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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Reliability and Confidence Interval Analysis of a CMC Turbine Stator Vane

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight, enable higher operating temperatures requiring less cooling and thus leading to increased engine efficiencies. However, these materials are brittle and show degradation with time at high operating temperatures due to creep as well as cyclic mechanical and thermal loads. In addition, these materials are heterogeneous in their make-up and various factors affect their properties in a specific design environment. Most of these advanced composites involve two- and three-dimensional fiber architectures and require a complex multi-step high temperature processing. Since there are uncertainties associated with each of these in addition to the variability in the constituent material properties, the observed behavior of composite materials exhibits scatter. Traditional material failure analyses employing a deterministic approach, where failure is assumed to occur when some allowable stress level or equivalent stress is exceeded, are not adequate for brittle material component design. Such phenomenological failure theories are reasonably successful when applied to ductile materials such as metals. Analysis of failure in structural components is governed by the observed scatter in strength, stiffness and loading conditions. In such situations, statistical design approaches must be used. Accounting for these phenomena requires a change in philosophy on the design engineer s part that leads to a reduced focus on the use of safety factors in favor of reliability analyses. The reliability approach demands that the design engineer must tolerate a finite risk of unacceptable performance. This risk of unacceptable performance is identified as a component's probability of failure (or alternatively, component reliability). The primary concern of the engineer is minimizing this risk in an economical manner. The methods to accurately determine the service life of an engine component with associated variability have become increasingly difficult. This results, in part, from the complex missions which are now routinely considered during the design process. These missions include large variations of multi-axial stresses and temperatures experienced by critical engine parts. There is a need for a convenient design tool that can accommodate various loading conditions induced by engine operating environments, and material data with their associated uncertainties to estimate the minimum predicted life of a structural component. A probabilistic composite micromechanics technique in combination with woven composite micromechanics, structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Furthermore, input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Since the measured data for the ceramic matrix composite properties is very limited, obtaining a probabilistic distribution with their corresponding parameters is difficult. In case of limited data, confidence bounds are essential to quantify the uncertainty associated with the distribution. Usually 90 and 95% confidence intervals are computed for material properties. Failure properties are then computed with the confidence bounds. Best estimates and the confidence bounds on the best estimate of the cumulative probability function for R-S (strength - stress) are plotted. The methodologies and the results from these analyses will be discussed in the presentation.

Murthy, Pappu L. N.↗
NASA NTRS1989

Tungsten fiber reinforced copper matrix composites: A review

Tungsten fiber reinforced copper matrix (W/Cu) composites have served as an ideal model system with which to analyze the properties of metal matrix composites. A series of research programs were conducted to investigate the stress-strain behavior of W/Cu composites; the effect of fiber content on the strength, modulus, and conductivity of W/Cu composites; and the effect of alloying elements on the behavior of tungsten wire and of W/Cu composites. Later programs investigated the stress-rupture, creep, and impact behavior of these composites at elevated temperatures. Analysis of the results of these programs as allows prediction of the effects of fiber properties, matrix properties, and fiber content on the properties of W/Cu composites. These analyses form the basis for the rule-of-mixtures prediction of composite properties which was universally adopted as the criteria for measuring composite efficiency. In addition, the analyses allows extrapolation of potential properties of other metal matrix composites and are used to select candidate fibers and matrices for development of tungsten fiber reinforced superalloy composite materials for high temperature aircraft and rocket engine turbine applications. The W/Cu composite efforts are summarized, some of the results obtained are described, and an update is provided on more recent work using W/Cu composites as high strength, high thermal conductivity composite materials for high heat flux, elevated temperature applications.

