This article focuses on the modeling and simulation of diffusion-controlled processes related to both materials processing such as heat treatments, and materials degradation from a practical perspective by using the one-dimensional (1-D) sharp interface approach. It describes various diffusion simulation models, such as one-phase simulations, moving phase-boundary simulations, and dispersed system simulations. The article presents case studies that illustrate some examples where diffusion simulations have been applied to industrial-based problems, with an emphasis on the approaches used and the lessons learned from performing such simulations.

In order to model macrosegregation, one must consider convection and the partitioning of segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the simulation of macrosegregation and microsegregation.

This article discusses the three different modeling approaches for grain structures formed during solidification of metallic alloys: direct modeling of dendritic structure, direct modeling of grain structure, and indirect modeling of grain structure. The main construction bases, the scale at which it applies, and the mathematical background are presented for each modeling approach. The article concludes with a table that presents a comparison of the main inputs/outputs, approximations, numerical methods, kinetics laws, and applications for the three approaches to modeling of dendritic grain solidification.

There is a need for models that predict the percentage and size of porosity formed during solidification in order to effectively predict mechanical properties. This article provides an overview of equations that govern pore formation. It reviews the four classes of models, highlighting both the benefits and drawbacks of each class. These classes include criteria functions, analytical models, continuum models, and kinetic models. The article also tabulates the criteria functions for porosity prediction.

This article reviews the topic of computational thermodynamics and introduces the calculation of solidification paths for casting alloys. It discusses the calculation of thermophysical properties and the fundamentals of the modeling of solidification processes. The article describes several commonly used microstructure simulation methods and presents ductile iron casting as an example to demonstrate the ability of microstructure simulation. The predictions for the major defects of casting, such as porosity, hot tearing, and macrosegregation, are highlighted. Finally, several industry applications are presented.

Homogenization, in a broad sense, refers to the processes designed to achieve uniform distribution of solutes or phases in a given matrix. This article addresses the root cause for inhomogeneities in cast components. It is nearly a standard industrial practice to homogenize alloys before thermomechanical processing. The article lists the objectives of homogenization and benefits of homogenization treatments. The benefits include increased resistance to pitting corrosion, increased resistance to stress-corrosion cracking, improved ductility, and uniform precipitate distribution during subsequent aging. The article provides a schematic illustration of an energy-dispersive X-ray spectroscope (EDS) scattered data of solute distributions across a dendrite due to microsegregation of chromium and molybdenum. It concludes with information on the computational modeling for simulation of microsegregation of chromium and molybdenum.

This article describes the fundamental concepts of heat treatment simulation, including the physical events and their interactions, the heat treatment simulation software, and the commonly used simulation strategies. It summarizes material data needed for heat treatment simulations and discusses reliable data sources as well as experimental and computational methods for material data acquisition. The article provides information on the process data needed for accurate heat treatment simulation and the methods for their determination. Methods for validating heat treatment simulations are also discussed with an emphasis on the underlying philosophy for the selection and design of validation tests. The article also discusses the applications, capabilities, and limitations of heat treatment simulations via selected industrial case studies for a better understanding of the effect of microstructure, distortion, residual stress, and cracking in gears, shafts, and bearing rings.

This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure and microstructure. The article describes the principles of the PF method and provides information on the applications of the PF method. The CA model is introduced as a computationally efficient method to predict grain structures in castings using the mesoscopic scale of individual grains. The article discusses the coupling of the CA to macroscopic calculation of heat, flow, and mass transfers in castings and applications to realistic casting conditions.

Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of the phase field method and the cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.

This article discusses continuum modeling, which is the most relevant approach in modeling grain growth, densification, and deformation during sintering. Continuum plasticity models are frequently used to describe the mechanical response of metal powders during compaction. The article illustrates the typical procedure for computer simulation for press and sinter process. It describes the procedure to obtain the material properties based on the generalized Shima-Oyane model. The article presents a wide variety of tests, accounting for data on the grain growth, densification, and distortion where these data help in the development of a constitutive model for sintering simulation. Finally, the article provides information on the simulation approaches used to optimize die compaction and sintering.

This article presents the governing equations and methodologies to model the press and sinter powder metallurgy, including continuum, micromechanical, multiparticle, and molecular dynamics approaches. It describes the constitutive relation for compaction and sintering. The article discusses the experimental determination of material properties and simulation verification for compaction and sintering. It reviews the use of modeling and simulation of press and sinter powder metallurgy, including gravitational distorting in sintering, compaction optimization, sintering optimization, and coupled press and sinter optimization.

