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NASA NTRS1995

Time-dependent deformation of titanium metal matrix composites

A three-dimensional finite element program called VISCOPAC was developed and used to conduct a micromechanics analysis of titanium metal matrix composites. The VISCOPAC program uses a modified Eisenberg-Yen thermo-viscoplastic constitutive model to predict matrix behavior under thermomechanical fatigue loading. The analysis incorporated temperature-dependent elastic properties in the fiber and temperature-dependent viscoplastic properties in the matrix. The material model was described and the necessary material constants were determined experimentally. Fiber-matrix interfacial behavior was analyzed using a discrete fiber-matrix model. The thermal residual stresses due to the fabrication cycle were predicted with a failed interface, The failed interface resulted in lower thermal residual stresses in the matrix and fiber. Stresses due to a uniform transverse load were calculated at two temperatures, room temperature and an elevated temperature of 650 C. At both temperatures, a large stress concentration was calculated when the interface had failed. The results indicate the importance of accuracy accounting for fiber-matrix interface failure and the need for a micromechanics-based analytical technique to understand and predict the behavior of titanium metal matrix composites.

Bigelow, C. A.↗

NASA NTRS1995

Thermoelastic Theory for the Response of Materials Functionally Graded in Two Directions with Applications to the Free-Edge Problem

A recently developed micromechanical theory for the thermoelastic response of functionally graded composites with nonuniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fiber spacing in two directions. In contrast to currently employed micromechanical approaches applied to functionally graded materials, which decouple the local and global effects by assuming the existence of a representative volume element at every point within the composite, the new theory explicitly couples the local and global effects. The analytical development is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense. Results are presented that illustrate the capability of the derived theory to capture local stress gradients at the free edge of a laminated composite plate due to the application of a uniform temperature change. It is further shown that it is possible to reduce the magnitude of these stress concentrations by a proper management of the microstructure of the composite plies near the free edge. Thus by an appropriate tailoring of the microstructure it is possible to reduce or prevent the likelihood of delamination at free edges of standard composite laminates.

Aboudi, Jacob↗

NASA NTRS1995

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

Pindera, Marek-Jerzy↗

NASA NTRS1993

Establishing the relationship between manufacturing and component performance in stretch formed thermoplastic composites

Flexible manufacturing methods are needed to reduce the cost of using advanced composites in structural applications. One method that allows for this is the stretch forming of long discontinuous fiber materials with thermoplastic matrices. In order to exploit this flexibility in an economical way, a thorough understanding of the relationship between manufacturing and component performance must be developed. This paper reviews some of the recent work geared toward establishing this understanding. Micromechanics models have been developed to predict the formability of the material during processing. The latest improvement of these models includes the viscoelastic nature of the matrix and comparison with experimental data. A finite element scheme is described which can be used to model the forming process. This model uses equivalent anisotropic viscosities from the micromechanics models and predicts the microstructure in the formed part. In addition, structural models have been built to account for the material property gradients that can result from the manufacturing procedures. Recent developments in this area include the analysis of stress concentrations and a failure model each accounting for the heterogeneous material fields.

Santare, Michael H.↗

NASA NTRS1995

Integrated Composite Analyzer With Damping Capabilities

Integrated Composite Analyzer with Damping Capabilities (ICAN/DAMP) computer program combines comprehensive linear analysis of multilayered fiber composite material in ICAN programs LEW-15832 and LEW-15592 with prediction of damping in polymer-matrix composite. Analysis contains essential features needed for effective design of structural components made from fiber composites, including micromechanical design features to predict ply-level hygral, thermal, and mechanical properties, and laminate-analysis features to account for interply layer effects. Incorporates new module for synthesizing material damping from micromechanics to laminate level. Written in FORTRAN 77.

