture analysis of AGR program matrix materials

We report the fuel form for high-temperature gas-cooled reactors consists of tristructural isotropic (TRISO) particles embedded in a matrix of graphite flake and carbonized resin. The process of overcoating particles prior to compacting yields a circumferential orientation of the graphite flake surrounding the TRISO particles, which is modified to varied extents when overcoated particles are pressed into the final fuel form. As graphite is highly anisotropic, the texture may impact the properties and performance of the fuel. Ellipsometry was used to measure the texture of the matrix for fueled compacts and unfueled “matrix-only” samples. Results indicated local texture related to the spherical particles in compacts associated with overcoating versus a more linear layered structure in “matrix-only” samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Workflow for High-throughput Screening of Enzyme Mutant Libraries Using Matrix-assisted Laser Desorption/Ionization Mass Spectrometry Analysis of Escherichia coli Colonies

High-throughput molecular screening of microbial colonies and DNA libraries are critical procedures that enable applications such as directed evolution, functional genomics, microbial identification, and creation of engineered microbial strains to produce high-value molecules. A promising chemical screening approach is the measurement of products directly from microbial colonies via optically guided matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS). Measuring the compounds from microbial colonies bypasses liquid culture with a screen that takes approximately 5 s per sample. We describe a protocol combining a dedicated informatics pipeline and sample preparation method that can prepare up to 3,000 colonies in under 3 h. The screening protocol starts from colonies grown on Petri dishes and then transferred onto MALDI plates via imprinting. The target plate with the colonies is imaged by a flatbed scanner and the colonies are located via custom software. The target plate is coated with MALDI matrix, MALDI-MS analyzes the colony locations, and data analysis enables the determination of colonies with the desired biochemical properties. This workflow screens thousands of colonies per day without requiring additional automation. The wide chemical coverage and the high sensitivity of MALDI-MS enable diverse screening projects such as modifying enzymes and functional genomics surveys of gene activation/inhibition libraries.

Choe, Kisurb↗
NASA NTRS1990

Matrix density effects on the mechanical properties of SiC fiber-reinforced silicon nitride matrix properties

The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.

Bhatt, Ramakrishna T.↗
NASA NTRS1990

Thermal and mechanical behavior of metal matrix and ceramic matrix composites

The present conference discusses local stresses in metal-matrix composites (MMCs) subjected to thermal and mechanical loads, the computational simulation of high-temperature MMCs' cyclic behavior, an analysis of a ceramic-matrix composite (CMC) flexure specimen, and a plasticity analysis of fibrous composite laminates under thermomechanical loads. Also discussed are a comparison of methods for determining the fiber-matrix interface frictional stresses of CMCs, the monotonic and cyclic behavior of an SiC/calcium aluminosilicate CMC, the mechanical and thermal properties of an SiC particle-reinforced Al alloy MMC, the temperature-dependent tensile and shear response of a graphite-reinforced 6061 Al-alloy MMC, the fiber/matrix interface bonding strength of MMCs, and fatigue crack growth in an Al2O3 short fiber-reinforced Al-2Mg matrix MMC.

Kennedy, John M.↗
NASA NTRS1991

Prediction of matrix fatigue crack initiation in notched SCS-6/Ti-15-3 metal matrix composites

Several lay-ups of SCS-6/Ti-15-3 metal matrix composites were tested in either a center hole or a double edge notched geometry. At different cyclic strss levels, the number of cycles required to develop matrix fatigue cracks at the notches was recorded. A fatigue strat-life curve was developed for the Ti-15-3 matrix material. This modified parameter predicted the number of cycles required for matrix crack initiation at the notches. The predictions were in good agreement with the experimental data.

Hillberry, B. M.↗
NASA NTRS1991

Predictions of the critical strain for matrix cracking of ceramic matrix composites

The critical strain for matrix cracking of ceramic matrix composites has been studied; emphasis is placed on the effects of the fiber/matrix debonding length and interfacial debonding energy. Based on a modified shear-lag model, stresses in the fiber and matrix have been found for both the bonded and debonded regions. An energy-balance approach, based upon the stress field, is then adopted to evaluate the critical strain for matrix cracking. From the general equation for the critical strain, close form solutions have been deduced for two limiting cases: complete debonding and perfect bonding. Numerical solutions are given for the cases of nonzero debonding energy and partial fiber debonding. The results show that the interfacial debonding energy, which has been ignored by most of the investigators, is an important factor in determining both the critical strain and the debonding length.

Kuo, Wen-Shyong↗