Modelling and Simulation in Materials Science and Engineering

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.

Homogeneous nucleation from aluminum (Al) melt was investigated by million-atom molecular dynamics simulations utilizing the second nearest neighbor modified embedded atom method potentials. The natural spontaneous homogenous nucleation from the Al melt was produced without any influence of pressure, free surface effects and impurities. Initially isothermal crystal nucleation from undercooled melt was studied at different constant temperatures, and later superheated Al melt was quenched with different cooling rates. The crystal structure of nuclei, critical nucleus size, critical temperature for homogenous nucleation, induction time, and nucleation rate were determined. The quenching simulations clearly revealed three temperature regimes: sub-critical nucleation, super-critical nucleation, and solid-state grain growth regimes. The main crystalline phase was identified as face-centered cubic, but a hexagonal close-packed (hcp) and an amorphous solid phase were also detected. The hcp phase was created due to the formation of stacking faults during solidification of Al melt. By slowing down the cooling rate, the volume fraction of hcp and amorphous phases decreased. After the box was completely solid, grain growth was simulated and the grain growth exponent was determined for different annealing temperatures.

Only few available interatomic interaction potentials implement the α ↔ γ phase transformation in iron by featuring a stable low-temperature bcc and high-temperature fcc lattice structure. Among these are the potentials by Meyer and Entel (1998 Phys. Rev. B 57 5140), by Müller et al (2007 J. Phys.: Condens. Matter 19 326220) and by Lee et al (2012 J. Phys.: Condens. Matter 24 225404). We study how these potentials model the phase transformation during heating and cooling; in order to help initiating the transformation, the simulation volume contains a grain boundary. For the martensitic transformation occurring on cooling an fcc structure, we additionally study two potentials that only implement a stable bcc structure of iron, by Zhou et al (2004 Phys. Rev. B 69 144113) and by Mendelev et al (2003 Philos. Mag. 83 3977). We find that not only the transition temperature depends on the potential, but that also the height of the energy barrier between fcc and bcc phase governs whether the transformation takes place at all. In addition, details of the emerging microstructure depend on the potential, such as the fcc/hcp fraction formed in the α → γ transformation, or the twinning induced in and the lattice orientation of the bcc phase in the γ → α transformation.

A one dimensional Bravais lattice model is applied to a superabundant vacancy (SAV) delta δ phase (Pd ₃VacD ₄—octahedral), in the palladium–deuterium system. SolidWorks is used to simulate the motion of atoms and ions in the lattice. These two approaches give identical results for the vibrations of the deuterons indicating that large vibrations of deuterons are possible when the microstructure is a mixture of beta deuteride and small volume percent delta SAV phase. These conditions result from the unique geometry and crystallography of δ phase. According to both the model and simulation, as the size of δ phase increases, opportunity for high amplitude vibrations of deuterons increases. Increasing temperature should have a similar effect.

The Open Visualization Tool (OVITO) is a new 3D visualization software designed for post-processing atomistic data obtained from molecular dynamics or Monte Carlo simulations. Unique analysis, editing and animations functions are integrated into its easy-to-use graphical user interface. The software is written in object-oriented C++, controllable via Python scripts and easily extendable through a plug-in interface. It is distributed as open-source software and can be downloaded from the website http://ovito.sourceforge.net/.

In this work we propose a new force field for modelling of adsorption of CO ₂, N ₂, O ₂ and Ar in all silica and Na ⁺ exchanged Si–Al zeolites. The force field has a standard molecular-mechanical functional form with electrostatic and Lennard-Jones interactions satisfying Lorentz–Berthelot mixing rules and thus has a potential for further extension in terms of new molecular types. The parameters for the zeolite framework atom types are optimized by an iterative procedure minimizing the difference with experimental adsorption data for a number of different zeolite structures and Si:Al ratios. The new force field shows a good agreement with available experimental data including those not used in the optimization procedure, and which also shows a reasonable transferability within different zeolite topologies. We suggest a potential usage in screening of different zeolite structures for carbon capture and storage process, and more generally, for separation of other gases.

