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MAC/GMC 4.0 User's Manual: Keywords Manual

This document is the second volume in the three volume set of User's Manuals for the Micromechanics Analysis Code with Generalized Method of Cells Version 4.0 (MAC/GMC 4.0). Volume 1 is the Theory Manual, this document is the Keywords Manual, and Volume 3 is the Example Problem Manual. MAC/GMC 4.0 is a composite material and laminate analysis software program developed at the NASA Glenn Research Center. It is based on the generalized method of cells (GMC) micromechanics theory, which provides access to the local stress and strain fields in the composite material. This access grants GMC the ability to accommodate arbitrary local models for inelastic material behavior and various types of damage and failure analysis. MAC/GMC 4.0 has been built around GMC to provide the theory with a user-friendly framework, along with a library of local inelastic, damage, and failure models. Further, applications of simulated thermo-mechanical loading, generation of output results, and selection of architectures to represent the composite material have been automated in MAC/GMC 4.0. Finally, classical lamination theory has been implemented within MAC/GMC 4.0 wherein GMC is used to model the composite material response of each ply. Consequently, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. This volume describes the basic information required to use the MAC/GMC 4.0 software, including a 'Getting Started' section, and an in-depth description of each of the 22 keywords used in the input file to control the execution of the code.

Bednarcyk, Brett A.↗

MAC/GMC 4.0 User's Manual: Example Problem Manual

This document is the third volume in the three volume set of User's Manuals for the Micromechanics Analysis Code with Generalized Method of Cells Version 4.0 (MAC/GMC 4.0). Volume 1 is the Theory Manual, Volume 2 is the Keywords Manual, and this document is the Example Problems Manual. MAC/GMC 4.0 is a composite material and laminate analysis software program developed at the NASA Glenn Research Center. It is based on the generalized method of cells (GMC) micromechanics theory, which provides access to the local stress and strain fields in the composite material. This access grants GMC the ability to accommodate arbitrary local models for inelastic material behavior and various types of damage and failure analysis. MAC/GMC 4.0 has been built around GMC to provide the theory with a user-friendly framework, along with a library of local inelastic, damage, and failure models. Further, application of simulated thermo-mechanical loading, generation of output results, and selection of architectures to represent the composite material, have been automated in MAC/GMC 4.0. Finally, classical lamination theory has been implemented within MAC/GMC 4.0 wherein GMC is used to model the composite material response of each ply. Consequently, the full range of GMC composite material capabilities is available for analysis of arbitrary laminate configurations as well. This volume provides in-depth descriptions of 43 example problems, which were specially designed to highlight many of the most important capabilities of the code. The actual input files associated with each example problem are distributed with the MAC/GMC 4.0 software; thus providing the user with a convenient starting point for their own specialized problems of interest.

Bednarcyk, Brett A.↗

Thermo-Mechanical Analyses of Dynamically Loaded Rubber Cylinders

Thick rubber components are employed by the Army to carry large loads. In tanks, rubber covers road wheels and track systems to protect roadways. It is difficult for design engineers to simulate the details of the hysteretic heating for large strain viscoelastic deformations. In this study, an approximation to the viscoelastic energy dissipated per unit time is investigated for use in estimating mechanically induced viscoelastic heating. Coupled thermo-mechanical simulations of large cyclic deformations of rubber cylinders are presented. The cylinders are first compressed axially and then cyclically loaded about the compressed state. Details of the algorithm and some computational issues are discussed. The coupled analyses are conducted for tall and short rubber cylinders both with and without imbedded metal disks.

Johnson, Arthur R.↗

Cyclic Load Effects on Long Term Behavior of Polymer Matrix Composites

A methodology to compute the fatigue life for different ratios, r, of applied stress to the laminate strength based on first ply failure criteria combined with thermal cyclic loads has been developed and demonstrated. Degradation effects resulting from long term environmental exposure and thermo-mechanical cyclic loads are considered in the simulation process. A unified time-stress dependent multi-factor interaction equation model developed at NASA Lewis Research Center has been used to account for the degradation of material properties caused by cyclic and aging loads. Effect of variation in the thermal cyclic load amplitude on a quasi-symmetric graphite/epoxy laminate has been studied with respect to the impending failure modes. The results show that, for the laminate under consideration, the fatigue life under combined mechanical and low thermal amplitude cyclic loads is higher than that due to mechanical loads only. However, as the thermal amplitude increases, the life also decreases. The failure mode changes from tensile under mechanical loads only to the compressive and shear at high mechanical and thermal loads. Also, implementation of the developed methodology in the design process has been discussed.