Sanfeliz, J. G.↗

NASA NTRS1995

Influence of fiber architecture on the elastic an d inelastic response of metal matrix composites

This three part paper focuses on the effect of fiber architecture (i.e., shape and distribution) on the elastic and inelastic response of metal matrix composites. The first part provides an annotative survey of the literature, presented as a historical perspective, dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix and metal matrix composites. Previous investigations dealing with both continuously and discontinuously reinforced composites are included. A summary of the state-of-the-art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of metal matrix composites. This micromechanics model, referred to as the generalized method of cells (GMC), is capable of predicting the overall, inelastic behavior of unidirectional, multi-phased composites given the properties of the constituents. In particular, the model is sufficiently general to predict the response of unidirectional composites reinforced by either continuous or discontinuous fibers with different inclusion shapes and spatial arrangements in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments regarding this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third pan provides qualitative results generated using GMC for a representative titanium matix composite system, SCS-6/TlMETAL 21S. Results are presented that correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep response, with both strong and weak fiber/matrix interfacial bonds. The fiber arrangements include square, square diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes include circular, square and cross-shaped cross sections. The effect of fiber volume fraction on the observed stress-strain response is also discussed, as the thus-far poorly documented strain rate sensitivity effect. In addition to the well documented features of architecture dependent response of continuously reinforced two-phase MMC's, new results involving continuous multi-phase internal architectures are presented. Specifically, stress strain and creep response of composites with different size fibers having different internal arrangements and bond strengths are investigated with the aim of determining the feasibility of using this approach to enhance the transverse toughness and creep resistance of TMC's.

Arnold, Steven M.↗

NASA NTRS1995

Micro-mechanics of micro-composites

The Structural Dynamics branch at NASA LaRC is working on developing an active passive mount system for vibration control. Toward this end a system utilizing piezoelectric actuators is currently being utilized. There are limitations to the current system related to space applications under which it is desired to eliminate deformations in the actuators associated with thermal effects. In addition, a material that is readily formable into complex shapes and whose mechanical properties can be optimized with regards to vibration control would be highly desirable. Microcomposite material are currently under study to service these needs. Microcomposite materials are essentially materials in which particles on the scale of microns are bound together with a polyimide (LaRC Si) that has been developed at LaRC. In particular a micro-composite consisting of LaRC Si binder and piezoelectric ceramic particles shows promise in satisfying the needs of the active passive mount project. The LaRC/ Si microcomposite has a unique combination of piezoelectric properties combined with a near zero coefficient of thermal expansion and easy machinability. The goal of this ASEE project is to develop techniques to analytically determine important material properties necessary to characterize the dynamic properties of actuators and mounts made from the LaRC Si / ceramic microcomposite. In particular, a generalized method of cells micromechanics originally developed at NASA Lewis is employed to analyze the microstructural geometry of the microcomposites and predict the overall mechanical properties of the material. A testing program has been established to evaluate and refine the GMC approach to these materials. In addition, a theory of mixtures analysis is being developed that utilizes the GMC micromechanics information to analyze complex behavior of the microcomposite material which has a near zero CTE.

Donovan, Richard P.↗

NASA NTRS1996

The Development of Computational Techniques for the Nonlinear Analysis of Composite Structures at High Temperature

The objective of this research project was to develop robust and efficient computational tools for deformation and life analysis techniques. This included: development of viscoplastic continuum models, associated numerical integration techniques, suitable micromechanics models/methods, and coupled deformation and damage algorithms. The work was involved with models/methods applicable to composite structures on both microscale and macroscale levels. The microscale analysis utilized Aboudi's generalized method of cells (GMS) micromechanical model as well as finite element models of similar composite architectures, i.e., square and hexagonal fiber pack models.

Keith, Theo G., Jr.↗

NASA NTRS1997

Computational Simulation of Composite Behavior

Composite microfracture technique developed here is based on the concept of global strain energy release rate. Step-by-step procedures were outlined to evaluate composite microfracture. The technique can predict microfracture initiation/propagation, predict the "structural fracture toughness", and establish the hierarchy of fracture modes. Both unidirectional and cross-ply metal-matrix composite laminates were evaluated for microfracture, subjected to thermal and mechanical loads. Five NASA reports were published as shown in the bibliography and several presentations were made at the technical conferences/ symposia. Work was also performed to develop simplified micromechanics and macromechanics for ceramic matrix composites. A novel fiber sub-structuring technique was developed, which divides the fiber into several "slices" and applies the micromechanics equation at the "slice" level, which are then integrated upwards to get the ply and the laminate properties. It allows for a more accurate representation of interfacial conditions such as partial interface bond etc. It also predicts the stress-strain behavior of a composite up to failure by taking into account material properties dependence upon temperature as well as stress redistribution that occurs due to damage initiation and propagation. A computer code CEMCAN (Ceramic Matrix Composites Analyzer) which includes all these capabilities has been developed as a part of this research activity.

