Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Weibull Distribution”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws

Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software

Nemeth, Noel↗
NASA NTRS2000

Rolling Bearing Life Prediction-Past, Present, and Future

Comparisons were made between the life prediction formulas of Lundberg and Palmgren, Ioannides and Harris, and Zaretsky and full-scale ball and roller bearing life data. The effect of Weibull slope on bearing life prediction was determined. Life factors are proposed to adjust the respective life formulas to the normalized statistical life distribution of each bearing type. The Lundberg-Palmgren method resulted in the most conservative life predictions compared to Ioannides and Harris, and Zaretsky methods which produced statistically similar results. Roller profile can have significant effects on bearing life prediction results. Roller edge loading can reduce life by as much as 98 percent. The resultant predicted life not only depends on the life equation used but on the Weibull slope assumed, the least variation occurring with the Zaretsky equation. The load-life exponent p of 10/3 used in the American National Standards Institute (ANSI)/American Bearing Manufacturers Association (ABMA)/International Organization for Standardization (ISO) standards is inconsistent with the majority roller bearings designed and used today.

Zaretsky, E V↗
NASA NTRS1989

Improved silicon carbide for advanced heat engines

The development of high strength, high reliability silicon carbide parts with complex shapes suitable for use in advanced heat engines is studied. Injection molding was the forming method selected for the program because it is capable of forming complex parts adaptable for mass production on an economically sound basis. The goals were to reach a Weibull characteristic strength of 550 MPa (80 ksi) and a Weibull modulus of 16 for bars tested in four-point loading. Statistically designed experiments were performed throughout the program and a fluid mixing process employing an attritor mixer was developed. Compositional improvements in the amounts and sources of boron and carbon used and a pressureless sintering cycle were developed which provided samples of about 99 percent of theoretical density. Strengths were found to improve significantly by annealing in air. Strengths in excess of 550 MPa (80 ksi) with Weibull modulus of about 9 were obtained. Further improvements in Weibull modulus to about 16 were realized by proof testing. This is an increase of 86 percent in strength and 100 percent in Weibull modulus over the baseline data generated at the beginning of the program. Molding yields were improved and flaw distributions were observed to follow a Poisson process. Magic angle spinning nuclear magnetic resonance spectra were found to be useful in characterizing the SiC powder and the sintered samples. Turbocharger rotors were molded and examined as an indication of the moldability of the mixes which were developed in this program.

Whalen, Thomas J.↗
NASA NTRS1995

Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models

The general goal of this project is to establish design protocols that enable the engineer to analyze and predict certain types of behavior in ceramic composites. Sections of the final report addresses the following: Description of the Problem that Motivated the Technology Development, Description of the New Technology that was Developed, Unique and Novel Features of the Technology and Results/Benefits of Application (year by year accomplishments), and Utilization of New Technology in Non-Aerospace Applications. Activities for this reporting period included the development of a design analysis as part of a cooperative agreement with general Electric Aircraft Engines. The effort focused on modifying the Toughened Ceramics Analysis and Reliability Evaluation of Structures (TCARES) algorithm for use in the design of engine components fabricated from NiAl. Other activities related to the development of an ASTM standard practice for estimating Weibull parameters. The standard focuses on the evaluation and reporting of uniaxial strength data, and the estimation of probability distribution parameters for ceramics which fail in a brittle fashion.

Duffy, Stephen F.↗
NASA NTRS1988

Strength distribution in commercial silicon carbide materials

Four-point flexural strength testing has been conducted in order to establish the baseline strength and reliability of four different commercial SiC types, in conjunction with reliable Weibull modulus values. Average strength of the samples ranged from 380 to 482 MPa at room temperature and 307 to 470 MPa at 1370 C. The strength scatter reflects the effect of flaw variability, which must be minimized to improve reliability in sintered SiC.

Dutta, Sunil↗
NASA NTRS1992

Extreme value statistics analysis of fracture strengths of a sintered silicon nitride failing from pores

Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.

Chao, Luen-Yuan↗
DOE OSTI2025

Additive manufacturing of mullite ceramic by digital light processing

Mullite material was successfully additively manufactured using digital light processing (DLP). The printed geometry involves a one-step process of pyrolysis, de-binding, and sintering under a plain atmosphere to achieve an average of 76 % ceramic yield and linear shrinkage of 12 %. Furthermore, the thermal profile was carefully controlled to obtain consistent phases in which the XRD shows a mullite phase. Here, in addition, the Weibull analysis was conducted on the sintered flexural specimens, showing a Weibull modulus (m) of 13.05 with a characteristic strength (σ 0 ) of 94.96 MPa. Synchrotron microtomography was performed on the sintered specimens, which showed two distinct porosity distributions (small and large). Large porosity (non-spherical elongated) is the primary cause of decreased material strength, while small porosity (spherical) is the sintering product. The measured thermal conductivity of the specimens was in the range of 2.7–3.1 W/m∙k and decreased with an increase in temperature. Lastly, large-scale prototypes were printed concurrently with a fine resolution of 25 μm without any compromise on the predetermined design and structure.