Shah, A. R.↗

Quantifying Uncertainties in the Thermo-Mechanical Properties of Particulate Reinforced Composites

The present paper reports results from a computational simulation of probabilistic particulate reinforced composite behavior. The approach consists use of simplified micromechanics of particulate reinforced composites together with a Fast Probability Integration (FPI) technique. Sample results are presented for a Al/SiC(sub p)(silicon carbide particles in aluminum matrix) composite. The probability density functions for composite moduli, thermal expansion coefficient and thermal conductivities along with their sensitivity factors are computed. The effect of different assumed distributions and the effect of reducing scatter in constituent properties on the thermal expansion coefficient are also evaluated. The variations in the constituent properties that directly effect these composite properties are accounted for by assumed probabilistic distributions. The results show that the present technique provides valuable information about the scatter in composite properties and sensitivity factors, which are useful to test or design engineers.

Mital, Subodh K.↗

Coupled Thermo-Mechanical Analyses of Dynamically Loaded Rubber Cylinders

A procedure that models coupled thermo-mechanical deformations of viscoelastic rubber cylinders by employing the ABAQUS finite element code is described. Computational simulations of hysteretic heating are presented for several tall and short rubber cylinders both with and without a steel disk at their centers. The cylinders are compressed axially and are then cyclically loaded about the compressed state. The non-uniform hysteretic heating of the rubber cylinders containing a steel disk is presented. The analyses performed suggest that the coupling procedure should be considered for further development as a design tool for rubber degradation studies.

Johnson, Arthur R.↗

Thermal-Mechanical Stability of Single Crystal Oxide Refractive Concentrators for High-Temperature Solar Thermal Propulsion

Single crystal oxides such as yttria-stabilized zirconia (Y2O3-ZrO2), yttrium aluminum garnet (Y3Al5O12, or YAG), magnesium oxide (MgO) and sapphire (Al2O3) are candidate refractive secondary concentrator materials for high temperature solar propulsion applications. However, thermo-mechanical reliability of these components in severe thermal environments during the space mission sun/shade transition is of great concern. Simulated mission tests are important for evaluating these candidate oxide materials under a variety of transient and steady-state heat flux conditions, and thus provide vital information for the component design. In this paper, a controlled heat flux thermal shock test approach is established for the single crystal oxide materials using a 3.0 kW continuous wave CO2 laser, with a wavelength 10.6 micron. Thermal fracture behavior and failure mechanisms of these oxide materials are investigated and critical temperature gradients are determined under various temperature and heating conditions. The test results show that single crystal sapphire is able to sustain the highest temperature gradient and heating-cooling rate, and thus exhibit the best thermal shock resistance, as compared to the yttria-stabilized zirconia, yttrium aluminum garnet, and magnesium oxide.

Zhu, Dongming↗

Thermal-Mechanical Stability of Single Crystal Oxide Refractive Concentrators for High-Temperature Solar Thermal Propulsion

Single crystal oxides such as yttria-stabilized zirconia (Y2O3-ZrO2), yttrium aluminum garnet (Y3Al5O12, or YAG), magnesium oxide (MgO) and sapphire (Al2O3) are candidate refractive secondary concentrator materials for high temperature solar propulsion applications. However, thermo-mechanical reliability of these components in severe thermal environments during the space mission sun/shade transition is of great concern. Simulated mission tests are important for evaluating these candidate oxide materials under a variety of transient and steady-state heat flux conditions, and thus provide vital information for the component design. In this paper, a controlled heat flux thermal shock test approach is established for the single crystal oxide materials using a 3.0 kW continuous wave CO2 laser, with a wavelength 10.6 micron. Thermal fracture behavior and failure mechanisms of these oxide materials are investigated and critical temperature gradients are determined under various temperature and heating conditions. The test results show that single crystal sapphire is able to sustain the highest temperature gradient and heating-cooling rate, and thus exhibit the best thermal shock resistance, as compared to the yttria-stabilized zirconia, yttrium aluminum garnet and magnesium oxide.

