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.

This article focuses on four industrial additive manufacturing approaches that are used to create polymer parts. The first section focuses on material extrusion, providing information on lumped-parameter material flow models and higher-fidelity models developed to estimate temperature distribution. The second section covers polymer powder-bed sintering/ fusion, discussing the different levels of scale used to address modeling and the impact of process settings: thermodynamics at the powder-bed surface, consolidation of adjacent particles in the fusion process, and fusion and molecular-level behavior within particles. The third section on vat photopolymerization (VPP) discusses two primary approaches to modeling VPP processes, namely a lumped-parameter approach to estimate cured regions in the vat, known as the Jacobs model, and a high-fidelity, continuum approach that uses finite-element methods. The final section is devoted to material jetting, focusing on simulations used to study droplet generation at the nozzle and droplet impact.

This article provides a detailed overview of the thermomechanical modeling of additive manufacturing (AM) process. It begins with information on a basic understanding of the formation of residual stress during AM processing followed by a discussion on models commonly applied in AM modeling, such as heat-input models, material models, and material activation models. Information on experimental setup for validation and simulation of directed-energy deposition model is then included. The article also provides information on moving-source and part-scale analyses to simulate the laser powder-bed fusion AM process.

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 provides an overview of cavitation erosion with a specific focus on the estimation of mass loss. It describes the mechanisms of cavitation erosion and the types of laboratory devices to evaluate the resistance to cavitation erosion of materials. The laboratory devices include rotating disks, vibratory devices, cavitating liquid jets, and high-speed cavitation tunnels. The article discusses materials selection and surface protection to prevent cavitation erosion. It reviews the fluid-structure interaction that plays a role in cavitation erosion particularly for compliant materials. The article provides information on the numerical prediction of cavitation erosion damage by the finite element method (FEM).

This article discusses two basic forms of extrusion: cold and hot. It provides information on three types of extrusion processes, namely, direct extrusion, reverse extrusion, and hydrostatic extrusion. The article also discusses the mechanics, analysis, tooling and die design of extrusion as well as thermodynamics. The finite-element method suitable for simulation of metal forming processes is explained. The article examines the extrusion defects that are divided into three different categories including surface, subsurface, and internal type. It includes information on friction and lubrication modeling of extrusion processes. The article also discusses the fundamentals of extrusion technology of titanium alloys and aluminum. It concludes with information on two forms of wear in extrusion, namely, adhesive and abrasive wear.

This article describes a method to predict mechanical properties of cast iron materials and illustrates how to use the predictions in computer-aided tools for the analysis of castings subjected to load. It outlines some ways to predict the hardness and elastic modulus of cast iron without going into dislocation theory. The article discusses modeling of hardness in cast iron based on a regular solution equation in which the properties of each phase depend on chemical composition and coarseness. It describes the evaluation of material parameters from the tensile stress-strain curve. The article concludes with an illustration of a finite-element method (FEM) model containing heterogeneous mechanical properties using local material definitions.

Designing of induction heating, or, generally electro technological installations, requires mathematical modeling for solving problems related to various physical phenomena, including electromagnetic (EM), thermal, mechanical, fluidic, and metallurgical fields. This article focuses on the solution of Maxwell's equations (MEs) and provides some basic information regarding the heat transfer and fluid equations, because these physical phenomena usually are strongly coupled to magnetic and electric fields. The solutions are usually obtained by using specific numerical methods such as finite-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method.

This article provides a discussion on probes for laboratory tests and resultant curves of industrial quenching processes. It describes the scope of the tests, and the calculation of heat-transfer coefficient (HTC) based on the tests. The article highlights the differences between the laboratory tests and characterization of industrial quenching processes. It reviews the importance of initial heat-flux density and first critical heat-flux density. The theoretical principle behind and the purpose of the temperature gradient method are discussed. The article provides information on the design of the probe, heat-extraction dynamics, and influence of wetting kinematics. It also includes discussions on the simplified 1-D temperature-distribution model, calculation of the HTC, and the finite-volume method for the heat-conduction equation.

This article summarizes many approaches that are used to simulate relaxation of bulk residual stresses in components. It presents analytical examples to highlight the complexity of residual stress and strain distributions observed in simple geometries, with ideal material behavior and trivial loading and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep, advanced constitutive models, and complicated stress and temperature loading histories.

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.

This article discusses a set of experimental and computational studies aimed at understanding the effect of various processing parameters on the extent of burr and other defect formation during sheet edge-shearing and slitting processes. It describes the development of experimentally validated finite-element models for analyzing the classes of shearing processes. The article also discusses the use of microstructural characterization with stereology to render three-dimensional volumetric parameters. It concludes with information on the numerical simulation of an edge-shearing process, along with sensitivity studies with respect to process and tool parameters.

This article begins with information on the fundamentals of chip formation process and general considerations for the modeling and simulation of machining processes. It focuses on smaller-scale models that seek to characterize the workpiece/tool/chip interface and behaviors closely associated with that. The article describes the advantages and disadvantages of various finite-element modeling approaches, namely, transient models, continuous cutting model, steady-state model, hybrid model, two-dimensional models, and three-dimensional models. It discusses flow stress measurements using constitutive and inverse testing methods and reviews tool design for chip removal. The article explains the effect of tool geometry on burr formation and the effect of coatings on tool temperatures. It concludes with information on tool wear, which is an unavoidable effect of metal cutting.

This article describes the applications of induction heat treatment of metals, including normalizing, annealing, hardening, and tempering and stress relieving. It discusses the simulation techniques of the electromagnetic and thermal processes that occur during induction heat treating. The article explains the finite-difference method, finite-element method, mutual impedance method, and boundary-element method for the numerical computation of the induction heat treating processes. It also discusses the direct and indirect coupling approaches for coupling the electromagnetic and heat-transfer problems. Modern computer simulation techniques are capable of effectively simulating electromagnetic and thermal phenomena for many processes that involve electromagnetic induction. The article considers the challenges faced by developers of modern simulation software.

Simulation programs are becoming more effective tools in reducing the need for physical testing and the avoidance of costly downstream problems by solving the problems upfront in the early development stage. This article provides a brief review of the history and applied analysis of simple forming operations. It focuses on metal stamping simulation based on the finite-element methods or model (FEM) with emphasis on software tools using the three-dimensional FEM technology. The article discusses two aspects of particular importance in finite-element analysis of sheet forming and springback analysis: the type of solution algorithm/governing equation and the type of element. The article provides information on various models for material yield criteria.

This article reviews the characterization methods for producing 3-D microstructural data sets. The methods include serial sectioning by mechanical material removal method and focused ion beam tomography method. The article describes how these data sets are used in realistic 3-D simulations of microstructural evolution during materials processing and materials response. It also explains how the 3-D experimental data are actually input and used in the simulations using phase-field modeling and finite-element modeling.

This article provides a summary of the overall development of the finite element method (FEM) and its contribution to the materials forming industry. It focuses on the overall philosophy and evolution of the FEM for solving bulk forming issues. A number of applications of FEM are presented in the order they would be used in a typical manufacturing process sequence: primary materials processing, hot forging and cold forming, and product assembly. The article discusses four FEM modules: the deformation model, the heat-transfer model, the microstructural model, and the carbon diffusion model. The article also covers material fracture and die stress analysis and reviews optimization of the design of forming processes.

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.

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.

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.