This article presents an approach to manage the uncertainty present in materials design. It describes inductive and deductive approaches to deal with uncertainty. The article focuses on providing an understanding of the opportunities for managing uncertainty and the decisions that influence the accuracy of the results. A design of experiments (DOE) represents a sequence of experiments to be performed, expressed in terms of factors set at specified levels. The article discusses the two types of DOEs: the full factorial design and the fractional factorial design. It explains the factors to be considered when selecting a procedure for propagating uncertainty. The article lists the categories of the popular types of uncertainty propagation methods, including simulation-based methods, local expansion methods, and numerical integration-based methods.

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.

Most modern instrumental techniques produce an output or signal that is not absolute. To obtain quantitative information, the raw output from an instrument must be converted into a physical quantity. This is done by standardizing or calibrating the raw response from an instrument and subsequently analyzing the uncertainty from both the calibration process and the measurement process. This article briefly summarizes the most common calibration and uncertainty analysis methods, namely external standard methods, abbreviated external standard methods, internal normalization, internal standard, standard addition, and serial dilution methods. In addition, it includes information on the traceability of true value of a measured quantity.

Neural networks permit the discovery of fundamental relationships and quantitative structure within vast arrays of ill-understood data. This article provides an overview of neural network modeling method, describing its overfitting nature. It discusses the use of neural networks in modeling noise and uncertainties in conducting experiments. The article also presents examples of the application of neural-network modeling to the behavior of metals.

Probability of detection (POD) assesses the performance of a non-destructive evaluation (NDE)-based inspection, which is a method used to determine the capability of an inspection as a function of defect type and defect size. This article provides an overview of the concept of POD, why it is needed, the history behind the development of POD, how POD assessments are performed, and how modeling and simulation can be integrated into the execution of a POD assessment. It describes the methods by which POD is determined. This includes detail on the experimental process to acquire the needed data, the mathematical methods to obtain a POD curve, and techniques to assess uncertainty in the POD curve as it is obtained from a limited data set. The concept of model-assisted POD (MAPOD) is introduced, with additional details and representative examples of MAPOD.

This article is a detailed account of the principles of electron-excited X-ray microanalysis. It begins by discussing the physical basis of electron-excited X-ray microanalysis and the advantages and limitations of energy dispersive spectrometry (EDS) and wavelength dispersive spectrometry for electron probe microanalysis. Key concepts for performing qualitative analysis and quantitative analysis by electron-excited X-ray spectrometry are then presented. Several sources that lead to measurement uncertainties in the k-ratio/matrix corrections protocol are provided, along with the significance of the raw analytical total. Sections on accuracy of the standards-based k-ratio/matrix corrections protocol with EDS and processes of analysis when severe peak overlap occurs are also included. The article provides information on low-atomic-number elements, iterative qualitative-quantitative analysis for complex compositions, and significance of standardless analysis in the EDS software. It ends with a section on the processes involved in elemental mapping for major and minor constituents.

The fracture-mechanics technology has significantly improved the ability to design safe and reliable structures and identify and quantify the primary parameters that affect structural integrity of materials. This article provides a discussion on fracture toughness of notched materials by explaining the ductile-to-brittle fracture transition and by correlating KId, KIc, and Charpy V-notch impact energy absorptions. It highlights the effects of constraint, temperature, and loading rate on the fracture transition. The article discusses the applications of fracture mechanism in limiting of operating stresses. It describes the mechanisms, testing methods, and effecting parameters of two main categories of fracture mechanics: linear-elastic fracture mechanics and elastic-plastic fracture mechanics. The article concludes with a discussion on the three major progressive stages of fatigue: crack initiation, crack growth, and fracture on the final cycle.

This article examines the factors influencing the fatigue behavior of an individual weldment, using extensive experimental data and a computer model, which simulates the fatigue resistance of weldments. It discusses the process of fatigue in weldments. The service conditions, which favor long crack growth and the conditions, which favor crack nucleation are contrasted. The article presents experimental data, which is used to show the effect of weldment geometry on fatigue resistance. Several useful geometry classification systems are compared. The article analyzes a computer model, which is employed to investigate the behavior of two hypothetical weldments, namely, a discontinuity-containing weldment and a discontinuity-free weldment.

Catastrophic failure best typifies the characteristic behavior of brittle solids in the presence of cracks or crack-like flaws under ambient conditions. This article provides a description of the concepts of fracture mechanics of brittle solids and focuses on the various testing methods developed to characterize the fracture behavior of brittle solids with examples. These include the fracture toughness test method and R-curve test method at ambient and elevated temperatures. The article also includes information on the evaluation of fracture-toughness test results and the behavior of R-curve.

