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Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes

The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.

Herencia-Zapana, Heber↗

Enhancing DSN Operations Efficiency with the Discrepancy Reporting Management System (DRMS)

The DRMS is the Discrepancy Reporting Management System used by the Deep Space Network (DSN). It uses a web interface and is a management tool designed to track and manage: data outage incidents during spacecraft tracks against equipment and software known as DRs (discrepancy Reports), to record "out of pass" incident logs against equipment and software in a Station Log, to record instances where equipment has be restarted or reset as Reset records, and to electronically record equipment readiness status across the DSN. Tracking and managing these items increases DSN operational efficiency by providing: the ability to establish the operational history of equipment items, data on the quality of service provided to the DSN customers, the ability to measure service performance, early insight into processes, procedures and interfaces that may need updating or changing, and the capability to trace a data outage to a software or hardware change. The items listed above help the DSN to focus resources on areas of most need.

Discrepancy Reporting Management Systems (DRMS)↗

Reliability and Creep/Fatigue Analysis of a CMC Component

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 and enable higher operating temperatures requiring less cooling; thus leading to increased engine efficiencies. There is a need for convenient design tools that can accommodate various loading conditions and material data with their associated uncertainties to estimate the minimum predicted life as well as the failure probabilities of a structural component. This paper presents a review of the life prediction and probabilistic analyses performed for a CMC turbine stator vane. A computer code, NASALife, is used to predict the life of a 2-D woven silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC) turbine stator vane due to a mission cycle which induces low cycle fatigue and creep. The output from this program includes damage from creep loading, damage due to cyclic loading and the combined damage due to the given loading cycle. Results indicate that the trends predicted by NASALife are as expected for the loading conditions used for this study. In addition, a combination of woven composite micromechanics, finite element 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. Input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Results indicate that reducing the scatter in proportional limit strength of the vane material has the greatest effect in improving the overall reliability of the CMC vane.

Murthy, Pappu L. N.↗

Subsonic Aircraft Safety Icing Study

NASA's Integrated Resilient Aircraft Control (IRAC) Project is one of four projects within the agency s Aviation Safety Program (AvSafe) in the Aeronautics Research Mission Directorate (ARMD). The IRAC Project, which was redesigned in the first half of 2007, conducts research to advance the state of the art in aircraft control design tools and techniques. A "Key Decision Point" was established for fiscal year 2007 with the following expected outcomes: document the most currently available statistical/prognostic data associated with icing for subsonic transport, summarize reports by subject matter experts in icing research on current knowledge of icing effects on control parameters and establish future requirements for icing research for subsonic transports including the appropriate alignment. This study contains: (1) statistical analyses of accident and incident data conducted by NASA researchers for this "Key Decision Point", (2) an examination of icing in other recent statistically based studies, (3) a summary of aviation safety priority lists that have been developed by various subject-matter experts, including the significance of aircraft icing research in these lists and (4) suggested future requirements for NASA icing research. The review of several studies by subject-matter experts was summarized into four high-priority icing research areas. Based on the Integrated Resilient Aircraft Control (IRAC) Project goals and objectives, the IRAC project was encouraged to conduct work in all of the high-priority icing research areas that were identified, with the exception of the developing of methods to sense and document actual icing conditions.

Jones, Sharon Monica↗

Fiber Optic Wing Shape Sensing on NASA's Ikhana UAV

This document discusses the development of fiber optic wing shape sensing on NASA's Ikhana vehicle. The Dryden Flight Research Center's Aerostructures Branch initiated fiber-optic instrumentation development efforts in the mid-1990s. Motivated by a failure to control wing dihedral resulting in a mishap with the Helios aircraft, new wing displacement techniques were developed. Research objectives for Ikhana included validating fiber optic sensor measurements and real-time wing shape sensing predictions; the validation of fiber optic mathematical models and design tools; assessing technical viability and, if applicable, developing methodology and approaches to incorporate wing shape measurements within the vehicle flight control system; and, developing and flight validating approaches to perform active wing shape control using conventional control surfaces and active material concepts.

