Modelling and Simulation in Materials Science and Engineering

An interatomic potential, traditionally regarded as a mathematical function, serves to depict atomic interactions within molecules or solids by expressing potential energy concerning atom positions. These potentials are pivotal in materials science and engineering, facilitating atomic-scale simulations, predictive material behavior, accelerated discovery, and property optimization. Notably, the landscape is evolving with machine learning transcending conventional mathematical models. Various machine learning-based interatomic potentials, such as artificial neural networks, kernel-based methods, deep learning, and physics-informed models, have emerged, each wielding unique strengths and limitations. These methods decode the intricate connection between atomic configurations and potential energies, offering advantages like precision, adaptability, insights, and seamless integration. The transformative potential of machine learning-based interatomic potentials looms large in materials science and engineering. They promise tailor-made materials discovery and optimized properties for specific applications. Yet, formidable challenges persist, encompassing data quality, computational demands, transferability, interpretability, and robustness. Tackling these hurdles is imperative for nurturing accurate, efficient, and dependable machine learning-based interatomic potentials primed for widespread adoption in materials science and engineering. This roadmap offers an appraisal of the current machine learning-based interatomic potential landscape, delineates the associated challenges, and envisages how progress in this domain can empower atomic-scale modeling of the composition-processing-microstructure-property relationship, underscoring its significance in materials science and engineering.

Science is and always has been based on data, but the terms 'data-centric' and the '4th paradigm' of materials research indicate a radical change in how information is retrieved, handled and research is performed. It signifies a transformative shift towards managing vast data collections, digital repositories, and innovative data analytics methods. The integration of artificial intelligence and its subset machine learning, has become pivotal in addressing all these challenges. This Roadmap on Data-Centric Materials Science explores fundamental concepts and methodologies, illustrating diverse applications in electronic-structure theory, soft matter theory, microstructure research, and experimental techniques like photoemission, atom probe tomography, and electron microscopy. While the roadmap delves into specific areas within the broad interdisciplinary field of materials science, the provided examples elucidate key concepts applicable to a wider range of topics. The discussed instances offer insights into addressing the multifaceted challenges encountered in contemporary materials research.

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/.

Bearing steels are complex materials composed of an iron matrix and a well defined and precise amount of several alloying elements. In order to improve sustainability and circularity, there is a tendency to increase the utilisation of scrap material for their production. The variability of the composition of scrap material has a direct impact on the properties of the final steels: There is less control on their composition due to the possible presence of larger amounts of tramp and alloying elements. One way to study the effect of tramp elements is by using universal machine learning interatomic potentials. These types of potential render the investigation of multi-element systems possible. They permit the study of interactions between iron atoms in the matrix and multiple concurrent tramp and alloying elements, a feature that is currently not available in classical potentials. In this work, we present a benchmark of four state-of-the-art universal machine learning interatomic potentials (Crystal Hamiltonian Graph Neural Network (Deng et al 2023 Nat. Mach. Intell. 5 1031–41) (v0.2.0 and v0.3.0), Materials 3-body Graph Network (Chen and Ping Ong 2022 Nat. Comput. Sci. 2 718–28), Multiple Atomic Cluster Expansion (Batatia et al 2022 Advances in Neural Information Processing Systems vol 35 pp 11423–36)) and SevenNet (Park et al 2024 J. Chem. Theory Comput. 20 4857–68), and study their applicability to the simulation of systems relevant to steels. For pure Fe, all potentials accurately predict the equilibrium lattice parameter, but the accuracy varies for other properties. For most solute–solute and solute–vacancy interactions all interatomic potentials tend to capture the general trends though there is a disparity in the predicted magnitudes. While currently 'off-the-shelf' universal machine learning interatomic potentials fail to predict some key properties, some of them show significant potential to serve as starting point for further training and refinement.