Mcdanels, David L.↗
NASA NTRS1990

Composites boost 21st-century aircraft engines

Research and development in light-weight, high-temperature composite materials for ultrahigh-bypass engines to be used in high-speed civil transport/rotocraft is presented. It is noted that the expected benefits to be attained by this R&D include weight reduction, lowered fuel consumption, and lower direct operating costs. A major effort underway in this area is the Advanced High Temperature Engine Materials Technology Program (HITEMP) of NASA, which focuses on providing revolutionary high-temperature composite materials: to 425 C (800 F) for polymer-matrix composites (PMCs), to 1250 C (2280 F) for metal-matrix/intermetallic-matrix composites (MMCs/IMCs), and to as high as 1650 C (3000 F) for ceramic-matrix composites (CMCs). Analytical modeling is being used to investigate the structural behavior of these advanced materials in six distinct areas: micromechanics, deformation and damage, fatigue, fracture, trade-off studies, and load definition. It is concluded that the development of advanced materials such as high-temperature composites is highly dependent on the availability of high-temperature fibers. The wide range of fiber characteristics needed will require the development of more than one fiber. In general, a candidate fiber should have low density, high strength, high stiffness, a CTE matching the matrix, chemical compatibility with the matrix, environmental stability and appropriate fiber diameter.

Stephens, Joseph R.↗
NASA NTRSDate not supplied

Challenges in Scaling Analysis from Coupons to Elements in 3D Woven Composites for a Launch Vehicle End-Ring Structure

The limitations of structural design with 3D woven composites based on homogenized material models characterized using coupon test data, representative unit cell analysis, or a combination of the two are discussed in the context of a space launch system (SLS)-scale end ring. Selected building block test configurations at the coupon, element, and subcomponent scales are described in detail. Highly instrumented tests and X-ray computed tomography inspections are used to characterize the structural behavior and associated damage progression with increasing load. It is shown that a single homogenized material constitutive relationship, applied at coupon and element scale, is not sufficient to model the structural response observed in both tests. In fact, substantially different stress-strain laws are required to predict the response of the coupon and element scale specimens, despite similar loading conditions. A model with discrete representation of the binder tows and cohesive interfaces to model matrix cracking shows much better agreement with the test data at the two length scales. Thus, evidence is provided showing that predictive structural analysis of 3D woven composites requires discrete representation of the tows, matrix cracking morphology, and their interactions in the structural configuration. With accurate knowledge of the element scale behavior, engineering approximations readily enable analysis scale-up to the subcomponent level.

Andrew C Bergan↗
NASA NTRSDate not supplied

LES Analysis of Loss Anomaly in a Turbine Blade with Large Trailing Edge Radius

There is great interest in the usage of Ceramic Matrix Composites (CMC) as a turbine blade material. CMCs can tolerate higher temperatures than alloyed metallic blades, resulting in better thermal efficiency of gas turbine engines. However, depending on the manufacturing process of the CMC, blades may have a larger trailing edge thickness. The design space therefore needs to be updated due to the resulting flow physics. Recently, experimental results acquired at NASA Glenn Transonic Turbine Blade Cascade Rig showed that a loss measure generally increased with increasing trailing edge thickness. For one case however, the losses initially decreased with increasing Reynolds number but rose and peaked at Re ~1.24x10 6 and then subsequently dropped to the original pre-peak trend. A possible cause of this intriguing phenomenon was speculated to be transonic vortex shedding, which is the mechanism of vortex shedding promoted by reflected shed pressure waves at the trailing edge at relatively high Reynolds numbers and higher Mach numbers. A Reynolds-averaged Navier-Stokes (RANS) analysis or a low-resolution large eddy simulation (LES) does not reproduce this apparent anomaly and thus it is worth performing a wall-resolved LES (the total mesh count of ~290 million cells) to investigate the aerodynamics of the CMC blade in the context of transonic vortex shedding. Our numerical results at Re=1,246,350 show that the pressure waves generated by the vortex shedding in the wake travel upstream and significantly influence the transition and separation on the suction side thus enhancing the said vortex shedding in the wake. This feedback seems not to hold under a low-Re condition (Re=621,900). The Reynolds number dependence was also examined by numerical perturbation of the pressure waves in the wake and by examining how such perturbation attenuates or endures. It is confirmed that the perturbation of the pressure waves is quickly damped.