The production of stamped parts from rolled aluminum sheets requires different tempers and different thermal routes. While the slip and hardening behavior of the alloy strongly depends on the temper and the process temperature, the crystallographic texture remains largely static. Although the plastic anisotropy of rolled sheet is largely a function of the crystallographic texture, a dependency of plastic anisotropy on the temper has been reported for 6xxx series alloys, indicating that slip and hardening behavior have some influence. A systematic investigation of the effect of the slip and hardening behavior on the plastic anisotropy, however, does not exist. In this study, a crystal plasticity fast Fourier transform framework is utilized to predict the r-values, a common measure for plastic anisotropy, of two widely used commercial aluminum alloys possessing different crystallographic textures, AA6016 and AA5182. To investigate the sensitivity of the r-values to changes in the modeling parameters, a suite of simulations is performed in which the modeling parameters are systematically changed, and the resulting changes to the predicted r-values are calculated. Furthermore, numerical parameters, such as the level of discretization and the number of simulated grains are studied. Results indicate that the predicted r-value is less dependent on changes to crystal plasticity modeling parameters than to the initial crystallographic texture. Resulting trends are discussed.

ATK-ForceField is a software package for atomistic simulations using classical interatomic potentials. It is implemented as a part of the Atomistix ToolKit (ATK), which is a Python programming environment that makes it easy to create and analyze both standard and highly customized simulations. This paper will focus on the atomic interaction potentials, molecular dynamics, and geometry optimization features of the software, however, many more advanced modeling features are available. The implementation details of these algorithms and their computational performance will be shown. We present three illustrative examples of the types of calculations that are possible with ATK-ForceField: modeling thermal transport properties in a silicon germanium crystal, vapor deposition of selenium molecules on a selenium surface, and a simulation of creep in a copper polycrystal.

The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.

We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis algorithms such as common neighbor analysis (CNA), centrosymmetry analysis, bond angle analysis, bond order analysis and Voronoi analysis. In addition we propose a simple extension to the CNA method that makes it suitable for multi-phase systems. Finally, we introduce a new structure identification algorithm, the neighbor distance analysis, which is designed to identify atomic structure units in grain boundaries.

Mixed-type dislocations are prevalent in metals and play an important role in their plastic deformation. Key characteristics of mixed-type dislocations cannot simply be extrapolated from those of dislocations with pure edge or pure screw characters. However, mixed-type dislocations traditionally received disproportionately less attention in the modeling and simulation community. In this work, we explore core structures of mixed-type dislocations in Al using three continuum approaches, namely, the phase-field dislocation dynamics (PFDD) method, the atomistic phase-field microelasticity (APFM) method, and the concurrent atomistic-continuum (CAC) method. Results are benchmarked against molecular statics. We advance the PFDD and APFM methods in several aspects such that they can better describe the dislocation core structure. In particular, in these two approaches, the gradient energy coefficients for mixed-type dislocations are determined based on those for pure-type ones using a trigonometric interpolation scheme, which is shown to provide better prediction than a linear interpolation scheme. The dependence of the in-slip-plane spatial numerical resolution in PFDD and CAC is also quantified.

In this work, selecting the equal-molar CoNiRu multi-principal element alloy (MPEA) as a model material, we study dislocation core structures starting from first principles. We begin by sifting through all possible configurations to find those corresponding to elastic stability and energetically favored face-centered cubic (fcc) phases and, then, for these configurations, employ a phase field-based model to predict the extent of dislocations lying within them. The main findings are that for the fcc phase, (i) large variations in atomic configuration for the same chemical composition can cause significant changes in the generalized stacking fault energy surface and (ii) the dispersion in defect fault energies are chiefly responsible for substantial variations in the intrinsic stacking fault (ISF) widths of screw and edge dislocations. For instance, positive the ISF energy can vary by 10 times, with the lower values correlated with entirely Ni and Ru atoms and higher values with only Co and Ru atoms across the slip plane. Variations in lattice parameter and stiffness tensor accompany local differences in atomic configuration are also taken into account but shown to play a lesser role. We find that the dislocation can experience profound variations (3–7-fold changes) in its associated ISF width along its line, with the screw dislocation experiencing a greater variation than the edge dislocation (6.02–43.22 Å for the screw dislocation, and 19.6–62.62 Å for the edge dislocation). We envision that the ab initio-informed phase-field modeling method developed here can be readily adapted to MPEAs with other chemical compositions.

