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Probability of stress-corrosion fracture under random loading.

A method is developed for predicting the probability of stress-corrosion fracture of structures under random loadings. The formulation is based on the cumulative damage hypothesis and the experimentally determined stress-corrosion characteristics. Under both stationary and nonstationary random loadings, the mean value and the variance of the cumulative damage are obtained. The probability of stress-corrosion fracture is then evaluated using the principle of maximum entropy. It is shown that, under stationary random loadings, the standard deviation of the cumulative damage increases in proportion to the square root of time, while the coefficient of variation (dispersion) decreases in inversed proportion to the square root of time. Numerical examples are worked out to illustrate the general results.

Yang, J.-N.

Forecasting Proximal Femur and Wrist Fracture Caused by a Fall to the Side during Space Exploration Missions to the Moon and Mars

The possibility of bone fracture in space is a concern due to the negative impact it could have on a mission. The Bone Fracture Risk Module (BFxRM) developed at the NASA Glenn Research Center is a statistical simulation that quantifies the probability of bone fracture at specific skeletal locations for particular activities or events during space exploration missions. This paper reports fracture probability predictions for the proximal femur and wrist resulting from a fall to the side during an extravehicular activity (EVA) on specific days of lunar and Martian exploration missions. The risk of fracture at the proximal femur on any given day of the mission is small and fairly constant, although it is slightly greater towards the end of the mission, due to a reduction in proximal femur bone mineral density (BMD). The risk of wrist fracture is greater than the risk of hip fracture and there is an increased risk on Mars since it has a higher gravitational environment than the moon. The BFxRM can be used to help manage the risk of bone fracture in space as an engineering tool that is used during mission operation and resource planning.

Lewandowski, Beth E.

Goal-directed ultrasound in the detection of long-bone fractures

BACKGROUND: New portable ultrasound (US) systems are capable of detecting fractures in the remote setting. However, the accuracy of ultrasound by physicians with minimal ultrasound training is unknown. METHODS: After one hour of standardized training, physicians with minimal US experience clinically evaluated patients presenting with pain and trauma to the upper arm or leg. The investigators then performed a long-bone US evaluation, recording their impression of fracture presence or absence. Results of the examination were compared with routine plain or computer aided radiography (CT). RESULTS: 58 patients were examined. The sensitivity and specificity of US were 92.9% and 83.3%, and of the physical examination were 78.6% and 90.0%, respectively. US provided improved sensitivity with less specificity compared with physical examination in the detection of fractures in long bones. CONCLUSION: Ultrasound scans by minimally trained clinicians may be used to rule out a long-bone fracture in patients with a medium to low probability of fracture.

Validation Studies

Geology of the Lachesis Tessera Quadrangle (V-18), Venus

The Lachesis Tessera Quadrangle (V-18) lies between 25deg and 50deg north, 300deg and 330deg east. Most of the quadrangle consists of "regional plains" (1) of Sedna and Guinevere Planitiae. A first draft of the geology has been completed, and the tentative number of mapped units by terrain type is: Tesserae - 2; plains - 4; ridge belts - 1; fracture belts - 1 (plus embayed fragments of possible additional belts); coronae - 3; central volcanoes - 1; shield flows - 2; paterae - 1; impact craters - 1; undifferentiated flows - 1; bright materials - 1. By far the areally most extensive materials are regional plains. These are mapped as two units, based on radar backscatter ("radar brightness"). The brighter unit appears to be younger than the darker unit. This inference is based on the common presence within the lighter unit of circular or nearly circular inliers of material with radar backscatter characteristic of the darker unit. The circular inliers are most likely low shield volcanoes, which are commonly present on the darker unit, that were only partially covered by the brighter unit. Clear cut examples of wrinkle ridges and fractures superposed on the darker unit but truncated by the brighter unit have not been found to date. These relationships indicate that the brighter unit is superposed on the darker unit, but that the difference in age between them is very small. Because they are so widespread, the regional plains are a convenient relative age time "marker." The number of impact craters superposed on these plains is too small to measure age differences (2), and thus we cannot estimate how much time elapsed between the emplacement of the darker and brighter regional plains units. More local plains units are defined by significantly lower radar backscatter or by a texture that is mottled at scores to hundreds of kilometers scale. A plains-like unit with a homogenous, bright diffuse backscatter is present as scattered exposures in the eastern part of the quadrangle. These exposures have been mapped as "bright material," but it is not clear at present if this is a valid unit or if it is part of the brighter regional plains unit. Tessera terrain is primarily found along the western border of the quadrangle, where Lachesis Tessera refers to the southern exposures, and Zirka Tessera refers to northern exposures. A second tessera unit has been mapped with the symbol "t?." This unit appears to be deformed by the requisite 2 sets of closely spaced structures, but it is so extensively flooded by regional plains materials that the structural fabric is partially obscured. Tessera terrain is present in the adjacent V-17 quadrangle, where both Lachesis Tessera and Zirka Tessera are areally more extensive than in V-18. Ridge and fracture belts are both present, but not as extensive as is the case in, for example, the Pandrosos Dorsa (3) and Lavinia Planitia (4) quadrangles. As is commonly the case, it is difficult to determine if the materials of these belts are older or younger than regional plains. A recent study using radar properties (5) demonstrated that at least most ridge belts appear to be older than regional plains. The materials of fracture belts probably are also older than regional plains, but the fractures themselves can be both older and younger than regional plains (e.g., 3).