Theory predicts limiting gliding velocities that dislocations cannot overcome. Computational and recent experiments have shown that these limiting velocities are soft barriers and dislocations can reach transonic speeds in high rate plastic deformation scenarios. In this paper we systematically examine the mobility of edge and screw dislocations in several face centered cubic (FCC) metals (Al, Au, Pt, and Ni) in the extreme large-applied-stress regime using molecular dynamics simulations. Our results show that edge dislocations are more likely to move at transonic velocities due to their high mobility and lower limiting velocity than screw dislocations. Importantly, among the considered FCC metals, the dislocation core structure determines the dislocation's ability to reach transonic velocities. This is likely due to the variation in stacking fault width due to relativistic effects near the limiting velocities.

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.

Over low and intermediate strain rates, plasticity in face centered cubic (FCC) metals is governed by the glide of dislocations, which manifest as complex networks that evolve with strain. Considering the elastic anisotropy of FCC metals, the characteristics of dislocation motion are also anisotropic (i.e. dislocation character angle-dependent), which is expected to notably influence the overall evolution of the dislocation network, and consequently, the plastic response of these materials. The aggregate influence of the anisotropy in the Peierls stress on the mechanical response of single crystal Ni was investigated in the present work using discrete dislocation dynamics simulations. Twenty initial dislocation networks, differing in their configuration and dislocation density, were deformed under uniaxial tension up to at least 0.9% strain, and the analysis of character-dependent dynamics showed a suppression of plasticity only for segments of nearly screw character. While the increased screw component of the Peierls stress raised the initial strain hardening rate, it also resulted in longer dislocation segments overall, contrary to the reasoning that longer pinned segments exhibit a lower resistance to motion and might give a weaker response. A non-linear superposition principle is demonstrated to predict the hardening reasonably well, considering the cumulative effects of forest and Peierls stress-related strengthening. Further analysis of the network topology revealed a tendency to maintain connectivity over the course of deformation for those networks simulated using an unequal Peierls stress. The general increases in hardening rate and network connectivity contrast with the localized reduction of dislocation motion, which occurred mainly for segments of nearly screw-type character.

Data-driven machine learning (ML) models of atomistic interactions are often based on flexible and non-physical functions that can relate nuanced aspects of atomic arrangements to predictions of energies and forces. As a result, these potentials are only as good as the training data (usually the results of so-called ab initio simulations), and we need to ensure that we have enough information to make a model sufficiently accurate, reliable and transferable. The main challenge stems from the fact that descriptors of chemical environments are often sparse, high-dimensional objects without a well-defined continuous metric. Therefore, it is rather unlikely that any ad hoc method for selecting training examples will be indiscriminate, and it is easy to fall into the trap of confirmation bias, where the same narrow and biased sampling is used to generate training and test sets. We will show that an approach derived from classical concepts of statistical planning of experiments and optimal design can help to mitigate such problems at a relatively low computational cost. The key feature of the method we will investigate is that it allows us to assess the quality of the data without obtaining reference energies and forces—a so-called offline approach. In other words, we are focusing on an approach that is easy to implement and does not require sophisticated frameworks that involve automated access to high performance computing.

FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by Moulinec and Suquet for the homogenization of composites. Since then many different approaches have been proposed for a more accurate and efficient resolution of the non-linear homogenization problem. Furthermore, the method has been pushed beyond its original purpose and has been adapted to a variety of problems including conventional and strain gradient plasticity, continuum and discrete dislocation dynamics, multi-scale modeling or homogenization of coupled problems such as fracture or multi-physics problems. In this paper, a comprehensive review of FFT approaches for micromechanical simulations will be made, covering the basic mathematical aspects and a complete description of a selection of approaches which includes the original basic scheme, polarization based methods, Krylov approaches, Fourier–Galerkin and displacement-based methods. Then, one or more examples of the applications of the FFT method in homogenization of composites, polycrystals or porous materials including the simulation of damage and fracture will be presented. The applications will also provide an insight into the versatility of the method through the presentation of existing synergies with experiments or its extension toward dislocation dynamics, multi-physics and multi-scale problems. Finally, the paper will analyze the current limitations of the method and try to analyze the future of the application of FFT approaches in micromechanics.

