Prestressed brittle structures.
Prestressed beams, columns and plates nonlinear response, statistical behavior and transverse cracking under axial compression, describing strength and stiffness
Barnett, R. L.↗
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Effect of size on cracking of materials
Brittle behavior of large mild steel elements, glass plasticity, and fatigue specimen size sensitivity are manifestations of strain-energy size effect. Specimens physical size effect on material cracking initiation occurs according to flaw distribution statistics. Fracture size effect depends on stability or instability of crack propagation.
Glucklick, J.↗
Analysis of the progressive failure of brittle matrix composites
This report investigates two of the most common modes of localized failures, namely, periodic fiber-bridged matrix cracks and transverse matrix cracks. A modification of Daniels' bundle theory is combined with Weibull's weakest link theory to model the statistical distribution of the periodic matrix cracking strength for an individual layer. Results of the model predictions are compared with experimental data from the open literature. Extensions to the model are made to account for possible imperfections within the layer (i.e., nonuniform fiber lengths, irregular crack spacing, and degraded in-situ fiber properties), and the results of these studies are presented. A generalized shear-lag analysis is derived which is capable of modeling the development of transverse matrix cracks in material systems having a general multilayer configuration and under states of full in-plane load. A method for computing the effective elastic properties for the damaged layer at the global level is detailed based upon the solution for the effects of the damage at the local level. This methodology is general in nature and is therefore also applicable to (0(sub m)/90(sub n))(sub s) systems. The characteristic stress-strain response for more general cases is shown to be qualitatively correct (experimental data is not available for a quantitative evaluation), and the damage evolution is recorded in terms of the matrix crack density as a function of the applied strain. Probabilistic effects are introduced to account for the statistical nature of the material strengths, thus allowing cumulative distribution curves for the probability of failure to be generated for each of the example laminates. Additionally, Oh and Finney's classic work on fracture location in brittle materials is extended and combined with the shear-lag analysis. The result is an analytical form for predicting the probability density function for the location of the next transverse crack occurrence within a crack bounded region. The results of this study verified qualitatively the validity of assuming a uniform crack spacing (as was done in the shear-lag model).
Thomas, David J.↗
The detection of fatigue cracks by nondestructive testing methods
X-radiographic penetrant, ultrasonic, eddy current, holographic, and acoustic emission techniques were optimized and applied to the evaluation of 2219-T87 aluminum alloy test specimens. One hundred eighteen specimens containing a total of 328 fatigue cracks were evaluated. The cracks ranged in length from 0.500 inch (1.27 cm) to 0.007 inch (0.018 cm) and in depth from 0.178 inch (0.451 cm) and 0.001 inch (0.003 cm). Specimen thicknesses were nominally 0.060 inch (0.152 cm) and 0.210 inch (0.532 cm) and surface finishes were nominally 32 and 125 rms and 64 and 200 rms respectively. Specimens were evaluated in the as-milled surface condition, in the chemically milled surface condition and, after proof loading, in a randomized inspection sequence. Results of the nondestructive test (NDT) evaluations were compared with actual crack size obtained by measurement of the fractured specimens. Inspection data was then analyzed to provide a statistical basis for determinating the threshold crack detection sensitivity (the largest crack size that would be missed) for each of the inspection techniques at a 95% probability and 95% confidence level.
Rummel, W. D.↗
The detection of fatigue cracks by nondestructive test methods
X-radiographic, penetrant, ultrasonic, and eddy current techniques were optimized and applied to the evaluation of 2219-T87 aluminum alloy test specimens. One hundred eighteen specimens containing a total of 328 fatigue cracks were evaluated. The cracks ranged in length from 1.27 to 0.018 cm and in depth from 0.451 to 0.003 cm. Specimen thicknesses were nominally 0.152 and 0.532 cm. Specimens were evaluated in the 'as-milled' surface condition, in the etched surface condition, and, after proof loading, in a randomized inspection sequence. Results of the nondestructive test evaluations were compared with actual crack size obtained by analysis of the fractured specimens. Inspection data were then analyzed to provide a statistical basis for determining the threshold crack detection sensitivity for each of the inspection techniques at a 95% probability and 95% confidence level.
Rummel, W. D.↗
The Effects of Salt Water on the Slow Crack Growth of Soda Lime Silicate Glass
The slow crack growth parameters of soda-lime silicate were measured in distilled and salt water of various concentrations in order to determine if stress corrosion susceptibility is affected by the presence of salt and the contaminate formation of a weak sodium film. Past research indicates that solvents effect 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 slow crack growth parameters A and n. However, for typical engineering purposes, the effect can be ignored.
