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NASA NTRS1993

Inelastic deformation of metal matrix composites

A theoretical model capable of predicting the thermomechanical response of continuously reinforced metal matrix composite laminates subjected to multiaxial loading was developed. A micromechanical model is used in conjunction with nonlinear lamination theory to determine inelastic laminae response. Matrix viscoplasticity, residual stresses, and damage to the fiber/matrix interfacial zone are explicitly included in the model. The representative cell of the micromechanical model is considered to be in a state of generalized plane strain, enabling a quasi two-dimensional analysis to be performed. Constant strain finite elements are formulated with elastic-viscoplastic constitutive equations. Interfacial debonding is incorporated into the model through interface elements based on the interfacial debonding theory originally presented by Needleman, and modified by Tvergaard. Nonlinear interfacial constitutive equations relate interfacial tractions to displacement discontinuities at the interface. Theoretical predictions are compared with the results of an experimental program conducted on silicon carbide/titanium (SiC/Ti) unidirectional, (O4), and angle-ply, (+34)(sub s), tubular specimens. Multiaxial loading included increments of axial tension, compression, torque, and internal pressure. Loadings were chosen in an effort to distinguish inelastic deformation due to damage from matrix plasticity and separate time-dependent effects from time-independent effects. Results show that fiber/matrix debonding is nonuniform throughout the composite and is a major factor in the effective response. Also, significant creep behavior occurs at relatively low applied stress levels at room temperature.

Lissenden, C. J.↗

NASA NTRS1993

Determination of fiber-matrix interface failure parameters from off-axis tests

Critical fiber-matrix (FM) interface strength parameters were determined using a micromechanics-based approach together with failure data from off-axis tension (OAT) tests. The ply stresses at failure for a range of off-axis angles were used as input to a micromechanics analysis that was performed using the personal computer-based MICSTRAN code. FM interface stresses at the failure loads were calculated for both the square and the diamond array models. A simple procedure was developed to determine which array had the more severe FM interface stresses and the location of these critical stresses on the interface. For the cases analyzed, critical FM interface stresses were found to occur with the square array model and were located at a point where adjacent fibers were closest together. The critical FM interface stresses were used together with the Tsai-Wu failure theory to determine a failure criterion for the FM interface. This criterion was then used to predict the onset of ply cracking in angle-ply laminates for a range of laminate angles. Predictions for the onset of ply cracking in angle-ply laminates agreed with the test data trends.

Naik, Rajiv A.↗

NASA NTRS1994

Assessment of impact damage of composite rocket motor cases

This contract reviewed the available literature on mechanisms of low velocity impact damage in filament wound rocket motor cases, MDE methods to quantify damage, critical coupon level test methods, manufacturing and material process variables and empirical and analytical modeling off impact damage. The critical design properties for rocket motor cases are biaxial hoop and axial tensile strength. Low velocity impact damage is insidious because it can create serious nonvisible damage at very low impact velocities. In thick rocket motor cases the prevalent low velocity impact damage is fiber fracture and matrix cracking adjacent to the front face. In contrast, low velocity loading of thin wall cylinders induces flexure, depending on span length and the flexure induces delamination and tensile cracking on the back face wall opposed to impact occurs due to flexural stresses imposed by impact loading. Important NDE methods for rocket motor cases are non-contacting methods that allow inspection from one side. Among these are vibrothermography, and pulse-echo methods based on acoustic-ultrasonic methods. High resolution techniques such as x-ray computed tomography appear to have merit for accurate geometrical characterization of local damage to support development of analytical models of micromechanics. The challenge of coupon level testing is to reproduce the biaxial stress state that the full scale article experiences, and to determine how to scale the composite structure to model full sized behavior. Biaxial tensile testing has been performed by uniaxially tensile loading internally pressurized cylinders. This is experimentally difficult due to gripping problems and pressure containment. Much prior work focused on uniaxial tensile testing of model filament wound cylinders. Interpretation of the results of some studies is complicated by the fact that the fabrication process did not duplicate full scale manufacturing. It is difficult to scale results from testing subscale cylinders since there are significant differences in out time of the resins relative to full scale cylinder fabrication, differences in hoop fiber tensioning and unsatisfactory coupon configurations. It appears that development of a new test method for subscale cylinders is merited. Damage tolerance may be improved by material optimization that uses fiber treatments and matrix modifications to control the fiber matrix interface bonding. It is difficult to develop process optimization in subscale cylinders without also modeling the longer out times resins experience in full scale testing. A major breakthrough in characterizing the effect of impact damage on residual strength, and understanding how to scale results of subscale evaluations, will be a sound micromechanical model that described progressive failure of the composite. Such models will utilize a three dimensional stress analysis due to the complex nature of low velocity impact stresses in thick composites. When these models are coupled with non-contact NDE methods that geometrically characterize the damage and acoustic methods that characterize the effective local elastic properties, accurate assessment of residual strength from impact damage may be possible. Directions for further development are suggested.

Paris, Henry G.↗

NASA NTRS1994

Planar rotational magnetic micromotors with integrated shaft encoder and magnetic rotor levitation

Deep x-ray lithography and electroplating may be combined to form a fabrication tool for micromechanical devices with large structural heights, to 500 micron, and extreme edge acuities, less than 0.1 micron-run-out per 100 micron of height. This process concept which originated in Germany as LIGA may be further extended by adding surface micromachining. This extension permits the fabrication of precision metal and plastic parts which may be assembled into three-dimensional micromechanical components and systems. The processing tool may be used to fabricate devices from ferromagnetic material such as nickel and nickel-iron alloys. These materials when properly heat treated exhibit acceptable magnetic behavior for current to flux conversion and marginal behavior for permanent magnet applications. The tool and materials have been tested via planar, magnetic, rotational micromotor fabrication. Three phase reluctance machines of the 6:4 configuration with 280 micron diameter rotors have been tested and analyzed. Stable rotational speeds to 34,000 rpm with output torques above 10 x 10(exp -9) N-m have been obtained. The behavior is monitored with integrated shaft encoders which are photodiodes which measure the rotor response. Magnetic levitation of the rotor via reluctance forces has been achieved and has reduced frictional torque losses to less than 1 percent of the available torque. The results indicate that high speed limits of these actuators are related to torque ripple. Hysteresis motors with magnetic bearings are under consideration and will produce high speed rotational machines with excellent sensor application potential.

Guckel, Henry↗

NASA NTRS1994

A methodology to predict damage initiation, damage growth and residual strength in titanium matrix composites

In this research, a methodology to predict damage initiation, damage growth, fatigue life, and residual strength in titanium matrix composites (TMC) is outlined. Emphasis was placed on micromechanics-based engineering approaches. Damage initiation was predicted using a local effective strain approach. A finite element analysis verified the prevailing assumptions made in the formulation of this model. Damage growth, namely, fiber-bridged matrix crack growth, was evaluated using a fiber bridging (FB) model which accounts for thermal residual stresses. This model combines continuum fracture mechanics and micromechanics analyses yielding stress-intensity factor solutions for fiber-bridged matrix cracks. It is assumed in the FB model that fibers in the wake of the matrix crack are idealized as a closure pressure, and an unknown constant frictional shear stress is assumed to act along the debond length of the bridging fibers. This frictional shear stress was used as a curve fitting parameter to the available experimental data. Fatigue life and post-fatigue residual strength were predicted based on the axial stress in the first intact 0 degree fiber calculated using the FB model and a three-dimensional finite element analysis.

Bakuckas, J. G., Jr.↗

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.↗