Dislocation plasticity in bcc metals at low temperatures and stresses is well known to be controlled by screw dislocation mobility. Screw dislocations move by the nucleation of kink-pairs on the dislocation line and is a relatively well studied phenomenon. However, how screw dislocation mobility is influenced by interfaces and surfaces has not been well-studied. To provide insight into the role interfaces play in screw dislocation mobility, this study proposes an empirical model to treat a grain boundary as a dislocation source, which is then implemented into kinetic Monte Carlo simulations for body-centered-cubic (bcc) metals. This effort focuses on the roles of kink nucleation and migration processes at the interface, comparing the energetics of these events on interfaces versus those on the interior of the dislocation line. The findings reveal that interfaces can either enhance dislocation motion or not affect it at all, depending on temperature, stress, and dislocation length. This work provides insights into the mesoscale behavior of bcc metals and bridges the gap between experimental observations and computational models at small scales.

This study focuses on the strain-rate dependence of mechanical properties of polymer matrix composites. The objective is to quantify the strain-rate strengthening effect on the ultimate tensile strength (UTS) of composites and to propose a residual strength prediction method that considers this effect. Firstly, the strain rate sensitivity of the material UTS was analyzed by fitting the S–N formula and Weibull distribution function to experimental data at different strain rates, respectively. Moreover, the strengthening effect of strain rate on the material UTS was quantified using the strain rate strengthening coefficient. Secondly, a new probabilistic residual strength model is constructed by coupling a statistical life formula into a generalized residual strength model. This model is independent of the stress level, takes into account the strengthening effect of strain rate, and has the capability of statistical analysis. Finally, the model is verified with the support of experimental data disclosed in the literature, and the results show that the strain rate consistency data obtained by multiplying the residual strength data by the strain rate strengthening factor of 1.3 are nearly all scattered within the 5%–95% confidence bands of the prediction results of the developed model. Also, the proposed model is a generalized model that is independent of the stress level, as indicated by the predictions achieved from only one set of model parameters.

In body-centered cubic metals such as molybdenum, screw dislocations critically govern the plastic deformation behavior of alloys. The presence of solute atoms in alloys can effectively alter the formation and movement of screw dislocations. In this study, we employed first-principles calculations to delve into the electronic origins of these influences. Initially, we constructed single atomic column and triple atomic column models to simulate the formation of screw dislocations with solute atoms. Our investigation revealed that tantalum (Ta) and tungsten (W) increase the formation energy of solute-dislocation interactions, while osmium (Os), iridium (Ir), and platinum (Pt) have the opposite effect. Subsequently, utilizing a screw dislocation dipole model under shear deformation, we explored the combined effects of solute atoms and deformation on dislocation core movement. We found that Os, Ir, and Pt, located as the first nearest neighbors of the dislocation core, exhibit an attractive effect on the dislocation core. Solute atoms at specific positions can alter the direction of dislocation slip, inducing cross-slip and enhancing material ductility. In contrast, under the same stress, Ta and W exhibit repulsion towards the dislocation core and cannot change the direction of dislocation slip, only altering the energy barrier for dislocation core movement. This work provides atomic-scale insights into solute-induced dislocation dynamics, offering guidelines for advanced Mo alloy design.

During the hydroforming process of the double-layer Y-shaped tube, defects such as wrinkling and rupture severely affect the forming quality. In this study, for the first time, hydroforming of multi-pass pipes is combined with crystal plasticity finite element modeling (CPFEM). A cross-scale simulation approach is proposed, where the displacement boundary conditions of the macroscopic finite element model are applied to the representative volume element through the submodel function in ABAQUS. A macroscopic–microscopic finite element model for the hydroforming of double-layer Y-shaped tube is established, and the deformation behavior in the representative region is systematically studied. The effects of non-uniform deformation on stress and strain are analyzed from the perspective of CPFEM, and the results are validated by hydroforming experiments. The results show that both macroscopic and microscopic finite element models exhibit good consistency with the experimental results. Considering the microstructure, initial stress concentrates on specific grains due to grain orientation differences. As work hardening occurs, slip systems in other grains are gradually activated, ultimately leading to a uniform stress distribution. The effect of the stress state on the slip mode is also discussed. The stress state and slip mode in the same regions of the inner and outer tubes are identical. Moreover, the cross-scale simulation can accurately predict the macroscopic deformation in the critical regions of the hydroforming tube, thus compensating for the limitations of traditional finite element simulations. This cross-scale numerical simulation method also lays the foundation for further research on the hydroforming of multi-pass pipes.