Over the past decade, there has been a resurgence in the importance of data-driven techniques in materials science and engineering. The utilization of state-of-the art algorithms, coupled with the increased availability of experimental and computational data, has led to the development of surrogate models offering the promise of rapid and accurate predictions of materials’ properties based solely on their structure or composition. Such machine learning (ML) models are trained on available past data and are thus susceptible to the intrinsic uncertainties/errors associate with these past measurements. The glass transition temperature ( T _g) of polymers, a property of paramount interest in polymer science, is one strong example of a material property that can show widespread variation in the final reported value as a result of a variety of intrinsic and extrinsic factors that occur during the experimental measurement process. In the current work, we curate a large database of T _g measurements from a variety of data sources and proceed to investigate the statistical nature of the inherent uncertainties in the database. Through the partitioning of the dataset using statistically relevant measures, we investigate the effect of variations in the dataset on the performance of the final ML model. We demonstrate that the measure of central tendency, median is a valid approximation when dealing with multiple reported values for T _g when dealing with multiple reported values of T _g for the same polymeric material. Moreover, the Bayesian model noise/uncertainty that emerges from our machine-learning pipeline is able to represent quantitatively the underlying noise/uncertainties in the experimental measurement of T _g.

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.

We generate representative structural models of amorphous carbon (a-C) from constant-volume quenching from the liquid with subsequent relaxation of internal stresses in molecular dynamics simulations using empirical and machine-learning interatomic potentials. By varying volume and quench rate we generate structures with a range of density and amorphous morphologies. We find that all a-C samples show a universal relationship between hybridization, bulk modulus and density despite having distinctly different cohesive energies. Differences in cohesive energy are traced back to slight changes in the distribution of bond-angles that is likely linked to thermal stability of these structures.

This paper presents the thermodynamic dislocation theory containing several modifications over its first version which was originally proposed by Langer, Bouchbinder, and Lookman [5]. Employing a small set of physics-based material parameters identified by the large scale least squares analysis, we show that the theory can fit the stress–strain curves of bcc crystals niobium, tantalum, tungsten, and vanadium over a wide range of temperatures and strain rates.

Tungsten components inside fusion reactors are subjected to extreme conditions, including an exceptionally high heat flux. This loading induces high stress levels, that may lead to brittle fracture. The current work aims to provide novel insights by relating the risk for brittle fracture to the tungsten microstructure and loadings conditions. To this end, a crystal plasticity framework is adopted with a temperature dependent slip resistance. The required parameters are obtained from experimental data in the literature. The risk for brittle fracture is assessed by means of Beremin's weakest-link theory. The brittle-to-ductile transition temperature (BDTT) found in literature can be accurately described with the presented framework. The simulation results reveal that the BDTT decreases linearly with the volume fraction of recrystallized grains in the microstructure. It is also shown that a sharp interface between rolled and recrystallized microscopic grains is more favourable in terms of risk for brittle fracture.

A molecular dynamics (MD) simulation method has been used to predict the interfacial behavior of single-wall carbon nanotube (CNT) reinforced aluminum (Al) composites. At the interface of the CNT and the Al, only van der Waals interaction was considered. The effect of CNT volume fraction and chirality on CNT pull-out has been studied for the first time with a proper distinction between them. The length of all the CNTs was kept constant throughout the study. The approach used in this work was validated with an earlier study. The present study revealed that the average pull-out load was found proportional to both the CNT volume fraction as well as the diameter. The smaller diameter CNTs improved the interfacial shear strength (ISS) at lower volume fraction significantly in comparison to that of the larger diameter CNTs. The highest improvement of 38.7% was observed in the ISS during pull-out of (6, 6) CNT at a CNT volume fraction of 3.17%. The average energy increment was found to be increasing with CNT volume fraction and was higher for larger diameter CNTs.

In steel, P and S cause serious grain boundary (GB) embrittlement, which is associated with high segregation energies. To investigate the origins of such high segregation energies of P and S, we applied the combination of ab initio local energy analysis and crystal orbital Hamiltonian population (COHP) analysis for the GB segregation of Al, Si, P, and S in bcc-Fe, which can provide local energetic and bonding views of segregation behavior of each solute, associated with the replacement between solute–Fe and Fe–Fe bonding at GB and bulk sites. The local energy analysis revealed that GB segregation of such solutes is mainly caused by the difference between local energy changes of Fe atoms adjacent to a solute atom in the GB and bulk sites, and that the local energy change of each Fe atom depends on the solute–Fe interatomic distance with a unique functional form for each solute species. The COHP analysis showed that such distance dependency of the Fe-atom local energy change is caused by that of solute–Fe bonding interactions, relative to the Fe–Fe ones, governed by the valence atomic-orbital characters of each solute species. P and S have smaller extents of atomic orbitals and larger numbers of valence electrons; thus, they greatly lower the local energies of Fe atoms at interatomic distances shorter than the bulk first-neighbor one, and they greatly increase those of Fe atoms at longer interatomic distances around the bulk second-neighbor one. Thus, high segregation energies of P and S occur at GB sites with short first-neighbor distances and reduced coordination numbers within the bulk second-neighbor distance. The GB embrittlement by P and S was also discussed by this local-bonding viewpoint. The combination of local energy and COHP analyses can provide novel insights into the behavior of solute elements in various materials.

