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NASA NTRS1993

Composite micromechanical modeling using the boundary element method

The use of the boundary element method for analyzing composite micromechanical behavior is demonstrated. Stress-strain, heat conduction, and thermal expansion analyses are conducted using the boundary element computer code BEST-CMS, and the results obtained are compared to experimental observations, analytical calculations, and finite element analyses. For each of the analysis types, the boundary element results agree reasonably well with the results from the other methodologies, with explainable discrepancies. Overall, the boundary element method shows promise in providing an alternative method to analyze composite micromechanical behavior.

Goldberg, Robert K.↗

NASA NTRS1991

Micromechanical studies of composites by BEM

Over the last five years BEM has been developed into a very effective tool for micromechanical studies of composites. The analyses developed range from static elastic analysis, steady state heat transfer, steady state and transient thermoelastic analysis, periodic and transient dynamic analysis. Currently some of these analyses are being extended to nonlinear micromechanical analyses involving viscoplasticity, elastoplasticity, combined plasticity fracture and creep. The paper describes some of the results for elastic analysis, heat transfer and thermoelastic analyses.

Banerjee, P. K.↗

NASA NTRS1993

Probabilistic micromechanics for high-temperature composites

The three-year program of research had the following technical objectives: the development of probabilistic methods for micromechanics-based constitutive and failure models, application of the probabilistic methodology in the evaluation of various composite materials and simulation of expected uncertainties in unidirectional fiber composite properties, and influence of the uncertainties in composite properties on the structural response. The first year of research was devoted to the development of probabilistic methodology for micromechanics models. The second year of research focused on the evaluation of the Chamis-Hopkins constitutive model and Aboudi constitutive model using the methodology developed in the first year of research. The third year of research was devoted to the development of probabilistic finite element analysis procedures for laminated composite plate and shell structures.

Reddy, J. N.↗

NASA NTRS1993

Micromechanical simulation of damage progression in carbon phenolic composites

Carbon/phenolic composites are used extensively as ablative insulating materials in the nozzle region of solid rocket motors. The current solid rocket motor (RSRM) on the space shuttle is fabricated from woven rayon cloth which is carbonized and then impregnated with the phenolic resin. These plies are layed up in the desired configuration and cured to form the finished part. During firing, the surface of the carbon/phenolic insulation is exposed to 5000 F gases from the rocket exhaust. The resin pyrolizes and the material chars to a depth which progresses with time. The rate of charring and erosion are generally predictable, and the insulation depth is designed to allow adequate safety margins over the firing time of the motor. However, anomalies in the properties and response of the carbon/phenolic materials can lead to severe material damage which may decrease safety margins to unacceptable levels. Three macro damage modes which were observed in fired nozzles are: ply lift, 'wedge out', and pocketing erosion. Ply lift occurs in materials with plies oriented nearly parallel to the surface. The damage occurs in a region below the charred material where material temperatures are relatively low - about 500 F. Wedge out occurs at the intersection of nozzle components whose plies are oriented at about 45 deg. The corner of the block of material breaks off along a ply interface. Pocketing erosion occurs in material with plies oriented normal to the surface. Thermal expansion is restrained in two directions resulting in large tensile strains and material failure normal to the surface. When a large section of material is removed as a result of damage, the insulation thickness is reduced which may lead to failure of the nozzle due to excessive heating of critical components. If these damage events cannot be prevented with certainty, the designer must increase the thickness of the insulator thus adding to both weight and cost. One of the difficulties in developing a full understanding of these macro damage mechanisms is that the loading environment and the material response to that environment are extremely complex. These types of damage are usually only observed in actual motor firings. Therefore, it is difficult and expensive to evaluate the reliability of new materials. Standard material tests which measure mechanical and thermal properties of test specimens can only provide a partial picture of how the material will respond in the service environment. The development of the ANALOG test procedure which can combine high heating rates and mechanical loads on a specimen will improve the understanding of the interactive effects of the various loads on the system. But a mechanistic model of material response which can account for the heterogeneity of the material, the progression of various micromechanical damage mechanisms, and the interaction of mechanical and thermal stresses on the material is required to accurately correlate material tests with response to service environments. A model based on fundamental damage mechanisms which is calibrated and verified under a variety of loading conditions will provide a general tool for predicting the response of rocket nozzles. The development of a micromechanical simulation technique was initiated and demonstrated to be effective for studying across-ply tensile failure of carbon/phenolic composites.