This article focuses on transport phenomena and modeling approaches that are specific to vapor-phase processes (VPP). It discusses the VPP for the synthesis of materials. The article reviews the basic notions of molecular collisions and gas flows, and presents transport equations. It describes the modeling of vapor-surface interactions and kinetics of hetereogeneous processes as well as the modeling and kinetics of homogenous reactions in chemical vapor deposition (CVD). The article provides information on the various stages of developing models for numerical simulation of the transport phenomena in continuous media and transition regime flows of VPP. It explains the methods used for molecular modeling in computational materials science. The article also presents examples that illustrate multiscale simulations of CVD or PVD processes and examples that focus on sputtering deposition and reactive or ion beam etching.

This article illustrates the simulation procedure of casting process. It describes important elements and points of the simulations. These include the setting of clear simulation objectives, selection of proper simulation code, hints in modeling of shape and phenomena, initial and boundary conditions, physical properties, enmeshing, and evaluation of simulation results. The article also provides some insights into the application of models to real world problem for foundry process engineers.

This article reviews the various aspects of the simulation of solidification microstructures and grain textures. It describes the grain structures and morphology of dendrites or eutectics that compose the internal structure of the grains. A particular emphasis has been put on the simulation of defects related to grain textures and microstructures. The article provides information on the application of the most important simulation approaches and the status of numerical simulation.

Diffusion is the process by which molecules, atoms, ions, point defects, or other particle types migrate from a region of higher concentration to one of lower concentration. This article focuses on the diffusivity data and modeling of lattice diffusion in solid-state materials, presenting their diffusion equations. It discusses different methods for evaluating the diffusivity of a material, including the measurement of diffusion coefficients, composition profiles, and layer growth widths. The article reviews the various types of direct and indirect diffusion experiments to extract tracer, intrinsic, and chemical diffusivities. It provides information on the applications of single-phase and multiphase diffusion.

The microstructure that develops during the solidification stage of cast iron largely influences the subsequent solid-state transformations and mechanical properties of the cast components. This article provides a brief introduction of methods that can be used for simulating the solidification microstructure of cast iron. Analytical as well as numerical models describing solidification phenomena at both macroscopic and microscopic scales are presented. The article introduces macroscopic transport equations and presents analytical microscopic models for solidification. These models include the dendrite growth models and the cooperative eutectic growth models. The article provides some solutions using numerical models to simulate the kinetics of microstructure formation in cast iron. It concludes with a discussion on cellular automaton (CA) technique that can handle complex topology changes and reproduce most of the solidification microstructure features observed experimentally.

This article discusses the fundamental aspects of phase-field microstructure modeling. It describes the evolution of microstructure modeling, including nucleation, growth, and coarsening. The article reviews two approaches used in the modeling nucleation of microstructure: the Langevin force approach and explicit nucleation algorithm. Calculation of activation energy and critical nucleus configuration is discussed. The article presents the deterministic phase-field kinetic equations for modeling growth and coarsening of microstructure. It also describes the material-specific model inputs, chemical free energy and kinetic coefficients, for phase-field microstructure modeling. The article provides four examples that illustrate some aspects of phase-field modeling.

This article discusses process simulation applications such as casting, powder metallurgy, machining, surface engineering, heat treatment, and joining. The implementation of modeling and simulation tools requires accurate descriptions of material properties and process boundary conditions. The article describes the role of input data and boundary conditions for process simulations. It provides information on the critical enablers of computational materials engineering, such as the computational speed, computational materials engineering software/hardware supply chain, and cost structure for virtual versus physical manufacturing and analysis.

This article provides a brief historical perspective, a classification of metallurgical processes, basic model development efforts, and an overview of the potential future directions for the modeling of metals processing. It describes the classification of material behavior models, which can be grouped broadly into three classes: statistical, phenomenological, and mechanistic models. The article also presents an overview of the potential directions for the modeling of metals processing.

Sintering is a thermal treatment process in which a powder or a porous material, already formed into the required shape, is converted into a useful article with the requisite microstructure. Sintering can be classified as solid-state, viscous, liquid-phase, and pressure-assisted (or pressure) sintering. This article provides information on the mechanisms and theoretical analysis of sintering and focuses on the types, mechanisms, process and microstructural variables, computer simulation, stages, and fundamentals of densification and grain growth of solid-state sintering and liquid-phase sintering. It describes the models for viscous sintering and the methods used in pressure-assisted sintering, namely, uniaxial hot pressing, hot isostatic pressing, sinter forging, and spark plasma sintering.