McGill, George E.

Probability of stress-corrosion fracture under random loading

Mathematical formulation is based on cumulative-damage hypothesis and experimentally-determined stress-corrosion characteristics. Under both stationary random loadings, mean value and variance of cumulative damage are obtained. Probability of stress-corrosion fracture is then evaluated, using principle of maximum entropy.

Yang, J. N.

Tectonic analysis of folds in the Colorado plateau of Arizona

Structural mapping and analysis of folds in Phanerozoic rocks in northern Arizona, using LANDSAT-1 imagery, yielded information for a tectonic model useful in identifying regional fracture zones within the Colorado Plateau tectonic province. Since the monoclines within the province developed as a response to differential movements of basement blocks along high-angle faults, the monoclinal fold pattern records the position and trend of many elements of the regional fracture system. The Plateau is divided into a mosaic of complex, polyhedral crustal blocks whose steeply dipping faces correspond to major fracture zones. Zones of convergence and changes in the trend of the monoclinal traces reveal the corners of the blocks. Igneous (and salt) diapirs have been emplaced into many of the designated zones of crustal weakness. As loci of major fracturing, folding, and probably facies changes, the fractures exert control on the entrapment of oil and gas.

Davis, G. H.

Time-dependent fracture strength of oriented polymers

A statistical consideration based upon a theory of microscopic molecular kinetics is developed to describe the time-dependent fracture process for oriented polymers. The interrelation between the macroscopic fracture strength and the microscopic behaviors is formulated with the aid of a double Fourier series expansion. The microscopic behavior in the vicinity of a point is expressed in the form of a spherical function which can be expanded into a series of symmetric tensorial terms. Subsequently, the fracture strength of polymers is evaluated in terms of both time and molecular orientation. By taking account of the individual values of the directional fraction of integrity, the time to fracture and the most probable direction of fracture within any volume element in a medium are predicted.

Mun, M. S.

Binomial Test Method for Determining Probability of Detection Capability for Fracture Critical Applications

The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that for a minimum flaw size and all greater flaw sizes, there is 0.90 probability of detection with 95% confidence (90/95 POD). Directed design of experiments for probability of detection (DOEPOD) has been developed to provide an efficient and accurate methodology that yields estimates of POD and confidence bounds for both Hit-Miss or signal amplitude testing, where signal amplitudes are reduced to Hit-Miss by using a signal threshold Directed DOEPOD uses a nonparametric approach for the analysis or inspection data that does require any assumptions about the particular functional form of a POD function. The DOEPOD procedure identifies, for a given sample set whether or not the minimum requirement of 0.90 probability of detection with 95% confidence is demonstrated for a minimum flaw size and for all greater flaw sizes (90/95 POD). The DOEPOD procedures are sequentially executed in order to minimize the number of samples needed to demonstrate that there is a 90/95 POD lower confidence bound at a given flaw size and that the POD is monotonic for flaw sizes exceeding that 90/95 POD flaw size. The conservativeness of the DOEPOD methodology results is discussed. Validated guidelines for binomial estimation of POD for fracture critical inspection are established.

Generazio, Edward R.

Probabilistic finite elements for fracture mechanics

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Besterfield, Glen

A model for the origin of Martian polygonal terrain

Extensive areas of the Martian northern plains in Utopia and Acidalia Planitiae are characterized by 'polygonal terrain.' Polygonal terrain consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on the Earth. However, the Martian polygons are orders of magnitude larger than these potential Earth analogs, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Stratigraphic studies show that the polygonally fractured material in Utopia Planitia was deposited on a land surface with significant topography, including scattered knobs and mesas, fragments of ancient crater rims, and fresh younger craters. Sediments or volcanics deposited over topographically irregular surfaces can experience differential compaction producing drape folds. Bending stresses due to these drape folds would be superposed on the pervasive tensile stresses due to desiccation or cooling, such that the probability of fracturing is enhanced above buried topographic highs and suppressed above buried topographic lows. Thus it was proposed that the scale of the Martian polygons is controlled by the spacing of topographic highs on the buried surface rather than by the physics of the shrinkage process.

Mcgill, G. E.