A wide range of deep learning-based machine learning (ML) techniques are extensively applied to the design of high-entropy alloys (HEAs), yielding numerous valuable insights. Kolmogorov–Arnold networks (KAN) is a recently developed architecture that aims to improve both the accuracy and interpretability of input features. In this work, we explore three different datasets for HEA design and demonstrate the application of KAN for both classification and regression models. In the first example, we use a KAN classification model to predict the probability of single-phase formation in high-entropy carbide ceramics based on various properties such as mixing enthalpy and valence electron concentration. In the second example, we employ a KAN regression model to predict the yield strength and ultimate tensile strength of HEAs based on their chemical composition and process conditions including annealing time, cold rolling percentage, and homogenization temperature. The third example involves a KAN classification model to determine whether a certain composition is an HEA or non-HEA, followed by a KAN regressor model to predict the bulk modulus of the identified HEA, aiming to identify HEAs with high bulk modulus. In all three examples, KAN either outperform or match the performance in terms of accuracy such as F1 score for classification and mean square error, and coefficient of determination (R²) for regression of the multilayer perceptron by demonstrating the efficacy of KAN in handling both classification and regression tasks. We provide a promising direction for future research to explore advanced ML techniques, which lead to more accurate predictions and better interpretability of complex materials, ultimately accelerating the discovery and optimization of HEAs with desirable properties.

Bearing steels are complex materials composed of an iron matrix and a well defined and precise amount of several alloying elements. In order to improve sustainability and circularity, there is a tendency to increase the utilisation of scrap material for their production. The variability of the composition of scrap material has a direct impact on the properties of the final steels: There is less control on their composition due to the possible presence of larger amounts of tramp and alloying elements. One way to study the effect of tramp elements is by using universal machine learning interatomic potentials. These types of potential render the investigation of multi-element systems possible. They permit the study of interactions between iron atoms in the matrix and multiple concurrent tramp and alloying elements, a feature that is currently not available in classical potentials. In this work, we present a benchmark of four state-of-the-art universal machine learning interatomic potentials (Crystal Hamiltonian Graph Neural Network (Deng et al 2023 Nat. Mach. Intell.5 1031–41) (v0.2.0 and v0.3.0), Materials 3-body Graph Network (Chen and Ping Ong 2022 Nat. Comput. Sci.2 718–28), Multiple Atomic Cluster Expansion (Batatia et al 2022 Advances in Neural Information Processing Systems vol 35 pp 11423–36)) and SevenNet (Park et al 2024 J. Chem. Theory Comput.20 4857–68), and study their applicability to the simulation of systems relevant to steels. For pure Fe, all potentials accurately predict the equilibrium lattice parameter, but the accuracy varies for other properties. For most solute–solute and solute–vacancy interactions all interatomic potentials tend to capture the general trends though there is a disparity in the predicted magnitudes. While currently 'off-the-shelf' universal machine learning interatomic potentials fail to predict some key properties, some of them show significant potential to serve as starting point for further training and refinement.

An interatomic potential, traditionally regarded as a mathematical function, serves to depict atomic interactions within molecules or solids by expressing potential energy concerning atom positions. These potentials are pivotal in materials science and engineering, facilitating atomic-scale simulations, predictive material behavior, accelerated discovery, and property optimization. Notably, the landscape is evolving with machine learning transcending conventional mathematical models. Various machine learning-based interatomic potentials, such as artificial neural networks, kernel-based methods, deep learning, and physics-informed models, have emerged, each wielding unique strengths and limitations. These methods decode the intricate connection between atomic configurations and potential energies, offering advantages like precision, adaptability, insights, and seamless integration. The transformative potential of machine learning-based interatomic potentials looms large in materials science and engineering. They promise tailor-made materials discovery and optimized properties for specific applications. Yet, formidable challenges persist, encompassing data quality, computational demands, transferability, interpretability, and robustness. Tackling these hurdles is imperative for nurturing accurate, efficient, and dependable machine learning-based interatomic potentials primed for widespread adoption in materials science and engineering. This roadmap offers an appraisal of the current machine learning-based interatomic potential landscape, delineates the associated challenges, and envisages how progress in this domain can empower atomic-scale modeling of the composition-processing-microstructure-property relationship, underscoring its significance in materials science and engineering.

