SEARCH · Search NASA

Results for “Weibull modulus,”

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.

SourceResearch connectionFrom yearThrough year

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

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Measuring the Weibull modulus of microscope slides

The objectives are that students will understand why a three-point bending test is used for ceramic specimens, learn how Weibull statistics are used to measure the strength of brittle materials, and appreciate the amount of variation in the strength of brittle materials with low Weibull modulus. They will understand how the modulus of rupture is used to represent the strength of specimens in a three-point bend test. In addition, students will learn that a logarithmic transformation can be used to convert an exponent into the slope of a straight line. The experimental procedures are explained.

Sorensen, Carl D.↗

NASA NTRS1996

Tensile Strength and Microstructural Characterization of Uncoated and Coated HPZ Ceramic Fibers

Tensile strengths of as-received HPZ fiber and those surface coated with BN, BN/SiC, and BN/Si3N4 have been determined at room temperature using a two-parameter Weibull distribution. Nominally approx. 0.4 micron BN and 0.2 micron SiC or Si3N4 coatings were deposited on the fibers by chemical vapor deposition using a continuous reactor. The average tensile strength of uncoated HPZ fiber was 2.0 +/- 0.56 GPa (290 +/- 81 ksi) with a Weibull modulus of 4.1. For the BN coated fibers, the average strength and the Weibull modulus increased to 2.39 +/- 0.44 GPa (346 +/- 64 ksi) and 6.5, respectively. The HPZ/BN/SiC fibers showed an average strength of 2.0 +/- 0.32 GPa (290 +/- 47 ksi) and Weibull modulus of 7.3. Average strength of the fibers having a dual BN/Si3N4 surface coating degraded to 1.15 +/- 0.26 GPa (166 +/- 38 ksi) with a Weibull modulus of 5.3. The chemical composition and thickness of the fiber coatings were determined using scanning Auger analysis. Microstructural analysis of the fibers and the coatings was carried out by scanning electron microscopy and transmission electron microscopy. A microporous silica-rich layer approx. 200 nm thick is present on the as-received HPZ fiber surface. The BN coatings on the fibers are amorphous to partly turbostratic and contaminated with carbon and oxygen. Silicon carbide coating was crystalline whereas the silicon nitride coating was amorphous. The silicon carbide and silicon nitride coatings are non-stoichiometric, non-uniform, and granular. Within a fiber tow, the fibers on the outside had thicker and more granular coatings than those on the inside.

Bansal, Narottam P.↗

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 NTRS1998

Effects of HF Treatments on Tensile Strength of Hi-Nicalon Fibers

Tensile strengths of as-received Hi-Nicalon fibers and those having a dual BN/SiC surface coating, deposited by chemical vapor deposition, have been measured at room temperature. These fibers were also treated with HF for 24 h followed by tensile strength measurements. Strengths of uncoated and BN/SiC coated Hi-Nicalon fibers extracted from celsian matrix composites, by dissolving away the matrix in HF for 24 h, were also determined. The average tensile strength of uncoated Hi-Nicalon was 3.19 +/- 0.73 GPa with a Weibull modulus of 5.41. The Hi-Nicalon/BN/SiC fibers showed an average strength of 3.04 q 0.53 GPa and Weibull modulus of 6.66. After HF treatments, the average strengths of the uncoated and BN/SiC coated Hi-Nicalon fibers were 2.69 +/- 0.67 GPa and 2.80 +/- 0.53 GPa and the Weibull moduli were 4.93 and 5.96, respectively. The BN/SiC coated fibers extracted from the celsian matrix composite exhibited a strength of 2.38 +/- 0.40 GPa and a Weibull modulus of 7.15. The strength of the uncoated Hi-Nicalon fibers in the composite was so severely degraded that they disintegrated into small fragments during extraction with HF. The uncoated fibers probably undergo mechanical surface damage during hot pressing of the composites. Also, the BN layer on the coated fibers acts as a compliant layer which protects the fibers from mechanical damage during composite processing. The elemental composition and thickness of the fiber coatings were deten-nined using scanning Auger analysis. Microstructural analyses of the fibers and the coatings were done by scanning electron microscopy and transmission electron microscopy. Strengths of fibers calculated using average and measured fiber diameters were in good agreement. Thus, the strength of fibers can be evaluated using an average fiber diameter instead of the measured diameter of each filament.

