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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Visualization techniques for the gyrokinetic tokamak simulation code

Gyrokinetic simulations of plasma microturbulence in tokamaks are challenging to visualize because the compute grid follows the magnetic field lines that spiral around the torus. We have overcome this challenge by developing three new approaches that improve visualization of gyrokinetics. Our techniques work directly with the topology of magnetic flux surfaces where the simulation stores variables in concentric rings on poloidal planes (vertical cross sections of the torus). Our visualization preview step triangulates each consecutive pair of rings to display the data on a poloidal plane. The second visualization technique follows spiral field lines around the torus and constructs polygons to visualize a flux surface. Third, the poloidal triangles are connected between planes to form prisms that compose a 3-D model of the entire torus. The visualization workflow produces detailed geometry that matches the high resolution, irregular compute grid for every time step. The surface and solid models are displayed in scientific visualization programs to effectively explore and communicate the results, including fluctuation of electron density, ion temperature, and electrostatic potential. Highly detailed renderings verify plasma behavior along magnetic field lines over time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Supersonic Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. Assessing the blade structural integrity is a complex task requiring an initial characterization of whether resonance is possible and then performing a forced response analysis if that condition is met. The standard technique for forced response analysis in rocket engine turbines is to decompose a computational fluid dynamics (CFD).generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies using cyclically symmetric structural dynamic models. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non ]harmonic excitation sources that become present in complex flows. This complex content can only be captured by a CFD flow field encompassing at least an entire revolution. A substantial development effort to create a series of software programs to enable application of the 360 degree forcing function in a frequency response analysis on cyclic symmetric models has been completed (to be described in a future paper), but the question still remains whether the frequency response analysis itself is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, of bladed-disks undergoing this complex flow environment have been performed. The first is of a bladed disk with each blade modeled by simple beam elements and the disk modeled with plates (using the finite element code MSC/NASTRAN). The focus of this model is to be representative of response of realistic bladed disks, and so the dimensions are roughly equivalent to the new J2X rocket engine 1st stage fuel pump turbine. The simplicity of the model allows the CFD load to be able to be readily applied, along with analytical and experimental variations in both the temporal and spatial fourier components of the excitation. In addition, this model is a first step in identifying response differences between transient and frequency forced response analysis techniques. The second phase assesses this difference for a much more realistic solid model of a bladed-disk in order to evaluate the effect of the spatial variation in loading on blade dominated modes. Neither research on the accuracy of the frequency response method when used in this context or a comprehensive study of the effect of test-observed variation on blade forced response have been found in the literature, so this research is a new contribution to practical structural dynamic analysis of gas turbines. The primary excitation of the upstream nozzles interacts with the blades on fuel pump of the J2X causes the 5th Nodal diameter modes to be excited, as explained by Tyler and Sofrin1, so a modal analysis was first performed on the beam/plate model and the 5ND bladed-disk mode at 40167 hz was identified and chosen to be the one excited at resonance (see figure 1). The first forced response analysis with this model focuses on identifying differences between frequency and transient response analyses. A hypothesis going into the analysis was that perhaps the frequency response was enforcing a temporal periodicity that did not really exist, and so therefore it would overestimate the response. As high dynamic response was a considerable source of stress in the J2X, examining this concept could potentially be beneficial for the program.

Brown, Andrew M.↗
DOE OSTI2023

Beneficial effect of copper on pitting resistance of Ni-Cr-Fe alloys

This study examines the effect of copper alloying on pitting resistance in a model solid solution FCC Ni-13%Cr-10%Fe alloy through potentiodynamic and potentiostatic polarization in 0.1 M NaCl in conjunction with an analysis using first-principles competitive electro-chemisorption modeling. The pitting potential increased with increasing Cu content in the alloy. Furthermore, the extent of metastable pit growth was suppressed and the incubation time for metastable to stable pit transition increased with Cu content. The first-principles competitive adsorption calculations suggested that Cu alloying suppresses chloride ion adsorption on the alloy surface in a simulated pit environment, which inhibits active dissolution at the pit bottom, enhances proton adsorption, and thereby increases the local pH at the pit bottom. In conclusion, we propose that these two effects of Cu in solid solution combine to reduce pit stability and may act in addition to the enrichment of Cu on the corroding pit surface.