Fitness-for-service assessment procedures can be used to assess the integrity, or remaining life, of components in service. Depending on the operating environment and the nature of the applied loading, a structure can fail by a number of different modes: brittle fracture, ductile fracture, plastic collapse, fatigue, creep, corrosion, and buckling. This article focuses on the broad categories of these failure modes: fracture, fatigue, environmental cracking, and high-temperature creep. It also discusses the benefits of a fitness-for-service approach.

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.

The goal of using nondestructive evaluation (NDE) in conjunction with failure analysis is to obtain the most comprehensive set of data in order to characterize the details of the damage and determine the factors that allowed the damage to occur. The NDE results can be used to determine optimal areas upon which to focus for sectioning and metallography in order to further investigate the condition of the component. This article provides information on the inspection method available for failure analysis, including standard methods such as visual testing, penetrant testing, and magnetic particle testing. It covers the effects of various factors on the properties of the part that may impact failure analysis, describes the characterization of damage modes and crack sizes, and finally discusses the processes involved in application of NDE results to failure analysis.

This article presents an approach to characterize the effects of surface treatments to enhance fatigue properties, with particular concern for wear, corrosion, and thermal effects. It discusses the considerations in selecting fabrication or subsequent surface processing procedures to improve fatigue resistance in terms of their respective effects on fatigue performance. The article details the experimental data sets representing specific materials, typical test geometries, and a range of different processing methods used to enhance resistance as compared to results for laboratory tests.

This article describes the test techniques that are available for monitoring crack initiation and crack growth and for obtaining information on fatigue damage in test specimens. These techniques include optical methods, the compliance method, electric potential measurement, and gel electrode imaging methods. The article discusses the magnetic techniques that are primarily used as inspection techniques for detecting fatigue cracks in structural components. It details the principles and operation procedures of the liquid penetrant methods, positron annihilation techniques, acoustic emission techniques, ultrasonic methods, eddy current techniques, infrared techniques, exoelectron methods, and gamma radiography. The article explains the microscopy methods used to determine fatigue crack initiation and propagation. These include electron microscopy, scanning tunneling microscopy, atomic force microscopy, and scanning acoustic microscopy. The article also reviews the X-ray diffraction technique used for determining the compositional changes, strain changes, and residual stress evaluation during the fatigue process.

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.

Computational fluid dynamics (CFD) is a computationally intensive three-dimensional simulation of thermal fluids systems where non-linear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid generation with complex geometries. It discusses the four-step procedures used in the CFD process for engineering design: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. The article also provides information on the engineering applications of the CFD. It concludes with a discussion on issues and directions for engineering CFD.

Computational fluid dynamics (CFD) is reserved for computationally intensive three-dimensional simulations of thermal fluids systems where nonlinear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts of numerical stability and accuracy are also reviewed. The article describes two approaches for grid generation with complex geometries: the use of unstructured grids and the use of special differencing methods on structured grids. The article describes the four-step procedures of the CFD process: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. It provides information on the applications of the engineering CFD. Issues and directions for the engineering CFD are also described.

Nonlinear ultrasonic nondestructive examination (NDE) techniques are based on nonlinear interaction of ultrasonic waves with the material to be characterized and defects to be detected. This article introduces the basic principles of nonlinear material-wave interaction, the origin of intrinsic nonlinearity in intact solids, and the main mechanisms of excess nonlinearity in damaged metals. It describes the measurement methods for nonlinear ultrasonic materials characterization and flaw-detection. The article schematically illustrates the instrumentation used for measurements of longitudinal wave and Rayleigh surface acoustic waves. It concludes with information on the applications of nonlinear ultrasonics.

Stress-corrosion cracking (SCC) occurs under service conditions, which can result, often without any prior warning, in catastrophic failure. Hydrogen embrittlement is distinguished from stress-corrosion cracking generally by the interactions of the specimens with applied currents. To determine the susceptibility of alloys to SCC and hydrogen embrittlement, several types of testing are available. This article describes the constant extension testing, constant load testing, constant strain-rate testing for smooth specimens and precracked or notched specimens of SCC. It provides information on the cantilever beam test, wedge-opening load test, contoured double-cantilever beam test, three-point and four-point bend tests, rising step-load test, disk-pressure test, slow strain-rate tensile test, and potentiostatic slow strain-rate tensile test for hydrogen embrittlement.

Modeling will help reduce machining problems and thereby enable more rapid introduction of high-performance materials and components. This article discusses the technical needs of aircraft engine and airframe structural components and modeling of heat-treat-induced residual stress by finite-element residual-stress analysis. It describes the two-dimensional (2-D) and three-dimensional (3-D) procedures involved in finite-element residual-stress analysis. The article deals with the 2-D and 3-D machining distortion validation on engine-disk-type components. It describes methods for obtaining machining-induced residual stresses, including detailed finite-element analysis of the cutting process, the simple fast-acting mechanistic model, and the semi-empirical linear stress model. The article concludes with information on the modeling benefits and implementation of modeling in a production environment.