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NASA NTRS1994

Using Finite-Element Analysis In Estimating Reliability

Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.

Zaretsky, Erwin V.↗

DOE OSTI2021

Ball-on-ring test validation for equibiaxial flexural strength testing of engineered ceramics

The validation of a ball-on-ring, equibiaxial flexural strength method to obtain the transverse rupture strength (TRS) of right cylindrical ceramic specimens was performed in this study. Validation of the test method was achieved using commercially available engineered high purity alumina disks and finite element (FE) model analysis. The validated fixture was then used to obtain the TRS and Weibull statistical analysis of MgO-partially stabilized zirconia (MSZ) and Y 2 O 3 -partially stabilized zirconia (YSZ) ceramic disks. TRS data for alumina, MSZ, and YSZ agreed with the TRS values reported in the literature. A statistically relevant number of samples (N > 30) for each material were tested to allow for a Weibull statistical analysis. Weibull parameters for these materials were within the expected values for engineered ceramics. The characteristic strength for alumina, MSZ, and YSZ were determined to be 289, 786, and 814 MPa, respectively. The Weibull modulus was determined between 10 and 25 for each material, which is typical of engineered ceramics. In addition, FE model results were in close agreement with experimental fracture values for the three ceramic materials tested in this study.

36 MATERIALS SCIENCE↗

NASA NTRS2002

Software for Statistical Analysis of Weibull Distributions with Application to Gear Fatigue Data: User Manual with Verification

The Weibull distribution has been widely adopted for the statistical description and inference of fatigue data. This document provides user instructions, examples, and verification for software to analyze gear fatigue test data. The software was developed presuming the data are adequately modeled using a two-parameter Weibull distribution. The calculations are based on likelihood methods, and the approach taken is valid for data that include type 1 censoring. The software was verified by reproducing results published by others.

Krantz, Timothy L.↗

NASA NTRS2002

Software for Statistical Analysis of Weibull Distributions with Application to Gear Fatigue Data: User Manual with Verification

The Weibull distribution has been widely adopted for the statistical description and inference of fatigue data. This document provides user instructions, examples, and verification for software to analyze gear fatigue test data. The software was developed presuming the data are adequately modeled using a two-parameter Weibull distribution. The calculations are based on likelihood methods, and the approach taken is valid for data that include type I censoring. The software was verified by reproducing results published by others.

Kranz, Timothy L.↗

NASA NTRS2014

A Reliability Model for Ni-BaTiO3-Based (BME) Ceramic Capacitors

The evaluation of multilayer ceramic capacitors (MLCCs) with base-metal electrodes (BMEs) for potential NASA space project applications requires an in-depth understanding of their reliability. The reliability of an MLCC is defined as the ability of the dielectric material to retain its insulating properties under stated environmental and operational conditions for a specified period of time t. In this presentation, a general mathematic expression of a reliability model for a BME MLCC is developed and discussed. The reliability model consists of three parts: (1) a statistical distribution that describes the individual variation of properties in a test group of samples (Weibull, log normal, normal, etc.), (2) an acceleration function that describes how a capacitors reliability responds to external stresses such as applied voltage and temperature (All units in the test group should follow the same acceleration function if they share the same failure mode, independent of individual units), and (3) the effect and contribution of the structural and constructional characteristics of a multilayer capacitor device, such as the number of dielectric layers N, dielectric thickness d, average grain size r, and capacitor chip size S. In general, a two-parameter Weibull statistical distribution model is used in the description of a BME capacitors reliability as a function of time. The acceleration function that relates a capacitors reliability to external stresses is dependent on the failure mode. Two failure modes have been identified in BME MLCCs: catastrophic and slow degradation. A catastrophic failure is characterized by a time-accelerating increase in leakage current that is mainly due to existing processing defects (voids, cracks, delamination, etc.), or the extrinsic defects. A slow degradation failure is characterized by a near-linear increase in leakage current against the stress time; this is caused by the electromigration of oxygen vacancies (intrinsic defects). The two identified failure modes follow different acceleration functions. Catastrophic failures follow the traditional power-law relationship to the applied voltage. Slow degradation failures fit well to an exponential law relationship to the applied electrical field. Finally, the impact of capacitor structure on the reliability of BME capacitors is discussed with respect to the number of dielectric layers in an MLCC unit, the number of BaTiO3 grains per dielectric layer, and the chip size of the capacitor device.

reliability↗

NASA NTRS1995

Real time acousto-ultrasonic NDE technique for monitoring damage in ceramic composites under dynamic loads