36 MATERIALS SCIENCE↗
NASA NTRS1982

Structural modeling of high Reynolds number wind tunnel models

A solid uninstrumented wing and a pressure instrumented wing having a tongue and groove type joint have been structurally modeled by using SPAR Structural Analysis System. The solid wing model can be analyzed by SPAR, using either solid elements or plate elements with reasonable accuracy. The instrumented wing models with tongue and groove joint can be modeled by using solid elements. A solid model representation for the wing with tongue and groove joint can be used for the cases where an error of 6 percent in deflections is acceptable.

Mehrotra, S. C.↗
NASA NTRSDate not supplied

Micrometeoroid and Orbital Debris (MMOD) Testing, Ballistic Limit Definition and Risk Assessment of the Exploration Extravehicular Mobility Unit (xEMU)

A well-known hazard associated with exposure to the space environment is the risk of failure due to an impact from a micrometeoroid and orbital debris (MMOD) particle. As NASA prepares to return astronauts to the moon with the Artemis program, the next generation of spacesuit is in development to support future extravehicular activities (EVAs.) An MMOD impact to the spacesuit is of great concern as a large leak could prevent an astronaut from safely reaching an airlock in time resulting in a loss of life. The exploration extravehicular mobility unit (xEMU) must meet MMOD requirements for multiple environments including those in low earth orbit (LEO) as well as the meteoroid and secondary lunar regolith ejecta environments found on the lunar surface. The subject of this paper is an internal xEMU configuration design developed by NASA Johnson Space Center (JSC) personnel. The xEMU shares similarities with the legacy Extravehicular Mobility Unit (EMU) spacesuit that is currently used for ISS EVAs, however differences in the layup (e.g., materials, thicknesses, and layers) of the fabric environmental protection garment (EPG), portable life support system (xPLSS) and helmet required an extensive test program to determine ballistic performance. Over 100 hypervelocity impact (HVI) tests were performed by the NASA/JSC HVIT and White Sands Test Facility (WSTF) teams on the xEMU EPG, xPLSS and helmet to generate ballistic limit equations (BLEs) for MMOD impacts. Additionally, over 50 low speed tests (< 1km/s) were performed by the NASA/JSC HVIT and Southwest Research Institute (SwRI) teams on the xEMU EPG, xPLSS and helmet to generate BLEs for lunar ejecta impacts. Post testing, ballistic limit equations (BLEs) used to define the performance of the various regions on the xEMU spacesuit were developed from a generic set of BLEs. The HVI and low speed testing was performed to establish a physical basis for the equations with the coefficients and exponents of the generic BLEs adjusted to fit the test data. The xEMU BLEs were added to the NASA/JSC software application used for spacecraft MMOD risk assessments (BUMPER-3). A finite element model (FEM) of the xEMU spacesuit, which defines the size and shape of the spacesuit as well as the locations of the various shielding configurations, was created based on a solid model provided by the xEMU program office. Using the FEM file and added xEMU BLEs, BUMPER-3 assessments of the xEMU spacesuit for probability of no penetration (PNP) were performed. For the LEO assessment of a typical ISS EVA, the orbital debris and meteoroids environments were defined using the latest engineering models, ORDEM 3.2 and MEM-3 respectively. The lunar surface assessment again used the MEM-3 engineering model to define the meteoroid environment along with the current released lunar surface ejecta model, NASA SP-8013 (developed during the Apollo Program). The Space Team in the Natural Environments Branch at Marshall Space Flight Center (MSFC) will soon release the new Lunar Meteoroid Ejecta Engineering Model (LMEEM), at which time the xEMU lunar surface EVA will be reassessed. Assessment of the MMOD risk for an 8-hour, 2-person EVA in both LEO and on the lunar surface showed that the xEMU spacesuit meets the program technical requirement of 1 in 2500 failure odds. Similar to the legacy EMU spacesuit, the majority of the MMOD risk (96% of the LEO EVA risk and 99% of the lunar surface EVA risk) is concentrated in regions of xEMU that are comprised primarily of softgoods (arms, legs, and gloves) rather than the hardgoods (xPLSS, hard upper torso and helmet).

