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 541 records · Page 30

Matrix glass vs. intruded glass in lunar breccia 15286

The viscous flow and crystallization behavior of the matrix composition of breccia 15286 have been determined in the 1159-1307 C and 644-770 C temperature ranges. The Shaw (1972) model and, to a slightly lesser extent, the semiempirical Bottinga and Weill (1972) model describe the variation of viscosity with temperature. The crystal growth rate has been determined over the temperature range 821-1185 C. Time-temperature-transformation, logarithmic cooling, and continuous cooling curves were constructed; a nucleation barrier of 60 kT at a relative undercooling of 0.2 is assumed. It is estimated that the matrix of 15286 breccia cooled at a rate greater than 80 K/min through the glass transition region. The increase in density that occurs when the matrix glass is annealed suggests that the breccia was formed by cooling from the molten state rather than by direct shock-induced transition from crystal to glass. Viscous sintering under continuous cooling and logarithmic cooling conditions is analyzed.

Handwerker, C. A.↗

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗

Space Shuttle communications RF switch matrix

The Shuttle Orbiter communications equipment includes phase modulation (PM) and frequency modulation (FM) channels. The PM section has the capability of routing high levels of energy (175 W) from any one of four transmitters to any one of four antennas, mutually exclusive. The FM channel uses a maximum of 15-W power routed from either of two transmitters to one of two antennas, mutually exclusive. The paper describes the design and the theory of a logic-controlled RF switch matrix devised for the purposes cited. Both PM and FM channels are computer-controlled with manual overrides. The logic interface is realized with CMOS logic for low power consumption and high noise immunity. The interior of the switch matrix is maintained at a pressure of 15 psi (90% nitrogen, 10% helium) by an electron beam-welded encapsulation. The computational results confirm the viability of the RF switch matrix concept.

Winch, R.↗

Analysis of a unidirectional composite containing broken fibers and matrix damage

An analytical solution is developed for the determination of the stresses and displacements in a unidirectional fiber-reinforced composite containing an arbitrary number of broken fibers as well as longitudinal yielding and splitting of the matrix. The solution is developed using a materials-modeling approach which is based on a shear-lag stress transfer mechanism. The equilibrium equation in the axial direction gives a pair of integral equations which are solved numerically. Excellent agreement is shown to exist between the solution and experimental results for notched unidirectional boron/aluminum laminates without splitting. For brittle matrix composites (i.e. epoxy) equally good results are indicated for both matrix yielding and splitting. For yielding without splitting the fracture strength depends on crack length while for large splitting it is crack length independent.

George, J. G.↗

Research on graphite reinforced glass matrix composites

High levels of mechanical performance in tension, flexure, fatigue, and creep loading situations of graphite fiber reinforced glass matrix composites are discussed. At test temperatures of up to 813 K it was found that the major limiting factor was the oxidative instability of the reinforcing graphite fibers. Particular points to note include the following: (1) a wide variety of graphite fibers were found to be comparable with the glass matrix composite fabrication process; (2) choice of fiber, to a large extent, controlled resultant composite performance; (3) composite fatigue performance was found to be excellent at both 300 K and 703 K; (4) composite creep and stress rupture at temperatures of up to 813 K was limited by the oxidative stability of the fiber; (5) exceptionally low values of composite thermal expansion coefficient were attributable to the dimensional stability of both matrix and fiber; and (6) component fabricability was demonstrated through the hot pressing of hot sections and brazing using glass and metal joining phases.

Prewo, K. M.↗

Analysis of a unidirectional composite containing broken fibers and matrix damage

An analytical solution is developed for the determination of the stresses and displacements in a unidirectional fiber-reinforced composite containing an arbitrary number of broken fibers as well as longitudinal yielding and splitting of the matrix. The solution is developed using a 'materials-modeling' approach which is based on a shear-lag stress transfer mechanism. The equilibrium equation in the axial direction gives a pair of integral equations which are solved numerically. Excellent agreement is shown to exist between the solution and experimental results for notched unidirectional boron/aluminum laminates without splitting. For brittle matrix composites (i.e., epoxy) equally good results are indicated for both matrix yielding and splitting. For yielding without splitting the fracture strength is found to depend on crack length while for large splitting it is crack length independent.