Bansal, Narottam P.↗

NASA NTRS2006

Slow Crack Growth and Fracture Toughness of Sapphire for the International Space Station Fluids and Combustion Facility

The fracture toughness, inert flexural strength, and slow crack growth parameters of the r- and a-planes of sapphire grown by the Heat Exchange Method were measured to qualify sapphire for structural use in the International Space Station. The fracture toughness in dry nitrogen, K(sub Ipb), was 2.31 +/- 0.12 MPa(square root of)m and 2.47 +/- 0.15 MPa(squre root of)m for the a- and r-planes, respectively. Fracture toughness measured in water via the operational procedure in ASTM C1421 was significantly lower, K(sub Ivb) = 1.95+/- 0.03 MPa(square root of)m, 1.94 +/- 0.07 and 1.77 +/- 0.13 MPa(square root of)m for the a- , m- and r-planes, respectively. The mean inert flexural strength in dry nitrogen was 1085 +/- 127 MPa for the r-plane and 1255 +/- 547 MPa for the a-plane. The power law slow crack growth exponent for testing in water was n = 21 +/- 4 for the r-plane and n (greater than or equal to) 31 for the a-plane. The power law slow crack growth coefficient was A = 2.81 x 10(exp -14) m/s x (MPa(squre root of)m)/n for the r-plane and A (approx. equals)2.06 x 10(exp -15) m/s x (MPa(square root of)m)/n for the a-plane. The r- and a-planes of sapphire are relatively susceptible to stress corrosion induced slow crack growth in water. However, failure occurs by competing modes of slow crack growth at long failure times and twinning for short failure time and inert environments. Slow crack growth testing needs to be performed at low failure stress levels and long failure times so that twinning does not affect the results. Some difficulty was encountered in measuring the slow crack growth parameters for the a-plane due to a short finish (i.e., insufficient material removal for elimination of the damage generated in the early grinding stages). A consistent preparation method that increases the Weibull modulus of sapphire test specimens and components is needed. This would impart higher component reliability, even if higher Weibull modulus is gained at the sacrifice of absolute strength of the component. The current specification frequently used for the preparation of sapphire test specimens and components (e.g., a "60/40" scratch-dig finish) is inadequate to avoid a short finish.

Salem, Jonathan A.↗

NASA NTRS1997

Estimation of Slow Crack Growth Parameters for Constant Stress-Rate Test Data of Advanced Ceramics and Glass by the Individual Data and Arithmetic Mean Methods

The two estimation methods, individual data and arithmetic mean methods, were used to determine the slow crack growth (SCG) parameters (n and D) of advanced ceramics and glass from a large number of room- and elevated-temperature constant stress-rate ('dynamic fatigue') test data. For ceramic materials with Weibull modulus greater than 10, the difference in the SCG parameters between the two estimation methods was negligible; whereas, for glass specimens exhibiting Weibull modulus of about 3, the difference was amplified, resulting in a maximum difference of 16 and 13 %, respectively, in n and D. Of the two SCG parameters, the parameter n was more sensitive to the estimation method than the other. The coefficient of variation in n was found to be somewhat greater in the individual data method than in the arithmetic mean method.

Choi, Sung R.↗

NASA NTRS1985

Densification and properties of alpha-silicon carbide

The sintering behavior of alpha-SiC with B and C sintering aids and without sintering aids was investigated experimentally. The sintering was performed for 30-60 min in argon flow at 2150 and 2200 C. The density of the sintered bars was determined by weighing and measuring the bars, four-point flexure tests were conducted on machined bars, and the Weibull modulus was determined by regression analysis. It is found that type 1 alpha-SiC powder, which does not densify, can be sintered to a high final density (in excess of 96 percent of the theoretical value) using B and C sintering aids. Flexure test results and Weibull modulus data suggest that the strength of the alpha-SiC ceramic is greatly affected by processing flaws and also by inclusions and machining flaws.

