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NASA NTRS2005

Comprehensive Micromechanics-Analysis Code - Version 4.0

Version 4.0 of the Micromechanics Analysis Code With Generalized Method of Cells (MAC/GMC) has been developed as an improved means of computational simulation of advanced composite materials. The previous version of MAC/GMC was described in "Comprehensive Micromechanics-Analysis Code" (LEW-16870), NASA Tech Briefs, Vol. 24, No. 6 (June 2000), page 38. To recapitulate: MAC/GMC is a computer program that predicts the elastic and inelastic thermomechanical responses of continuous and discontinuous composite materials with arbitrary internal microstructures and reinforcement shapes. The predictive capability of MAC/GMC rests on a model known as the generalized method of cells (GMC) - a continuum-based model of micromechanics that provides closed-form expressions for the macroscopic response of a composite material in terms of the properties, sizes, shapes, and responses of the individual constituents or phases that make up the material. Enhancements in version 4.0 include a capability for modeling thermomechanically and electromagnetically coupled ("smart") materials; a more-accurate (high-fidelity) version of the GMC; a capability to simulate discontinuous plies within a laminate; additional constitutive models of materials; expanded yield-surface-analysis capabilities; and expanded failure-analysis and life-prediction capabilities on both the microscopic and macroscopic scales.

Arnold, S. M.↗
NASA NTRS1991

Micromechanics analysis of space simulated thermal stresses in composites. I - Theory and unidirectional laminates. II - Multidirectional laminates and failure predictions

A micromechanics analysis is used to study the effects of constituent properties on thermally induced stresses in continuous fiber reinforced composites. A finite element formulation is described, and results are presented for unidirectional carbon/epoxy laminates. It is shown that significant stresses develop in composites exposed to thermal excursions typical of spacecraft operating environments and that the fiber thermoelastic properties have a minimal effect on the magnitude of these stresses. The finite element micromechanics analysis is then extended to the study of multidirectional laminates using a simple global/local formulation. Damage initiation predictions are compared with experimental data, and factors controlling the initiation of damage are identified. Ways of improving the durability of composites are discussed.

Bowles, David E.↗
NASA NTRS2005

Development, Implementation and Application of Micromechanical Analysis Tools for Advanced High Temperature Composites

This document contains the final report to the NASA Glenn Research Center (GRC) for the research project entitled Development, Implementation, and Application of Micromechanical Analysis Tools for Advanced High-Temperature Composites. The research supporting this initiative has been conducted by Dr. Brett A. Bednarcyk, a Senior Scientist at OM in Brookpark, Ohio from the period of August 1998 to March 2005. Most of the work summarized herein involved development, implementation, and application of enhancements and new capabilities for NASA GRC's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) software package. When the project began, this software was at a low TRL (3-4) and at release version 2.0. Due to this project, the TRL of MAC/GMC has been raised to 7 and two new versions (3.0 and 4.0) have been released. The most important accomplishments with respect to MAC/GMC are: (1) A multi-scale framework has been built around the software, enabling coupled design and analysis from the global structure scale down to the micro fiber-matrix scale; (2) The software has been expanded to analyze smart materials; (3) State-of-the-art micromechanics theories have been implemented and validated within the code; (4) The damage, failure, and lifing capabilities of the code have been expanded from a very limited state to a vast degree of functionality and utility; and (5) The user flexibility of the code has been significantly enhanced. MAC/GMC is now the premier code for design and analysis of advanced composite and smart materials. It is a candidate for the 2005 NASA Software of the Year Award. The work completed over the course of the project is summarized below on a year by year basis. All publications resulting from the project are listed at the end of this report.

Source record↗
NASA NTRS1992

A macro-micromechanics analysis of a notched metal matrix composite

Macro- and micromechanics analysis were conducted to determine the matrix and fiber behaviors near the notch in a center-notched metal-matrix composite. In this approach, the macrolevel analysis models the entire notched specimen using a 3D finite element program that uses the vanishing-fiber-diameter model to simulate the elastic-plastic behavior of the matrix and the elastic behavior of the fiber. The microlevel behavior is analyzed using a discrete fiber-matrix model containing one fiber and the surrounding matrix. The viability of this analysis is demonstrated using results for a boron/aluminum monolayer.

Bigelow, Catherine A.↗
NASA NTRS1990

A macro-micromechanics analysis of a notched metal matrix composite

A macro-micromechanics analysis was formulated to determine the matrix and fiber behavior near the notch tip in a center-notched metal matrix composite. Results are presented for a boron/aluminum monolayer. The macro-level analysis models the entire notched specimen using a three dimensional finite element program which uses the vanishing-fiber-diameter model to model the elastic-plastic behavior of the matrix and the elastic behavior of the fiber. The micro-behavior is analyzed using a Discrete Fiber-Matrix (DFM) model containing one fabric and the surrounding matrix. The dimensions of the DFM model were determined by the ply thickness and the fiber volume fraction and corresponded to the size of the notch-tip element in the macro-level analysis. The boundary conditions applied to the DFM model were determined from the macro-level analysis. Stress components within the DFM model were calculated and stress distributions are presented along selected planes and surfaces within the DFM model, including the fiber-matrix interface. Yielding in the matrix was examined at the notch tip in both the macro- and micro-level analyses. The DFM model predicted higher stresses (24 percent) in the fiber compared to the global analysis. In the notch-tip element, the interface stresses indicated that a multi-axial criterion may be required to predict interfacial failure. The DFM analysis predicted yielding to initiate in the notch-tip element at a stress level 28 percent lower than predicted by the global analysis.

