This article provides a summary of the overall development of the finite element method (FEM) and its contribution to the materials forming industry. It presents an overview of FEM methodologies and applications in the order of their usage in typical manufacturing (bulk forming process) process sequence: primary materials processing, hot forging and cold forming, and product assembly. The article discusses the material fracture and dies stress analysis and presents the optimization techniques used in 2-D and 3-D preform die design.

Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs.

This article provides an explanation on how crystal plasticity is implemented within finite element formulations by the use of physical length scales: crystal scale and continuum scale. It provides theoretical formulations for kinematic framework for deforming crystals and polycrystals, elastic and plastic behaviors of single crystals, refinements to the single-crystal constitutive, and crystal-scale finite-element. The article also presents examples that illustrate the capabilities of the formulations at the length scales.

When complex designs, transient loadings, and nonlinear material behavior must be evaluated, computer-based techniques are used. This is where the finite-element analysis (FEA) is most applicable and provides considerable assistance in design analysis as well as failure analysis. This article provides a general view on the applicability of finite-element modeling in conducting analyses of failed components. It highlights the uses of finite-element modeling in the area of failure analysis and design, with emphasis on structural analysis. The discussion covers the general development and both general- and special-purpose applications of FEA. The special-purpose applications of FEA covered are piping and pressure vessel analysis, impact analysis, and microelectronic and microelectromechanical systems analysis. The article provides case histories that involved the use of FEA in failure analysis.

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.

Ultrasound is an ideal modality for nondestructive evaluation (NDE) because it enables the interior of objects to be assessed without the safety and access issues associated with radiography. This article summarizes the history of array usage in NDE and its relationship to medical applications. It discusses the mathematics behind classical beamforming, full matrix capture, and total focusing methods of imaging. The article shows how ultrasonic array data can be simulated by direct numerical methods (most commonly using finite-element methods), analytical methods, or hybrid methods. It also considers various methods of comparing the performance of arrays and imaging algorithms. The article provides a comparison of various advanced and nonlinear imaging algorithm and looks at some practical industrial applications of arrays. It concludes with some future perspectives for arrays in NDE.

This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.

This article provides general guidelines for casting design to provide progressive solidification, minimize heat concentration, eliminate cores, and prevent distortion. Casting design also affects tolerances. Casting tolerances depend on the alloy being poured, the size of the casting, and the molding method used. Designers can predict the effect of the design on the structure of the final part using solidification simulation models, namely finite element and finite difference models, and rapid prototyping. The article concludes with a short note on how the quality is assured in the foundry.

This article summarizes some of the issues and approaches in performing computational analyses of mechanical behavior, distortion, and hot tearing during solidification. It presents the governing equations and describes the methods used to solve them. The article reviews the finite element formulation, multidomain approaches, and arbitrary Lagrangian Eulerian method in solidification modeling. It illustrates the sand casting of braking disks and continuous casting of steel slabs.

This article discusses physical analysis, including slab method and upper-bound method and slip-line field analysis, for calculating stress states in plastic deformation processes. It presents various validation standards and models for evaluating the criterion of fracture for use in finite-element analyses of deformation processing. The article reviews the Cockcroft-Latham criterion of fracture and its reformulated extension for analysing the fracture locus for compression. It concludes with information on fundamental fracture models.

Hot-die forging and isothermal forging are unique forging methods developed to forge materials that are difficult or impossible to forge by conventional means. This article presents a comparative study on hot-die forging and isothermal forging. It discusses forging parameters, process selection considerations, design guidelines, alloy types and selection, and the advantages and disadvantages of hot-die forging and isothermal forging. The article discusses the application of the finite-element analysis modeling to design.

Coextrusion is defined as the simultaneous extrusion of two or more metals to form an integral product that can be carried out using conventional extrusion or drawing equipment at a temperature appropriate to the metal system being formed. This article discusses the applications, billet configurations, and metal flow modes of coextrusion. It presents the analytical studies of coextrusion: deformation energy methods, lower-bound (slab) analyses, upper-bound analyses, and finite-element analyses. These studies are used to identify the regime of material properties and process variables for which sound extrusions can be obtained. The article concludes with a discussion on the state-of-the-art of coextrusion that assists in developing process models, which accurately describe both the macroscopic and microscopic aspects of a process.

