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An initial evaluation of upgraded boron fibers in an epoxy matrix is performed. Data generated on the program show that fiber strength does increase as a consequence of the upgrading treatment. However, the interlaninar shear strength of upgraded fiber composites is lower than that for an untreated fiber composite. In the limited tests performed, the increased fiber strength failed to translate into the composite.
A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.
Fiber-reinforced composites and design analysis methods for these materials are being developed because of the vast potential of composites for decreasing weight and/or increasing use temperature capability in aerospace systems. These composites have potential for use in airbreathing engine components as well as aeronautical and space vehicle structures. Refractory wire-superalloy composites for use up to 2200 F or more and metal-matrix composites for lower temperature applications such as aerospace structures and turbojet fan and compressor blades are under investigation and are discussed. The development of a number of resin systems, including the polyimides and polyphenylquinoxalines, is described and their potential for use at temperatures approaching 315 C (600 F) is indicated. Various molecular modifications that improve processability and/or increase thermal and oxidative resistance of the resins are also described. Structural analysis methods are discussed for determining the stresses and deformations in complex composite systems. Consideration is also given to residual stresses resulting from the curing process and to the foreign object damage problem in fan blade applications.
A general expression is given for the derivative of the C sub 4 - inverse of a differentiable matrix A whenever that derivative, as well as the derivative of A, exists.
The problem is considered of classifying into one of m distinct n-variate classes an arbitrary n-channel multispectral measurement vector x. The classification procedure used is the maximum likelihood procedure. Information loss in compressing the n-channel data to k channels is taken to be the difference in the average interclass divergences (or probability of misclassification) in n-space and in k-space. Data compression is accomplished by kxn linear transformation i.e., multiplication of the spectral n-vector by a kxn matrix of rank k.
The development of an analytic procedure for the calculation of nonequilibrium boundary layer flows over surfaces of arbitrary catalycities is described. An existing equilibrium boundary layer integral matrix code was extended to include nonequilibrium chemistry while retaining all of the general boundary condition features built into the original code. For particular application to the pitch-plane of shuttle type vehicles, an approximate procedure was developed to estimate the nonequilibrium and nonisentropic state at the edge of the boundary layer.
This paper examines the fracture mechanisms which occur in the matrix and interfacial region surrounding a fiber when the fiber fails under axial load. Both tensile and compressive behavior of carbon fibers in an epoxy-novolac system are treated for specimens having very low fiber concentrations. First, the fracture mechanisms are isolated and identified and then means for controlling the propagation or containment of fiber fractures are explored. Sequences of photographs showing progressive damage with increasing load are presented for each loading condition. Effects of fiber orientation are also treated.
Recently a high-modulus and high-strength organic fiber, identified as PRD-49-III by the manufacturer, became commercially available. To assess the fiber performance and its potential as a reinforcement for fiber composites, the tensile properties of the fiber in an epoxy matrix were determined. During this study over 6000 fiber/epoxy strands were made using the filament winding process; these strands were representative samples taken from over 60 lb of single-end fiber. The fiber uniformity, its strength distribution at room and LN2 temperature, stress-strain characteristics, and the strain rate effect on the fiber strength were evaluated.
Models for unsteady water transport in fuel cell configurations of Bacon-Pratt and Whitney type are derived. Tests with a specially constructed isothermal cell producing no water and order of magnitude analysis show that diffusion through the liquid alone cannot account for the observed behavior. An analytical solution which includes diffusion in both the liquid and the gas spaces of the matrix is in better agreement with the data than models which consider diffusion in either the liquid or in the gas phase alone.
An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.
An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.
Matrix operator theory is used to calculate the reflected and transmitted radiance of photons that have interacted with plane-parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo are tabulated. The forward peak and other features in the single-scattered phase function cause the radiance in many cases to be very different from that for Rayleigh scattering. In particular, the variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked and the relative limb darkening under very thick layers is greater for haze M than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = 0 is always greater and the cloud albedo is always less for haze M than for Rayleigh layers.
Polyurethanes derived from hydroxy terminated polyperfluoro propylene oxide prepolymers were evaluated as matrix resins for filament wound composites which would be exposed to liquid (and 100% gaseous) oxygen environments. A number of structural modifications were brought about by variations in prepolymer molecular weight, and alternative curing agents which allowed retention of the oxygen compatibility. Although satisfactory performance was achieved at sub-ambient temperatures, the derived composites suffered considerable property loss at ambient or slightly elevated temperatures. To attain overall effectiveness of the composite system, upgrading of the polymer thermomechanical properties must first be achieved.
FORTRAN computer subroutines stemming from requirements to process state variable system equations for systems of high order are presented. They find the characteristic equation of a matrix using the method of Danilevsky, the number of roots with positive real parts using the Routh-Horwitz alternate formulation, convert a state variable system description to a Laplace transfer function using the method of Bollinger, and evaluate that transfer function and obtain its frequency response. A sample problem is presented to demonstrate use of the subroutines.
A summary of modifications to Aerotherm's Boundary Layer Integral Matrix Procedure (BLIMP) code is presented. These modifications represent a preliminary effort to make BLIMP compatible with other JANNAF codes and to adjust the code for specific application to rocket nozzle flows. Results of the initial verification of the code for prediction of rocket nozzle type flows are discussed. For those cases in which measured free stream flow conditions were used as input to the code, the boundary layer predictions and measurements are in excellent agreement. In two cases, with free stream flow conditions calculated by another JANNAF code (TDK) for use as input to BLIMP, the predictions and the data were in fair agreement for one case and in poor agreement for the other case. The poor agreement is believed to result from failure of the turbulent model in BLIMP to account for laminarization of a turbulent flow. Recommendations for further code modifications and improvements are also presented.
The relation of microstructure to the mechanical strength and stress corrosion resistance of highest strength and overaged tempers of BAR and 7050 aluminum alloys was investigated. Comparison is made with previously studied 7075 aluminum alloy. Optical microscopy, transmission electron microscopy, and differential scanning calorimetry were used to characterize the grain morphology, matrix microstructure, and grain boundary microstructure of these tempers. Grain boundary interparticle spacing was significant to stress corrosion crack propagation for all three alloys; increasing interparticle spacing led to increased resistance to crack propagation. In addition, the fire grain size in Bar and 7050 appears to enhance crack propagation. The highest strength temper of 7050 has a comparatively high resistance to crack initiation. Overall stress corrosion behavior is dependent on environment pH, and evaluation over a range of pH is recommended.
Description of the characteristics of PLZT-matrix type block data composers operated in the strain-biased, scattering, differential phase, and edge-effect modes. The operation peculiarities of each of these four modes are discussed, and their respective merits are compared.
A numerical generalized-capacity-matrix technique is developed for application to aerodynamic flow computations. This technique allows the very fast direct (noniterative) numerical elliptic solvers to be used in problems with arbitrary internal boundaries and with a wide class of boundary conditions, including numerical application of the Kutta condition on an airfoil without iteration. Accuracy, speed, and usefulness of the technique are demonstrated with linear problems for potential flows over airfoil shapes. The method's main advantages, however, can be exploited within iterative procedures for a variety of complex flow problems governed by systems of equations not necessarily elliptic or linear.