Dutta, S.↗

NASA NTRS1992

Design prediction for long term stress rupture service of composite pressure vessels

Extensive stress rupture studies on glass composites and Kevlar composites were conducted by the Lawrence Radiation Laboratory beginning in the late 1960's and extending to about 8 years in some cases. Some of the data from these studies published over the years were incomplete or were tainted by spurious failures, such as grip slippage. Updated data sets were defined for both fiberglass and Kevlar composite stand test specimens. These updated data are analyzed in this report by a convenient form of the bivariate Weibull distribution, to establish a consistent set of design prediction charts that may be used as a conservative basis for predicting the stress rupture life of composite pressure vessels. The updated glass composite data exhibit an invariant Weibull modulus with lifetime. The data are analyzed in terms of homologous service load (referenced to the observed median strength). The equations relating life, homologous load, and probability are given, and corresponding design prediction charts are presented. A similar approach is taken for Kevlar composites, where the updated stand data do show a turndown tendency at long life accompanied by a corresponding change (increase) of the Weibull modulus. The turndown characteristic is not present in stress rupture test data of Kevlar pressure vessels. A modification of the stress rupture equations is presented to incorporate a latent, but limited, strength drop, and design prediction charts are presented that incorporate such behavior. The methods presented utilize Cartesian plots of the probability distributions (which are a more natural display for the design engineer), based on median normalized data that are independent of statistical parameters and are readily defined for any set of test data.

Robinson, Ernest Y.↗

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.↗

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 NTRS1990

Reliability analysis of a structural ceramic combustion chamber

The Weibull modulus, fracture toughness and thermal properties of a silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Weibull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effect of data censoring, FEM mesh refinement, and fracture criterion were considered in the analysis.

Salem, Jonathan A.↗

NASA NTRS1991

Reliability analysis of a structural ceramic combustion chamber

Salem, Jonathan A.↗

NASA NTRS2005

Fabrication and Probabilistic Fracture Strength Prediction of High-Aspect-Ratio Single Crystal Silicon Carbide Microspecimens With Stress Concentration

Single crystal silicon carbide micro-sized tensile specimens were fabricated with deep reactive ion etching (DRIE) in order to investigate the effect of stress concentration on the room-temperature fracture strength. The fracture strength was defined as the level of stress at the highest stressed location in the structure at the instant of specimen rupture. Specimens with an elliptical hole, a circular hole, and without a hole (and hence with no stress concentration) were made. The average fracture strength of specimens with a higher stress concentration was larger than the average fracture strength of specimens with a lower stress concentration. Average strength of elliptical-hole, circular-hole, and without-hole specimens was 1.53, 1.26, and 0.66 GPa, respectively. Significant scatter in strength was observed with the Weibull modulus ranging between 2 and 6. No fractographic examination was performed but it was assumed that the strength controlling flaws originated from etching grooves along the specimen side-walls. The increase of observed fracture strength with increasing stress concentration was compared to predictions made with the Weibull stress-integral formulation by using the NASA CARES/Life code. In the analysis isotropic material and fracture behavior was assumed - hence it was not a completely rigorous analysis. However, even with these assumptions good correlation was achieved for the circular-hole specimen data when using the specimen data without stress concentration as a baseline. Strength was over predicted for the elliptical-hole specimen data. Significant specimen-to-specimen dimensional variation existed in the elliptical-hole specimens due to variations in the nickel mask used in the etching. To simulate the additional effect of the dimensional variability on the probabilistic strength response for the single crystal specimens the ANSYS Probabilistic Design System (PDS) was used with CARES/Life.