Slattery, Kerry T.↗

NASA NTRS1994

Micromechanical characterization of nonlinear behavior of advanced polymer matrix composites

Due to the presence of curing stresses and oriented crystalline structures in the matrix of polymer matrix fiber composites, the in situ nonlinear properties of the matrix are expected to be rather different from those of the bulk resin. A plane stress micromechanical model was developed to retrieve the in situ elastic-plastic properties of Narmco 5260 and Amoco 8320 matrices from measured elastic-plastic properties of IM7/5260 and IM7/8320 advance composites. In the micromechanical model, the fiber was assumed to be orthotropically elastic and the matrix to be orthotropic in elastic and plastic properties. The results indicate that both in situ elastic and plastic properties of the matrices are orthotropic.

Gates, Thomas S.↗

NASA NTRS1994

Micromechanical Modeling of the Thermal Expansion of Graphite/copper Composites with Nonuniform Microstructure

Two micromechanical models were developed to investigate the thermal expansion of graphite/copper (Gr/Cu) composites. The models incorporate the effects of temperature-dependent material properties, matrix inelasticity, initial residual stresses due to processing history, and nonuniform fiber distribution. The first model is based on the multiple concentric cylinder geometry, with each cylinder treated as a two-phase composite with a characteristic fiber volume fractions. By altering the fiber volume fraction of the individual cylinders, unidirectional composites with radially nonuniform fiber distributions can be investigated using this model. The second model is based on the inelastic lamination theory. By varying the fiber content in the individual laminae, composites with nonuniform fiber distribution in the thickness direction can be investigated. In both models, the properties of the individual regions (cylinders or laminae) are calculated using the method of cells micromechanical model. Classical incremental plasticity theory is used to model the inelastic response of the copper matrix at the microlevel. The models were used to characterize the effects of nonuniform fiber distribution on the thermal expansion of Gr/Cu. These effects were compared to the effects of matrix plasticity, choice of stress-free temperature, and slight fiber misalignment. It was found that the radially nonuniform fiber distribution has little effect on the thermal expansion of Gr/Cu but could become significant for composites with large fiber-matrix transverse CTE and Young's modulus mismatch. The effect of nonuniform fiber distribution in the through-thickness direction of a laminate was more significant, but only approached that of the stress-free temperature for the most extreme cases that include large amounts of bending. Subsequent comparison with experimental thermal expansion data indicated the need for more accurate characterization of the graphite fiber thermomechanical properties. Correlation with cyclic data revealed the presence of a mechanism not considered in the developed models. The predicted response did, however, exhibit ratcheting behavior that has been observed experimentally in Gr/Cu. Finally, simulation of the actual fiber distribution of particular specimens had little effect on the predicted thermal expansion.

Bednarcyk, Brett A.↗

NASA NTRS1996

Simplified Micromechanics of Plain Weave Composites

A micromechanics based methodology to simulate the complete hygro-thermomechanical behavior of plain weave composites is developed. This methodology is based on micromechanics and the classical laminate theory. The methodology predicts a complete set of thermal, hygral and mechanical properties of plain woven composites, generates necessary data for use in a finite element structural analysis, and predicts stresses all the way from the laminate to the constituent level. This methodology is used in conjunction with a composite mechanics code to analyze and predict the properties/response of a generic graphite/epoxy woven textile composite and a plain weave ceramic composite. The fiber architecture, including the fiber waviness and fiber end distributions through the thickness, is properly accounted for. Predicted results compare reasonably well with those from detailed three-dimensional finite element analyses as well as available experimental data. However, the main advantage of the proposed methodology is its high computational efficiency as compared with three-dimensional finite element analyses.