Micrometeoroid↗
NASA NTRSDate not supplied

Micrometeoroid and Orbital Debris (MMOD) Testing, Ballistic Limit Equation Definition and Risk Assessment of the Exploration Extravehicular Mobility Unit (xEMU)

A well-known hazard associated with exposure to the space environment is the risk of failure due to an impact from a micrometeoroid and orbital debris (MMOD) particle. As NASA prepares to return astronauts to the moon with the Artemis program, the next generation of spacesuit is in development to support future extravehicular activities (EVAs.) An MMOD impact to the spacesuit is of great concern as a large leak could prevent an astronaut from safely reaching an airlock in time resulting in a loss of life. The exploration extravehicular mobility unit (xEMU) must meet MMOD requirements for multiple environments including those in low earth orbit (LEO) as well as the meteoroid and secondary lunar regolith ejecta environments found on the lunar surface. The subject of this paper is an internal xEMU configuration design developed by NASA Johnson Space Center (JSC) personnel. This paper will expand on the hypervelocity impact (HVI) testing and ballistic limit equation (BLE) definition work that was partially presented at the 2nd International Orbital De-bris (IOC-II) Conference held in Sugar Land, TX in December 2023. The xEMU shares similarities with the legacy Extravehicular Mobility Unit (EMU) spacesuit that is currently used for ISS EVAs, however differences in the layup (e.g., materials, thicknesses, and layers) of the fabric environmental protection garment (EPG), portable life support system (xPLSS) and helmet required an extensive test program to determine ballistic performance. Over 100 hypervelocity impact (HVI) tests were performed by the NASA/JSC HVIT and White Sands Test Facility (WSTF) teams on the xEMU EPG, xPLSS and helmet to generate ballistic limit equations (BLEs) for MMOD impacts. Additionally, over 50 low speed tests (< 1km/s) were performed by the NASA/JSC HVIT and Southwest Research Institute (SwRI) teams on the xEMU EPG, xPLSS and helmet to generate BLEs for lunar ejecta impacts. Post testing, ballistic limit equations used to define the performance of the various regions on the xEMU spacesuit were developed from a generic set of BLEs. The HVI and low speed testing was performed to establish a physical basis for the equations with the co-efficients and exponents of the generic BLEs adjusted to fit the test data. The xEMU BLEs were added to the NASA/JSC software application used for space-craft MMOD risk assessments (BUMPER-3). A finite element model (FEM) of the xEMU spacesuit, which defines the size and shape of the spacesuit as well as the locations of the various shielding configurations, was created based on a solid model provided by the xEMU program office. Using the FEM file and added xEMU BLEs, BUMPER-3 assessments of the xEMU spacesuit for probability of no penetration (PNP) were performed. For the LEO assessment of a typical ISS EVA, the orbital debris and meteoroids environments were defined using the latest engineering models, ORDEM 3.2 and MEM-3 respectively. The lunar sur-face assessment again used the MEM-3 engineering model to define the meteoroid environ-ment along with the current released lunar surface ejecta model, NASA SP-8013 (developed during the Apollo Program). The Space Team in the Natural Environments Branch at Mar-shall Space Flight Center (MSFC) will soon release the new Lunar Meteoroid Ejecta Engineering Model (LMEEM), at which time the xEMU lunar surface EVA will be reassessed. Assessment of the MMOD risk for an 8-hour, 2-person EVA in both LEO and on the lunar surface showed that the xEMU spacesuit meets the program technical requirement of 1 in 2500 failure odds. Similar to the legacy EMU spacesuit, the majority of the MMOD risk (96% of the LEO EVA risk and 99% of the lunar surface EVA risk) is concentrated in regions of xEMU that are comprised primarily of softgoods (arms, legs, and gloves) rather than the hardgoods (xPLSS, hard upper torso and helmet).