Bigelow, C. A.↗
NASA NTRS1995

Application of the boundary element method to the micromechanical analysis of composite materials

A new boundary element formulation for the micromechanical analysis of composite materials is presented in this study. A unique feature of the formulation is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one-dimensional integrations. To demonstrate the applicability of the formulations, several example problems including elastic and thermal analysis of laminated composites and elastic analyses of woven composites are presented and the boundary element results compared to experimental observations and/or results obtained through alternate analytical procedures. While several issues remain to be addressed in order to make the methodology more robust, the formulations presented here show the potential in providing an alternative to traditional finite element methods, particularly for complex composite architectures.

Goldberg, R. K.↗
NASA NTRS1987

A micromechanics analysis of the influence of the interface on the performance of polymer-matrix composites

A specially developed two-dimensional finite element micromechanics analysis was used to predict the transverse tensile response of three different carbon fiber-reinforced, polymer matrix unidirectional composites. Experimental data were available for four different fiber sizings. The composites were tested both dry and moisture-conditioned, at room and elevated temperatures. Analytical/experimental correlations are presented and discussed.

Adams, Donald F.↗
NASA NTRS1986

A micromechanics analysis of the influence of the interface on the performance of polymer-matrix composites

A specially developed two-dimensional finite element micromechanics analysis was used to predict the transverse tensile response of three different carbon fiber-reinforced, polymer matrix unidirectional composites. Experimental data were available for four different fiber sizings. The composites were tested both dry and moisture-conditioned, at room and elevated temperatures. Analytical/experimental correlations are presented and discussed.

Adams, Donald F.↗
NASA NTRS1990

Micromechanics analysis of space simulated thermal deformations and stresses in continuous fiber reinforced composites

Space simulated thermally induced deformations and stresses in continuous fiber reinforced composites were investigated with a micromechanics analysis. The investigation focused on two primary areas. First, available explicit expressions for predicting the effective coefficients of thermal expansion (CTEs) for a composite were compared with each other, and with a finite element (FE) analysis, developed specifically for this study. Analytical comparisons were made for a wide range of fiber/matrix systems, and predicted values were compared with experimental data. The second area of investigation focused on the determination of thermally induced stress fields in the individual constituents. Stresses predicted from the FE analysis were compared to those predicted from a closed-form solution to the composite cylinder (CC) model, for two carbon fiber/epoxy composites. A global-local formulation, combining laminated plate theory and FE analysis, was used to determine the stresses in multidirectional laminates. Thermally induced damage initiation predictions were also made.

Bowles, David E.↗
NASA NTRS1994

Micromechanics Analysis Code (MAC) User Guide: Version 1.0

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions it must be based on a micromechanics approach which utilizes physically based deformation and life constitutive models and allows one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Here the user guide for the recently developed, computationally efficient and comprehensive micromechanics analysis code, MAC, who's predictive capability rests entirely upon the fully analytical generalized method of cells, GMC, micromechanics model is described. MAC is a versatile form of research software that 'drives' the double or triple ply periodic micromechanics constitutive models based upon GMC. MAC enhances the basic capabilities of GMC by providing a modular framework wherein (1) various thermal, mechanical (stress or strain control), and thermomechanical load histories can be imposed; (2) different integration algorithms may be selected; (3) a variety of constituent constitutive models may be utilized and/or implemented; and (4) a variety of fiber architectures may be easily accessed through their corresponding representative volume elements.

Wilt, T. E.↗
NASA NTRS1999

Micromechanics Analysis Code With Generalized Method of Cells (MAC/GMC): User Guide

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions it must be based on a micromechanics approach which utilizes physically based deformation and life constitutive models and allows one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Here the user guide for the recently developed, computationally efficient and comprehensive micromechanics analysis code, MAC, who's predictive capability rests entirely upon the fully analytical generalized method of cells, GMC, micromechanics model is described. MAC/ GMC is a versatile form of research software that "drives" the double or triply periodic micromechanics constitutive models based upon GMC. MAC/GMC enhances the basic capabilities of GMC by providing a modular framework wherein 1) various thermal, mechanical (stress or strain control) and thermomechanical load histories can be imposed, 2) different integration algorithms may be selected, 3) a variety of material constitutive models (both deformation and life) may be utilized and/or implemented, and 4) a variety of fiber architectures (both unidirectional, laminate and woven) may be easily accessed through their corresponding representative volume elements contained within the supplied library of RVEs or input directly by the user, and 5) graphical post processing of the macro and/or micro field quantities is made available.