Zhu, Dongming↗

Effect of Cyclic Thermo-Mechanical Loads on Fatigue Reliability in Polymer Matrix Composites

A methodology to compute probabilistic fatigue life of polymer matrix laminated composites has been developed and demonstrated. Matrix degradation effects caused by long term environmental exposure and mechanical/thermal cyclic loads are accounted for in the simulation process. A unified time-temperature-stress dependent multi-factor interaction relationship developed at NASA Lewis Research Center has been used to model the degradation/aging of material properties due to cyclic loads. The fast probability integration method is used to compute probabilistic distribution of response. Sensitivities of fatigue life reliability to uncertainties in the primitive random variables (e.g., constituent properties, fiber volume ratio, void volume ratio, ply thickness, etc.) computed and their significance in the reliability- based design for maximum life is discussed. The effect of variation in the thermal cyclic loads on the fatigue reliability for a (0/+/- 45/90)(sub s) graphite/epoxy laminate with a ply thickness of 0.127 mm, with respect to impending failure modes has been studied. The results show that, at low mechanical cyclic loads and low thermal cyclic amplitudes, fatigue life for 0.999 reliability is most sensitive to matrix compressive strength, matrix modulus, thermal expansion coefficient, and ply thickness. Whereas at high mechanical cyclic loads and high thermal cyclic amplitudes, fatigue life at 0.999 reliability is more sensitive to the shear strength of matrix, longitudinal fiber modulus, matrix modulus, and ply thickness.

Shah, A. R.↗

Space radiation effects on the thermo-mechanical behavior of graphite-epoxy composites

This investigation of composite material properties utilized T300/934 graphite-epoxy that was subjected to 1.0 MeV electron radiation for a total dose of 1.0 x 10 to the 10th rads at a rate of 5.0 x 10 to the 7th rads/hour, simulating a worst-case exposure equivalent to 30 years in space. Mechanical testing was performed on 4-ply unidirectional laminates over the temperature range of -250 F (116 K) to +250 F (394 K). In-plane elastic tensile and shear properties as well as strength were obtained. The results show that electron radiation degrades the epoxy matrix and produces products that volatilize at the temperatures considered. These degradation products plasticize the epoxy at elevated temperatures and embrittle it at low temperatures, thereby altering the mechanical properties of the composite.

Milkovich, Scott M.↗

Concurrent material-fabrication optimization of metal-matrix laminates under thermo-mechanical loading

A methodology is developed to tailor fabrication and material parameters of metal-matrix laminates for maximum loading capacity under thermomechanical loads. The stresses during the thermomechanical response are minimized subject to failure constrains and bounds on the laminate properties. The thermomechanical response of the laminate is simulated using nonlinear composite mechanics. Evaluations of the method on a graphite/copper symmetric cross-ply laminate were performed. The cross-ply laminate required different optimum fabrication procedures than a unidirectional composite. Also, the consideration of the thermomechanical cycle had a significant effect on the predicted optimal process.

Saravanos, D. A.↗

Coupled Multi-Disciplinary Optimization for Structural Reliability and Affordability

A computational simulation method is presented for Non-Deterministic Multidisciplinary Optimization of engine composite materials and structures. A hypothetical engine duct made with ceramic matrix composites (CMC) is evaluated probabilistically in the presence of combined thermo-mechanical loading. The structure is tailored by quantifying the uncertainties in all relevant design variables such as fabrication, material, and loading parameters. The probabilistic sensitivities are used to select critical design variables for optimization. In this paper, two approaches for non-deterministic optimization are presented. The non-deterministic minimization of combined failure stress criterion is carried out by: (1) performing probabilistic evaluation first and then optimization and (2) performing optimization first and then probabilistic evaluation. The first approach shows that the optimization feasible region can be bounded by a set of prescribed probability limits and that the optimization follows the cumulative distribution function between those limits. The second approach shows that the optimization feasible region is bounded by 0.50 and 0.999 probabilities.

Abumeri, Galib H.↗

Prediction of thermal-stress and deformations due to phase change in solidifying objects via flux/stress based finite element representations

The paper presents numerical simulations for the prediction of thermal-stress and deformation fields resulting from phase change in solidifying bodies employing new finite element representations. The formulations herein demonstrated provide different perspectives and physical interpretation for the modeling/analysis of thermo-mechanical problems and possess several inherent advantages. In comparison to traditional approaches for solving similar problems, the paper employs new flux/stress based representations to enhance the overall effectiveness. Comparative numerical applications validate applicability of the formulations for predicting the temperature induced deformations and stresses resulting from effects due to phase change.

