Results for “MATRIX” — Page 8

NASA NTRS1977

Petrology of crystalline matrix breccias from Apollo 17 rake samples

The petrology, mineralogy, and composition of 13 crystalline matrix breccias from the Apollo 17 rake samples are described. The breccias have matrices of uniform modal mineralogy (plagioclase, 50-54%; olivine and pyroxene, 41-46%) but diverse textures. Clast characteristics, including the proportion of plagioclase, the composition in comparison with matrix, and the textures of different clast types, are reported. The majority of bulk matrix compositions plot on or very near the plagioclase-olivine cotectic in the system olivine-anorthite-silica. If the matrix compositions represent impact total melts, the inferred cotectic control requires that the source material was itself an igneous differentiate with compositions along the plagioclase-olivine cotectic. Alternatively, the proximity of the matrix compositions to the plagioclase-olivine cotectic could be accounted for if the breccia matrices represent a suite of impact-generated partial melts.

Warner, R. D.↗

NASA NTRS1982

Development, implementation, and test results on integrated optics switching matrix

A small integrated optics switching matrix, which was developed, implemented, and tested, indicates high performance. The matrix serves as a model for the design of larger switching matrices. The larger integrated optics switching matrix should form the integral part of a switching center with high data rate throughput of up to 300 megabits per second. The switching matrix technique can accomplish the design goals of low crosstalk and low distortion. About 50 illustrations help explain and depict the many phases of the integrated optics switching matrix. Many equations used to explain and calculate the experimental data are also included.

Rutz, E.↗

NASA NTRS1985

Thermal expansion of selected graphite reinforced polyimide-, epoxy-, and glass-matrix composite

The thermal expansion of three epoxy-matrix composites, a polyimide-matrix composite and a borosilicate glass-matrix composite, each reinforced with continuous carbon fibers, has been measured and compared. The expansion of a composite with a rubber toughened epoxy-matrix and P75S carbon fibers was very different from the expansion of two different single phase epoxy-matrix composites with P75S fibers although all three had the same stacking sequence. Reasonable agreement was obtained between measured thermal-expansion data and results from classical laminate theory. The thermal expansion of a material may change markedly as a result of thermal cycling. Microdamage, induced by 250 cycles between -156 C and 121 C in the graphite/polyimide laminate, caused a 53 percent decrease in the coefficient of thermal expansion. The thermal expansion of the graphite/glass laminate was not changed by 100 thermal cycles from -129 C to 38 C; however, a residual strain of about 10 x 10 to the minus 6 power was measured for the laminate tested.

Tompkins, S. S.↗

NASA NTRS1987

On the eigenvalue and eigenvector derivatives of a general matrix

The existence of differentiable eigenvalues and eigenvectors for a general matrix is addressed. The eigenspace which contains differentiable eigenvectors is determined and computed by using the concept of subspace intersection in conjunction with the singular value decomposition algorithm. The differentiable eigenvectors associated with repeated eigenvalues should be simultaneously the eigenvectors of the general matrix and its corresponding sensitivity matrix. Furthermore, the derivatives for differentiable eigenvectors associated with repeated eigenvalues can be computed using higher order derivatives of the matrix, whereas the corresponding eigenvalue derivatives are the eigenvalues of the sensitivity matrix.

Juang, Jer-Nan↗

NASA NTRS1987

The matrix exponential in transient structural analysis

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Minnetyan, Levon↗

NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1988

Fatigue testing and damage development in continuous fiber reinforced metal matrix composites

A general overview of the fatigue behavior of metal matrix composites (MMC) is presented. The first objective is to present experimental procedures and techniques for conducting a meaningful fatigue test to detect and quantify fatigue damage in MMC. These techniques include interpretation of stress-strain responses, acid etching of the matrix, edge replicas of the specimen under load, radiography, and micrographs of the failure surfaces. In addition, the paper will show how stiffness loss in continuous fiber reinforced metal matrix composites can be a useful parameter for detecting fatigue damage initiation and accumulation. Second, numerous examples of how fatigue damage can initiate and grow in various MMC are given. Depending on the relative fatigue behavior of the fiber and matrix, and the interface properties, the failure modes of MMC can be grouped into four categories: (1) matrix dominated, (2) fiber dominated, (3) self-similar damage growth, and (4) fiber/matrix interfacial failures. These four types of damage will be discussed and illustrated by examples with the emphasis on the fatigue of unnotched laminates.

