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NASA NTRS1999

High Temperature Mechanical Characterization and Analysis of Al2O3 /Al2O3 Composition

Sixteen ply unidirectional zirconia coated single crystal Al2O3 fiber reinforced polycrystalline Al2O3 was tested in uniaxial tension at temperatures to 1400 C in air. Fiber volume fractions ranged from 26 to 31%. The matrix has primarily open porosity of approximately 40%. Theories for predicting the Young's modulus, first matrix cracking stress, and ultimate strength were applied and evaluated for suitability in predicting the mechanical behavior of Al2O3/Al2O3 composites. The composite exhibited pseudo tough behavior (increased area under the stress/strain curve relative to monolithic alumina) from 22 to 1400 C. The rule-of-mixtures provides a good estimate of the Young's modulus of the composite using the constituent properties from room temperature to approximately 1200 C for short term static tensile tests in air. The ACK theory provides the best approximation of the first matrix cracking stress while accounting for residual stresses at room temperature. Difficulties in determining the fiber/matrix interfacial shear stress at high temperatures prevented the accurate prediction of the first matrix cracking stress above room temperature. The theory of Cao and Thouless, based on Weibull statistics, gave the best prediction for the composite ultimate tensile strength.

Gyekenyesi, John Z.↗

NASA NTRS1999

Problems Associated with Statistical Pattern Recognition of Acoustic Emission Signals in a Compact Tension Fatigue Specimen

Acoustic emission (AE) data were acquired during fatigue testing of an aluminum 2024-T4 compact tension specimen using a commercially available AE system. AE signals from crack extension were identified and separated from noise spikes, signals that reflected from the specimen edges, and signals that saturated the instrumentation. A commercially available software package was used to train a statistical pattern recognition system to classify the signals. The software trained a network to recognize signals with a 91-percent accuracy when compared with the researcher's interpretation of the data. Reasons for the discrepancies are examined and it is postulated that additional preprocessing of the AE data to focus on the extensional wave mode and eliminate other effects before training the pattern recognition system will result in increased accuracy.

Hinton, Yolanda L.↗

NASA NTRS2004

Microstructural Evaluation of KM4 and SR3 Samples Subjected to Various Heat Treatments

The gamma-gamma microstructures of two advanced powder metallurgy disk alloys, KM4 and SR3, were quantified after a series of heat treatments using transmission electron microscopy and image analysis. Relationships between the heat treatments and the resulting gamma distributions were evaluated. Statistical correlations between the gamma distributions and the reported tensile strengths, creep resistances, and dwell crack growth resistances were separately assessed for each alloy. To avoid the effects of grain size related mechanisms, the grain size of the samples used in the correlations for each alloy were limited to narrow ranges of about 1.5 in ASTM grain size number. In both alloys, yield and tensile strength increased with increasing fraction of medium sized gamma. The strength increased as the size of the medium gamma decreased and the size of the fine gamma increased. Time to 0.2 percent creep in SR3 increased with increasing medium gamma volume fraction, and decreasing fine gamma sizes. However, 0.2 percent creep time was not clearly correlated with the gamma microstructures of KM4 specimens, apparently due to effects of stabilization heat treatments which greatly suppress creep resistance. Dwell fatigue crack growth rate decreased with increasing medium gamma volume fraction, indicating more medium gamma is beneficial. The crack growth rate also decreased with decreasing gamma size, indicating finer gamma is better.

Ellis, David↗

NASA NTRS2004

A Hierarchical Approach to Fracture Mechanics

Recent research conducted under NASA LaRC's Creativity and Innovation Program has led to the development of an initial approach for a hierarchical fracture mechanics. This methodology unites failure mechanisms occurring at different length scales and provides a framework for a physics-based theory of fracture. At the nanoscale, parametric molecular dynamic simulations are used to compute the energy associated with atomic level failure mechanisms. This information is used in a mesoscale percolation model of defect coalescence to obtain statistics of fracture paths and energies through Monte Carlo simulations. The mathematical structure of predicted crack paths is described using concepts of fractal geometry. The non-integer fractal dimension relates geometric and energy measures between meso- and macroscales. For illustration, a fractal-based continuum strain energy release rate is derived for inter- and transgranular fracture in polycrystalline metals.

Saether, Erik↗

NASA NTRS1986

Grain boundary oxidation and its effects on high temperature fatigue life

Fatigue lives at elevated temperatures are often shortened by creep and/or oxidation. Creep causes grain boundary void nucleation and grain boundary cavitation. Grain boundary voids and cavities will accelerate fatigue crack nucleation and propagation, and thereby shorten fatigue life. The functional relationships between the damage rate of fatigue crack nucleation and propagation and the kinetic process of oxygen diffusion depend on the detailed physical processes. The kinetics of grain boundary oxidation penetration was investigated. The statistical distribution of grain boundary penetration depth was analyzed. Its effect on high temperature fatigue life are discussed. A model of intermittent micro-ruptures of grain boundary oxide was proposed for high temperature fatigue crack growth. The details of these studies are reported.