Evolution of composition patterns in the annealed, single-crystal surface alloy film is considered in the presence of the spinodal decomposition, the compositional stress and the diffusion anisotropy. While the former two effects contribute to overall phase separation, the anisotropy, correlated with the surface crystallographic orientation, guides the in-plane formation and orientation of a pattern. The impacts of the anisotropy parameters on patterns are systematically computed for [110], [100], and [111]-oriented fcc cubic alloy surfaces.

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.

The phase transition process between solid phases plays a critical role in defining the microstructural characteristics of many metals and alloys. Therefore, accurate reproduction of phase transformations enables significant predictive abilities in material modeling which cannot be otherwise achieved. At the atomistic scale, phase transitions naturally occur in modeling as large numbers of atoms in a system relax to their equilibrium phase over a relatively long time scale. However, the accuracy of the simulations in predicting the equilibrium phase for a given pressure, temperature, and solute concentration are often inadequate. Sufficient calibration for a given atomistic potential to reliably reflect these properties is often not achieved because methods of determining the transformation face a number of limitations including high computational cost and sometimes poor accuracy of the results. Herein, we review the methods which have been used to determine equilibrium phase transition conditions at the discrete atom scale and compare their relative efficiency and efficacy.

Atomistic modeling of fracture is intended to illuminate the complex response of atoms in the very high stressed region just ahead of a sharp crack. Accurate modeling of the atomic scale fracture is crucial for describing the intrinsic nature of a material (intrinsic ductility/brittleness), chemical effects in the crack-tip vicinity, the crack interaction with different defects in solids such as grain boundaries, solutes, precipitates, dislocations, voids, etc. Here, different methods for atomistic modeling of fracture are compared in their ability to obtain quantitatively useful results that are in agreement with the basic principles of linear elastic fracture mechanics (LEFM). We demonstrate that the complicated atomic crack-tip behavior is precisely described in simulations of semi-infinite cracks, where the loading is uniquely controlled by the applied stress intensity factor K. Such ‘ K-test’ simulations are shown to be equally applicable in crystalline and amorphous materials, and to be suitable for quantitative evaluation of various critical stress intensity factors, the overall material fracture toughness, and quantitative comparison with theories. We further demonstrate that the simulation of a nanoscale center-crack tension (CCT) specimen often leads to the results that do not satisfy the conditions for application of LEFM. The simulated intrinsic fracture toughness, one of the basic material properties, using CCT test geometry is shown to be dependent on the crack size and far-field loading. In general, this study resolves quantitative differences between several methods for atomistic modeling of fracture and recommends that application of simulations based on nanoscale finite size cracks not be pursued.

Crystal plasticity is mediated through dislocations, which form knotted configurations in a complex energy landscape. Once they disentangle and move, they may also be impeded by permanent obstacles with finite energy barriers or frustrating long-range interactions. The outcome of such complexity is the emergence of dislocation avalanches as the basic mechanism of plastic flow in solids at the nanoscale. While the deformation behavior of bulk materials appears smooth, a predictive model should clearly be based upon the character of these dislocation avalanches and their associated strain bursts. We provide here a comprehensive overview of experimental observations, theoretical models and computational approaches that have been developed to unravel the multiple aspects of dislocation avalanche physics and the phenomena leading to strain bursts in crystal plasticity.

In materials science the orientation of a crystal lattice is described by means of a rotation relative to an external reference frame. A number of rotation representations are in use, including Euler angles, rotation matrices, unit quaternions, Rodrigues–Frank vectors and homochoric vectors. Each representation has distinct advantages and disadvantages with respect to the ease of use for calculations and data visualization. It is therefore convenient to be able to easily convert from one representation to another. However, historically, each representation has been implemented using a set of often tacit conventions; separate research groups would implement different sets of conventions, thereby making the comparison of methods and results difficult and confusing. This tutorial article aims to resolve these ambiguities and provide a consistent set of conventions and conversions between common rotational representations, complete with worked examples and a discussion of the trade-offs necessary to resolve all ambiguities. Additionally, an open source Fortran-90 library of conversion routines for the different representations is made available to the community.