An interdisciplinary analysis of multispectral satellite data for selected cover types in the Colorado mountains, using automatic data processing techniques

The author has identified the following significant results. In the San Juan Mountains there exists a group of structural and topographic features which suggest a common origin. The relative positions of the San Juan Depression with the Silverton and Lake City Calderas indicate they are possibly on the edge of a large circular feature. Comparison with the 1:250,000 scale Durango Geologic Map reveals a series of radial and arcuate faults concentric with the major circular feature. Such a fracture pattern implies that the circular feature may represent the extent of a major domal uplift in the area. The uplift was very likely due to the sub-crustal emplacement of the parent magma of the San Juan volcanics and intrusives. The broad doming led to the formation of a zone of tensional ring fractures which acted as conduits of release for the magma and the eventual development of the various calderas. The ring fracturing was probably incomplete with hinging occurring in the southern and southwestern portions of the dome accounting for the lack of development of caldera structures in that portion of the area.

Hoffer, R. M.

NASA NDE Program

The current activities in the National Aeronautics and Space Administration Nondestructive Evaluation (NDE) Program are presented. The topics covered include organizational communications, orbital weld inspection, electric field imaging, fracture critical probability of detection validation, monitoring of thermal protection systems, physical and document standards, image quality indicators, integrity of composite pressure vessels, and NDE for additively manufactured components.

Generazio, Ed

Consistent Practices for the Probability of Detection (POD) of Fracture Critical Metallic Components Project

NASA-STD-5009 requires that successful flaw detection by NDE methods be statistically qualified for use on fracture critical metallic components, but does not standardize practices. This task works towards standardizing calculations and record retention with a web-based tool, the NNWG POD Standards Library or NPSL. Test methods will also be standardized with an appropriately flexible appendix to -5009 identifying best practices. Additionally, this appendix will describe how specimens used to qualify NDE systems will be cataloged, stored and protected from corrosion, damage, or loss.

Hughitt, Brian

Experimental Validation of a Module Cell Cracking Model

The What's Cracking app can predict how changes in crystalline silicon photovoltaic (PV) module materials, design, and mounting affect its susceptibility for cell fracture under uniform loading. This work has experimentally validated the app. A set of commercial crystalline silicon PV modules was obtained for this study. The modules were uniformly loaded at three different mounting points, and their subsequent cell fractures were recorded. A large sample size allowed for the development of an experimental statistical model for cell fracture. Here, the comparison of the experiment to predictions from the app is in excellent agreement. Both experimental and modeling results also elucidate how moving the module mounting points toward the center of the module increases the probability of cell fracture.

14 SOLAR ENERGY

Uniform Mechanical Loading Can Test for Nonuniform Loading Durability

In this work, we present a method to evaluate the equivalency between any module mechanical loading conditions. The method is developed to address the specific failure mode of glass fracture and is based on Weibull analysis and weakest link theory. It considers the varying stress profile across the module to calculate the probability of glass fracture, which is used as the metric of equivalency. An idealized nonuniform loading scheme is employed to demonstrate the method and introduce the concept of the equivalent uniform load factor: a factor applied to the maximum pressure of the nonuniform load to obtain the equivalent uniform load value. It is demonstrated that this factor is less than unity for all nonuniform load cases considered, including snow and various characters of wind loading. These significant results suggest that uniform loading may be reliably, and practically, employed to evaluate photovoltaic module glass for nonuniform loading durability.

14 SOLAR ENERGY

Reusable solid rocket motor case - Optimum probabilistic fracture control

A methodology for the reliability analysis of a reusable solid rocket motor case is discussed in this paper. The analysis is based on probabilistic fracture mechanics and probability distribution for initial flaw sizes. The developed reliability analysis can be used to select the structural design variables of the solid rocket motor case on the basis of minimum expected cost and specified reliability bounds during the projected design life of the case. Effects on failure prevention plans such as nondestructive inspection and the material erosion between missions can also be considered in the developed procedure for selection of design variables. The reliability-based procedure that has been discussed in this paper can easily be modified to consider other similar structures of reusable space vehicle systems with different fracture control plans.

Hanagud, S.

Probabilistic Fracture Mechanics and Optimum Fracture Control Analytical Procedures for a Reusable Solid Rocket Motor Case

A methodology for the reliability analysis of a reusable solid rocket motor case is discussed. The analysis is based on probabilistic fracture mechanics and probability distribution for initial flaw sizes. The developed reliability analysis is used to select the structural design variables of the solid rocket motor case on the basis of minimum expected cost and specified reliability bounds during the projected design life of the case. Effects of failure prevention plans such as nondestructive inspection and the material erosion between missions are also considered in the developed procedure for selection of design variables. The reliability-based procedure can be modified to consider other similar structures of reusable space vehicle systems with different failure prevention plans.

Hanagud, S.