Research effort was directed towards developing a near real-time, acousto-ultrasonic (AU), nondestructive evaluation (NDE) tool to study the failure mechanisms of ceramic composites. Progression of damage is monitored in real-time by observing the changes in the received AU signal during the actual test. During the real-time AU test, the AU signals are generated and received by the AU transducers attached to the specimen while it is being subjected to increasing quasi-static loads or cyclic loads (10 Hz, R = 1.0). The received AU signals for 64 successive pulses were gated in the time domain (T = 40.96 micro sec) and then averaged every second over ten load cycles and stored in a computer file during fatigue tests. These averaged gated signals are representative of the damage state of the specimen at that point of its fatigue life. This is also the first major attempt in the development and application of real-time AU for continuously monitoring damage accumulation during fatigue without interrupting the test. The present work has verified the capability of the AU technique to assess the damage state in silicon carbide/calcium aluminosilicate (SiC/CAS) and silicon carbide/ magnesium aluminosilicate (SiC/MAS) ceramic composites. Continuous monitoring of damage initiation and progression under quasi-static ramp loading in tension to failure of unidirectional and cross-ply SiC/CAS and quasi-isotropic SiC/MAS ceramic composite specimens at room temperature was accomplished using near real-time AU parameters. The AU technique was shown to be able to detect the stress levels for the onset and saturation of matrix cracks, respectively. The critical cracking stress level is used as a design stress for brittle matrix composites operating at elevated temperatures. The AU technique has found that the critical cracking stress level is 10-15% below the level presently obtained for design purposes from analytical models. An acousto-ultrasonic stress-strain response (AUSSR) model for unidirectional and cross-ply ceramic composites was formulated. The AUSSR model predicts the strain response to increasing stress levels using real-time AU data and classical laminated plate theory. The Weibull parameters of the AUSSR model are used to calculate the design stress for thermo-structural applications. Real-time AU together with the AUSSR model was used to study the failure mechanisms of SiC/CAS ceramic composites under static and fatigue loading. An S-N curve was generated for a cross-ply SiC/CAS ceramic composite material. The AU results are corroborated and complemented by other NDE techniques, namely, in-situ optical microscope video recordings and edge replication.

Tiwari, Anil↗

NASA NTRS2018

Weibull-Based Stochastic Simulation of Mud-Crack Damage Formation in an Environmental Barrier Coating

The integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC (Micromechanics Analysis Code/Generalized Method of Cells) multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button-sized disk-shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300 degrees Centigrade to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.

Residual Tensile Stress↗

DOE OSTI2021

A time-dependent chloride diffusion model for predicting initial corrosion time of reinforced concrete with slag addition

The effect of granulated blast furnace slag (GBFS) addition on the threshold chloride concentration (TCC) for rebar corrosion was investigated. A modified diffusion model, coupled with a time-dependent effective diffusion coefficient and surface chloride concentration, was proposed to predict the chloride profile. The corrosion initiation time was estimated based on the model predictions and the measured TCC. The results indicate that adding GBFS decreases the TCC by lowering the pH value of the pore solution. The evolution of corrosion potential and current density is found to obey a 3-parameter Weibull distribution. MIP tests show that adding GBFS contributes to refinement of pore structure by decreasing the fraction of large capillary pores. The time-dependent model exhibits good predictive strength and helps understand how GBFS addition delays the corrosion initiation by retarding the chloride diffusion, though a lower TCC is obtained.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A method for predicting failure statistics for steady state elevated temperature structural components

This paper presents the initial development of a high temperature life prediction method that accounts for the variability in the material properties of Grade 91 steel. The method accounts for material variability by fitting a variable 3-parameter Weibull distribution to experimental rupture data and accounts for the variability of creep deformation on the steady-state stresses via a Monte Carlo approach. To ensure reasonable computational times, the model represents the material as an extremely viscous Stokes fluid with a non-Newtonian viscosity, therefore solving the stress relaxation problem with a steady, static, instead of transient, analysis. Furthermore, the complete statistical analysis combines this model for creep deformation with a probabilistic model for creep rupture to evaluate the probability of premature failure for a set of sample problems, comparing the predicted failure statistics to the design life predicted by the ASME Boiler and Pressure Vessel Code rules.

42 ENGINEERING↗

DOE OSTI2022

Stress-controlled fatigue of HfNbTaTiZr high-entropy alloy and associated deformation and fracture mechanisms

The stress-controlled fatigue tests are carried out at a stress ratio of 0.1 and a frequency of 10 Hz, and span both low-cycle and high-cycle regimes by varying the applied stress amplitudes. The high-cycle fatigue regime gives a fatigue strength of 497 MPa and a fatigue ratio of 0.44. At equivalent conditions, the alloy's fatigue strength is greater than all other high-entropy alloys (HEAs) with reported high-cycle fatigue data, dilute body-centered cubic alloys, and many structural alloys such as steels, titanium alloys, and aluminum alloys. Through in-depth analyses of crack-propagation trajectories, fracture-surface morphologies and deformation plasticity by means of various microstructural analysis techniques and theoretical frameworks, the alloy's remarkable fatigue resistance is attributed to delayed crack initiation in the high-cycle regime, which is achieved by retarding the formation of localized persistent slip bands, and its good resistance to crack propagation in the low-cycle regime, which is accomplished by intrinsic toughening backed up by extrinsic toughening. Additionally, the stochastic nature of the fatigue data is neatly captured with a 2-parameter Weibull model.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Flexural strength of a conventionally processed and additively manufactured debased 94% alumina