Computer simulation of microstructural evolution during hot rolling of steels is a major topic of research and development in academia and industry. This article describes the methodology and procedures commonly employed to develop microstructural evolution models to simulate microstructural evolution in steels. It presents an example of the integration of finite element modeling and microstructural evolution models for the simulation of metal flow and microstructural evolution in a hot rolling process.

This article focuses on the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. It informs that workability depends on the local conditions of stress, strain, strain rate, and temperature in combination with material factors. The article discusses the common testing techniques and process variables for workability prediction. It illustrates the simple and most widely used fracture criterion proposed by Cockcroft and Latham and provides a workability analysis using the fracture limit line. The article describes various workability tests, such as the tension test, ring compression test, plane-strain compression test, bend test, indentation test, and forgeability test. It concludes with information on the role of the finite-element modeling software used in workability analysis.

The purposes and methods of fatigue modeling and simulation in high-cycle fatigue (HCF) regime are to design either failsafe components or components with a finite life and to quantify remaining life of components with pre-existing cracks using fracture mechanics, with the intent of monitoring via an inspection scheme. This article begins with a discussion on the stages of the fatigue damage process. It describes hierarchical multistage fatigue modeling and several key points regarding the physics of crack nucleation and microstructurally small crack propagation in the HCF regime. The article provides a description of the microstructure-sensitive modeling to model fatigue of several classes of advanced engineering alloys. It describes the various modeling and design processes designed against fatigue crack initiation. The article concludes with a discussion on the challenges in microstructure-sensitive fatigue modeling.

This article considers the two primary methods used for ultrasonic inspection: pulse-echo and the transmission methods. Pulse-echo inspection can be accomplished with longitudinal, shear, surface (Rayleigh), or Lamb (plate) waves using a diverse range of transducers. The article discusses the principles of each of these inspection methods. It describes the applications and the basic data formats for single-element transducer-based systems, including A-scans, B-scans, and C-scans. The article provides information on electronic equipment used for ultrasonic inspection. It also describes how specific material conditions produce and modify A-scan indications. The article provides information on the controls and their functions for the display unit of the electronic equipment. It describes the techniques used for the identification and characterization of flaws, namely, surface (Rayleigh) wave and ultrasonic polar scan techniques.

Fatigue failures may occur in components subjected to fluctuating (time-dependent) loading as a result of progressive localized permanent damage described by the stages of crack initiation, cyclic crack propagation, and subsequent final fracture after a given number of load fluctuations. This article begins with an overview of fatigue properties and design life. This is followed by a description of the two approaches to fatigue, namely infinite-life criterion and finite-life criterion, along with information on damage tolerance criterion. The article then discusses the characteristics of fatigue fractures followed by a discussion on the effects of loading and stress distribution, and material condition on the microstructure of the material. In addition, general prevention and characteristics of corrosion fatigue, contact fatigue, and thermal fatigue are also presented.

This article begins with discussion on forgeability and the factors affecting the forgeability of aluminum and aluminum alloys. It describes the types of forging methods and equipment and reviews critical elements in the overall aluminum forging process: die materials, die design, and die manufacture. The article discusses the critical aspects of various manufacturing elements of aluminum alloy forging, including the preparation of the forging stock, preheating stock, die heating, lubrication, trimming, forming and repair, cleaning, heat treatment, and inspection. It concludes with a discussion on the forging of advanced aluminum materials and aluminum alloy precision forgings.

Failure analysis is generally defined as the investigation and analysis of parts or structures that have failed or appeared to have failed to perform their intended duty. Methods of field inspection and initial examination are also critical factors for both reconstruction analysts and materials failure analysts. This article focuses on the general methods and approaches from the perspective of a reconstruction analyst. It describes the elements of accident reconstruction, which have conceptual similarity with the principles for failure analysis of material incidents that are less complex than a large-scale accident. The approach presented is that the analysis and reconstruction is based on the physical evidence. The article provides a brief review of some general concepts on the use and limitations of advanced data acquisition tools and computer modeling. Legal implications of destructive testing are discussed in detail.

Computational fluid dynamics (CFD) is one of the tools available for understanding and predicting the performance of thermal-fluids systems. This article qualitatively describes the basic principles of CFD. The numerical methods, such as geometry description and discretization, used to solve the CFD equations are discussed. The article demonstrates the application of CFD to a few casting problems.