LES↗
DOE OSTI2020

Engineered Cementitious Composites (ECC) with limestone calcined clay cement (LC 3 )

Recent research have recognized that coupled use of calcined clay, limestone and cement clinker in concrete is viable to reduce environmental footprints at manufacture and to enhance material durability. In this study, a novel application of the limestone calcined clay cement (LC 3 ) is demonstrated by substituting the Ordinary Portland Cement (OPC) in Engineered Cementitious Composites (ECC). The composite mechanical properties including σ-δ and σ-ε relationships and residual crack widths were evaluated to 28 days under uniaxial tension. Matrix chemistry was characterized using thermogravimetric analysis and X-ray diffraction, while the pore structure of matrices and composites was analyzed using mercury intrusion porosimetry. The LC 3 -based ECC showed more rapid early strength development but lower 28-day strength (~32 MPa) due to a 20% higher water-to-solid ratio for attaining adequate workability and fiber dispersion. Nevertheless, the tensile strain capacity of LC 3 -based ECC achieved over 6% with an average residual crack width less than 50 μm. Additionally, the composite pore structure exhibited a decreasing volume fraction of large pores and voids (>100 nm) after substituting LC 3 for OPC. Here, the use of LC 3 marginally decreased the embodied material energy and cost, but led to about 32% and 28% reductions in CO 2 emissions compared to traditional OPC-based ECC and concrete, respectively. As a preliminary study, LC 3 -based ECC shows promise as a greener ductile concrete compared with OPC-based ECC.

36 MATERIALS SCIENCE↗
NASA NTRS2003

Solutions for Hot Situations

From the company that brought the world an integral heating and cooling food service system after originally developing it for NASA's Apollo Program, comes yet another orbital offshoot: a product that can be as thin as paper and as strong as steel. Nextel Ceramic Textiles and Composites from 3M Company offer space-age protection and innovative solutions for hot situations, ranging from NASA to NASCAR. With superior thermal protection, Nextel fabrics, tape, and sleevings outperform other high temperature textiles such as aramids, carbon, glass, and quartz, permitting engineers and manufacturers to handle applications up to 2,500 F (1,371 C). The stiffness and strength of Nextel Continuous Ceramic Fibers make them a great match for improving the rigidity of aluminum in metal matrix composites. Moreover, the fibers demonstrate low shrinkage at operating temperatures, which allow for the manufacturing of a dimensionally stable product. These novel fibers also offer excellent chemical resistance, low thermal conductivity, thermal shock resistance, low porosity, and unique electrical properties.

Source record↗
NASA NTRS2015

Oxide_Oxide Ceramic Matrix Composite (CMC) Exhaust Mixer Development in the NASA Environmentally Responsible Aviation (ERA) Project

Rolls-Royce North American Technologies, Inc. (LibertyWorksLW) began considering the development of CMC exhaust forced mixers in 2008, as a means of obtaining reduced weight and hotter operating temperature capability, while minimizing shape distortion during operation, which would improve mixing efficiency and reduce fuel burn. Increased component durability, enhanced ability to fabricate complex-shaped components, and engine noise reduction are other potential advantages of CMC mixers (compared to metallic mixers). In 2010, NASA was pursuing the reduction of NOx emissions, fuel burn, and noise from turbine engines in Phase I of the Environmentally Responsible Aviation (ERA) Project. ERA subtasks, including those focused on CMC components, were formulated with the goal of maturing technology from proof of concept validation (TRL 3) to a systemsubsystem or prototype demonstration in a relevant environment (TRL 6). In April 2010, the NASA Glenn Research Center (GRC) and LibertyWorks jointly initiated a CMC Exhaust System Validation Program within the ERA Project, teaming on CMC exhaust mixer development for subsonic jet engines capable of operating with increased performance. Our initial focus was on designing, fabricating, and characterizing the thrust and acoustic performance of a roughly quarter-scale 16-lobe oxide oxide CMC mixer and tail cone along with a conventional low bypass exhaust nozzle. Support Services, LLC (Allendale, MI) and ATK COI Ceramics, Inc. (COIC, in San Diego, CA) supported the design of a subscale nozzle assembly that consisted of an oxide oxide CMC mixer and center body, with each component mounted on a metallic attachment ring. That design was based upon the operating conditions a mixer would experience in a turbofan engine. Validation of the aerodynamic and acoustic performance of the subscale mixer via testing and the achievement of TRL 4 encouraged the NASALWCOIC team to move to the next phase where a full scale CMC mixer sized for a RR AE3007 engine and a compatible attachment flange were designed, followed by CMC component fabrication by COIC, and vibration testing at GRC under conditions simulating the structural and dynamic environment encountered during engine operation. AFRL (WPAFB) supported this testing by performing 3D laser vibrometry to identify the mixer mode shapes and modal frequencies. The successful fabrication and testing of such a component has been achieved. The CMC mixer demonstrated good durability during vibration testing at room and elevated temperature (TRL5). This has cleared the article for a ground-based test on a Rolls-Royce AE3007 engine, where the performance and benefits of the component can be further assessed.