Nemeth, Noel N.↗

NASA NTRS2020

Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating

The FEAMAC/CARES program, which integrates finite element analysis (FEA) with the MAC/GMC (Micromechanics Analysis Code with Generalized Method of Cells) and the CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures / Life Prediction) programs, was used to simulate the formation of mudcracks during the cooling of a multilayered environmental barrier coating (EBC) deposited on a silicon carbide substrate. FEAMAC/CARES combines the MAC/GMC multiscale micromechanics analysis capability (primarily developed for composite materials) with the CARES/Life probabilistic multiaxial failure criteria (developed for brittle ceramic materials) and Abaqus (Dassault Systèmes) FEA. In this report, elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio elements enabled the formation of crack boundaries, leading to development of mudcrack-patterned damage. Finite element models of a disk-shaped three-dimensional specimen and a twodimensional model of a through-the-thickness cross section subjected to progressive cooling from 1,300 °C to an ambient temperature of 23 °C were made. Mudcrack damage in the coating resulted from the buildup of residual tensile stresses between the individual material constituents because of thermal expansion mismatches between coating layers and the substrate. A two-parameter Weibull distribution characterized the coating layer stochastic strength response and allowed the effect of the Weibull modulus on the formation of damage and crack segmentation lengths to be studied. The spontaneous initiation of cracking and crack coalescence resulted in progressively smaller mudcrack cells as cooling progressed, consistent with a fractal-behaved fracture pattern. Other failure modes such as delamination, and possibly spallation, could also be reproduced. The physical basis assumed and the heuristic approach employed, which involves a simple stochastic cellular automaton methodology to approximate the crack growth process, are described. The results ultimately show that a selforganizing mudcrack formation can derive from a Weibull distribution that is used to describe the stochastic strength response of the bulk brittle ceramic material layers of an EBC.

Nemeth, Noel N.↗

NASA NTRS2018

Simulation of Stochastic 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 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 1300oC 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↗

NASA NTRS1977

Ceramics for the advanced automotive gas turbine engine: A look at a single shaft design

The results of a preliminary analysis of a single shaft regenerative design with a single stage radial turbine are presented to show the fuel economy that can be achieved at high turbine inlet temperatures, with this particular advanced design, if the turbine tip speed and regenerator inlet temperature are not limited. The engine size was 100 hp for application to a 3500 lb auto. The fuel economy was analyzed by coupling the engine to the auto through a continuously variable speed-ratio transmission and operating the system at constant turbine inlet temperature over the Composite Driving Cycle. The fuel was gasoline and the analysis was for a 85 F day. With a turbine inlet temperature of 2500 F the fuel economy was 26.2 mpg, an improvement of 18 percent over that of 22.3 mpg with a turbine inlet temperature of 1900 F. The turbine tip speed needed for best economy with the 2500 F engine was 2530 ft/sec. The regenerator temperature was approximately 2200 F at idle. Disk stresses were estimated for one single stage radial turbine and two two-stage radial-axial turbines and compared with maximum allowable stress curves estimated for a current ceramic material. Results show a need for higher Weibull Modulus, higher strength ceramics.

Nosek, S. M.↗

NASA NTRS1985

Effect of hot isostatic pressing on the properties of sintered alpha silicon carbide

Two lots of alpha silicon carbide were isostatically hot-pressed under 138 MPa for 2 h in Ar at temperatures up to 2200 C. Nearly theoretically dense specimens resulted. Hot isostatic pressing increased both room-temperature strength and 1200 C strength, and resulted in improved reliability. One lot of material which was pressed at 2200 C showed increases of about 20 percent in room-temperature strength and about 50 percent in 1200 C flexural strength; the Weibull modulus improved about 100 percent.

Watson, G. K.↗

NASA NTRS1985

The effects of surface finish and grain size on the strength of sintered silicon carbide

The effects of surface treatment and microstructure, especially abnormal grain growth, on the strength of sintered SiC were studied. The surfaces of sintered SiC were treated with 400, 800 and 1200 grit diamond wheels. Grain growth was induced by increasing the sintering times at 2050 C. The beta to alpha transformation occurred during the sintering of beta-phase starting materials and was often accompanied by abnormal grain growth. The overall strength distributions were established using Weibull statistics. The strength of the sintered SiC is limited by extrinsic surface flaws in normal-sintered specimens. The finer the surface finish and grain size, the higher the strength. But the strength of abnormal sintering specimens is limited by the abnormally grown large tabular grains. The Weibull modulus increases with decreasing grain size and decreasing grit size for grinding.

You, Y. H.↗