Micrometeoroid↗
NASA NTRS2002

Preliminary Sizing Completed for Single- Stage-To-Orbit Launch Vehicles Powered By Rocket-Based Combined Cycle Technology

Single-stage-to-orbit (SSTO) propulsion remains an elusive goal for launch vehicles. The physics of the problem is leading developers to a search for higher propulsion performance than is available with all-rocket power. Rocket-based combined cycle (RBCC) technology provides additional propulsion performance that may enable SSTO flight. Structural efficiency is also a major driving force in enabling SSTO flight. Increases in performance with RBCC propulsion are offset with the added size of the propulsion system. Geometrical considerations must be exploited to minimize the weight. Integration of the propulsion system with the vehicle must be carefully planned such that aeroperformance is not degraded and the air-breathing performance is enhanced. Consequently, the vehicle's structural architecture becomes one with the propulsion system architecture. Geometrical considerations applied to the integrated vehicle lead to low drag and high structural and volumetric efficiency. Sizing of the SSTO launch vehicle (GTX) is itself an elusive task. The weight of the vehicle depends strongly on the propellant required to meet the mission requirements. Changes in propellant requirements result in changes in the size of the vehicle, which in turn, affect the weight of the vehicle and change the propellant requirements. An iterative approach is necessary to size the vehicle to meet the flight requirements. GTX Sizer was developed to do exactly this. The governing geometry was built into a spreadsheet model along with scaling relationships. The scaling laws attempt to maintain structural integrity as the vehicle size is changed. Key aerodynamic relationships are maintained as the vehicle size is changed. The closed weight and center of gravity are displayed graphically on a plot of the synthesized vehicle. In addition, comprehensive tabular data of the subsystem weights and centers of gravity are generated. The model has been verified for accuracy with finite element analysis. The final trajectory was rerun using OTIS (Boeing Corporation's trajectory optimization software package), and the sizing output was incorporated into a solid model of the vehicle using PRO/Engineer computer-aided design software (Parametric Technology Corporation, Waltham, MA).

Roche, Joseph M.↗
NASA NTRS1990

Control/structure interaction conceptual design tool

The JPL Control/Structure Interaction Program is developing new analytical methods for designing micro-precision spacecraft with controlled structures. One of these, the Conceptual Design Tool, will illustrate innovative new approaches to the integration of multi-disciplinary analysis and design methods. The tool will be used to demonstrate homogeneity of presentation, uniform data representation across analytical methods, and integrated systems modeling. The tool differs from current 'integrated systems' that support design teams most notably in its support for the new CSI multi-disciplinary engineer. The design tool will utilize a three dimensional solid model of the spacecraft under design as the central data organization metaphor. Various analytical methods, such as finite element structural analysis, control system analysis, and mechanical configuration layout, will store and retrieve data from a hierarchical, object oriented data structure that supports assemblies of components with associated data and algorithms. In addition to managing numerical model data, the tool will assist the designer in organizing, stating, and tracking system requirements.

Briggs, Hugh C.↗
NASA NTRS1992

Geometric modeling for computer aided design

The goal was the design and implementation of software to be used in the conceptual design of aerospace vehicles. Several packages and design studies were completed, including two software tools currently used in the conceptual level design of aerospace vehicles. These tools are the Solid Modeling Aerospace Research Tool (SMART) and the Environment for Software Integration and Execution (EASIE). SMART provides conceptual designers with a rapid prototyping capability and additionally provides initial mass property analysis. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand alone analysis codes that result in the streamlining of the exchange of data between programs, reducing errors and improving efficiency.