The production of stamped parts from rolled aluminum sheets requires different tempers and different thermal routes. While the slip and hardening behavior of the alloy strongly depends on the temper and the process temperature, the crystallographic texture remains largely static. Although the plastic anisotropy of rolled sheet is largely a function of the crystallographic texture, a dependency of plastic anisotropy on the temper has been reported for 6xxx series alloys, indicating that slip and hardening behavior have some influence. A systematic investigation of the effect of the slip and hardening behavior on the plastic anisotropy, however, does not exist. In this study, a crystal plasticity fast Fourier transform framework is utilized to predict the r-values, a common measure for plastic anisotropy, of two widely used commercial aluminum alloys possessing different crystallographic textures, AA6016 and AA5182. To investigate the sensitivity of the r-values to changes in the modeling parameters, a suite of simulations is performed in which the modeling parameters are systematically changed, and the resulting changes to the predicted r-values are calculated. Furthermore, numerical parameters, such as the level of discretization and the number of simulated grains are studied. Results indicate that the predicted r-value is less dependent on changes to crystal plasticity modeling parameters than to the initial crystallographic texture. Resulting trends are discussed.

The microstructural origin of strain hardening during plastic deformation in stage II deformation of face-centered cubic (fcc) metals can be attributed to the increase in dislocation density resulting in a formation of dislocation networks. Although this is a well known relation, the complexity of dislocation multiplication processes and details about the formation of dislocation networks have recently been revealed by discrete dislocation dynamics (DDD) simulations. It has been observed that dislocations, after being generated by multiplication mechanisms, show a limited expansion within their slip plane before they get trapped in the network by dislocation reactions. This mechanism involves multiple slip systems and results in a heterogeneous dislocation network, which is not reflected in most dislocation-based continuum models. We approach the continuum modeling of dislocation networks by using data science methods to provide a link between discrete dislocations and the continuum level. For this purpose, we identify relevant correlations that feed into a model for dislocation networks in a dislocation-based continuum theory of plasticity. As a key feature, the model combines the dislocation multiplication with the limitation of the travel distance of dislocations by formation of stable dislocation junctions. The effective mobility of the network is determined by a range of dislocation spacings which reproduces the scattering travel distances of generated dislocation as observed in DDD. The model is applied to a high-symmetry fcc loading case and compared to DDD simulations. The results show a physically meaningful microstructural evolution, where the generation of new dislocations by multiplication mechanisms is counteracted by a formation of a stable dislocation network. In conjunction with DDD, we observe a steady state interplay of the different mechanisms.

A one dimensional Bravais lattice model is applied to a superabundant vacancy (SAV) delta δ phase (Pd ₃VacD ₄—octahedral), in the palladium–deuterium system. SolidWorks is used to simulate the motion of atoms and ions in the lattice. These two approaches give identical results for the vibrations of the deuterons indicating that large vibrations of deuterons are possible when the microstructure is a mixture of beta deuteride and small volume percent delta SAV phase. These conditions result from the unique geometry and crystallography of δ phase. According to both the model and simulation, as the size of δ phase increases, opportunity for high amplitude vibrations of deuterons increases. Increasing temperature should have a similar effect.

We propose a combined computational approach based on the multi-phase-field and the lattice Boltzmann method for the motion of solid particles under the action of capillary forces. The accuracy of the method is analyzed by comparison with the analytic solutions for the motion of two parallel plates of finite extension connected by a capillary bridge. The method is then used to investigate the dynamics of multiple spherical solid bodies connected via capillary bridges. The amount of liquid connecting the spheres is varied, and the influence of the resulting liquid-morphology on their dynamics is investigated. It is shown that the method is suitable for a study of liquid-phase sintering which includes both phase transformation and capillary driven rigid body motion.

Whether a metallic material fractures by brittle cleavage or by ductile rupture is primarily governed by the competition between cleavage and dislocation emission at the crack tip. The linear elastic fracture mechanics (LEFM) based criterion of Griffith, respectively the one for dislocation emission of Rice, are sufficiently reliable for determining the possible crack tip propagation mechanisms in isotropic crystalline metals. However, the applicability of these criteria is questionable when non-cubic, anisotropic solids are considered, as e.g. ordered intermetallic TiAl phases, where slip systems are limited and elastic anisotropy is pronounced. We study brittle versus ductile failure mechanisms in face-centered tetragonal TiAl and hexagonal Ti ₃Al using large-scale atomistic simulations and compare our findings to the predictions of LEFM-based criteria augmented by elastic anisotropy. We observe that the augmented Griffith and Rice criteria are reliable for determining the direction dependent crack tip mechanisms, if all the available dislocation slip systems are taken into account. Yet, atomistic simulations are necessary to understand crack blunting due to mixed mechanisms, or shear instabilities other than dislocation emission. The results of our systematic study can be used as basis for modifications of the Griffith/Rice criteria in order to incorporate such effects.