exhaust nozzles↗
DOE OSTI2025

Multiscale Modeling of the Mechanical Response of Silicon Carbide Composite Within the Accelerated Fuel Qualification Framework

The accelerated fuel qualification (AFQ) framework has been used for the initial development of multiscale modeling of silicon carbide (SiC) fiber reinforced composite (SiC-SiC). The AFQ framework provides a methodology to leverage physics-informed multiscale modeling along with a reduced set of empirical test data to reduce the time and cost of licensing and qualification of new nuclear fuel systems while maintaining the overall nuclear power plant safety case. SiC-SiC is being proposed for in-core applications, most notably fuel cladding, for current and next-generation nuclear reactors because of its high temperature stability, irradiation tolerance, and ability to withstand many accident conditions. As these composites exhibit multiscale architectures and complex microstructure-based fracture mechanics, it is an appealing use case for the AFQ methodology. While the end goal of this work is a single multiscale model that can be used for predictive in-core performance, current focus is on the individual various length scale models. Four individual models have been initially developed from microscale to engineering system level to capture key physics-based effects across different length scales. These models include a microscale homogenized tow model, a mesoscale fast Fourier transform–based weave model that integrates the homogenized tow model, a mesoscale finite element–based weave model, and a system-level BISON fuel performance model. Results of these models have undergone an initial comparison with separate-effects test data showing a good match to experimental results. By using the AFQ framework during model development, several near-term benefits have been secured including a reduction in development time for the SiC-SiC cladding, more targeted irradiation testing, and a better understanding of uncertainty.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1986

Evaluation of carbon-carbon for space engine nozzle

An investigation is underway to determine the suitability of carbon-carbon composite materials for lightweight nozzle extensions on the Orbit Transfer Vehicle (OTV). The best combinations of fiber precursor, matrix material, and oxidation protection coatings are being evaluated in a series of hot-fire tests in an O sub 2/H sub 2 rocket nozzle environment. Evaluation criteria include life expectancy (recession), strength to weight, producibility, maturity, and cost. A data base of carbon-carbon performance in the OTV nozzle environment will be established which may be used in designing a full-scale OTV nozzle extension.

Suhoza, J. P.↗
NASA NTRS2003

A Study of Technical Engineering Peer Reviews at NASA

This report describes the state of practices of design reviews at NASA and research into what can be done to improve peer review practices. There are many types of reviews at NASA: required and not, formalized and informal, programmatic and technical. Standing project formal reviews such as the Preliminary Design Review and Critical Design Review are a required part of every project and mission development. However, the technical, engineering peer reviews that support teams' work on such projects are informal, some times ad hoc, and inconsistent across the organization. The goal of this work is to identify best practices and lessons learned from NASA's experience, supported by academic research and methodologies to ultimately improve the process. This research has determined that the organization, composition, scope, and approach of the reviews impact their success. Failure Modes and Effects Analysis (FMEA) can identify key areas of concern before or in the reviews. Product definition tools like the Project Priority Matrix, engineering-focused Customer Value Chain Analysis (CVCA), and project or system-based Quality Function Deployment (QFD) help prioritize resources in reviews. The use of information technology and structured design methodologies can strengthen the engineering peer review process to help NASA work towards error-proofing the design process.