Additive manufacturing↗
NASA NTRS1992

Long-life assessment of graphite epoxy materials for Space Station Freedom pressure vessels

Graphite/epoxy composite overwrapped pressure vessels are being considered for use on Space Station Freedom because of their light weight and high efficiency. These composite pressure vessels weigh roughly one-third of comparable all-metal aluminum pressure vessels, and could result in a 15,000-lb weight saving for the propulsion and fluid management and distribution systems. These vessels must resist failures under sustained pressure loads for crew safety considerations and adequate protection of the space structure during their 30-yr life. Weibull statistical analysis techniques have been applied, and a model developed, for predicting long-term stress-rupture behavior based on published short-term test data on composite strands and pressure vessels. Graphite/epoxy materials are calculated to have a 99.99-percent probability of surviving stress rupture for 30 yr under a sustained load of 50 percent ultimate failure strength. Stress-rupture lifetimes are predicted to increase as the size of the pressure vessels increases in support of the viscoelastic load-transfer mechanism proposed for stress rupture of fiber/epoxy composite materials.

Thomas, Donald A.↗
NASA NTRS1985

Improved silicon nitride for advanced heat engines

The AiResearch Casting Company baseline silicon nitride (92 percent GTE SN-502 Si sub 3 N sub 4 plus 6 percent Y sub 2 O sub 3 plus 2 percent Al sub 2 O sub 3) was characterized with methods that included chemical analysis, oxygen content determination, electrophoresis, particle size distribution analysis, surface area determination, and analysis of the degree of agglomeration and maximum particle size of elutriated powder. Test bars were injection molded and processed through sintering at 0.68 MPa (100 psi) of nitrogen. The as-sintered test bars were evaluated by X-ray phase analysis, room and elevated temperature modulus of rupture strength, Weibull modulus, stress rupture, strength after oxidation, fracture origins, microstructure, and density from quantities of samples sufficiently large to generate statistically valid results. A series of small test matrices were conducted to study the effects and interactions of processing parameters which included raw materials, binder systems, binder removal cycles, injection molding temperatures, particle size distribution, sintering additives, and sintering cycle parameters.

Yeh, H. C.↗
NASA NTRSDate not supplied

Microscale Constitutive Model Sensitivity on Multiscale Modeling of Fiber Reinforced Composites

Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to microscale variability during manufacturing, making failure predictions difficult. The impact microscale variability has on macroscale mechanical response is difficult to predict due to the computational efficiency needed to simulate many, large, high fidelity, microscale models. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using an efficient micromechanical. Mesoscale models were created where element sizes equaled microstructure size, and properties were assigned through sampling of microscale simulation results. First, this study showed the effect of using Weibull scaling on constituent matrix strength on macroscale response. Then, a comparison was made between different element sizes and experiments. Finally, model dimensions were fixed, and the effect of randomly distributed local properties alone was examined. Results showed that the scatter of strength and stiffness in the experiments could be predicted well using images of the microscale fiber morphologies and that using stochastic properties produced a 3% coefficient of variation of strength for all experiments.

statistical microstructure↗
NASA NTRS1988

Improved silicon carbide for advanced heat engines

This is the third annual technical report for the program entitled, Improved Silicon Carbide for Advanced Heat Engines, for the period February 16, 1987 to February 15, 1988. The objective of the original program was the development of high strength, high reliability silicon carbide parts with complex shapes suitable for use in advanced heat engines. Injection molding is the forming method selected for the program because it is capable of forming complex parts adaptable for mass production on an economically sound basis. The goals of the revised program are to reach a Weibull characteristic strength of 550 MPa (80 ksi) and a Weibull modulus of 16 for bars tested in 4-point loading. Two tasks are discussed: Task 1 which involves materials and process improvements, and Task 2 which is a MOR bar matrix to improve strength and reliability. Many statistically designed experiments were completed under task 1 which improved the composition of the batches, the mixing of the powders, the sinter and anneal cycles. The best results were obtained by an attritor mixing process which yielded strengths in excess of 550 MPa (80 ksi) and an individual Weibull modulus of 16.8 for a 9-sample group. Strengths measured at 1200 and 1400 C were equal to the room temperature strength. Annealing of machined test bars significantly improved the strength. Molding yields were measured and flaw distributions were observed to follow a Poisson process. The second iteration of the Task 2 matrix experiment is described.