Keith, Theo G., Jr.↗

NASA NTRS1998

Analysis of Curved Sandwich Panels Subjected to Combined Temperature Gradient and Mechanical Loads

The results of a detailed study of the nonlinear response of curved sandwich panels with composite face sheets and subjected to a temperature gradient through-the-thickness combined with mechanical loadings are presented. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical panels subjected to combined pressure loading, edge shortening or extension, edge shear and a temperature gradient through the thickness. The results show the effects of variations in the loading and the panel aspect ratio, on the nonlinear response and its sensitivity to changes in the various panel, effective layer and micromechanical parameters.

Noor, Ahmed K.↗

NASA NTRS1998

PCEMCAN - Probabilistic Ceramic Matrix Composites Analyzer: User's Guide, Version 1.0

PCEMCAN (Probabalistic CEramic Matrix Composites ANalyzer) is an integrated computer code developed at NASA Lewis Research Center that simulates uncertainties associated with the constituent properties, manufacturing process, and geometric parameters of fiber reinforced ceramic matrix composites and quantifies their random thermomechanical behavior. The PCEMCAN code can perform the deterministic as well as probabilistic analyses to predict thermomechanical properties. This User's guide details the step-by-step procedure to create input file and update/modify the material properties database required to run PCEMCAN computer code. An overview of the geometric conventions, micromechanical unit cell, nonlinear constitutive relationship and probabilistic simulation methodology is also provided in the manual. Fast probability integration as well as Monte-Carlo simulation methods are available for the uncertainty simulation. Various options available in the code to simulate probabilistic material properties and quantify sensitivity of the primitive random variables have been described. The description of deterministic as well as probabilistic results have been described using demonstration problems. For detailed theoretical description of deterministic and probabilistic analyses, the user is referred to the companion documents "Computational Simulation of Continuous Fiber-Reinforced Ceramic Matrix Composite Behavior," NASA TP-3602, 1996 and "Probabilistic Micromechanics and Macromechanics for Ceramic Matrix Composites", NASA TM 4766, June 1997.

Shah, Ashwin R.↗

NASA NTRS1998

Flow/Damage Surfaces for Fiber-Reinforced Metals Having Different Periodic Microstructures

Flow/damage surfaces can be defined in terms of stress, inelastic strain rate, and internal variables using a thermodynamics framework. A macroscale definition relevant to thermodynamics and usable in an experimental program is employed to map out surfaces of constant inelastic power in various stress planes. The inelastic flow of a model silicon carbide/ titanium composite system having rectangular, hexagonal, and square diagonal fiber packing arrays subjected to biaxial stresses is quantified by flow/damage surfaces that are determined numerically from micromechanics, using both finite element analysis and the generalized method of cells. Residual stresses from processing are explicitly included and damage in the form of fiber-matrix debonding under transverse tensile and/or shear loading is represented by a simple interface model. The influence of microstructural architecture is largest whenever fiber-matrix debonding is not an issue; for example in the presence of transverse compressive stresses. Additionally, as the fiber volume fraction increases, so does the effect of microstructural architecture. With regard to the micromechanics analysis, the overall inelastic flow predicted by the generalized method of cells is in excellent agreement with that predicted using a large number of displacement-based finite elements.

Lissenden, Cliff J.↗

NASA NTRS1998

Flow/Damage Surfaces for Fiber-Reinforced Metals having Different Periodic Microstructures

Flow/damage surfaces can be defined in terms of stress, inelastic strain rate, and internal variables using a thermodynamics framework. A macroscale definition relevant to thermodynamics and usable in an experimental program is employed to map out surfaces of constant inelastic power in various stress planes. The inelastic flow of a model silicon carbide/ titanium composite system having rectangular, hexagonal, and square diagonal fiber packing, arrays subjected to biaxial stresses is quantified by flow/damage surfaces that are determined numerically from micromechanics. using both finite element analysis and the generalized method of cells. Residual stresses from processing are explicitly included and damage in the form of fiber-matrix debonding under transverse tensile and/or shear loading is represented by a simple interface model. The influence of microstructural architecture is largest whenever fiber-matrix debonding is not an issue, for example in the presence of transverse compressive stresses. Additionally, as the fiber volume fraction increases, so does the effect of microstructural architecture. With regard to the micromechanics analysis, the overall inelastic flow predicted by the generalized method of cells is in excellent agreement with that predicted using a large number of displacement-based finite elements.