Mital, Subodh K.↗

NASA NTRS1996

Micromechanics for particulate reinforced composites

A set of micromechanics equations for the analysis of particulate reinforced composites is developed using the mechanics of materials approach. Simplified equations are used to compute homogenized or equivalent thermal and mechanical properties of particulate reinforced composites in terms of the properties of the constituent materials. The microstress equations are also presented here to decompose the applied stresses on the overall composite to the microstresses in the constituent materials. The properties of a 'generic' particulate composite as well as those of a particle reinforced metal matrix composite are predicted and compared with other theories as well as some experimental data. The micromechanics predictions are in excellent agreement with the measured values.

Murthy, Pappu L. N.↗

NASA NTRS1996

Critique of Macro Flow/Damage Surface Representations for Metal Matrix Composites Using Micromechanics

Guidance for the formulation of robust, multiaxial, constitutive models for advanced materials is provided by addressing theoretical and experimental issues using micromechanics. The multiaxial response of metal matrix composites, depicted in terms of macro flow/damage surfaces, is predicted at room and elevated temperatures using an analytical micromechanical model that includes viscoplastic matrix response as well as fiber-matrix debonding. Macro flow/damage surfaces (i.e., debonding envelopes, matrix threshold surfaces, macro 'yield' surfaces, surfaces of constant inelastic strain rate, and surfaces of constant dissipation rate) are determined for silicon carbide/titanium in three stress spaces. Residual stresses are shown to offset the centers of the flow/damage surfaces from the origin and their shape is significantly altered by debonding. The results indicate which type of flow/damage surfaces should be characterized and what loadings applied to provide the most meaningful experimental data for guiding theoretical model development and verification.

Lissenden, Cliff J.↗

NASA NTRS1997

Probabilistic Micromechanics and Macromechanics for Ceramic Matrix Composites

The properties of ceramic matrix composites (CMC's) are known to display a considerable amount of scatter due to variations in fiber/matrix properties, interphase properties, interphase bonding, amount of matrix voids, and many geometry- or fabrication-related parameters, such as ply thickness and ply orientation. This paper summarizes preliminary studies in which formal probabilistic descriptions of the material-behavior- and fabrication-related parameters were incorporated into micromechanics and macromechanics for CMC'S. In this process two existing methodologies, namely CMC micromechanics and macromechanics analysis and a fast probability integration (FPI) technique are synergistically coupled to obtain the probabilistic composite behavior or response. Preliminary results in the form of cumulative probability distributions and information on the probability sensitivities of the response to primitive variables for a unidirectional silicon carbide/reaction-bonded silicon nitride (SiC/RBSN) CMC are presented. The cumulative distribution functions are computed for composite moduli, thermal expansion coefficients, thermal conductivities, and longitudinal tensile strength at room temperature. The variations in the constituent properties that directly affect these composite properties are accounted for via assumed probabilistic distributions. Collectively, the results show that the present technique provides valuable information about the composite properties and sensitivity factors, which is useful to design or test engineers. Furthermore, the present methodology is computationally more efficient than a standard Monte-Carlo simulation technique; and the agreement between the two solutions is excellent, as shown via select examples.

Murthy, Pappu L. N.↗

NASA NTRS1998

Micromechanical Prediction of the Effective Coefficients of Thermo-Piezoelectric Multiphase Composites

The micromechanical generalized method of cells model is employed for the prediction of the effective elastic, piezoelectric, dielectric, pyroelectric and thermal-expansion constants of multiphase composites with embedded piezoelectric materials. The predicted effective constants are compared with other micromechanical methods available in the literature and good agreements are obtained.