Whalen, Thomas J.↗
DOE OSTI2025

Federated Learning for Efficient Condition Monitoring and Anomaly Detection in Industrial Cyber-Physical Systems

Detecting and localizing anomalies in cyber-physical systems (CPS) has become increasingly challenging as systems grow in complexity, particularly due to varying sensor reliability and node failures in distributed environments. While federated learning (FL) offers a foundation for distributed model training, existing approaches lack mechanisms to handle these CPS-specific challenges. This paper presents an enhanced FL framework that introduces three key innovations: adaptive model aggregation based on sensor reliability, dynamic node selection for resource optimization, and Weibull-based checkpointing for fault tolerance. Our framework enables reliable condition monitoring while addressing the computational and reliability challenges of industrial CPS deployments. Experiments on NASA Bearing and Hydraulic System Datasets demonstrate superior performance over state-of-the-art FL methods, achieving 99.5% AUC-ROC in anomaly detection and maintaining accuracy under node failures. Statistical validation using Mann-Whitney (U) test confirms significant improvements (p < 0.05) in both detection accuracy and computational efficiency across diverse operational scenarios.1

Marfo, William [University of Texas at El Paso,Dep↗
NASA NTRS1989

Strength distribution of reinforcing fibers in a Nicalon fiber/chemically vapor infiltrated silicon carbide matrix composite

The strength distribution of fibers within a two-dimensional laminate ceramic/ceramic composite consisting of an eight harness satin weave of Nicalon continuous fiber within a chemically vapor infiltrated SiC matrix was determined from analysis of the fracture mirrors of the fibers. Comparison of the fiber strengths and the Weibull moduli with those for Nicalon fibers prior to incorporation into composites suggests that possible fiber damage may occur either during the weaving or during another stage of the composite manufacture. Observations also indicate that it is the higher-strength fibers which experience the greatest extent of fiber pullout and thus make a larger contribution to the overall composite toughness than do the weaker fibers.

Eckel, Andrew J.↗
NASA NTRS1976

Failure rate analysis of Goddard Space Flight Center spacecraft performance during orbital life

The reported study presents the results of analyses conducted with the aid of both Duane and Weibull growth models. The failure rate values provided may be useful for estimating future space performance, and comparing past, present, and future space performance. Failure rate data from thermal-vacuum system tests are examined and related to the space values. Attention is given to the data base, the time distribution of space malfunctions, limitations on data, and average component reliability for three years in space.

Norris, H. P.↗
NASA NTRS1987

Statistical study of thermal fracture of ceramic materials in the water quench test

The Weibull statistical theory of fracture was applied to thermal shock of ceramics in the water quench test. Transient thermal stresses and probability of failure were calculated for a cylindrical specimen cooled by convection. The convective heat transfer coefficient was calibrated using the time to failure which was measured with an acoustic emission technique. Theoretical failure probability distributions as a function of time and quench temperature compare favorably with experimental results for three high-alumina ceramics and a glass.

Rogers, Wayne P.↗
DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗
NASA NTRS1992

Scale effects on the transverse tensile strength of graphite epoxy composites

The influence of material volume on the transverse tensile strength of AS4/3501-6 graphite epoxy composites was investigated. Tensile tests of 90 degree laminates with 3 different widths and 5 different thicknesses were conducted. A finite element analysis was performed to determine the influence of the grip on the stress distribution in the coupons and explain the tendency for the distribution of failure locations to be skewed toward the grip. Specimens were instrumented with strain gages and extensometers to insure good alignment and to measure failure strains. Data indicated that matrix dominated strength properties varied with the volume of material that was stressed, with the strength decreasing as volume increased. Transverse strength data were used in a volumetric scaling law based on Weibull statistics to predict the strength of 90 degree laminates loaded in three point bending. Comparisons were also made between transverse strength measurements and out-of-plane interlaminar tensile strength measurements from curved beam bending tests. The significance of observed scale effects on the use of tests for material screening, quality assurance, and design allowables is discussed.

Obrien, T. Kevin↗
DOE OSTI2023

Understanding the effect of specimen size on the properties of fine-grain isotropic nuclear graphite for irradiation studies: Mechanical properties

Programs at Oak Ridge National Laboratory are investigating the effects of neutron irradiation in the High Flux Isotope Reactor (HFIR) on properties of fine-grain isotropic nuclear graphites. Specimens were irradiated in the HFIR flux trap, which requires using specimens that are smaller than the sizes recommended by ASTM standards. Here, this work has investigated whether subsized specimens can be used to reliably predict strength behavior. The results show that (1) tensile strength was loosely coupled to specimen volume, (2) the compression specimens had a slightly higher strength for larger volumes, (3) the uniaxial flexural strength was nearly independent of specimen effective area for one orientation whereas the other orientation showed a slight strength–size scaling Weibull behavior, and (4) equibiaxial flexural strength followed traditional strength–size scaling Weibull behavior. These results suggest that fine-grain graphite is more similar to ceramics than to medium- and large-grained graphite with respect to both the strength-limiting flaws (Griffith theory) and the effect of machining on the strength behavior. This work shows that using specimens that are smaller than ASTM recommendations are suitable for investigating the strength changes caused by neutron irradiation because the primary interest is the relative change in the strength distribution parameters rather than their absolute values.

36 MATERIALS SCIENCE↗