Liu, H. W.↗

NASA NTRS2008

Multiscale Modeling of Intergranular Fracture in Aluminum: Constitutive Relation For Interface Debonding

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum-atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum-atomistic interface, and continues its propagation in the atomistic environment. This study is a step towards relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

Yamakov, V.↗

NASA NTRS1975

Assessment of NDE reliability data

Twenty sets of relevant nondestructive test (NDT) reliability data were identified, collected, compiled, and categorized. A criterion for the selection of data for statistical analysis considerations was formulated, and a model to grade the quality and validity of the data sets was developed. Data input formats, which record the pertinent parameters of the defect/specimen and inspection procedures, were formulated for each NDE method. A comprehensive computer program was written and debugged to calculate the probability of flaw detection at several confidence limits by the binomial distribution. This program also selects the desired data sets for pooling and tests the statistical pooling criteria before calculating the composite detection reliability. An example of the calculated reliability of crack detection in bolt holes by an automatic eddy current method is presented.

Yee, B. G. W.↗

NASA NTRS1998

High Temperature Mechanical Characterization of Ceramic Matrix Composites

A high temperature mechanical characterization laboratory has been assembled at NASA Lewis Research Center. One contribution of this work is to test ceramic matrix composite specimens in tension in environmental extremes. Two high temperature tensile testing systems were assembled. The systems were assembled based on the performance and experience of other laboratories and meeting projected service conditions for the materials in question. The systems use frames with an electric actuator and a center screw. A PC based data acquisition and analysis system is used to collect and analyze the data. Mechanical extensometers are used to measure specimen strain. Thermocouples, placed near the specimen, are used to measure the specimen gage section temperature. The system for testing in air has a resistance element furnace with molybdenum disilicide elements and pneumatic grips with water cooling attached to hydraulic alignment devices. The system for testing in an inert gas has a graphite resistance element furnace in a chamber with rigidly mounted, water cooled, hydraulically actuated grips. Unidirectional SiC fiber reinforced reaction bonded Si3N4 and triaxially woven, two dimensional, SiC fiber reinforced enhanced SiC composites were tested in unidirectional tension. Theories for predicting the Young's modulus, modulus near the ultimate strength, first matrix cracking stress, and ultimate strength were applied and evaluated for suitability in predicting the mechanical behavior of SiC/RBSN and enhanced SiC/SiC composites. The SiC/RBSN composite exhibited pseudo tough behavior (increased area under the stress/strain curve) from 22 C to 1500 C. The rule of mixtures provides a good estimate of the Young's modulus of the SiC/RBSN composite using the constituent properties from room temperature to 1440 C for short term static tensile tests in air or nitrogen. The rule of mixtures significantly overestimates the secondary modulus near the ultimate strength. The ACK theory provides the best approximation of the first matrix cracking stress when residual stresses are ignored. The theory of Cao and Thouless, based on Weibull statistics, gave the best prediction for the composite ultimate strength. The enhanced SiC/SiC composite exhibited nonlinear stress/strain behavior from 24 C to 1370 C in air with increased ultimate strain when compared to monolithic SiC. The theory of Yang and Chou with the assumption of a frictional fiber/matrix interface provided the best estimate of the Young's modulus. The theory of Cao and Thouless gave the best estimate for the ultimate strength.

Gyekenyesi, John Z.↗

NASA NTRS2017

Structural Design Parameters for Germanium

The fracture toughness and slow crack growth parameters of germanium supplied as single crystal beams and coarse grain disks were measured. Although germanium is anisotropic (A* 1.7), it is not as anisotropic as SiC, NiAl, or Cu. Thus the fracture toughness was similar on the 100, 110, and 111 planes, however, measurements associated with randomly oriented grinding cracks were 6 to 30 higher. Crack extension in ring loaded disks occurred on the 111 planes due to both the lower fracture energy and the higher stresses on stiff 111 planes. Germanium exhibits a Weibull scale effect, but does not exhibit significant slow crack growth in distilled water. (n 100), implying that design for quasi static loading can be performed with scaled strength statistics. Practical values for engineering design are a fracture toughness of 0.69 0.02 MPam (megapascals per square root meter) and a Weibull modulus of m 6 2. For well ground and reasonable handled coupons, average fracture strength should be greater than 40 megapascals. Aggregate, polycrystalline elastic constants are Epoly 131 gigapascals, vpoly 0.22.

fracture toughness↗

NASA NTRS2016

Effects of Aqueous Solutions on the Slow Crack Growth of Soda-Lime-Silicate Glass

The slow crack growth (SCG) parameters of soda-lime-silicate were measured in distilled and saltwater of various concentrations in order to determine if the presence of salt and the contaminate formation of a weak sodium film affects stress corrosion susceptibility. Past research indicates that solvents affect the rate of crack growth; however, the effects of salt have not been studied. The results indicate a small but statistically significant effect on the SCG parameters A and n at high concentrations; however, for typical engineering purposes, the effect can be ignored.