Aboudi, Jacob↗

NASA NTRS1999

Micromechanics Analysis Code Post-Processing (MACPOST) User Guide

As advanced composite materials have gained wider usage. the need for analytical models and computer codes to predict the thermomechanical deformation response of these materials has increased significantly. Recently, a micromechanics technique called the generalized method of cells (GMC) has been developed, which has the capability to fulfill this -oal. Tc provide a framework for GMC, the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) has been developed. As MAC/GMC has been updated, significant improvements have been made to the post-processing capabilities of the code. Through the MACPOST program, which operates directly within the MSC/PATRAN graphical pre- and post-processing package, a direct link between the analysis capabilities of MAC/GMC and the post-processing capabilities of MSC/PATRAN has been established. MACPOST has simplified the production, printing. and exportation of results for unit cells analyzed by MAC/GMC. MACPOST allows different micro-level quantities to be plotted quickly and easily in contour plots. In addition, meaningful data for X-Y plots can be examined. MACPOST thus serves as an important analysis and visualization tool for the macro- and micro-level data generated by MAC/GMC. This report serves as the user's manual for the MACPOST program.

Goldberg, Robert K.↗

NASA NTRS2000

Micromechanical and Electrical Properties of Monolithic Aluminum Nitride at High Temperatures

Micromechanical spectroscopy of aluminum nitride reveals it to possess extremely low background internal friction at less than 1x10(exp-4) logarithmic decrement (log dec) from 20 to 1200 T. Two mechanical loss peaks were observed, the first at 350 C approximating a single Debye peak with a peak height of 60x10(exp-4) log dec. The second peak was seen at 950 'C with a peak height of 20x 10' log dec and extended from 200 to over 1200 C. These micromechanical observations manifested themselves in the electrical behavior of these materials. Electrical conduction processes were predominately intrinsic. Both mechanical and electrical relaxations appear to be thermally activated processes, with activation energies of 0.78 and 1.32 eV respectively.

Goldsby, Jon C.↗

NASA NTRS2001

Micromechanical and Electrical Properties of Monolithic Aluminum Nitride at High Temperatures

Micromechanical spectroscopy of aluminum nitride reveals it to possess extremely low background internal friction at less than 1 x 10 (exp -4) logarithmic decrement (log dec.) from 20 to 1200 C. Two mechanical loss peaks were observed, the first at 350 C approximating a single Debye peak with a peak height of 60 x 10 (exp -4) log dec. The second peak was seen at 950 C with a peak height of 20 x 10 (exp -4) log dec. and extended from 200 to over 1200 C. These micromechanical observations manifested themselves in the electrical behavior of these materials. Electrical conduction processes were predominately intrinsic. Both mechanical and electrical relaxations appear to be thermally activated processes, with activation energies of 0.78 and 1.32 eV respectively.

Goldsby, Jon C.↗

NASA NTRS1945

Micromechanical Study of Metals

The Institut Scientifique Experimental des Transports at Moscow established toward the end of 1925 had since its inception included in its program the study of the mechanism of plastic deformation and the problems associated with it with reference to the materials of the means of transport. Before the program thus determined upon could be carried out, it was necessary to adopt a method of research, or, more exactly, a system of such methods. Because of the modest equipment of the laboratory of the recently established institute, the choice of any particular method was determined not only by the advantages it offered but also by the resources available. As a result of a series of studies and investigations, a method was determined upon which in this paper will be denoted as the micromechanical method. The underlying basis of this method is already known. As will be seen from the description that follows, the micromechanical method is merely a combination of the micrographic study of plastic deformations with mechanical tests on small specimens. It is a well-known fact that a number of investigators have largely employed and still are employing these two procedures and have thereby obtained good results. The authors of the present paper have found it useful to combine the two methods, by making the two studies simultaneously on the sane specimen.

Velikov, P. A.↗

NASA NTRS2005

Role of Probabilistic Micromechanics Modeling in Establishing Design Allowables in Composites