Deformation microstructure heterogeneities play a pivotal role during dislocation patterning and interface network restructuring. Thereby, they affect indirectly how the microstructure recrystallizes. Given this relevance, it has become common practice to study the evolution of deformation microstructure heterogeneities with 3D experiments and full-field crystal plasticity computer simulations including tools such as the spectral method. Quantifying material point to grain or phase boundary distances, though, is a practical challenge with spectral method crystal plasticity models because these discretize the material volume rather than mesh explicitly the grain and phase boundary interface network. This limitation calls for specific data post-processing methods to quantify the spatial correlations between state variable values at each material point and the points’ corresponding distance to the closest grain or phase boundary. This work contributes to the development of advanced such post-processing routines. Specifically, two grain reconstruction and three distancing methods are developed for solving above challenge. The individual strengths and limitations of these methods surplus the efficiency of their parallel implementation is assessed with an exemplary Düsseldorf Advanced Material Simulation Kit large scale crystal plasticity study. We apply the new tool to assess the evolution of subtle stress and disorientation gradients towards grain boundaries.

Only few available interatomic interaction potentials implement the α ↔ γ phase transformation in iron by featuring a stable low-temperature bcc and high-temperature fcc lattice structure. Among these are the potentials by Meyer and Entel (1998 Phys. Rev. B 57 5140), by Müller et al (2007 J. Phys.: Condens. Matter 19 326220) and by Lee et al (2012 J. Phys.: Condens. Matter 24 225404). We study how these potentials model the phase transformation during heating and cooling; in order to help initiating the transformation, the simulation volume contains a grain boundary. For the martensitic transformation occurring on cooling an fcc structure, we additionally study two potentials that only implement a stable bcc structure of iron, by Zhou et al (2004 Phys. Rev. B 69 144113) and by Mendelev et al (2003 Philos. Mag. 83 3977). We find that not only the transition temperature depends on the potential, but that also the height of the energy barrier between fcc and bcc phase governs whether the transformation takes place at all. In addition, details of the emerging microstructure depend on the potential, such as the fcc/hcp fraction formed in the α → γ transformation, or the twinning induced in and the lattice orientation of the bcc phase in the γ → α transformation.

Dislocations can provide short circuit diffusion paths for atoms resulting in a dislocation climb motion referred to as self-climb. A variational principle is presented for the analysis of problems in which fast dislocation core diffusion is the dominant mechanism for material redistribution. The linear element based self-climb model, developed in our previous work [1] Liu, Cocks and Tarleton (2020 J. Mech. Phys. Solids 135 103783), is significantly accelerated here, by employing a new finite element discretisation method. The speed-up in computation enables us to use the self-climb model as an effective numerical technique to simulate emergent dislocation behaviour involving both self-climb and glide. The formation of prismatic loops from the break-up of different types of edge dislocation dipoles are investigated based on this new method. We demonstrate that edge dipoles sequentially pinch-off prismatic loops, rather than spontaneously breaking-up into a string of loops, to rapidly decrease the total dislocation energy.

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.

A flow stress model which considers the processing conditions for a given alloy composition as well as the microchemistry of the alloy allows for integrated optimization of alloy composition, thermal treatments and forming operations to achieve the desired properties in the most efficient processing route. In the past, a statistical flow stress model for cell forming metals, 3IVM+ (3 Internal Variable Model), has been used for through process modeling of sheet production. However, this model was restricted to a given alloy in the state in which it was calibrated. In this work, the existing 3IVM+ model is augmented with an analytical solute strengthening model which uses input from ab initio simulations. Furthermore, a new particle strengthening model for non-shearable precipitates has been introduced which takes Orowan looping at low temperatures and dislocation climb at high temperatures into account. Hence, the present modeling approach considers the strengthening contributions from solutes, precipitates and forest dislocations. Three case studies on the alloys AA 1110, AA 3003 and AA 8014 are presented to assess the performance of the model in simulating the yield stress and flow stress of Al alloys over a wide range of temperatures and strain rates.