Goree, J. G.↗

New approach to the solution of large, full matrix equations

A new approach to the solution of matrix equations resulting from integral equations is presented and applied to the solution of two-dimensional Neumann problems describing the inviscid, incompressible flow past an airfoil. The problem is reformulated in terms of a preselected set of mode functions giving an equivalent matrix equation to be solved for the mode-function expansion coefficients. Because of the inherent smoothness of the original problem, the coefficient problem can be solved approximately without significantly affecting the accuracy of the final solution. Very promising two-dimensional results are obtained and the extension of the method to three-dimensional problems is investigated. On the basis of these results it is shown that the computing time for the matrix solution for a large three-dimensional panel method calculation could be reduced by an order of magnitude compared with that required for a direct solution.

Clark, R. W.↗

Degradation Mechanisms in Aluminum Matrix Composites: Alumina/Aluminum and Boron/Aluminum

The effects of fabrication and long term thermal exposure (up to 10,000 hours at 590 K) on two types of aluminum matrix composites were examined. An alumina/aluminum composite, was made of continuous alpha Al2O3 fibers in a matrix of commercially pure aluminum alloyed with 2.8% lithium. The mechanical properties of the material, the effect of isothermal exposure, cyclic thermal exposure, and fatigue are presented. Two degradation mechanisms are identified. One was caused by formation of a nonstoichiometric alumina during fabrication, the other by a loss of lithium to a surface reaction during long term thermal exposure. The other composite, boron/aluminum, made of boron fibers in an aluminum matrix, was investigated using five different aluminum alloys for the matrices. The mechanical properties of each material and the effect of isothermal and cyclic thermal exposure are presented. The effects of each alloy constituent on the degradation mechanisms are discussed. The effects of several reactions between alloy constituents and boron fibers on the composite properties are discussed.

Olsen, G. C.↗

Integrating matrix formulations for vibrations of rotating beams including the effects of concentrated masses

By expressing partial differential equations of motion in matrix notation, utilizing the integrating matrix as a spatial operator, and applying the boundary conditions, the resulting ordinary differential equations can be cast into standard eigenvalue form upon assumption of the usual time dependence. As originally developed, the technique was limited to beams having continuous mass and stiffness properties along their lengths. Integrating matrix methods are extended to treat the differential equations governing the flap, lag, or axial vibrations of rotating beams having concentrated masses. Inclusion of concentrated masses is shown to lead to the same kind of standard eigenvalue problem as before, but with slightly modified matrices.

Lakin, W. D.↗

Matrix differentiation formulas

A compact differentiation technique (without using indexes) is developed for scalar functions that depend on complex matrix arguments which are combined by operations of complex conjugation, transposition, addition, multiplication, matrix inversion and taking the direct product. The differentiation apparatus is developed in order to simplify the solution of extremum problems of scalar functions of matrix arguments.

Usikov, D. A.↗

Characterization of the matrix glass transition in carbon-epoxy laminates using the CSD test geometry

A new test geometry, referred to as centro-symmetric deformation (CSD), is proposed for characterizing the viscoelastic behavior of the matrix of carbon-epoxy laminates. The sample consists of a thin disk, typically 6-14 plies thick, having a nominal diameter of 30 mm. The disk is freely supported on a circular anvil; the load is applied to the center of the disk using an 8-mm-diameter ball bearing nosepiece. The CSD test geometry provides viscoelastic dispersion data which are independent of the angular orientation of the sample. The test geometry is sufficiently sensitive to matrix changes to allow its use for postcuring, humidity, crosslink density, and other matrix change studies. Test results are presented for a carbon-epoxy laminate.

Sternstein, S. S.↗

Analysis of stress-strain, fracture and ductility behavior of aluminum matrix composites containing discontinuous silicon carbide reinforcement

Mechanical properties and stress-strain behavior for several types of commercially fabricated aluminum matrix composites, containing up to 40 vol % discontinuous SiC whisker, nodule, or particulate reinforcement were evaluated. It was found that the elastic modulus of the composites was isotropic, to be independent of type of reinforcement, and to be controlled solely by the volume percentage of SiC reinforcement present. The yield/tensile strengths and ductility were controlled primarily by the matrix alloy and temper condition. Ductility decreased with increasing reinforcement content, however, the fracture strains observed were higher than those reported in the literature for this type of composite. This increase in fracture strain is attributed to cleaner matrix powder and increased mechanical working during fabrication. Conventional aluminum and titanium structural alloys were compared and have shown that the properties of these low cost, lightweight composites have good potential for application to aerospace structures.

