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NASA NTRS1987

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Gyekenyesi, J. P.↗

NASA NTRS1972

Analysis of stress-rupture data from S-glass composites.

Both composite and free strands have been tested to study matrix effectiveness. Glass from different lots were used, and processing parameters were varied to demonstrate the effects of material variability. The statistical patterns that emerge from these experiments show that lifetime distributions are characteristically skewed. As a class, the lifetime distributions are well approximated by the reduced form of the Weibull distribution. The strength retention data display little early degradation. The retained-strength distributions can also be classed as Weibull distributions. A statistical model applied to the data gives predictions of progressive failure, strength retention path, and expected life for two basic types of internal fracture processes.

Robinson, E. Y.↗

NASA NTRS1990

Calculation of Weibull strength parameters, Batdorf flaw density constants and related statistical quantities using PC-CARES

This manual describes the operation and theory of the PC-CARES (Personal Computer-Ceramic Analysis and Reliability Evaluation of Structures) computer program for the IBM PC and compatibles running PC-DOS/MS-DOR OR IBM/MS-OS/2 (version 1.1 or higher) operating systems. The primary purpose of this code is to estimate Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities. Included in the manual is the description of the calculation of shape and scale parameters of the two-parameter Weibull distribution using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. The methods for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull line, as well as the techniques for calculating the Batdorf flaw-density constants are also described.

Szatmary, Steven A.↗

NASA NTRS1992

Mechanical properties of silicate glasses exposed to a low-Earth orbit

The effects of a 5.8 year exposure to low earth orbit environment upon the mechanical properties of commercial optical fused silica, low iron soda-lime-silica, Pyrex 7740, Vycor 7913, BK-7, and the glass ceramic Zerodur were examined. Mechanical testing employed the ASTM-F-394 piston on 3-ball method in a liquid nitrogen environment. Samples were exposed on the Long Duration Exposure Facility (LDEF) in two locations. Impacts were observed on all specimens except Vycor. Weibull analysis as well as a standard statistical evaluation were conducted. The Weibull analysis revealed no differences between control samples and the two exposed samples. We thus concluded that radiation components of the Earth orbital environment did not degrade the mechanical strength of the samples examined within the limits of experimental error. The upper bound of strength degradation for meteorite impacted samples based upon statistical analysis and observation was 50 percent.

Wiedlocher, David E.↗

DOE OSTI2025

Statistical fracture behavior of doped UO 2 using a ball-on-ring equibiaxial flexure test method

Metal oxide dopants, such as titanium and chromium oxides, have garnered considerable attention for their potential to increase grain size (≥ 30 µm) in UO 2 fuel, purportedly enhancing fission gas retention during reactor operation. Fuel performance is significantly impacted by fuel fracture behavior, so it is important to understand the effects of enhanced grain size and dopant content on UO 2 fuel fracture. UO 2 pellets were doped with 0.1 wt% TiO 2 and 0.3 wt% Cr 2 O 3 to alter density and grain size. Inductively coupled plasma mass spectroscopy measured dopant levels pre- and post-sintering. X-ray diffraction revealed lattice changes and microstrain via Rietveld refinement. Field emission scanning electron microscopy determined grain sizes of approximately 30 µm for TiO 2 doping and 7 µm for Cr 2 O 3 doping. Transverse rupture strength tests were performed on over 30 samples per dataset to obtain characteristic strength and Weibull modulus. Results indicate no statistical difference in fracture strength between 0.1 wt% TiO 2 doped UO 2 and undoped UO 2 , while 0.3 wt% Cr 2 O 3 doped UO 2 exhibited a 20% decrease in fracture strength. Doped UO 2 samples also showed reduced Weibull modulus compared to undoped UO 2 , suggesting increased scatter in fracture strength. This study's findings suggest that titanium and chromium oxide doping in UO 2 , regardless of grain size, induce residual stresses, decreasing fracture strength and increasing variability in fracture behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1987

Weibull Distribution From Interval Inspection Data

Most likely failure sequence assumed. Memorandum discusses application of Weibull distribution to statistics of failures of turbopump blades. Is generalization of well known exponential random probability distribution and useful in describing component-failure modes including aging effects. Parameters found from experimental data by method of maximum likelihood.