Schwing, James L.↗
NASA NTRS1995

Integration of design, structural, thermal and optical analysis: And user's guide for structural-to-optical translator (PATCOD)

Electronic integration of design and analysis processes was achieved and refined at Langley Research Center (LaRC) during the development of an optical bench for a laser-based aerospace experiment. Mechanical design has been integrated with thermal, structural and optical analyses. Electronic import of the model geometry eliminates the repetitive steps of geometry input to develop each analysis model, leading to faster and more accurate analyses. Guidelines for integrated model development are given. This integrated analysis process has been built around software that was already in use by designers and analysis at LaRC. The process as currently implemented used Pro/Engineer for design, Pro/Manufacturing for fabrication, PATRAN for solid modeling, NASTRAN for structural analysis, SINDA-85 and P/Thermal for thermal analysis, and Code V for optical analysis. Currently, the only analysis model to be built manually is the Code V model; all others can be imported for the Pro/E geometry. The translator from PATRAN results to Code V optical analysis (PATCOD) was developed and tested at LaRC. Directions for use of the translator or other models are given.

Amundsen, R. M.↗
NASA NTRS2014

Space Launch System Base Heating Test: Sub-Scale Rocket Engine/Motor Design, Development and Performance Analysis

The Space Launch System (SLS) base heating test is broken down into two test programs: (1) Pathfinder and (2) Main Test. The Pathfinder Test Program focuses on the design, development, hot-fire test and performance analyses of the 2% sub-scale SLS core-stage and booster element propulsion systems. The core-stage propulsion system is composed of four gaseous oxygen/hydrogen RS-25D model engines and the booster element is composed of two aluminum-based model solid rocket motors (SRMs). The first section of the paper discusses the motivation and test facility specifications for the test program. The second section briefly investigates the internal flow path of the design. The third section briefly shows the performance of the model RS-25D engines and SRMs for the conducted short duration hot-fire tests. Good agreement is observed based on design prediction analysis and test data. This program is a challenging research and development effort that has not been attempted in 40+ years for a NASA vehicle.

Mehta, Manish↗
NASA NTRS2002

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

Powers, Lynn M.↗
NASA NTRS1990

Application of three-dimensional Bezier patches in grid generation

Bezier and B-spline patches are popular tools in surface modeling. With these methods, a surface is represented by the tensor product of univariate approximations. The extension of this concept to three dimensions is obvious and can be applied to the problem of grid generation. This report will demonstrate how three dimensional patches can be used in solid modeling and in the generation of grids. Examples will be given demonstrating the ability to generate three dimensional grids directly from a wire frame without having to first set up the boundary surfaces. Many geometric grid properties can be imposed by the proper choice of the control net.

Mastin, C. Wayne↗
NASA NTRS2004

JWST ISIM Distortion Analysis Challenge

Very tight distortion requirements are imposed on the JWST's ISM structure due to the sensitivity of the telescope's mirror segment and science instrument positioning. The ISIM structure is a three dimensional truss with asymmetric gusseting and metal fittings. One of the primary challenges for ISIM's analysis team is predicting the thermal distortion of the structure both from the bulk cooldown from ambient to cryo, and the smaller temperature changes within the cryogenic operating environment. As a first cut to estimate thermal distortions, a finite element model of bar elements was created. Elements representing joint areas and metal fittings use effective properties that match the behavior of the stack-up of the composite tube, gusset and adhesive under mechanical and thermal loads. These properties were derived by matching tip deflections of a solid model simplified T-joint. Because of the structure s asymmetric gusseting, this effective property model is a first attempt at predicting rotations that cannot be captured with a smeared CTE approach. In addition to the finite element analysis, several first order calculations have been performed to gauge the feasibility of the material design. Because of the stringent thermal distortion requirements at cryogenic temperatures, a composite tube material with near zero or negative CTE is required. A preliminary hand analysis of the contribution of the various components along the distortion path between FGS and the other instruments, neglecting second order effects were examined. A plot of bounding tube longitudinal and transverse CTEs for thermal stability requirements was generated to help determine the feasibility of meeting these requirements. This analysis is a work in progress en route to a large degree of freedom hi-fidelity FEA model for distortion analysis. Methods of model reduction, such as superelements, are currently being investigated.