One of the major challenges in designing with any new material, and particularly with advanced composite materials, is the fidelity of material design allowables. In the case of composite materials, the concern arises from the inherent nature of these materials, i.e., their heterogeneous make-up and the various factors that affect their properties in a specific design environment. Composites have various scales - micro, macro, laminate and structural, as well as numerous other fabrication related parameters. Many advanced composites in aerospace applications involve complex two- and three-dimensional fiber architectures and requires high-temperature processing. Since there are uncertainties associated with each of these, the observed behavior of composite materials shows scatter. Evaluating the effect of each of these variables on the observed scatter in composite properties solely by teSting is cost and time prohibitive. One alternative is to evaluate these effects by computational simulation. The authors have developed probabilistic composite micromechanics techniques by combining woven composite micromechanics and Fast Probability Integration (FPI) techniques to address these issues. In this paper these techniques will be described and demonstrated through selected examples. Results in the form of cumulative distribution functions (CDF) of the composite properties of a MI (melt-infiltrated) SiC/SiC (silicon carbide fiber in a silicon carbide matrix) Composite will be presented. A CDF is a relationship defined by the value of the property (the response variable) with respect to the cumulative probability of occurrence. Furthermore, input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Sensitivity information is very valuable in quality control. How these results can be utilized to develop design allowables so that these materials may be used by structural analysts/designers will also be discussed.

Mital, Subodh K.↗

NASA NTRS2001

Micromechanics-Based Inelastic Finite Element Analysis Accomplished Via Seamless Integration of MAC/GMC

A critical issue in the micromechanics-based analysis of composite structures becomes the availability of a computationally efficient homogenization technique: one that is 1) Capable of handling the sophisticated, physically based, viscoelastoplastic constitutive and life models for each constituent; 2) Able to generate accurate displacement and stress fields at both the macro and the micro levels; 3) Compatible with the finite element method. The Generalized Method of Cells (GMC) developed by Paley and Aboudi is one such micromechanical model that has been shown to predict accurately the overall macro behavior of various types of composites given the required constituent properties. Specifically, the method provides "closed-form" expressions for the macroscopic composite response in terms of the properties, size, shape, distribution, and response of the individual constituents or phases that make up the material. Furthermore, expressions relating the internal stress and strain fields in the individual constituents in terms of the macroscopically applied stresses and strains are available through strain or stress concentration matrices. These expressions make possible the investigation of failure processes at the microscopic level at each step of an applied load history.

Arnold, Steven M.↗

NASA NTRS2005

Micromechanics, Fracture Mechanics and Gas Permeability of Composite Laminates for Cryogenic Storage Systems

A micromechanics method is developed to investigate microcrack propagation in a liquid hydrogen composite tank at cryogenic temperature. The unit cell is modeled using square and hexagonal shapes depends on fiber and matrix layout from microscopic images of composite laminates. Periodic boundary conditions are applied to the unit cell. The temperature dependent properties are taken into account in the analysis. The laminate properties estimated by the micromechanics method are compared with empirical solutions using constituent properties. The micro stresses in the fiber and matrix phases based on boundary conditions in laminate level are calculated to predict the formation of microcracks in the matrix. The method is applied to an actual liquid hydrogen storage system. The analysis predicts micro stresses in the matrix phase are large enough to cause microcracks in the composite. Stress singularity of a transverse crack normal to a ply-interface is investigated to predict the fracture behavior at cryogenic conditions using analytical and finite element analysis. When a transverse crack touches a ply-interface of a composite layer with same fiber orientation, the stress singularity is equal to 1/2. When the transverse crack propagates to a stiffer layer normal to the ply-direction, the singularity becomes less than 1/2 and vice versa. Finite element analysis is performed to predict the fracture toughness of a laminated beam subjected to fracture loads measured by four-point bending tests at room and cryogenic temperatures. As results, the fracture load at cryogenic temperature is significantly lower than that at room temperature. However, when thermal stresses are taken into consideration, for both cases of room and cryogenic temperatures, the difference of the fracture toughness becomes insignificant. The result indicates fracture toughness is a characteristic property, which is independent to temperature changes. The experimental analysis is performed to investigate the effect of cryogenic cycling on permeability for various composite material systems. Textile composites have lower permeability than laminated composites even with increasing number of cryogenic cycle. Nano-particles dispersed in laminated composites do not show improvement on permeability. The optical inspection is performed to investigate the microcrack propagation and void content in laminated composites and compared the microscopic results before and after cryogenic cycling.

Choi, Sukjoo↗