Science is and always has been based on data, but the terms 'data-centric' and the '4th paradigm' of materials research indicate a radical change in how information is retrieved, handled and research is performed. It signifies a transformative shift towards managing vast data collections, digital repositories, and innovative data analytics methods. The integration of artificial intelligence and its subset machine learning, has become pivotal in addressing all these challenges. This Roadmap on Data-Centric Materials Science explores fundamental concepts and methodologies, illustrating diverse applications in electronic-structure theory, soft matter theory, microstructure research, and experimental techniques like photoemission, atom probe tomography, and electron microscopy. While the roadmap delves into specific areas within the broad interdisciplinary field of materials science, the provided examples elucidate key concepts applicable to a wider range of topics. The discussed instances offer insights into addressing the multifaceted challenges encountered in contemporary materials research.

Materials and manufacturing engineering are continuing to advance in part to computational materials and process modeling and associated linkages with associated interdisciplinary efforts across all engineering, manufacturing, and quality disciplines. Computational modeling has enabled virtual processing, prediction and assessment of potential new materials and manufacturing processes, without or with limited need to perform costly and time-consuming physical trials. Development and integration of computational materials and process engineering requires a number of seemingly disparate critical technical elements, making this evolving computational capability very complicated. Accurate and validated models are supporting rapid material, process, and component development, and additionally qualification and certification of new final products through integrated computational materials engineering (ICME). These capabilities are driving further industrial utilization of computational material and process modeling with formalized linkages and integration within multidisciplinary engineering workflows. Past utilization, present applications and potential future development activities indicate that industry has now fully embraced the tools and methods, and overarching engineering framework of ICME.

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry, and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

The irradiation of the target surface by an ultrafast femtosecond (fs) laser pulse produces the extreme non-equilibrium states of matter and subsequent phase transformations. Computational modeling and simulation is a very important tool for gaining insight into the physics processes that govern the laser–matter interactions, and, specifically, for quantitative understanding the laser light absorption, electron–ion energy exchange, spallation, melting, warm dense matter regime, vaporization, and expansion of plasma plume. High-fidelity predictive modeling of a variety of these multi-physics processes that take place at various time and length scales is extremely difficult, requiring the coupled multi-physics and multi-scale models. This topical review covers progress and advances in developing the modeling approaches and performing the state-of-the-art simulations of fs laser-pulse interactions with solids and plasmas. A complete kinetic description of a plasma based on the most accurate Vlasov–Maxwell set of equations is first presented and discussed in detail. After that an exact kinetic model that encompasses the microscopic motions of all the individual particles, their charge and current densities, generated electric and magnetic fields, and the effects of these fields on the motion of charged particles in a plasma is briefly reviewed. The methodology of kinetic particle-in-cell (PIC) approach that is well suitable for computational studies of the non-linear processes in laser–plasma interactions is then presented. The hydrodynamic models used for the description of plasmas under the assumption of a local thermodynamic equilibrium include the two-fluid and two-temperature model and its simplifications. The two-temperature model coupled with molecular dynamics (MD) method is finally discussed. Examples are illustrated from research areas such as applications of the fully kinetic, PIC, hydrodynamic, and MD models to studies of ultrafast laser–matter interactions. Challenges and prospects in the development of computational models and their applications to the modeling of ultrafast intense laser–solid and laser–plasma interactions are overviewed.

The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models can be envisaged in terms of the evolution of order-parameter-like variables that strive to minimize a free energy functional which incorporates interface energy-like terms, i.e., as a phase field theory. We show that dislocation density variables obey non-standard conservation laws. These lead, in conjunction with the externally supplied work, to evolution equations that go beyond the classical framework of Allen-Cahn vs. Cahn-Hilliard equations. The approach is applied to the evolution of dislocation patterns in materials with B1(NaCl) lattice structure and it is demonstrated that it gives access to the formation of cellular dislocation patterns, and the concomitant emergence of both incidental and geometrically necessary dislocation boundaries.