Tamma, K. K.↗

Probabilistic Evaluation of Advanced Ceramic Matrix Composite Structures

The objective of this report is to summarize the deterministic and probabilistic structural evaluation results of two structures made with advanced ceramic composites (CMC): internally pressurized tube and uniformly loaded flange. The deterministic structural evaluation includes stress, displacement, and buckling analyses. It is carried out using the finite element code MHOST, developed for the 3-D inelastic analysis of structures that are made with advanced materials. The probabilistic evaluation is performed using the integrated probabilistic assessment of composite structures computer code IPACS. The affects of uncertainties in primitive variables related to the material, fabrication process, and loadings on the material property and structural response behavior are quantified. The primitive variables considered are: thermo-mechanical properties of fiber and matrix, fiber and void volume ratios, use temperature, and pressure. The probabilistic structural analysis and probabilistic strength results are used by IPACS to perform reliability and risk evaluation of the two structures. The results will show that the sensitivity information obtained for the two composite structures from the computational simulation can be used to alter the design process to meet desired service requirements. In addition to detailed probabilistic analysis of the two structures, the following were performed specifically on the CMC tube: (1) predicted the failure load and the buckling load, (2) performed coupled non-deterministic multi-disciplinary structural analysis, and (3) demonstrated that probabilistic sensitivities can be used to select a reduced set of design variables for optimization.

Abumeri, Galib H.↗

Tracking and Control of Gas Turbine Engine Component Damage/Life

This paper describes damage mechanisms and the methods of controlling damages to extend the on-wing life of critical gas turbine engine components. Particularly, two types of damage mechanisms are discussed: creep/rupture and thermo-mechanical fatigue. To control these damages and extend the life of engine hot-section components, we have investigated two methodologies to be implemented as additional control logic for the on-board electronic control unit. This new logic, the life-extending control (LEC), interacts with the engine control and monitoring unit and modifies the fuel flow to reduce component damages in a flight mission. The LEC methodologies were demonstrated in a real-time, hardware-in-the-loop simulation. The results show that LEC is not only a new paradigm for engine control design, but also a promising technology for extending the service life of engine components, hence reducing the life cycle cost of the engine.

Jaw, Link C.↗

Vibration Testing of Stirling Power Convertors

The NASA John H. Glenn Research Center (GRC) and the U.S. Department of Energy (DOE) are currently developing a high efficient, long life, free piston Stirling convertor for use as an advanced spacecraft power system for future NASA missions. As part of this development, a Stirling Technology Demonstrator Convertor (TDC), developed by Stirling Technology Company (STC) for DOE, was vibration tested at GRC s Structural Dynamics Laboratory (SDU7735) in November- December 1999. This testing demonstrated that the Stirling TDC is able to withstand the harsh random vibration (20 to 2000 Hertz) seen during a typical spacecraft launch and survive with no structural damage or functional power performance degradation, thereby enabling its usage in future spacecraft power systems. The Stirling Vibration Test Team at NASA GRC and STC personnel conducted tests on a single 55 electric watt TDC. The purpose was to characterize the TDC s structural response to vibration and determine if the TDC could survive the vibration criteria established by the Jet Propulsion Laboratory (JPL) for launch environments. The TDC was operated at full-stroke and full power conditions during the vibration testing. The TDC was tested in two orientations, with the direction of vibration parallel and perpendicular to the TDC s moving components (displacer and piston). The TDC successfully passed a series of sine and random vibration tests. The most severe test was a 12.3 Grms random vibration test (peak vibration level of 0.2 g2/Hz from 50 to 250 Hertz) with test durations of 3 minutes per axis. The random vibration test levels were chosen to simulate, with margin, the maximum anticipated launch vibration conditions. As a result of this very successful vibration testing and successful evaluations in other key technical readiness areas, the Stirling power system is now considered a viable technology for future application for NASA spacecraft missions. Possible usage of the Stirling power system would be to supply on- board electric spacecraft power for future NASA Deep-Space Missions, performing as an attractive alternative to Radioisotope Thermoelectric Generators (RTG). Usage of the Stirling technology is also being considered as the electric power source for future Mars rovers, whose mission profiles may exclude the use of photovoltaic power systems (such as exploring at high Martian latitudes or for missions of lengthy durations). GRC s Thermo-Mechanical Systems Branch (5490) provides Stirling technology expertise under a Space Act Agreement with the DOE. Additional vibration testing, by GRC s Structural Systems Dynamics Branch (7733, is planned to continue to demonstrate the Stirling power system s vibration capability as its technology and flight system designs progress.