Rheinfurth, Mario H.↗

NASA NTRS1971

Estimating Weibull parameters for materials

The statistical analysis of strength and fracture of materials in general, with application to fiber composites are discussed. The weakest link model is considered in a fairly general form, and the resulting equations are demonstrated by using a Weibull distribution for flaws. This distribution appears naturally in a variety of problems, and therefore additional attention is devoted to analysis and statistical estimation connected with this distribution. Special working charts are included to facilitate interpretation of observed data and estimation of parameters. Implications of the size effect are considered for various kinds of flaw distributions. Failure and damage in a fiber-reinforced system are described. Some useful graphs are included for predicting the strength of such a system. Recent data on organic-fiber (PRD 49) composite material is analyzed by the Weibull distribution with the methods presented.

Robinson, E. Y.↗

NASA NTRS1977

A Weibull characterization for tensile fracture of multicomponent brittle fibers

A statistical characterization for multicomponent brittle fibers in presented. The method, which is an extension of usual Weibull distribution procedures, statistically considers the components making up a fiber (e.g., substrate, sheath, and surface) as separate entities and taken together as in a fiber. Tensile data for silicon carbide fiber and for an experimental carbon-boron alloy fiber are evaluated in terms of the proposed multicomponent Weibull characterization.

Barrows, R. G.↗

NASA NTRS1988

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

Pai, Shantaram S.↗

NASA NTRS1989

Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics

The calculation of shape and scale parametes of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by using the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program.

Shantaram, S. Pai↗

NASA NTRS1993

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗

NASA NTRS1977

Lifetimes of fiber composites under sustained tensile loading

Results are presented for a study intended to summarize lifetime data on several fiber/epoxy composite materials subjected to sustained uniaxial tensile loading, to report preliminary results of an accelerated test method for predicting the life of simple composites, and to describe related work in progress on pressure vessels and other filament-wound structures. The lifetime performance of the tested composites was compared by plotting the percent of ultimate strength (applied fiber stress normalized with respect to fiber failure stress in a composite) versus lifetime. In terms of performance in long-term tensile applications, the tested composites are ranked in the following order: graphite/epoxy, Be wire/epoxy, Aramid/epoxy, and S-glass/epoxy. The accelerated test using temperature and stress to simulate the passage of time proves to be encouraging, at least in the case of the Aramid/epoxy composite. The potential of a statistical analysis based on Weibull distribution analyses or a power law relationship is demonstrated.

Chiao, T. T.↗

NASA NTRS1978

Rolling element fatigue testing of gear materials

Rolling element fatigue lives of eleven alloys were evaluated. The eleven alloys studied were three nitriding alloys (Super Nitralloy, Nitralloy 135, and Nitralloy N), four case carburizing alloys (AISI 9310, CBS 600, CBS 1000M and Vasco X-2), and four throughhardening alloys (Vasco Matrix II,AISI W-1, AISI S-2 and AISI O-2). Several different heat treatments and/or melting processes were studied on the three carburizing alloy steels. Metallurgical analyses were made before and after the RC rig tests. Test data were statistically analyzed using the Weibull distribution function. B-10 lives were compared versus VIM-VAR AISI M-50 and carburized VAR AISI 9310, as reference alloys.

Nahm, A. H.↗

NASA NTRS1990

Tensile adhesion testing methodology for thermally sprayed coatings

The structure of thermally sprayed coatings consists of lamellae which are oriented parallel to the substrate surface. The lamellae separate and fracture by distinctive mechanisms which are reflected in the failure morphology, and these may be described as adhesive (between the coating and substrate), cohesive (within the coating), or mixed mode. There is a large variability in the failure stress for any nominally identical group of coatings. A lower bound for the fracture toughness of alumina coatings can be calculated as 0.2 MNm exp -3/2. The coating strength values may also be treated as belonging to the statistical distribution of the Weibull function. The Weibull modulus of the coating strength varied from 1.4 to 3.8. This analysis infers that the flaw size within coatings is highly variable and that the flaws are nonuniformly dispersed. The present work focuses on the question of whether tensile adhesion tests are an appropriate testing method for thermally sprayed materials.