salt↗

NASA NTRS2018

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

Corbetta, M.↗

NASA NTRS2019

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

stochastic calculus↗

NASA NTRS1992

An energy analysis of crack-initiation and arrest in epoxy

The objective of this work is to study fracture processes such as crack initiation and arrest in epoxy. A compact tension specimen with displacement-controlled loading is employed to observe multiple crack initiations and arrests. The energy release rate at crack initiation is significantly higher than that at crack arrest, as has been observed elsewhere. In this study, the difference between these energy release rates is found to depend on specimen size (scale effect), and is quantitatively related to the fracture surface morphology. The scale effect, similar to that in strength theory, is conventionally attributed to the statistics of defects which control the fracture process. Triangular shaped ripples, deltoids, are formed on the fracture surface of the epoxy during the slow sub-critical crack growth, prior to the smooth mirrorlike surface characteristic of fast cracks. The deltoids are complimentary on the two crack faces which excludes any inelastic deformation from consideration. The deltoids are analogous to the ripples created on a river surface downstream from a small obstacle. However, in spite of the expectation based on this analogy and the observed scale effect, there are no 'defects' at the apex of the deltoids detectable down to the 0.1 micron level. This suggests that the formation of deltoids during the slow process of subcritical crack growth is an intrinsic feature of the fracture process itself, triggered by inhomogeneity of material on a submicron scale. This inhomogeneity may be related to a fluctuation in the cross-link density of the epoxy.

Chudnovsky, A.↗

NASA NTRS2013

Cohesive Modeling of Transverse Cracking in Laminates with a Single Layer of Elements per Ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks

VanDerMeer, Frans P.↗

NASA NTRS1983

Failure during thermal cycling of plasma-sprayed thermal barrier coatings

The thermal cycling behavior of plasma-sprayed ZrO2-12 wt pct Y2O3 coatings was studied. Coatings were produced with and without bond coats of Ni-Cr-Al-Zr and in some cases the substrates were heated to above the optimum temperature prior to spraying. The coatings (attached to the substrate) were thermal cycled to 1200 C and their cracking behavior was followed by acoustic emission (AE) techniques. It was possible to examine the failure mechanisms by statistical analysis of the AE data and to evaluate the influence of preheating and bond coating. It is shown that the AE spectrum changes when a bond coat is used because of the presence of microcracks which, in turn, dissipate energy and improve the coating integrity. The preheating effect is reflected by a decrease in the peak count rate and an increase in the temperature at which AE activity is initiated.

Berndt, C. C.↗

NASA NTRS1988

Kuhn-Tucker optimization based reliability analysis for probabilistic finite elements

The fusion of probability finite element method (PFEM) and reliability analysis for fracture mechanics is considered. Reliability analysis with specific application to fracture mechanics is presented, and computational procedures are discussed. Explicit expressions for the optimization procedure with regard to fracture mechanics are given. The results show the PFEM is a very powerful tool in determining the second-moment statistics. The method can determine the probability of failure or fracture subject to randomness in load, material properties and crack length, orientation, and location.

Liu, W. K.↗

NASA NTRS1991

A statistical approach to the brittle fracture of a multi-phase solid

A stochastic damage model is proposed to quantify the inherent statistical distribution of the fracture toughness of a brittle, multi-phase solid. The model, based on the macrocrack-microcrack interaction, incorporates uncertainties in locations and orientations of microcracks. Due to the high concentration of microcracks near the macro-tip, a higher order analysis based on traction boundary integral equations is formulated first for an arbitrary array of cracks. The effects of uncertainties in locations and orientations of microcracks at a macro-tip are analyzed quantitatively by using the boundary integral equations method in conjunction with the computer simulation of the random microcrack array. The short range interactions resulting from surrounding microcracks closet to the main crack tip are investigated. The effects of microcrack density parameter are also explored in the present study. The validity of the present model is demonstrated by comparing its statistical output with the Neville distribution function, which gives correct fits to sets of experimental data from multi-phase solids.

Liu, W. K.↗

NASA NTRS2011

Statistical Analysis of an Infrared Thermography Inspection of Reinforced Carbon-Carbon

Each piece of flight hardware being used on the shuttle must be analyzed and pass NASA requirements before the shuttle is ready for launch. One tool used to detect cracks that lie within flight hardware is Infrared Flash Thermography. This is a non-destructive testing technique which uses an intense flash of light to heat up the surface of a material after which an Infrared camera is used to record the cooling of the material. Since cracks within the material obstruct the natural heat flow through the material, they are visible when viewing the data from the Infrared camera. We used Ecotherm, a software program, to collect data pertaining to the delaminations and analyzed the data using Ecotherm and University of Dayton Log Logistic Probability of Detection (POD) Software. The goal was to reproduce the statistical analysis produced by the University of Dayton software, by using scatter plots, log transforms, and residuals to test the assumption of normality for the residuals.

Comeaux, Kayla↗