Toughness↗
Grain boundary oxidation and an analysis of the effects of oxidation on fatigue crack nucleation life
The effects of preoxidation on subsequent fatigue life were studied. Surface oxidation and grain boundary oxidation of a nickel-base superalloy (TAZ-8A) were studied at 600 to 1000 C for 10 to 1000 hours in air. Surface oxides were identified and the kinetics of surface oxidation was discussed. Grain boundary oxide penetration and morphology were studied. Pancake type grain boundary oxide penetrates deeper and its size is larger, therefore, it is more detrimental to fatigue life than cone-type grain boundary oxide. Oxide penetration depth, a (sub m), is related to oxidation temperature, T, and exposure time, t, by an empirical relation of the Arrhenius type. Effects of T and t on statistical variation of a (sub m) were analyzed according to the Weibull distribution function. Once the oxide is cracked, it serves as a fatigue crack nucleus. Statistical variation of the remaining fatigue life, after the formation of an oxide crack of a critical length, is related directly to the statistical variation of grain boundary oxide penetration depth.
Oshida, Y.↗
Flight inspection data and crack initiation times
Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.
Johnson, W. S.↗
Effect of Broaching Machining Parameters, Residual Stresses and Cold Work on Fatigue Life of Ni-based Turbine Disk P/M Alloy at 650°C
A study was performed to examine the effect of various broaching machining parameters on high temperature fatigue lives of a nickel-based Low Solvus High Refractory (LSHR) powder metallurgy disk alloy. The work was done to gain a better understanding of the effect of various broaching variables on the integrity and the durability of these fracture critical components. The influence of tool wear and broaching speed were examined in terms of their effect on residual stresses, cold work and surface roughness. These variables were shown to have a substantial effect on fatigue lives and the failure mode. The relationships between these parameters and fatigue crack initiation mechanisms are detailed. Statistical analyses evaluating these relationships are presented.
fatigue↗
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.↗
A statistical, micromechanical theory of the compressive strength of brittle materials
A general theory of the compressive strength of brittle materials is presented. This theory proposes that failure is brought about by structural weakening from accumulated crack damage which increases with the stress level. The statistics of the flaw distribution and the mechanism of crack initiation and extension are important. A sample calculation using the theory is given to demonstrate its application
Adams, M.↗
Design of ceramic components with the NASA/CARES computer program
The ceramics analysis and reliability evaluation of structures (CARES) computer program is described. The primary function of the code is to calculate the fast-fracture reliability or failure probability of macro-scopically isotropic ceramic components. These components may be subjected to complex thermomechanical loadings, such as those found in heat engine applications. CARES uses results from MSC/NASTRAN or ANSYS finite-element analysis programs to evaluate how inherent surface and/or volume type flaws component reliability. CARES utilizes the Batdorf model and the two-parameter Weibull cumulative distribution function to describe the effects of multiaxial stress states on material strength. The principle of independent action (PIA) and the Weibull normal stress averaging models are also included. Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities are estimated from four-point bend bar or uniform uniaxial tensile specimen fracture strength data. Parameter estimation can be performed for a single or multiple failure modes by using a least-squares analysis or a maximum likelihood method. Kolmogorov-Smirnov and Anderson-Darling goodness-to-fit-tests, 90 percent confidence intervals on the Weibull parameters, and Kanofsky-Srinivasan 90 percent confidence band values are also provided. Examples are provided to illustrate the various features of CARES.
Nemeth, Noel N.↗
Ceramics Analysis and Reliability Evaluation of Structures (CARES). Users and programmers manual
This manual describes how to use the Ceramics Analysis and Reliability Evaluation of Structures (CARES) computer program. The primary function of the code is to calculate the fast fracture reliability or failure probability of macroscopically isotropic ceramic components. These components may be subjected to complex thermomechanical loadings, such as those found in heat engine applications. The program uses results from MSC/NASTRAN or ANSYS finite element analysis programs to evaluate component reliability due to inherent surface and/or volume type flaws. CARES utilizes the Batdorf model and the two-parameter Weibull cumulative distribution function to describe the effect of multiaxial stress states on material strength. The principle of independent action (PIA) and the Weibull normal stress averaging models are also included. Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities are estimated from four-point bend bar or unifrom uniaxial tensile specimen fracture strength data. Parameter estimation can be performed for single or multiple failure modes by using the least-square analysis or the maximum likelihood method. Kolmogorov-Smirnov and Anderson-Darling goodness-of-fit tests, ninety percent confidence intervals on the Weibull parameters, and Kanofsky-Srinivasan ninety percent confidence band values are also provided. The probabilistic fast-fracture theories used in CARES, along with the input and output for CARES, are described. Example problems to demonstrate various feature of the program are also included. This manual describes the MSC/NASTRAN version of the CARES program.