Berndt, Christopher C.↗

NASA NTRS1991

Comparison of Weibull strength parameters from flexure and spin tests of brittle materials

Fracture data from five series of four point bend tests of beam and spin tests of flat annular disks were reanalyzed. Silicon nitride and graphite were the test materials. The experimental fracture strengths of the disks were compared with the predicted strengths based on both volume flaw and surface flaw analyses of four point bend data. Volume flaw analysis resulted in a better correlation between disks and beams in three of the five test series than did surface flaw analysis. The Weibull (moduli) and characteristic gage strengths for the disks and beams were also compared. Differences in the experimental Weibull slopes were not statistically significant. It was shown that results from the beam tests can predict the fracture strength of rotating disks.

Holland, Frederic A., Jr.↗

NASA NTRS2011

Rolling-Element Fatigue Testing and Data Analysis - A Tutorial

In order to rank bearing materials, lubricants and other design variables using rolling-element bench type fatigue testing of bearing components and full-scale rolling-element bearing tests, the investigator needs to be cognizant of the variables that affect rolling-element fatigue life and be able to maintain and control them within an acceptable experimental tolerance. Once these variables are controlled, the number of tests and the test conditions must be specified to assure reasonable statistical certainty of the final results. There is a reasonable correlation between the results from elemental test rigs with those results obtained with full-scale bearings. Using the statistical methods of W. Weibull and L. Johnson, the minimum number of tests required can be determined. This paper brings together and discusses the technical aspects of rolling-element fatigue testing and data analysis as well as making recommendations to assure quality and reliable testing of rolling-element specimens and full-scale rolling-element bearings.

Vlcek, Brian L.↗

DOE OSTI2022

Equibiaxial Flexure Strength of a Superfine-Grained Nuclear Graphite

The strength of advanced graphite is reported in accordance with ASTM D7846-16 using a two-parameter Weibull distribution for uniaxial strength testing. The rule of thumb for Weibull distributions is to use a minimum of 30 strength measurements to have a high level of confidence in the Weibull characteristic strength and the Weibull modulus. These large sample sets for statistical confidence are easily obtained for as-manufactured graphite, but determination of the Weibull two-factor parameters on graphite that has been exposed to neutron irradiation is nearly impossible due to irradiation testing restraints on specimen size and space limitations in test reactors for the accommodation of specimens. These restrictions have resulted in irradiation programs that use sub-sized specimens to measure uniaxial strength change, but the specimen geometries still hinder the number of replicate specimens for each irradiation condition. In contrast, this work used an advanced ceramic standard, ASTM C1499-05, as the foundation for equibiaxial strength testing of a superfine-grained nuclear graphite to investigate the irradiation-induced strength change and any changes to the two-parameter Weibull distribution. The goal was to investigate the effect of specimen size on the two-parameter Weibull distribution parameters in support of the small specimens and geometry desired for irradiation. A study of the effect of a reduced sample population was also undertaken to investigate the reliability of using the two-parameter Weibull distribution to study changes to the materials properties caused by neutron irradiation damage. The results of this work suggest that these equibiaxial specimens would be ideal for statistically significant studies of the effects of irradiation on the Weibull characteristic strength (but not the modulus) and for providing a method for surveillance specimen campaigns for future operating commercial reactors.

Campbell, Anne↗

NASA NTRS1988

Statistical analysis of censored motion sickness latency data using the two-parameter Weibull distribution

The suitability of the two-parameter Weibull distribution for describing highly censored cat motion sickness latency data was evaluated by estimating the parameters with the maximum likelihood method and testing for goodness of fit with the Kolmogorov-Smirnov statistic. A procedure for determining confidence levels and testing for significance of the difference between Weibull parameters is described. Computer programs for these procedures may be obtained from an archival source.

Park, Won J.↗