In this paper, nickel-based single crystal thin-walled specimens with different bending angles were designed. The effect of crystal orientation on the fatigue properties of thin-walled specimens with film cooling hole at 900℃ was investigated by using crystal plastic slip theory. The results show that the mises stress around the film cooling hole under three crystal orientations [001], [011] and [111] is concentrated in the vertical loading direction, forming four banded stripes, and the order of maximum mises stress is [111] > [011] > [001]. The change of crystal orientation leads to the difference of stress distribution and stress gradient, and the stress gradient increases with the increase of curvature. The distribution of maximum shear stress under different crystal orientations is different, and the change of bending degree does not affect its direction distribution. In addition, the activation of the octahedral slip system around the film cooling hole under different crystal orientations was analyzed. It was found that the number of octahedral slip systems activated by [001] and [011] orientations was the same, while the number of octahedral slip systems activated by [111] orientation was less.

Radioactive fission gases such as Xe and Kr play a decisive role in the thermal transport of UO2 under nuclear reactor operating conditions. Here, systematic molecular dynamics simulations are performed to understand the effect of fission gases on the thermal conductivity and structural properties of UO2 . The conductivity deteriorates significantly in the presence of fission gases. The
strong phonon-disorder scattering leads to overdamping of the phonon modes, particularly impacting the midfrequency region, leading to substantial decay in conductivity. We unveil the interplay of anharmonicity and disorder in conductivity. Significant decay in conductivity is attributed to the phonon-disorder scattering at low temperatures and anharmonic phonon-phonon scattering at high temperatures. To analyze the high-temperature structural stability, we compute the radial distribution function, mean square displacements, and diffusion coefficients; an early onset of superionic diffusion is observed in UO2 with fission gases compared to pristine UO2 .

An interatomic potential for the Ti-V binary alloy focusing on evolution of defects, including ones arising as a result of the irradiation process, was constructed within the Lipnitskii-Saveliev approach, which accurately takes into account three-particle interactions and the sum of all multi-particle interactions of a higher order in the framework of the centrally symmetric approximation. In the new potential, Ti-V interactions were fitted to the DFT data on set of model structures with different coordination numbers, including ones with vacancies. The properties used for fitting are accurately reproduced by the present potentials for both pure elements and alloy systems. The potential was tested on the binding energies between Ti atoms and self-point defects in bcc V, elastic moduli, thermal expansion and melting point of some alloys, and diffusion. We obtained qualitative agreement for these properties with available theoretical and experimental data. Finally, we investigated evolution of excess vacancies in the V-4 at. \% Ti alloy at 700 K, which are typical conditions of vanadium-based alloys for fusion applications. We found that no vacancy loop is formed in the alloy in contrast to the pure V, which agrees with the experimental observations. The potential is expected to be especially suitable for irradiation simulations of vanadium based V-Ti alloys.

The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models can be envisaged in terms of the evolution of order-parameter-like variables that strive to minimize a free energy functional which incorporates interface energy-like terms, i.e., as a phase field theory. We show that dislocation density variables obey non-standard conservation laws. These lead, in conjunction with the externally supplied work, to evolution equations that go beyond the classical framework of Allen-Cahn vs. Cahn-Hilliard equations. The approach is applied to the evolution of dislocation patterns in materials with B1(NaCl) lattice structure and it is demonstrated that it gives access to the formation of cellular dislocation patterns, and the concomitant emergence of both incidental and geometrically necessary dislocation boundaries.

