Search Results for statistical distributions

Statistical techniques provide the design engineer with a powerful tool for the analysis of failure data. By means of an actual case study, steps required to design a test yielding statistically meaningful data and procedures used in graphical analysis of results are presented. The Weibull distribution is the statistical model used as a basis for these techniques. This method of failure analysis provides the engineer with clear, positive design direction.

This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable definitions, how uncertainty is quantified, and input for the associated random variables, as well as the characterization of the response uncertainty. Next, it focuses on specific and generic uncertainty propagation techniques: first- and second-order reliability methods, the response surface method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling as well as several statistical techniques. Finally, it illustrates some of the techniques with application problems for which probabilistic analysis is an essential element.

In this study, the failure modes of cartwheel and mechanical properties of materials have been analyzed. The results show that rim cracking is always initiated from stringer-type alumina cluster and driven by a combination effect of mechanical and thermal load. The strength, toughness, and ductility are mainly determined by the carbon content of wheel steels. The fatigue crack growth resistance is insensitive to composition and microstructure, while the fatigue crack initiation life increases with the decrease of austenite grain size and pearlite colony size. The dynamic fracture toughness, KID, is obviously lower than static fracture toughness, KIC, and has the same trend as KIC. The ratio of KID/sigma YD is the most reasonable parameter to evaluate the fracture resistance of wheel steels with different composition and yield strength. Decreasing carbon content is beneficial to the performance of cartwheel.

This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.

Several heavy truck Cr-Mo steel steering arms in service less than three years fractured during stationary or low-speed turning maneuvers that required power-assisted steering. Metallographic examination of the cracked AISI 4135 arms, heat treated to a hardness of 285 to 341 HB, revealed that fatigue crack initiation occurred from the tip of oxide scale inclusions forged into the U-shaped arm at the inside radius. Corrective action involved redesigning the steering arm to increase the minimum forging radius and reduce the stress level at the inner-bend radius, and reducing the level of power assistance to the wheels to encourage the driver to put the vehicle in motion prior to turning.

The quantitative characterization of fracture surface geometry, that is, quantitative fractography, can provide useful information regarding the microstructural features and failure mechanisms that govern material fracture. This article is devoted to the fractographic techniques that are based on fracture profilometry. This is followed by a section describing the methods based on scanning electron microscope fractography. The article also addresses procedures for three-dimensional fracture surface reconstruction. In each case, sufficient methodological details, governing equations, and practical examples are provided.

Graphitization, the formation of graphite nodules in carbon and low alloy steels, contributes to many failures in high-temperature environments. Three such failures in power-generating systems were analyzed to demonstrate the unpredictable nature of this failure mechanism and its effect on material properties and structures. In general, the more randomly distributed the nodules, the less effect they have on structural integrity. In the cases examined, the nodules were found to be organized in planar arrays, indicating they might have an effect on material properties. Closer inspection, however, revealed that the magnitude of the effect depends on the relative orientation of the planar arrangement and principle tensile stress. For normal orientation, the effect of embrittlement tends to be most severe. Conversely, when the orientation is parallel, the nodules have little or no effect. The cases examined show that knowledge is incomplete in regard to graphitization, and the prediction of its occurrence is not yet possible.

This article briefly introduces the concepts of failure analysis and root cause analysis (RCA), and the role of failure analysis as a general engineering tool for enhancing product quality and failure prevention. It reviews four fundamental categories of physical root causes, namely, design deficiencies, material defects, manufacturing/installation defects, and service life anomalies, with examples. The article describes several common charting methods that may be useful in performing an RCA. It also discusses other failure analysis tools, including review of all sources of input and information, people interviews, laboratory investigations, stress analysis, and fracture mechanics analysis. The article concludes with information on the categories of failure and failure prevention.

This article briefly introduces the concepts of failure analysis, including root-cause analysis (RCA), and the role of failure analysis as a general engineering tool for enhancing product quality and failure prevention. It initially provides definitions of failure on several different levels, followed by a discussion on the role of failure analysis and the appreciation of quality assurance and user expectations. Systematic analysis of equipment failures reveals physical root causes that fall into one of four fundamental categories: design, manufacturing/installation, service, and material, which are discussed in the following sections along with examples. The tools available for failure analysis are then covered. Further, the article describes the categories of mode of failure: distortion or undesired deformation, fracture, corrosion, and wear. It provides information on the processes involved in RCA and the charting methods that may be useful in RCA and ends with a description of various factors associated with failure prevention.

Despite extensive aircraft landing gear design analyses and tests performed by designers and manufacturers, and the large number of trouble-free landings, aircraft users have experienced problems with and failures of landing gear components. Different data banks and over 200 failure analysis reports were surveyed to provide an overview of structural landing gear component failures as experienced by the Canadian Forces over the last 20 years on more than 20 aircraft types, and to assess trends in failure mechanisms and causes. Case histories were selected to illustrate typical problems, troublesome failure mechanisms, the role of high strength aluminum alloys and steels, and situations where fracture mechanics analyses provided insight into the failures. The two main failure mechanisms were: fatigue occurring mainly in steel components, and corrosion related problems with aluminum alloys. Very few overload failures were noted. A number of causes were identified: design deficiencies and manufacturing defects leading mainly to fatigue failures, and poor materials selection and improper maintenance as the principal causes of corrosion-related failures. The survey showed that a proper understanding of the failure mechanisms and causes, by thorough failure analysis, provides valuable feedback information to designers, operators and maintenance personnel for appropriate corrective actions to be taken.