Chao, Lawrence P.↗
NASA NTRS1997

Durability and Life of Ceramic Matrix Composites in Combustion Environment

It is now generally recognized that the next frontier in the commercial air travel will be achieved by an optimum combination of the concepts being used for the air and space transports. It will depend upon the new engines specifically designed to meet the demanding strength, temperature, environment and economy requirements. The successful development of an advanced propulsion system for a 21st Century High Speed Civil Transport will require key advances in the combustor system. Minimizing nitrous oxide (NO(x)) emission is critical, since the deleterious interaction within the ozone layer would occur at the proposed vehicle cruise level of about 75,000 feet. In order to achieve the low NOx levels an efficient combustor operating at controlled equivalence ratios and high combustion temperatures are required. This requires a combustor, whose one portion will be operating in an oxidizing environment while the other portion will operate in a reducing environment. This rather unusual requirement has introduced considerable challenge to the materials scientists and engineers, the development of material systems capable of long-life at high temperatures (up to 3000 F) in an oxidizing and/or reducing environment.

Tewari, Surendra↗
DOE OSTI2021

Roadmap for thermal property measurements of Molten Salt Reactor systems

Thermal properties of molten salts, both with and without fissile and fertile material, are fundamental to modeling and simulation that supports design, construction, operation, and accident progression evaluation of molten salt reactors. This roadmap provides guidance to the research community on the types and amounts of required data for base, or carrier, salt systems, recommends simulated burnup fuel salt compositions to evaluate, and provides a technical foundation for a focused salt property evaluation matrix. The property values generated from both computation and experimental methods are used to develop models that constitute the Molten Salt Thermal Properties Database (MSTDB). While the building blocks of MSTDB are fundamental in nature, its data facilitates constructing engineering models that allow stakeholders to investigate the behavior of specific compositions of interest and supports broader modeling and simulation of MSRs through coupling to multi-physics, multi-scale mass accountancy tools.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2015

Mechanical Properties and Real-Time Damage Evaluations of Environmental Barrier Coated SiC/SiC CMCs Subjected to Tensile Loading Under Thermal Gradients

SiC/SiC ceramic matrix composites (CMCs) require new state-of-the art environmental barrier coatings (EBCs) to withstand increased temperature requirements and high velocity combustion corrosive combustion gasses. The present work compares the response of coated and uncoated SiC/SiC CMC substrates subjected to simulated engine environments followed by high temperature mechanical testing to asses retained properties and damage mechanisms. Our focus is to explore the capabilities of electrical resistance (ER) measurements as an NDE technique for testing of retained properties under combined high heat-flux and mechanical loading conditions. Furthermore, Acoustic Emission (AE) measurements and Digital Image Correlation (DIC) were performed to determine material damage onset and accumulation.

Ceramic matrix composites↗
DOE OSTI2023

FWP FEAA149: “Next Generation Environmental Barrier Coatings”

Environmental barrier coatings (EBCs) are required coatings for utilization of SiC/SiC ceramic matrix composite (CMC) components in gas turbines, where the EBC represents the life-limiting factor for such components. EBC/CMC systems have shown success in aero-engine applications with increased turbine inlet temperatures and improved efficiencies, which are achieved through higher temperature stability, lower density, and decreased reliance on cooling air compared to traditional superalloys. While industrial gas turbines (IGTs) do not currently utilize SiC/SiC CMCs, the current shift towards low-carbon or carbon-free fuel sources for power generation could result in a need for EBC/CMC components with higher temperature capabilities. In this work, three tasks were outlined to improve understanding of EBC lifetimes to encourage use in IGTs with carbon-free fuel such as hydrogen: 1. Define the bond coating oxidation kinetics and EBC failure criteria, 2. Measure thermal expansion coefficients of each layered material, and 3. Perform advanced characterization and modeling to assess EBC lifetimes. Cyclic steam oxidation tests were conducted on various EBC/Si/SiC chemistries and EBC/SiC architectures to define substrate oxidation kinetics and EBC failure modes. An open-source code was developed to quantify the undulating thermally grown oxide thickness with thousands of measurements from specimen cross-section images. Bond coating oxidation kinetics were determined and used to develop a kinetic and thermodynamic model for predicting EBC lifetimes. High-temperature Raman spectroscopy was utilized for determining the SiO 2 thermally grown oxide phase transformation as the life-limiting feature for EBCs. Model efforts supported the claim that the SiO 2 phase transformation causes elevated stress during thermal cycling with associated cracking that decreases the adhesion strength of the EBC, eventually resulting in coating spallation. The finite element model subroutine will be made publicly available upon internal review. Further development of an EBC lifetime model for IGTs involves definition of a critical SiO 2 thickness for EBC spallation and must also consider both environmental (gas velocity, pressure, etc.) and specimen (EBC dopants, layer architectures, etc.) effects into predicted bond coating oxidation kinetics for long-lifetime components.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Advances in Ceramic Matrix Composite Blade Damping Characteristics for Aerospace Turbomachinery Applications