Cifie, Emmanuel↗
NASA NTRS2002

Analysis of Composite Skin-Stiffener Debond Specimens Using Volume Elements and a Shell/3D Modeling Technique

The debonding of a skin/stringer specimen subjected to tension was studied using three-dimensional volume element modeling and computational fracture mechanics. Mixed mode strain energy release rates were calculated from finite element results using the virtual crack closure technique. The simulations revealed an increase in total energy release rate in the immediate vicinity of the free edges of the specimen. Correlation of the computed mixed-mode strain energy release rates along the delamination front contour with a two-dimensional mixed-mode interlaminar fracture criterion suggested that in spite of peak total energy release rates at the free edge the delamination would not advance at the edges first. The qualitative prediction of the shape of the delamination front was confirmed by X-ray photographs of a specimen taken during testing. The good correlation between prediction based on analysis and experiment demonstrated the efficiency of a mixed-mode failure analysis for the investigation of skin/stiffener separation due to delamination in the adherents. The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to three-point bending is also demonstrated. The global structure was modeled with shell elements. A local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination front was used to capture the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/3D simulations were in good agreement with results obtained from full solid models. The good correlations of the results demonstrated the effectiveness of the shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents.

Krueger, Ronald↗
NASA NTRS2002

Application of the Shell/3D Modeling Technique for the Analysis of Skin-Stiffener Debond Specimens

The application of a shell/3D modeling technique for the simulation of skin/stringer debond in a specimen subjected to three-point bending is demonstrated. The global structure was modeled with shell elements. A local three-dimensional model, extending to about three specimen thicknesses on either side of the delamination front was used to capture the details of the damaged section. Computed total strain energy release rates and mixed-mode ratios obtained from shell/13D simulations were in good agreement with results obtained from full solid models. The good correlations of the results demonstrated the effectiveness of the shell/3D modeling technique for the investigation of skin/stiffener separation due to delamination in the adherents.

Krueger, Ronald↗
NASA NTRS1992

Application of three-dimensional Bezier patches in grid generation

Bezier and B-spline patches are popular tools in surface modeling. With these methods, a surface is represented by the tensor product of univariate approximations. The extension of this concept to three-dimensions is obvious and can be applied to the problem of grid generation. This report will demonstrate how three-dimensional patches can be used in solid modeling and in the generation of grids. Examples will be given demonstrating the ability to generate three-dimensional grids directly from a wire frame without having to first set up the boundary surfaces. Many geometric grid properties can be imposed by the proper choice of the control net.

Mastin, C. Wayne↗
NASA NTRS1992

Evaluation of microcrack thermal shock damage in ceramics: Modeling and experiment

In this paper we present an experimental and theoretical study of the effect of microcrack damage on ceramic properties. For the experimental investigation, ceramic samples of aluminum oxide and reaction bonded silicon nitride (RBSN) are used. Thermal shock treatment from different temperatures up to 1000 C is applied to produce the microcracks. Both surface and bulk ultrasonic wave methods are used to correlate the change of elastic constants to microstructural degradation and to determine the change in elastic anisotropy induced by microcrack damage. For the theoretical investigation, damage mechanics, which relates microstructural damage to material service life and mechanical failure, is used. The change in elastic properties due to microcrack damage calculated from the theoretical model is compared with the experimental results for determination of the applicability of damage theory. It is shown that two independent experimental methods (bulk wave and surface wave) give the same results for shear moduli of damaged ceramics. The experimental results aagree reasonably well with the moduli predicted from the cracked solid model.

Chu, Y. C.↗