This article focuses primarily on what an analyst should know about applying X-ray diffraction (XRD) residual stress measurement techniques to failure analysis. Discussions are extended to the description of ways in which XRD can be applied to the characterization of residual stresses in a component or assembly. The article describes the steps required to calibrate instrumentation and to validate stress measurement results. It presents a practical approach to sample selection and specimen preparation, measurement location selection, and measurement depth selection, as well as an outline on measurement validation. The article also provides information on stress-corrosion cracking and corrosion fatigue. The importance of residual stress in fatigue is described with examples. The article explains the effects of heat treatment and manufacturing processes on residual stress. It concludes with a section on the XRD stress measurements in multiphase materials and composites and in locations of stress concentration.

X-ray diffraction (XRD) residual-stress analysis is an essential tool for failure analysis. This article focuses primarily on what the analyst should know about applying XRD residual-stress measurement techniques to failure analysis. Discussions are extended to the description of ways in which XRD can be applied to the characterization of residual stresses in a component or assembly and to the subsequent evaluation of corrective actions that alter the residual-stress state of a component for the purposes of preventing, minimizing, or eradicating the contribution of residual stress to premature failures. The article presents a practical approach to sample selection and specimen preparation, measurement location selection, and measurement depth selection; measurement validation is outlined as well. A number of case studies and examples are cited. The article also briefly summarizes the theory of XRD analysis and describes advances in equipment capability.

This article describes concepts and tools that can be used by the failure analyst to understand and address deformation, cracking, or fracture after a stress-related failure has occurred. Issues related to the determination and use of stress are detailed. Stress is defined, and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear elastic fracture mechanics analysis, with some mention of elastic-plastic fracture mechanics analysis. The article describes the probabilistic aspects of fatigue and fracture. Information on crack-growth simulation of the material is also provided.

A failure analysis case study on railroad rails is presented. The work, performed under the sponsorship of the Department of Transportation, addresses the problem of shell and detail fracture formation in standard rails. Fractographic and metallographic results coupled with hardness and residual stress measurements are presented. These results suggest that the shell fractures form on the plane of maximum residual tensile stresses. The formation of the shells is aided by the presence of defects in the material in these planes of maximum residual stress. The detail fracture forms as a perturbation from the shell crack under cyclic loading and is constrained to develop as an embedded flaw in the early stages of growth because the crack is impeded at the gage side and surface of the rail head by compressive longitudinal stresses.

The failure of T12 reheater tubes that had been in service for only 3000 h was investigated. The thickness of the tubes was visibly reduced by heavy oxidation corrosion on the inner and outer walls. The original pearlite substrate completely decomposed. Uniform oxide scale observed on the inner wall showed obvious vapor oxidation corrosion characteristics. Corrosion originated in the grain boundary, and selective oxidation occurred due to ion diffusion in the substrate. The layered oxide scale on the inner wall is related to the different diffusion rates for different cations. Exposure to high temperature corrosive flux accelerated the corrosion on the outer wall. Microstructure degradation and the corrosion characteristics observed indicate that the tubes failed primarily because of overheating, which is confirmed by calculations.

Rolling-contact fatigue (RCF) is a common failure mode in components subjected to rolling or rolling-sliding contact. This article provides a basic understanding of RCF and a broad overview of materials and manufacturing techniques commonly used in industry to improve component life. A brief discussion on coatings to improve surface-initiated fatigue and wear is included, due to the similarity to RCF and the increasing criticality of this failure mode. The article presents a working knowledge of Hertzian contact theory, describes the life prediction of rolling-element bearings, and provides information on physics and testing of rolling-contact fatigue. Processes commonly used to produce bearings for demanding applications are also covered.

The Rocky Point Viaduct, located near Port Orford, OR, was replaced after only 40 years of service. A beam from the original viaduct was studied in detail to determine the mechanisms contributing to severe corrosion damage to the structure. Results are presented from the delamination survey, potential and corrosion mapping, concrete chemistry, and concrete physical properties. The major cause of corrosion damage appears to have been the presence of both pre-existing and environmentally-delivered chlorides in the concrete.

This article addresses some established protocols for characterizing thermoplastics and whether they are homogeneous resins, alloyed, or blended compositions or highly modified thermoplastic composites. It begins with a discussion on characterizing mechanical, rheological, and thermal properties of polymer. This is followed by a section describing molecular weight determination using viscosity measurements. Next, the article discusses the use of cone and plate and parallel plate geometries in melt rheology. It then reviews the processes involved in the analysis of thermoplastic resins by chromatography. Finally, the article covers three operations of thermoanalysis, namely differential scanning calorimetry, thermogravimetric analysis, and thermomechanical testing.