Richards, Lance↗

Thermal and Environmental Barrier Coating Development for Advanced Propulsion Engine Systems

Ceramic thermal and environmental barrier coatings (TEBCs) are used in gas turbine engines to protect engine hot-section components in the harsh combustion environments, and extend component lifetimes. Advanced TEBCs that have significantly lower thermal conductivity, better thermal stability and higher toughness than current coatings will be beneficial for future low emission and high performance propulsion engine systems. In this paper, ceramic coating design and testing considerations will be described for turbine engine high temperature and high-heat-flux applications. Thermal barrier coatings for metallic turbine airfoils and thermal/environmental barrier coatings for SiC/SiC ceramic matrix composite (CMC) components for future supersonic aircraft propulsion engines will be emphasized. Further coating capability and durability improvements for the engine hot-section component applications can be expected by utilizing advanced modeling and design tools.

Zhu, Dongming↗

Real-time In-Flight Strain and Deflection Monitoring with Fiber Optic Sensors

This viewgraph presentation reviews Dryden's efforts to develop in-flight monitoring based on Fiber Optics. One of the motivating factors for this development was the breakup of the Helios aircraft. On Ikhana the use of fiber optics for wing shape sensing is being developed. They are being used to flight validate fiber optic sensor measurements and real-time wing shape sensing predictions on NASA's Ikhana vehicle; validate fiber optic mathematical models and design tools; Assess technical viability and, if applicable, develop methodology and approach to incorporate wing shape measurements within the vehicle flight control system, and develop and flight validate advanced approaches to perform active wing shape control.

Richards, Lance↗

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.↗

Multiuser Collaboration with Networked Mobile Devices

In this paper we describe a multiuser collaboration infrastructure that enables multiple mission scientists to remotely and collaboratively interact with visualization and planning software, using wireless networked personal digital assistants(PDAs) and other mobile devices. During ground operations of planetary rover and lander missions, scientists need to meet daily to review downlinked data and plan science activities. For example, scientists use the Science Activity Planner (SAP) in the Mars Exploration Rover (MER) mission to visualize downlinked data and plan rover activities during the science meetings [1]. Computer displays are projected onto large screens in the meeting room to enable the scientists to view and discuss downlinked images and data displayed by SAP and other software applications. However, only one person can interact with the software applications because input to the computer is limited to a single mouse and keyboard. As a result, the scientists have to verbally express their intentions, such as selecting a target at a particular location on the Mars terrain image, to that person in order to interact with the applications. This constrains communication and limits the returns of science planning. Furthermore, ground operations for Mars missions are fundamentally constrained by the short turnaround time for science and engineering teams to process and analyze data, plan the next uplink, generate command sequences, and transmit the uplink to the vehicle [2]. Therefore, improving ground operations is crucial to the success of Mars missions. The multiuser collaboration infrastructure enables users to control software applications remotely and collaboratively using mobile devices. The infrastructure includes (1) human-computer interaction techniques to provide natural, fast, and accurate inputs, (2) a communications protocol to ensure reliable and efficient coordination of the input devices and host computers, (3) an application-independent middleware that maintains the states, sessions, and interactions of individual users of the software applications, (4) an application programming interface to enable tight integration of applications and the middleware. The infrastructure is able to support any software applications running under the Windows or Unix platforms. The resulting technologies not only are applicable to NASA mission operations, but also useful in other situations such as design reviews, brainstorming sessions, and business meetings, as they can benefit from having the participants concurrently interact with the software applications (e.g., presentation applications and CAD design tools) to illustrate their ideas and provide inputs.

ground operations↗

Coupled Thermo-Electro-Magneto-Elastic Response of Smart Stiffened Panels

This report documents the procedures developed for incorporating smart laminate and panel analysis capabilities within the HyperSizer aerospace structural sizing software package. HyperSizer analyzes stiffened panels composed of arbitrary composite laminates through stiffener homogenization, or "smearing " techniques. The result is an effective constitutive equation for the stiffened panel that is suitable for use in a full vehicle-scale finite element analysis via MSC/NASTRAN. The existing thermo-elastic capabilities of HyperSizer have herein been extended to include coupled thermo-electro-magneto-elastic analysis capabilities. This represents a significant step toward realization of design tools capable of guiding the development of the next generation of smart aerospace structures. Verification results are presented that compare the developed smart HyperSizer capability with an ABAQUS piezoelectric finite element solution for a facesheet-flange combination. These results show good agreement between HyperSizer and ABAQUS, but highlight a limitation of the HyperSizer formulation in that constant electric field components are assumed.

