Search Results for extreme-value distribution

This article details factors that have been used for evaluating the susceptibility of alloys to stress-corrosion cracking. Many considerations impacting the validity and accuracy of information gathered from laboratory testing programs are reviewed. The article highlights the main characteristics of probability distributions, such as normal distribution, log-normal distribution, exponential distribution, Poisson distribution, and extreme-value distribution. It also provides information on the statistical concepts to produce effective test programs.

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.

This article discusses the need for design allowables, development of design allowables, and important factors that affect the selection of the allowable. It provides a comparison between lamina and laminate allowables. The article discusses laminate results and specific techniques used in the statistical development of allowable values.

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.

This article presents effective stress equations that are based on the von Mises criterion, the Tresca criterion, and the Huddleston criterion. It describes the calculation of effective stresses for different cases: elastic stresses, steady-state creep stresses, stresses in a fully plastic case, and thermal stresses in a tube. The article illustrates the comparison of life predictions by the stress criteria and presents a simple mean diameter hoop stress equation, which is used for designing components. It also provides information on the multiaxial creep ductility of tubular components and multiaxial testing methods.

Induction heating has the ability to concentrate the electromagnetic field and heat within a certain area of the workpiece. This article provides a detailed discussion on the end heating of bars, rods, and billets using solenoid inductors, oval inductors, and channel inductors. It reviews the importance of computer modeling in predicting the impact of different, interrelated, and nonlinear factors on the transitional and final thermal conditions of billets and bars. The article describes the most appropriate processes to improve end heating process effectiveness. Induction bending of narrow circumferential band of pipe or tube is also discussed. The article concludes with a discussion on stress relieving of pipe ends and welded areas.

Induction heating computations deal with a multiphysics problem containing analysis of several coupled physical fields such as electromagnetic, temperature, mechanical, and metallurgical. In order to solve coupled electromagnetic-temperature field problems, it is necessary to develop suitable algorithms and numerical procedures, which make it possible to deal with these nonlinear coupled problems. This article focuses on the most common approaches to coupled electromagnetic and heat transfer problems, namely, weak-, quasi-, and hard-coupled formulations.

There are two parts to deal with uncertainty in fatigue design: determining the distributions of possible values for all uncertain inputs and calculating the probability of failure due to all the uncertain inputs. This article discusses the sources of uncertainty in a fatigue analysis, such as the material properties, distribution of applied stress levels within a given environment, environments or loading intensities, and modeling or prediction. It presents a probabilistic approach for analyzing the uncertainties and determining the level of reliability (probability of failure).

The most popular metal hot working processes for which induction heating is applied are forging, forming, extrusion, and rolling. This article focuses on estimation techniques to determine basic induction heating process parameters, including coil power, length of heating line, and frequency selection. It discusses three modes of heat transfer: conduction, convection, and radiation, in induction heating. The article describes the factors affected by a distortion of the magnetic field at the coil end through a schematic illustration of distribution of three magnetic force components experienced by the turns of the coil. It concludes with information on some case studies of numerical simulation.

This article discusses the two extremes of solute redistribution, equilibrium solidification and nonequilibrium Gulliver-Scheil solidification, for which solid redistribution of solute within the primary solid phase is the distinguishing parameter. The process and material parameters that control microsegregation are discussed in relation to the manifestations of microsegregation in simple and then increasingly complex alloy systems. The measurement and kinetics of microsegregation are discussed for the binary isomorphous systems: titanium-molybdenum; binary eutectic systems: aluminum-copper and aluminum-silicon; binary peritectic systems: copper-zinc; multicomponent eutectic systems: Al-Si-Cu-Mg; and for systems with both eutectic and peritectic reactions: Fe-C-Cr and nickel-base superalloy.

This article provides a brief introduction to lubrication as a method to reduce friction between two surfaces. It discusses the surface characteristics of parts and explores how lubrication helps separate two contacting surfaces and thereby decreases the coefficient of friction. The article details the classifications of lubrication regimes, namely, boundary, mixed, hydrodynamic, and elastohydrodynamic lubrications. It discusses the various types of lubricant materials and additives, including liquid lubricants, solid lubricants, gaseous lubricants, greases, green lubricants, and nanomaterials. The article also reviews the properties of lubricants. It describes the tribological evaluation of lubricants, including stribeck test, four-ball test, block-on-ring test, pin-in-vee test, and reciprocating motion test.