Nemeth, Noel N.↗
Replacement/Refurbishment of JSC/NASA POD Specimens
The NASA Special NDE certification process requires demonstration of NDE capability by test per NASA-STD-5009. This test is performed with fatigue cracked specimens containing very small cracks. The certification test results are usually based on binomial statistics and must meet a 90/95 Probability of Detection (POD). The assumption is that fatigue cracks are tightly closed, difficult to detect, and inspectors and processes passing such a test are well qualified for inspecting NASA fracture critical hardware. The JSC NDE laboratory has what may be the largest inventory that exists of such fatigue cracked NDE demonstration specimens. These specimens were produced by the hundreds in the late 1980s and early 1990s. None have been produced since that time and the condition and usability of the specimens are questionable.
Castner, Willard L.↗
Damage Mechanisms and Controlled Crack Propagation in a Hot Pressed Silicon Nitride Ceramic
The subcritical growth of cracks from pre-existing flaws in ceramics can severely affect the structural reliability of a material. The ability to directly observe subcritical crack growth and rigorously analyze its influence on fracture behavior is important for an accurate assessment of material performance. A Mode I fracture specimen and loading method has been developed which permits the observation of stable, subcritical crack extension in monolithic and toughened ceramics. The test specimen and procedure has demonstrated its ability to generate and stably propagate sharp, through-thickness cracks in brittle high modulus materials. Crack growth for an aluminum oxide ceramic was observed to be continuously stable throughout testing. Conversely, the fracture behavior of a silicon nitride ceramic exhibited crack growth as a series of subcritical extensions which are interrupted by dynamic propagation. Dynamic initiation and arrest fracture resistance measurements for the silicon nitride averaged 67 and 48 J/sq m, respectively. The dynamic initiation event was observed to be sudden and explosive. Increments of subcritical crack growth contributed to a 40 percent increase in fracture resistance before dynamic initiation. Subcritical crack growth visibly marked the fracture surface with an increase in surface roughness. Increments of subcritical crack growth loosen ceramic material near the fracture surface and the fracture debris is easily removed by a replication technique. Fracture debris is viewed as evidence that both crack bridging and subsurface microcracking may be some of the mechanisms contributing to the increase in fracture resistance. A Statistical Fracture Mechanics model specifically developed to address subcritical crack growth and fracture reliability is used together with a damaged zone of material at the crack tip to model experimental results. A Monte Carlo simulation of the actual experiments was used to establish a set of modeling input parameters. It was demonstrated that a single critical parameter does not characterize the conditions required for dynamic initiation. Experimental measurements for critical crack lengths, and the energy release rates exhibit significant scatter. The resulting output of the model produces good agreement with both the average values and scatter of experimental measurements.
Calomino, Anthony Martin↗
A Multi-Parameter Approach for Calculating Crack Instability
An accurate fracture control analysis of spacecraft pressure systems, boosters, rocket hardware and other critical low-cycle fatigue cases where the fracture toughness highly impacts cycles to failure requires accurate knowledge of the material fracture toughness. However, applicability of the measured fracture toughness values using standard specimens and transferability of the values to crack instability analysis of the realistically complex structures is refutable. The commonly used single parameter Linear Elastic Fracture Mechanics (LEFM) approach which relies on the key assumption that the fracture toughness is a material property would result in inaccurate crack instability predictions. In the past years extensive studies have been conducted to improve the single parameter (K-controlled) LEFM by introducing parameters accounting for the geometry or in-plane constraint effects]. Despite the importance of the thickness (out-of-plane constraint) effects in fracture control problems, the literature is mainly limited to some empirical equations for scaling the fracture toughness data] and only few theoretically based developments can be found. In aerospace hardware where the structure might have only one life cycle and weight reduction is crucial, reducing the design margin of safety by decreasing the uncertainty involved in fracture toughness evaluations would result in lighter hardware. In such conditions LEFM would not suffice and an elastic-plastic analysis would be vital. Multi-parameter elastic plastic crack tip field quantifying developments combined with statistical methods] have been shown to have the potential to be used as a powerful tool for tackling such problems. However, these approaches have not been comprehensively scrutinized using experimental tests. Therefore, in this paper a multi-parameter elastic-plastic approach has been used to study the crack instability problem and the transferability issue by considering the effects of geometrical constraints as well as the thickness. The feasibility of the approach has been examined using a wide range of specimen geometries and thicknesses manufactured from 7075-T7351 aluminum alloy.
Zanganeh, M.↗
Random loading fatigue crack growth: Crack closure considerations
The prediction of fatigue crack growth is an important element of effective fracture control for metallic structures and mechanical components, especially in the aerospace industry. The prediction techniques available and applied today are mostly based on fatigue crack growth measurements determined in constant amplitude testing. However, while many service loadings are constant amplitude, many more loadings are random amplitude. An investigation to determine which statistics of random loadings are relevant to fatigue crack closure was conducted. The fundamentals of random processes and crack closure are briefly reviewed, then the relevance of certain random process parameters to the crack closure calculation are discussed qualitatively. A course for further research is outlined.
Ortiz, Keith↗
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, John P.↗