For advanced aerospace propulsion systems, development of ceramic matrix composite integrally-bladed turbine disk technology is attractive for a number of reasons. The high strength-to-weight ratio of ceramic composites helps to reduce engine weight and the one-piece construction of a blisk will result in fewer parts count, which should translate into reduced operational costs. One shortcoming with blisk construction, however, is that blisks may be prone to high cycle fatigue due to their structural response to high vibration environments. Use of ceramic composites is expected to provide some internal damping to reduce the vibratory stresses encountered due to unsteady flow loads through the bladed turbine regions. A goal of our research was to characterize the vibration viscous damping behavior of C/SiC composites. The vibration damping properties were measured and calculated. Damping appeared to decrease with an increase in the natural frequency. While the critical damping amount of approximately 2% is required for typical aerospace turbomachinery engines, the C/SiC damping at high frequencies was less than 0.2% from our study. The advanced high-performance aerospace propulsion systems almost certainly will require even more damping than what current vehicles require. A purpose of this paper is to review some work on C/SiC vibration damping by the authors for the NASA CMC turbine blisk development program and address an importance of the further investigation of the blade vibration damping characteristics on candidate CMC materials for the NASA s advanced aerospace turbomachinery engine systems.

Min, James B.↗
NASA NTRS2008

Current Computational Challenges for CMC Processes, Properties, and Structures

In comparison to current state-of-the-art metallic alloys, ceramic matrix composites (CMC) offer a variety of performance advantages, such as higher temperature capability (greater than the approx.2100 F capability for best metallic alloys), lower density (approx.30-50% metal density), and lower thermal expansion. In comparison to other competing high-temperature materials, CMC are also capable of providing significantly better static and dynamic toughness than un-reinforced monolithic ceramics and significantly better environmental resistance than carbon-fiber reinforced composites. Because of these advantages, NASA, the Air Force, and other U.S. government agencies and industries are currently seeking to implement these advanced materials into hot-section components of gas turbine engines for both propulsion and power generation. For applications such as these, CMC are expected to result in many important performance benefits, such as reduced component cooling air requirements, simpler component design, reduced weight, improved fuel efficiency, reduced emissions, higher blade frequencies, reduced blade clearances, and higher thrust. Although much progress has been made recently in the development of CMC constituent materials and fabrication processes, major challenges still remain for implementation of these advanced composite materials into viable engine components. The objective of this presentation is to briefly review some of those challenges that are generally related to the need to develop physics-based computational approaches to allow CMC fabricators and designers to model (1) CMC processes for fiber architecture formation and matrix infiltration, (2) CMC properties of high technical interest such as multidirectional creep, thermal conductivity, matrix cracking stress, damage accumulation, and degradation effects in aggressive environments, and (3) CMC component life times when all of these effects are interacting in a complex stress and service environment. To put these computational issues in perspective, the various modeling needs within these three areas are briefly discussed in terms of their technical importance and their key controlling mechanistic factors as we know them today. Emphasis is placed primarily on the SiC/SiC ceramic composite system because of its higher temperature capability and enhanced development within the CMC industry. A brief summary is then presented concerning on-going property studies aimed at addressing these CMC modeling needs within NASA in terms of their computational approaches and recent important results. Finally an overview perspective is presented on those key areas where further CMC computational studies are needed today to enhance the viability of CMC structural components for high-temperature applications.

DiCarlo, James↗
NASA NTRS1989

Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites

Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.

Arenz, R. J.↗