Johnson, W. S.↗

NASA NTRS1989

The role of rapid solidification processing in the fabrication of fiber reinforced metal matrix composites

Advanced composite processing techniques for fiber reinforced metal matrix composites require the flexibility to meet several widespread objectives. The development of uniquely desired matrix microstructures and uniformly arrayed fiber spacing with sufficient bonding between fiber and matrix to transmit load between them without degradation to the fiber or matrix are the minimum requirements necessary of any fabrication process. For most applications these criteria can be met by fabricating composite monotapes which are then consolidated into composite panels or more complicated components such as fiber reinforced turbine blades. Regardless of the end component, composite monotapes are the building blocks from which near net shape composite structures can be formed. The most common methods for forming composite monotapes are the powder cloth, foil/fiber, plasma spray, and arc spray processes. These practices, however, employ rapid solidification techniques in processing of the composite matrix phase. Consequently, rapid solidification processes play a vital and yet generally overlooked role in composite fabrication. The future potential of rapid solidification processing is discussed.

Locci, Ivan E.↗

NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Baritzhack, Itzhack Y.↗

NASA NTRS1989

Nature and origin of matrix in the unique type 3 chondrite, Kakangari

The characteristics of the matrix of the Kakangari type-3 chondrite were investigated using high-resolution TEM and AEM. It was found that the textural and mineralogical characteristics of the fine-grained matrix of Kakangari are different from those of the other chondrite groups. Unlike the matrix phases present in the CV3 and CO3 chondrites, the matrix mineralogy of Kakangari contains clear information regarding its possible origin and thermal history. Data obtained are most consistent with an origin of Kakangari by annealing, without melting at high temperature (possibly during a chondrule-forming thermal event), of clusters or aggregates of ultrafine-grained amorphous or crystalline phases. The precursor materials were most likely to have been a mixture of nebula and presolar dust. Chondrules in Kakangari were probably formed from identical precursors to the matrix, but reached temperatures sufficiently high to produce melting.

Brearley, Adrian J.↗

NASA NTRS1990

Parametric studies to determine the effect of compliant layers on metal matrix composite systems

Computational simulation studies are conducted to identify compliant layers to reduce matrix stresses which result from the coefficient of thermal expansion mismatch and the large temperature range over which the current metal matrix composites will be used. The present study includes variations of compliant layers and their properties to determine their influence on unidirectional composite and constituent response. Two simulation methods are used for these studies. The first approach is based on a three-dimensional linear finite element analysis of a 9 fiber unidirectional composite system. The second approach is a micromechanics based nonlinear computer code developed to determine the behavior of metal matrix composite system for thermal and mechanical loads. The results show that an effective compliant layer for the SCS 6 (SiC)/Ti-24Al-11Nb (Ti3Al + Nb) and SCS 6 (SiC)/Ti-15V-3Cr-3Sn-3Al (Ti-15-3) composite systems should have modulus 15 percent that of the matrix and a coefficient of thermal expansion of the compliant layer roughly equal to that of the composite system without the CL. The matrix stress in the longitudinal and the transverse tangent (loop) direction are tensile for the Ti3Al + Nb and Ti-15-3 composite systems upon cool down from fabrication. The fiber longitudinal stress is compressive from fabrication cool down. Addition of a recommended compliant layer will result in a reduction in the composite modulus.

Caruso, J. J.↗

NASA NTRS1990

Observations of fatigue crack initiation and damage growth in notched titanium matrix composites

The purpose was to characterize damage initiation and growth in notched titanium matrix composites at room temperature. Double edge notched or center open hole SCS-6/Ti-15-3 specimens containing 0 deg plies or containing both 0 and 90 deg plies were fatigued. The specimens were tested in the as-fabricated (ASF) and in heat-treated conditions. A local strain criterion using unnotched specimen fatigue data was successful in predicting fatigue damage initiation. The initiation stress level was accurately predicted for both a double edge notched unidirectional specimen and a cross-plied center hole specimen. The fatigue produced long multiple cracks growing from the notches. These fatigue cracks were only in the matrix material and did not break the fibers in their path. The combination of matrix cracking and fiber/matrix debonding appears to greatly reduce the stress concentration around the notches. The laminates that were heat treated showed a different crack growth pattern. In the ASF specimens, matrix cracks had a more tortuous path and showed considerable more crack branching. For the same specimen geometry and cyclic stress, the (0/90/0) laminate with a hole had far superior fatigue resistance than the matrix only specimen with a hole.

Naik, R. A.↗

NASA NTRS1989

Comparison of two matrix data structures for advanced CSM testbed applications

The first section describes data storage schemes presently used by the Computational Structural Mechanics (CSM) testbed sparse matrix facilities and similar skyline (profile) matrix facilities. The second section contains a discussion of certain features required for the implementation of particular advanced CSM algorithms, and how these features might be incorporated into the data storage schemes described previously. The third section presents recommendations, based on the discussions of the prior sections, for directing future CSM testbed development to provide necessary matrix facilities for advanced algorithm implementation and use. The objective is to lend insight into the matrix structures discussed and to help explain the process of evaluating alternative matrix data structures and utilities for subsequent use in the CSM testbed.