Bednarcyk, Brett A.↗

NASA Tech Briefs, September 2009

opics covered include: Filtering Water by Use of Ultrasonically Vibrated Nanotubes; Computer Code for Nanostructure Simulation; Functionalizing CNTs for Making Epoxy/CNT Composites; Improvements in Production of Single-Walled Carbon Nanotubes; Progress Toward Sequestering Carbon Nanotubes in PmPV; Two-Stage Variable Sample-Rate Conversion System; Estimating Transmitted-Signal Phase Variations for Uplink Array Antennas; Board Saver for Use with Developmental FPGAs; Circuit for Driving Piezoelectric Transducers; Digital Synchronizer without Metastability; Compact, Low-Overhead, MIL-STD-1553B Controller; Parallel-Processing CMOS Circuitry for M-QAM and 8PSK TCM; Differential InP HEMT MMIC Amplifiers Embedded in Waveguides; Improved Aerogel Vacuum Thermal Insulation; Fluoroester Co-Solvents for Low-Temperature Li+ Cells; Using Volcanic Ash to Remove Dissolved Uranium and Lead; High-Efficiency Artificial Photosynthesis Using a Novel Alkaline Membrane Cell; Silicon Wafer-Scale Substrate for Microshutters and Detector Arrays; Micro-Horn Arrays for Ultrasonic Impedance Matching; Improved Controller for a Three-Axis Piezoelectric Stage; Nano-Pervaporation Membrane with Heat Exchanger Generates Medical-Grade Water; Micro-Organ Devices; Nonlinear Thermal Compensators for WGM Resonators; Dynamic Self-Locking of an OEO Containing a VCSEL; Internal Water Vapor Photoacoustic Calibration; Mid-Infrared Reflectance Imaging of Thermal-Barrier Coatings; Improving the Visible and Infrared Contrast Ratio of Microshutter Arrays; Improved Scanners for Microscopic Hyperspectral Imaging; Rate-Compatible LDPC Codes with Linear Minimum Distance; PrimeSupplier Cross-Program Impact Analysis and Supplier Stability Indicator Simulation Model; Integrated Planning for Telepresence With Time Delays; Minimizing Input-to-Output Latency in Virtual Environment; Battery Cell Voltage Sensing and Balancing Using Addressable Transformers; Gaussian and Lognormal Models of Hurricane Gust Factors; Simulation of Attitude and Trajectory Dynamics and Control of Multiple Spacecraft; Integrated Modeling of Spacecraft Touch-and-Go Sampling; Spacecraft Station-Keeping Trajectory and Mission Design Tools; Efficient Model-Based Diagnosis Engine; and DSN Simulator.

Source record↗

Challenges and Lessons Learned From Resurrecting a Legacy Research Flight Controller

Resurrecting the legacy Inner Loop Thrust Vectoring research flight controller to investigate the tail shock region brought unique challenges. This report documents these challenges and lessons learned from a stability and controls perspective. The flight test approach for flight envelope expansion and probing tests, as well as limited flight test results, are presented. Recent advances in sonic boom reduction technology have contributed to a resurgent interest in civilian supersonic cruise flight. These advances have focused only on fore body shaping, however, and little, if any, experimental flight data are available to develop and validate design tools for the tail shock region. In January of 2009, the NASA Dryden Flight Research Center completed research flights to investigate the tail shock region of a highly modified F-15 aircraft by probing the shock waves around it, using another F-15 aircraft. To adjust the lift distribution and plume shape, a decade-old research flight controller from the Inner Loop Thrust Vectoring project was required. To investigate the tail shock region, the lift distribution was changed by adjusting the canard position, and the plume shape was changed by adjusting the nozzle area and thrust vectoring.