Lissenden, Cliff J.↗

NASA NTRS1999

Rate Dependent Deformation and Strength Analysis of Polymer Matrix Composites

A research program is being undertaken to develop rate dependent deformation and failure models for the analysis of polymer matrix composite materials. In previous work in this program, strain-rate dependent inelastic constitutive equations used to analyze polymers have been implemented into a mechanics of materials based composite micromechanics method. In the current work, modifications to the micromechanics model have been implemented to improve the calculation of the effective inelastic strain. Additionally, modifications to the polymer constitutive model are discussed in which pressure dependence is incorporated into the equations in order to improve the calculation of constituent and composite shear stresses. The Hashin failure criterion is implemented into the analysis method to allow for the calculation of ply level failure stresses. The deformation response and failure stresses for two representative uniaxial polymer matrix composites, IM7/977-2 and AS4-PEEK, are predicted for varying strain rates and fiber orientations. The predicted results compare favorably to experimentally obtained values.

Goldberg, Robert K.↗

NASA NTRS1998

Progressive Failure And Life Prediction of Ceramic and Textile Composites

An engineering approach to predict the fatigue life and progressive failure of multilayered composite and textile laminates is presented. Analytical models which account for matrix cracking, statistical fiber failures and nonlinear stress-strain behavior have been developed for both composites and textiles. The analysis method is based on a combined micromechanics, fracture mechanics and failure statistics analysis. Experimentally derived empirical coefficients are used to account for the interface of fiber and matrix, fiber strength, and fiber-matrix stiffness reductions. Similar approaches were applied to textiles using Repeating Unit Cells. In composite fatigue analysis, Walker's equation is applied for matrix fatigue cracking and Heywood's formulation is used for fiber strength fatigue degradation. The analysis has been compared with experiment with good agreement. Comparisons were made with Graphite-Epoxy, C/SiC and Nicalon/CAS composite materials. For textile materials, comparisons were made with triaxial braided and plain weave materials under biaxial or uniaxial tension. Fatigue predictions were compared with test data obtained from plain weave C/SiC materials tested at AS&M. Computer codes were developed to perform the analysis. Composite Progressive Failure Analysis for Laminates is contained in the code CPFail. Micromechanics Analysis for Textile Composites is contained in the code MicroTex. Both codes were adapted to run as subroutines for the finite element code ABAQUS and CPFail-ABAQUS and MicroTex-ABAQUS. Graphic user interface (GUI) was developed to connect CPFail and MicroTex with ABAQUS.

Xue, David Y.↗

NASA NTRS1999

Strain Rate Dependent Modeling of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Strain rate dependent inelastic constitutive equations have been developed to model the polymer matrix, and have been incorporated into a micromechanics approach to analyze polymer matrix composites. The Hashin failure criterion has been implemented within the micromechanics results to predict ply failure strengths. The deformation model has been implemented within LS-DYNA, a commercially available transient dynamic finite element code. The deformation response and ply failure stresses for the representative polymer matrix composite AS4/PEEK have been predicted for a variety of fiber orientations and strain rates. The predicted results compare favorably to experimentally obtained values.

Goldberg, Robert K.↗

NASA NTRS1998

Constitutive Modeling of the Mechanical Properties of Optical Fibers

Micromechanical modeling of the composite mechanical properties of optical fibers was conducted. Good agreement was obtained between the values of Young's modulus obtained by micromechanics modeling and those determined experimentally for a single mode optical fiber where the wave guide and the jacket are physically coupled. The modeling was also attempted on a polarization-maintaining optical fiber (PANDA) where the wave guide and the jacket are physically decoupled, and found not to applicable since the modeling required perfect bonding at the interface. The modeling utilized constituent physical properties such as the Young's modulus, Poisson's ratio, and shear modulus to establish bounds on the macroscopic behavior of the fiber.

Moeti, L.↗

NASA NTRS2001

Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems

In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalent-continuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.

Odegard, Gregory M.↗