Arnold, S. M.↗
NASA NTRS1996

Micromechanics Analysis Code (MAC). User Guide: Version 2.0

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions it must be based on a micromechanics approach which utilizes physically based deformation and life constitutive models and allows one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Here the user guide for the recently developed, computationally efficient and comprehensive micromechanics analysis code's (MAC) who's predictive capability rests entirely upon the fully analytical generalized method of cells (GMC), micromechanics model is described. MAC is a versatile form of research software that 'drives' the double or triply periodic micromechanics constitutive models based upon GMC. MAC enhances the basic capabilities of GMC by providing a modular framework wherein (1) various thermal, mechanical (stress or strain control) and thermomechanical load histories can be imposed, (2) different integration algorithms may be selected, (3) a variety of constituent constitutive models may be utilized and/or implemented, and (4) a variety of fiber and laminate architectures may be easily accessed through their corresponding representative volume elements.

Wilt, T. E.↗
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 NTRS1997

Micromechanics Analysis Code (MAC) Developed

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers in performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions, it must be based on a micromechanics approach that uses physically based deformation and life constitutive models, and it must allow one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Only then can such a model be used by a material scientist to investigate the effect of different deformation mechanisms on the overall response of the composite and, thereby, identify the appropriate constituents for a given application. However, if a micromechanical model is to be used in a large-scale structural analysis it must be (1) computationally efficient, (2) able to generate accurate displacement and stress fields at both the macro and micro level, and (3) compatible with the finite element method. In addition, new advancements in processing and fabrication techniques now make it possible to engineer the architectures of these advanced composite systems. Full utilization of these emerging manufacturing capabilities require the development of a computationally efficient micromechanics analysis tool that can accurately predict the effect of microstructural details on the internal and macroscopic behavior of composites. Computational efficiency is required because (1) a large number of parameters must be varied in the course of engineering (or designing) composite materials and (2) the optimization of a material's microstructure requires that the micromechanics model be integrated with optimization algorithms. From this perspective, analytical approaches that produce closed-form expressions which describe the effect of a material's internal architecture on the overall material behavior are preferable to numerical methods such as the finite element or finite difference schemes.

Source record↗
NASA NTRS1994

Micromechanical analysis of thermo-inelastic multiphase short-fiber composites

A micromechanical formulation is presented for the prediction of the overall thermo-inelastic behavior of multiphase composites which consist of short fibers. The analysis is an extension of the generalized method of cells that was previously derived for inelastic composites with continuous fibers, and the reliability of which was critically examined in several situations. The resulting three dimensional formulation is extremely general, wherein the analysis of thermo-inelastic composites with continuous fibers as well as particulate and porous inelastic materials are merely special cases.

Aboudi, Jacob↗
NASA NTRS1988

Micromechanical analysis of the time-dependent response of unidirectional composites

The micromechanical model of Aboudi (1982, 1984, and 1986) is used to predict the time-dependent creep behavior of viscoelastic-matrix composites with unidirectional elastic-fiber reinforcement. The derivation of the model and its numerical implementation are outlined, and predictions for T300/934 CFRP at 72 and 250 F are compared with experimental measurements in extensive tables and graphs. Good agreement is demonstrated, and the applicability of the present approach to composite laminates and hybrid materials such as ARALL is indicated.

Yancey, R. N.↗
NASA NTRS1985

Delamination micromechanics analysis

A three-dimensional finite element analysis was developed which includes elastoplastic, orthotropic material response, and fracture initiation and propagation. Energy absorption due to physical failure processes characteristic of the heterogeneous and anisotropic nature of composite materials is modeled. A local energy release rate in the presence of plasticity was defined and used as a criterion to predict the onset and growth of cracks in both micromechanics and macromechanics analyses. This crack growth simulation technique is based upon a virtual crack extension method. A three-dimensional finite element micromechanics model is used to study the effects of broken fibers, cracked matrix and fiber-matrix debond on the fracture toughness of the unidirectional composite. The energy release rates at the onset of unstable crack growth in the micromechanics analyses are used as critical energy release rates in the macromechanics analysis. This integrated micromechanical and macromechanical fracture criterion is shown to be very effective in predicting the onset and growth of cracks in general multilayered composite laminates by applying the criterion to a single-edge notched graphite/epoxy laminate subjected to implane tension normal to the notch.

Adams, D. F.↗
NASA NTRS2002

Incorporation of Mean Stress Effects into the Micromechanical Analysis of the High Strain Rate Response of Polymer Matrix Composites

The results presented here are part of an ongoing research program, to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. A micromechanics approach is employed in this work, in which state variable constitutive equations originally developed for metals have been modified to model the deformation of the polymer matrix, and a strength of materials based micromechanics method is used to predict the effective response of the composite. In the analysis of the inelastic deformation of the polymer matrix, the definitions of the effective stress and effective inelastic strain have been modified in order to account for the effect of hydrostatic stresses, which are significant in polymers. Two representative polymers, a toughened epoxy and a brittle epoxy, are characterized through the use of data from tensile and shear tests across a variety of strain rates. Results computed by using the developed constitutive equations correlate well with data generated via experiments. The procedure used to incorporate the constitutive equations within a micromechanics method is presented, and sample calculations of the deformation response of a composite for various fiber orientations and strain rates are discussed.

Goldberg, Robert K.↗