Mechanical strength of a 94 wt% debased alumina was measured using ASTM-C1161 specimens fabricated via conventional and lithography-based ceramic manufacturing (LCM) methods. The effects of build orientation and a 1500°C wet hydrogen fire added to the LCM firing sequence on strength were evaluated. Additionally, a Weibull fit to the conventional flexural specimen data yielded 20 and 356 MPa for the modulus and characteristic strength, respectively. Weibull fits of the data from the LCM specimens yielded moduli between 7.5 and 11.3 and characteristics strengths between 333 and 339 MPa. A Weibull fit to data from LCM specimens subjected to the wet hydrogen fire yielded 14.2 and 376 MPa for the modulus and characteristic strength, respectively. The 95% confidence intervals for all Weibull parameters are reported. Average Archimedes bulk densities of LCM and conventional specimens were 3.732 and 3.730 g/cm 3 , respectively. Process dependent differences in surface morphology were observed in scanning electron microscope (SEM) images of specimen surfaces. SEM images of LCM specimen cross-sections showed alumina grain texture dependent on build direction, but no evidence of porosity concentrated in planes between printed layers. Fracture surfaces of LCM and conventionally processed specimens revealed hackle lines and mirror regions indicative of fracture initiation at the sample surface rather than the interior.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Initial development of a high temperature life prediction method directly accounting for variability in material properties

This report presents the initial development of a life prediction method that accounts for the variability of the material properties in Grade 91 steel. We account for material variability by both fitting a variable 3-parameter Weibull distribution to the rupture data of the material and by quantifying the effect that the creep deformation properties have on stresses via a Monte Carlo approach. To ensure a reasonable time frame when applying Monte Carlo to the creep stress, we propose a methodology that models the material as an extremely viscous Stokes flow with a non-Newtonian viscosity, therefore solving the problem in a single step. We use the final probabilistic model for structural failure developed in this document to evaluate a Flat Head Vessel designed with the Section III, Division 5 ASME Boiler Pressure and Vessel Code rules with a 100,000h design life and assess its probability of premature failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1973

Modern methodology of designing target reliability into rotating mechanical components

Experimentally determined distributional cycles-to-failure versus maximum alternating nominal strength (S-N) diagrams, and distributional mean nominal strength versus maximum alternating nominal strength (Goodman) diagrams are presented. These distributional S-N and Goodman diagrams are for AISI 4340 steel, R sub c 35/40 hardness, round, cylindrical specimens 0.735 in. in diameter and 6 in. long with a circumferential groove 0.145 in. radius for a theoretical stress concentration = 1.42 and 0.034 in. radius for a stress concentration = 2.34. The specimens are subjected to reversed bending and steady torque in specially built, three complex-fatigue research machines. Based on these results, the effects on the distributional S-N and Goodman diagrams and on service life of superimposing steady torque on reversed bending are established, as well as the effect of various stress concentrations. In addition a computer program for determining the three-parameter Weibull distribution representing the cycles-to-failure data, and two methods for calculating the reliability of components subjected to cumulative fatigue loads are given.

Kececioglu, D. B.↗

NASA NTRS1981

Statistical distribution of mechanical properties for three graphite-epoxy material systems

Graphite-epoxy composites are playing an increasing role as viable alternative materials in structural applications necessitating thorough investigation into the predictability and reproducibility of their material strength properties. This investigation was concerned with tension, compression, and short beam shear coupon testing of large samples from three different material suppliers to determine their statistical strength behavior. Statistical results indicate that a two Parameter Weibull distribution model provides better overall characterization of material behavior for the graphite-epoxy systems tested than does the standard Normal distribution model that is employed for most design work. While either a Weibull or Normal distribution model provides adequate predictions for average strength values, the Weibull model provides better characterization in the lower tail region where the predictions are of maximum design interest. The two sets of the same material were found to have essentially the same material properties, and indicate that repeatability can be achieved.

Reese, C.↗

NASA NTRS1985

Weibull distribution based on maximum likelihood with interval inspection data

The two Weibull parameters based upon the method of maximum likelihood are determined. The test data used were failures observed at inspection intervals. The application was the reliability analysis of the SSME oxidizer turbine blades.

Rheinfurth, M. H.↗

NASA NTRS1988

Monolithic ceramic analysis using the SCARE program

The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.

Manderscheid, Jane M.↗

NASA NTRS1988

Computerized life and reliability modelling for turboprop transmissions

A generalized life and reliability model is presented for parallel shaft geared prop-fan and turboprop aircraft transmissions. The transmission life and reliability model is a combination of the individual reliability models for all the bearings and gears in the main load paths. The bearing and gear reliability models are based on classical fatigue theory and the two parameter Weibull failure distribution. A computer program was developed to calculate the transmission life and reliability. The program is modular. In its present form, the program can analyze five different transmission arrangements. However, the program can be modified easily to include additional transmission arrangements. An example is included which compares the life of a compound two-stage transmission with the life of a split-torque, parallel compound two-stage transmission, as calculated by the computer program.

Savage, M.↗

NASA NTRS1988

Computerized life and reliability modelling for turboprop transmissions

Savage, M.↗