This article reviews the essential parts of the complex process of quantitative image analysis to assist automatic image analysis in laboratories. It describes the basic difference between the bias of classical manual stereological analysis and quantitative image analysis. The article concentrates on the basic properties of digital measurements that are the core of quantitative image analysis. It provides a brief description of the specimen and apparatus preparation as well as the image acquisition. The article explains how to evaluate stereological parameters and provides the general rules and guidelines for optimization of image processing algorithms from the viewpoint of shape quantification. It concludes with examples that demonstrate the usefulness of automatic image analysis in comparison to manual methods.

Induction heating is a combination of several interrelated physical phenomena, including heat transfer, electromagnetics, and metallurgy. This article presents a brief review of different heat transfer modes, namely, heat conduction, thermal radiation, and convection. It focuses on the specifics of induction heating and heat treating applications. The article discusses the nonlinear and interrelated nature of a particular heat transfer phenomenon, physical property, and skin effect. It also presents simple case studies and general physical laws governing different heat transfer modes. The article also discusses the basic concepts of direct current and alternating current circuits, and reviews the theory of electromagnetic fields.

This article provides a detailed account of x-ray diffraction (XRD) residual-stress techniques. It begins by describing the principles of XRD stress measurement, followed by a discussion on the most common methods of XRD residual-stress measurement. Some of the procedures required for XRD residual-stress measurement are then presented. The article provides information on measurement of subsurface stress gradients and stress relaxation caused by layer removal. The article concludes with a section on examples of applications of XRD residual-stress measurement that are typical of industrial metallurgical, process development, and failure analysis investigations undertaken at Lambda Research.

This article discusses some of the statistical aspects of design from an engineer's perspective. It reviews the commonly used statistical terms and distributions for providing some guidance on the practical engineering applications of these distributions. The article describes the basic statistical procedures that can be used to address variability and uncertainty in an engineering analysis. It contains a table that lists the relevant statistics standards published by the American Society of Testing and Materials.

This article describes the effects of furnace atmospheric elements, including air, water vapor, molecular nitrogen, carbon dioxide, and carbon monoxide, on steels. It provides useful information on six groups of commercially important prepared atmospheres classified by the American Gas Association on the basis of the method of preparation or on the original constituents employed. These groups are designated and defined as follows: Class 100, exothermic base; Class 200, prepared nitrogen base; Class 300, endothermic base; Class 400, charcoal base; Class 500, exothermic-endothermic base; and Class 600, ammonia base. These are subclassified and numerically designated to indicate variations in the method by which they are prepared. The article also contains a table that lists significant furnace atmospheres and typical applications.

This article provides the basics of overall quench process distortion. It describes the influence of quenching processes on the generation of distortion. Examples for the distortion behavior of different types of components are presented. Then, comparisons between different quenching processes are provided. The article presents some possibilities for minimization of shape changes by the quenching process itself. Several suggestions are given for quenching processes in evaporating fluids. An example is provided for out-of-roundness reduction for rings by well-defined inhomogeneous quenching in a gas nozzle field. Another example shows how intensive and high-speed quenching can help to reduce the bending of shafts with an asymmetrical cross-section. The last example shows the result when external loads and nonsymmetric quenching act together. The article also presents test samples for the judgment about distortion potential arising from heat treatment equipment.

A newly developed theory on plasticity makes it possible to include elastic effects, which play a major role when using blunt hardness indenters. This article reviews the new theory and explains several phenomena associated with practical hardness testing. In the indentation hardness test, a blunt indenter that approximates a flat punch is forced into a plane surface. The effective cone angle for most indenters is such that some upward flow results even when there is sufficient material surrounding the indenter to provide a full elastic constraint. When loaded by a blunt indenter, materials with high values of Young's Modulus of Elasticity/uniaxial flow stress (E/Y) (metals) appear to develop a Hertzian stress distribution over the contact. In contrast, materials with low values of E/Y (glasses and polymers) develop a uniform distribution of stress.

This article provides guidelines for the assessment of model quality in materials science and engineering. It discusses the fundamentals of model quality assessment and the calibration of mechanistic material models. The article reviews the considerations for the model verification during software implementation planning to identify suitable programs, software components, and programming languages. It describes the validity tests used in model validation, including boundary-value tests, degenerate problem tests, sensitivity tests, and benchmarking. The article also presents an example of model calibration, verification, and validation for the prediction of martensite start temperature of steels.

This article presents definitions, equations, and notational conventions that are used widely in statistical analysis. It provides information on a basic framework for the selection of a statistical test. The article outlines the basic elements common to all statistical tests. Illustrations of specific statistical tests and the concept of confidence limits are introduced. The article provides an overview of sampling issues, with guidance on both selecting a sampling method and determining the number of units to sample. One-way analysis of the variance, correlation, and simple regression are also illustrated.