Mcdanels, D. L.↗

The effect of matrix properties and fiber properties on impact failure mechanics

The low-velocity impact problem in graphite/epoxy composite sheets must be solved before large amounts of that material can be used in commercial aircraft. Many of the low-velocity impacts that affect aircraft parts occur during normal ground operations and maintenance. Service equipment and tools have masses above 1 kg, and at velocities of less than 3 m/s can impact structural parts with energies higher than composites can endure without degradation of stiffness or strength. Simple solutions were developed for large-mass, low-velocity impacts which can be modeled as quasi-static events. Static test data and impact data show that the fiber properties control the impact energy which can be absorbed before penetration. Matrix shear strength and peel resistance control the extent of delamination. Comparison of results from tough matrix and brittle matrix composites show that although tough matrices reduce the extent of delamination, they lead to more fiber damage in the contact area.

Elber, W.↗

Improved high temperature resistant matrix resins

The objective was to develop organic matrix resins suitable for service at temperatures up to 644 K (700 F) and at air pressures up to 0.4 MPa (60 psia) for time durations of a minimum of 100 hours. Matrix resins capable of withstanding these extreme oxidative environmental conditions would lead to increased use of polymer matrix composites in aircraft engines and provide significant weight and cost savings. Six linear condensation, aromatic/heterocyclic polymers containing fluorinated and/or diphenyl linkages were synthesized. The thermo-oxidative stability of the resins was determined at 644 K and compressed air pressures up to 0.4 MPa. Two formulations, both containing perfluoroisopropylidene linkages in the polymer backbone structure, exhibited potential for 644 K service to meet the program objectives. Two other formulations could not be fabricated into compression molded zero defect specimens.

Chang, G. E.↗

Composite Property Dependence on the Fiber, Matrix, and the Interphase

The matrix properties of a difunctional epoxy, Epon 828, were varied. The Hercules type A fiber was also utilized in this investigation. The fiber and the interface between fiber and matrix were examined in terms of shear strength. Micrographs of the epoxy matrix are presented.

Drzal, L. T.↗

High Temperature Polymer Matrix Composites

These are the proceedings of the High Temperature Polymer Matrix Composites Conference held at the NASA Lewis Research Center on March 16 to 18, 1983. The purpose of the conference is to provide scientists and engineers working in the field of high temperature polymer matrix composites an opportunity to review, exchange, and assess the latest developments in this rapidly expanding area of materials technology. Technical papers are presented in the following areas: (1) matrix development; (2) adhesive development; (3) characterization; (4) environmental effects; and (5) applications.

Source record↗

Bismaleimides and related maleimido polymers as matrix resins

Significant processing and property improvements can be achieved by copolymerization of state-of-the-art bisimides with various vinyl stilbazole derivatives to give both fire resistance and high-temperature properties from hot-melt compositions. Significant improvement in mechanical properties is achieved through these modifications, which may make these new matrix resins ideal candidates for fireworthy secondary graphite composite structures. Phosphorous modifications of maleimido polymers through phosphonate structure and tricyclophosphazene derivatives provide families of new matrix resins for short-time applications in severe thermo-oxidative environments. With further research these may provide matrix resins for long-term thermo-oxidative stability of advanced composites at temperatures up to 400 to 500 C.

Parker, J. A.↗

A comparison of measured and calculated thermal stresses in a hybrid metal matrix composite spar cap element

A hybrid spar of titanium with an integrally brazed composite, consisting of an aluminum matrix reinforced with boron-carbide-coated fibers, was heated in an oven and the resulting thermal stresses were measured. Uniform heating of the spar in an oven resulted in thermal stresses arising from the effects of dissimilar materials and anisotropy of the metal matrix composite. Thermal stresses were calculated from a finite element structural model using anisotropic material properties deduced from constituent properties and rules of mixtures. Comparisons of calculated thermal stresses with measured thermal stresses on the spar are presented. It was shown that failure to account for anisotropy in the metal matrix composite elements would result in large errors in correlating measured and calculated thermal stresses. It was concluded that very strong material characterization efforts are required to predict accurate thermal stresses in anisotropic composite structures.

Jenkins, J. M.↗