Hughes, Bill↗

Damage-mitigating control of a reusable rocket engine for high performance and extended life

The goal of damage mitigating control in reusable rocket engines is to achieve high performance with increased durability of mechanical structures such that functional lives of the critical components are increased. The major benefit is an increase in structural durability with no significant loss of performance. This report investigates the feasibility of damage mitigating control of reusable rocket engines. Phenomenological models of creep and thermo-mechanical fatigue damage have been formulated in the state-variable setting such that these models can be combined with the plant model of a reusable rocket engine, such as the Space Shuttle Main Engine (SSME), for synthesizing an optimal control policy. Specifically, a creep damage model of the main thrust chamber wall is analytically derived based on the theories of sandwich beam and viscoplasticity. This model characterizes progressive bulging-out and incremental thinning of the coolant channel ligament leading to its eventual failure by tensile rupture. The objective is to generate a closed form solution of the wall thin-out phenomenon in real time where the ligament geometry is continuously updated to account for the resulting deformation. The results are in agreement with those obtained from the finite element analyses and experimental observation for both Oxygen Free High Conductivity (OFHC) copper and a copper-zerconium-silver alloy called NARloy-Z. Due to its computational efficiency, this damage model is suitable for on-line applications of life prediction and damage mitigating control, and also permits parametric studies for off-line synthesis of damage mitigating control systems. The results are presented to demonstrate the potential of life extension of reusable rocket engines via damage mitigating control. The control system has also been simulated on a testbed to observe how the damage at different critical points can be traded off without any significant loss of engine performance. The research work reported here is built upon concepts derived from the disciplines of Controls, Thermo-fluids, Structures, and Materials. The concept of damage mitigation, as presented in this report, is not restricted to control of rocket engines. It can be applied to any system where structural durability is an important issue.

Ray, Asok↗

Understanding of the Dynamics of the Stirling Convertor Advanced by Structural Testing

The NASA Glenn Research Center, the U.S. Department of Energy, and the Stirling Technology Company (STC) are developing a highly efficient, long-life, free-piston Stirling convertor for use as an advanced spacecraft power system for future NASA missions, including deep-space and Mars surface applications. As part of this development, four structural dynamic test programs were recently performed on Stirling Technology Demonstration Convertors (TDC's) that were designed and built by STC under contract to the Department of Energy. This testing was performed in Glenn's Structural Dynamics Laboratory and Microgravity Emissions Laboratory. The first test program, in November and December 1999, demonstrated that the Stirling TDC could withstand the harsh random vibration experienced during a typical spacecraft launch and survive with no structural damage or functional power performance degradation. This was a critical step in enabling the use of Stirling convertors for future spacecraft power systems. The most severe test was a 12.3grms random vibration test, with test durations of 3 min per axis. The random vibration test levels were chosen to simulate, with margin, the maximum anticipated launch vibration conditions. The Microgravity Emissions Laboratory is typically used to measure the dynamics produced by operating space experiments and the resulting impact to the International Space Station's microgravity environment. For the second Stirling dynamic test program, performed in January 2001, the Microgravity Emissions Laboratory was used to characterize the structure-borne disturbances produced by the normal operation of a pair of Stirling convertors. The forces and moments produced by the normal operation of a Stirling system must be recognized and controlled, if necessary, so that other nearby spacecraft components, such as cameras, are not adversely affected. The Stirling convertor pair emitted relatively benign tonal forces at its operational frequency and associated harmonics. Therefore, Stirling power systems will not disturb spacecraft science experiments if minimal appropriate mounting efforts are made. The third test program, performed in February and May 2001, resulted in a modal characterization of a Stirling convertor. Since the deflection of the TDC piston rod, under vibration excitation, was of particular interest, the outer pressure shell was removed to allow access to the rod. Through this testing, the Stirling TDC's natural frequencies and modes were identified. This knowledge advanced our understanding of the successful 1999 vibration test and may be utilized to optimize the output power of future Stirling designs. The fourth test program, in April 2001, was conducted to characterize the structural response of a pair of Stirling convertors, as a function of their mounting interface stiffness. The test results provide guidance for the Stirling power package interface design. Properly designed, the interface may lead to increased structural capability and power performance beyond what was demonstrated in the successful 1999 vibration test. Dynamic testing performed to date at Glenn has shown that the Stirling convertors can withstand liftoff random vibration environments and meet "good neighbor" vibratory emission requirements. Furthermore, the future utilization of the information obtained during the tests will allow the corporation selected to be the Stirling system integrator to optimize their convertor and system interfaces designs. Glenn's Thermo-Mechanical Systems Branch provides Stirling technology expertise under a Space Act Agreement with the Department of Energy. Additional vibration testing by Glenn's Structural Systems Dynamics Branch is planned to continue to demonstrate the Stirling power system's vibration capability as its technology and flight system designs progress.

Hughes, William O.↗