Dees, Ray A.↗

Ka-Band Waveguide Two-Way Hybrid Combiner for MMIC Amplifiers

The design, simulation, and characterization of a novel Ka-band (32.05 0.25 GHz) rectangular waveguide two-way branch-line hybrid unequal power combiner (with port impedances matched to that of a standard WR-28 waveguide) has been created to combine input signals, which are in phase and with an amplitude ratio of two. The measured return loss and isolation of the branch-line hybrid are better than 22 and 27 dB, respectively. The measured combining efficiency is 92.9 percent at the center frequency of 32.05 GHz. This circuit is efficacious in combining the unequal output power from two Ka-band GaAs pseudomorphic high electron mobility transistor (pHEMT) monolithic microwave integrated circuit (MMIC) power amplifiers (PAs) with high efficiency. The component parts include the branch-line hybrid-based power combiner and the MMIC-based PAs. A two-way branch-line hybrid is a four-port device with all ports matched; power entering port 1 is divided in phase, and into the ratio 2:1 between ports 3 and 4. No power is coupled to port 2. MMICs are a type of integrated circuit fabricated on GaAs that operates at microwave frequencies, and performs the function of signal amplification. The power combiner is designed to operate over the frequency band of 31.8 to 32.3 GHz, which is NASA's deep space frequency band. The power combiner would have an output return loss better than 20 dB. Isolation between the output port and the isolated port is greater than 25 dB. Isolation between the two input ports is greater than 25 dB. The combining efficiency would be greater than 90 percent when the ratio of the two input power levels is two. The power combiner is machined from aluminum with E-plane split-block arrangement, and has excellent reliability. The flexibility of this design allows the combiner to be customized for combining the power from MMIC PAs with an arbitrary power output ratio. In addition, it allows combining a low-power GaAs MMIC with a high-power GaN MMIC. The arbitrary port impedance allows matching the output impedance of the MMIC PA directly to the waveguide impedance without transitioning first into a transmission line with characteristic impedance of 50 ohms. Thus, by eliminating the losses associated with a transition, the overall SSPA efficiency is enhanced. For reducing the cost and weight when required in very large quantities, such as in the beam-forming networks of phased-array antenna systems, the combiner can be manufactured using metal-plated plastic. Two hybrid unequal power combiners can be cascaded to realize a non-binary combiner (for e.g., a three-way) and can be synergistically optimized for low VSWR (voltage standing wave ratio), low insertion loss, high isolation, and wide bandwidth using commercial off-the-shelf electromagnetic software design tools.

Simons, Rainee N.↗

Cast Glance Near Infrared Imaging Observations of the Space Shuttle During Hypersonic Re-Entry

High resolution calibrated infrared imagery of the Space Shuttle was obtained during hypervelocity atmospheric entries of the STS-119, STS-125 and STS128 missions and has provided information on the distribution of surface temperature and the state of the airflow over the windward surface of the Orbiter during descent. This data collect was initiated by NASA s Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) team and incorporated the use of air- and land-based optical assets to image the Shuttle during atmospheric re-entry. The HYTHIRM objective is to develop and implement a set of mission planning tools designed to establish confidence in the ability of an existing optical asset to reliably acquire, track and return global quantitative surface temperatures of the Shuttle during entry. On Space Shuttle Discovery s STS-119 mission, NASA flew a specially modified thermal protection system tile and instrumentation package to monitor heating effects from boundary layer transition during re-entry. On STS-119, the windward airflow on the port wing was deliberately disrupted by a four-inch wide and quarter-inch tall protuberance built into the modified tile. In coordination with this flight experiment, a US Navy NP-3D Orion aircraft was flown 28 nautical miles below Discovery and remotely monitored surface temperature of the Orbiter at Mach 8.4 using a long-range infrared optical package referred to as Cast Glance. Approximately two months later, the same Navy Cast Glance aircraft successfully monitored the surface temperatures of the Orbiter Atlantis traveling at approximately Mach 14.3 during its return from the successful Hubble repair mission. In contrast to Discovery, Atlantis was not part of the Boundary Layer Transition (BLT) flight experiment, thus the vehicle was not configured with a protuberance on the port wing. In September 2009, Cast Glance was again successful in capturing infrared imagery and monitoring the surface temperatures on Discovery s next flight, STS-128. Again, NASA flew a specially modified thermal protection system tile and instrumentation package to monitor heating effects from boundary layer transition during re-entry. During this mission, Cast Glance was able to image laminar and turbulent flow phenomenology optimizing data collection for Mach 14.7. The purpose of this paper is to describe key elements associated with STS-119/125/128 mission planning and execution from the perspective of the Cast Glance flight crew that obtained the imagery. The paper will emphasize a human element of experience, expertise and adaptability seamlessly coupled with Cast Glance system and sensor technology required to manually collect the required imagery. Specific topics will include a near infrared (NIR) camera upgrade that was implemented just prior to the missions, how pre-flight radiance modeling was utilized to optimize the IR sensor configuration, communications, the development of aircraft test support positions based upon Shuttle trajectory information, support to contingencies such as Shuttle one orbit wave-offs/west coast diversions and then the Cast Glance perspective during an actual Shuttle imaging mission.