Regelbrugge, M. E.↗

NASA NTRS1989

Fatigue testing and damage development in continuous fiber reinforced metal matrix composites

A general overview of the fatigue behavior of metal matrix composites (MMC) is presented. The first objective is to present experimental procedures and techniques for conducting a meaningful fatigue test to detect and quantify fatigue damage in MMC. These techniques include interpretation of stress-strain responses, acid etching of the matrix, edge replicas of the specimen under load, radiography, and micrographs of the failure surfaces. In addition, the paper will show how stiffness loss in continuous fiber reinforced metal matrix composites can be a useful parameter for detecting fatigue damage initiation and accumulation. Second, numerous examples of how fatigue damage can initiate and grow in various MMC are given. Depending on the relative fatigue behavior of the fiber and matrix, and the interface properties, the failure modes of MMC can be grouped into four categories: (1) matrix dominated, (2) fiber dominated, (3) self-similar damage growth, and (4) fiber/matrix interfacial failures. These four types of damage will be discussed and illustrated by examples with the emphasis on the fatigue of unnotched laminates.

Johnson, W. S.↗

NASA NTRS1990

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1990

Isothermal and nonisothermal fatigue behavior of a metal matrix composite

The isothermal and nonisothermal fatigue resistance of a metal matrix composite (MMC) consisting of Ti-15V-3Cr-3Al-3Sn (Ti-15-3) matrix reinforced by 33 vol pct continuous SiC fibers was investigated. The fibers were nominally oriented parallel to the specimen axis. Isothermal fatigue tests were performed in air at 300 and 550 C. The MMC had good isothermal fatigue resistance at low cyclic stress, with fatigue cracks initiating from fiber-matrix interfaces and foil laminations. At high cyclic stresses, stress relaxation in the matrix reduced isothermal composite fatigue resistance at 550 C. Nonisothermal fatigue loading substantially degraded composite fatigue resistnce. This degradation was produced by a thermomechanical fatigue damage mechanism associated with the fiber-matrix interfaces.

Gabb, T. P.↗

NASA NTRS1989

Mechanisms controlling fatigue damage development in continuous fiber reinforced metal matrix composites

Damage in continuous fiber reinforced metal matrix composite materials can be quite complex since there are a number of different constituents (fiber, matrix, and the fiber/matrix interface) that can fail. Multidirectional lay-ups have an even greater number of possible damage orientations and mechanisms. Based on the simplifying assumption of equivalent constituent strain states in the absence of damage, a strain based failure criteria may be applied to determine when and where initial damage will occur. Based on the relative strain to fatigue failure of the fiber and matrix, the possible damage mechanisms of an MMC can be grouped into three categories: (1) matrix dominated, (2) fiber dominated, and (3) self-similar damage growth. A fourth type of damage development, fiber/matrix interface failure, is dependent on the relative strength of the fiber/matrix interface and the matrix yield strength. These four types of damage are discussed and illustrated by examples.

Johnson, W. S.↗

NASA NTRS1990

Parametric studies to determine the effect of compliant layers on metal matrix composite systems

Computational simulation studies are conducted to identify compliant layers to reduce matrix stresses which result from the coefficient of thermal expansion mismatch and the large temperature range over which the current metal matrix composites will be used. The present study includes variations of compliant layers and their properties to determine their influence on unidirectional composite and constituent response. Two simulation methods are used for these studies. The first approach is based on a three-dimensional linear finite element analysis of a 9 fiber unidirectional composite system. The second approach is a micromechanics based nonlinear computer code developed to determine the behavior of metal matrix composite system for thermal and mechanical loads. The results show that an effective compliant layer for the SCS 6 (SiC)/Ti-24Al-11Nb (Ti3Al + Nb) and SCS 6 (SiC)/Ti-15V-3Cr-3Sn-3Al (Ti-15-3) composite systems should have modulus 15 percent that of the matrix and a coefficient of thermal expansion of the compliant layer roughly equal to that of the composite system without the CL. The matrix stress in the longitudinal and the transverse tangent (loop) direction are tensile for the Ti3Al + Nb and Ti-15-3 composite systems upon cool down from fabrication. The fiber longitudinal stress is compressive from fabrication cool down. Addition of a recommended compliant layer will result in a reduction in the composite modulus.

Caruso, J. J.↗