Tack, Steve↗

Design of a Microwave Assisted Discharge Inductive Plasma Accelerator

A new plasma accelerator concept that employs electrodeless plasma preionization and pulsed inductive acceleration is presented. Preionization is achieved through an electron cyclotron resonance discharge that produces a weakly-ionized plasma at the face of a conical theta pinch-shaped inductive coil. The presence of the preionized plasma allows for current sheet formation at lower discharge voltages than those found in other pulsed inductive accelerators. The location of an electron cyclotron resonance discharge can be controlled through the design of the applied magnetic field in the thruster. A finite-element model of the magnetic field was used as a design tool, allowing for the implementation of an arrangement of permanent magnets that yields a small volume of preionized propellant at the coil face. This allows for current sheet formation at the face of the inductive coil, minimizing the initial inductance of the pulse circuit and maximizing the potential efficiency of the new accelerator.

Hallock, Ashley K.↗

NASA Subsonic Rotary Wing Project-Multidisciplinary Analysis and Technology Development: Overview

This slide presentation reviews the objectives of the Multidisciplinary Analysis and Technology Development (MDATD) in the Subsonic Rotary Wing project. The objectives are to integrate technologies and analyses to enable advanced rotorcraft and provide a roadmap to guide Level 1 and 2 research. The MDATD objectives will be met by conducting assessments of advanced technology benefits, developing new or enhanced design tools, and integrating Level 2 discipline technologies to develop and enable system-level analyses and demonstrations.

Yamauchi, Gloria K.↗

Modeling Guidelines for Code Generation in the Railway Signaling Context

Modeling guidelines constitute one of the fundamental cornerstones for Model Based Development. Their relevance is essential when dealing with code generation in the safety-critical domain. This article presents the experience of a railway signaling systems manufacturer on this issue. Introduction of Model-Based Development (MBD) and code generation in the industrial safety-critical sector created a crucial paradigm shift in the development process of dependable systems. While traditional software development focuses on the code, with MBD practices the focus shifts to model abstractions. The change has fundamental implications for safety-critical systems, which still need to guarantee a high degree of confidence also at code level. Usage of the Simulink/Stateflow platform for modeling, which is a de facto standard in control software development, does not ensure by itself production of high-quality dependable code. This issue has been addressed by companies through the definition of modeling rules imposing restrictions on the usage of design tools components, in order to enable production of qualified code. The MAAB Control Algorithm Modeling Guidelines (MathWorks Automotive Advisory Board)[3] is a well established set of publicly available rules for modeling with Simulink/Stateflow. This set of recommendations has been developed by a group of OEMs and suppliers of the automotive sector with the objective of enforcing and easing the usage of the MathWorks tools within the automotive industry. The guidelines have been published in 2001 and afterwords revisited in 2007 in order to integrate some additional rules developed by the Japanese division of MAAB [5]. The scope of the current edition of the guidelines ranges from model maintainability and readability to code generation issues. The rules are conceived as a reference baseline and therefore they need to be tailored to comply with the characteristics of each industrial context. Customization of these recommendations has been performed for the automotive control systems domain in order to enforce code generation [7]. The MAAB guidelines have been found profitable also in the aerospace/avionics sector [1] and they have been adopted by the MathWorks Aerospace Leadership Council (MALC). General Electric Transportation Systems (GETS) is a well known railway signaling systems manufacturer leading in Automatic Train Protection (ATP) systems technology. Inside an effort of adopting formal methods within its own development process, GETS decided to introduce system modeling by means of the MathWorks tools [2], and in 2008 chose to move to code generation. This article reports the experience performed by GETS in developing its own modeling standard through customizing the MAAB rules for the railway signaling domain and shows the result of this experience with a successful product development story.

Ferrari, Alessio↗

A Brief Introduction to the Theory of Friction Stir Welding

Friction stir welding (FSW) is a solid state welding process invented in 1991 at The Welding Institute in the United Kingdom. A weld is made in the FSW process by translating a rotating pin along a weld seam so as to stir the sides of the seam together. FSW avoids deleterious effects inherent in melting and is already an important welding process for the aerospace industry, where welds of optimal quality are demanded. The structure of welds determines weld properties. The structure of friction stir welds is determined by the flow field in the weld metal in the vicinity of the weld tool. A simple kinematic model of the FSW flow field developed at Marshall Space Flight Center, which enables the basic features of FSW microstructure to be understood and related to weld process parameters and tool design, is explained.

Nunes, Arthur C., Jr.↗