Bearing steels are complex materials composed of an iron matrix and a well defined and precise amount of several alloying elements. In order to improve sustainability and circularity, there is a tendency to increase the utilisation of scrap material for their production. The variability of the composition of scrap material has a direct impact on the properties of the final steels: There is less control on their composition due to the possible presence of larger amounts of tramp and alloying elements. One way to study the effect of tramp elements is by using universal machine learning interatomic potentials. These types of potential render the investigation of multi-element systems possible. They permit the study of interactions between iron atoms in the matrix and multiple concurrent tramp and alloying elements, a feature that is currently not available in classical potentials. In this work, we present a benchmark of four state-of-the-art universal machine learning interatomic potentials (Crystal Hamiltonian Graph Neural Network (Deng et al 2023 Nat. Mach. Intell.5 1031–41) (v0.2.0 and v0.3.0), Materials 3-body Graph Network (Chen and Ping Ong 2022 Nat. Comput. Sci.2 718–28), Multiple Atomic Cluster Expansion (Batatia et al 2022 Advances in Neural Information Processing Systems vol 35 pp 11423–36)) and SevenNet (Park et al 2024 J. Chem. Theory Comput.20 4857–68), and study their applicability to the simulation of systems relevant to steels. For pure Fe, all potentials accurately predict the equilibrium lattice parameter, but the accuracy varies for other properties. For most solute–solute and solute–vacancy interactions all interatomic potentials tend to capture the general trends though there is a disparity in the predicted magnitudes. While currently 'off-the-shelf' universal machine learning interatomic potentials fail to predict some key properties, some of them show significant potential to serve as starting point for further training and refinement.

In the present study, an atomistic K-test framework for the fracture toughness assessment of generally oriented grain boundaries (GBs) (tilt, twist, mixed) and triclinic single crystals is investigated. Boundary conditions for the modelling of cracks along the interfaces of bicrystals are derived based on the $6{\text{th}}$-order Stroh formalism and compared with established approaches. Thereby, especially the oscillations in the relevant field quantities due to mode I loading are critically assessed. It is found that for engineering applications, these oscillations do not compromise the validity of the employed approach since they are confined to a negligibly small region at the crack tip. Next, the $6{\text{th}}$-order Stroh approach is used to investigate crack propagation along GBs under mode I loading. A crack identification and crack tip tracing scheme is included to update the imposed boundary conditions during the simulations. Lastly, a physically-motivated method is discussed and incorporated, which allows for the unambiguous determination of the fracture toughness, including challenging setups such as generally oriented GBs. The so-established K-test setup is validated with a series of numerical examples.

The anisotropy of crystal structures mandates the direction dependence of materials' mechanical properties. Key properties of interest are the Young's modulus and Poisson ratio in the small strain limit, and the ideal tensile strength in the large strain regime. To date, atomistic computations of these properties have been conducted using two approaches. The first approach explicitly calculates the stress–strain response using computational tensile test experiments. The second approach computes the single crystal elastic constants then derives the mechanical properties using analytical equations. The two approaches have been used interchangeably and their equivalence not assessed. This work systematically computes the mechanical properties of 13 BCC and 12 face centered cubic (FCC) metals via the two approaches using first principles density functional theory calculations and hypothesize the robustness of the first approach. Analysis of the results has revealed the shortcomings of the elastic constants method in detecting instabilities in the structures captured by the first principles computational tensile test approach. Large discrepancies in calculations of Young's moduli using the latter approach are herein reported, as well as auxetic repossess and large Poisson ratio for some metals. Beyond the small strain results, we systematically examined the lateral strain response up to 0.5 applied strain in 3 crystallographic directions and reported large changes in slopes and peculiarities around the Bain transformation strain. From the computational stress–strain results, we validated empirical equations in the literature relating the ideal strength to the direction-dependent Young's modulus and the Bain strain along [001] in BCC and [110] in FCC but also presented further relations for other crystallographic directions. In conclusion, we believe that the elastic constants approach, while computationally efficient, has to be used with caution and should be validated against the computational tensile tests. In addition, we highlight the importance of examining different crystallographic directions with possibly desirable properties.

Theory predicts limiting gliding velocities that dislocations cannot overcome. Computational and recent experiments have shown that these limiting velocities are soft barriers and dislocations can reach transonic speeds in high rate plastic deformation scenarios. In this paper we systematically examine the mobility of edge and screw dislocations in several face centered cubic (FCC) metals (Al, Au, Pt, and Ni) in the extreme large-applied-stress regime using molecular dynamics simulations. Our results show that edge dislocations are more likely to move at transonic velocities due to their high mobility and lower limiting velocity than screw dislocations. Importantly, among the considered FCC metals, the dislocation core structure determines the dislocation's ability to reach transonic velocities. This is likely due to the variation in stacking fault width due to relativistic effects near the limiting velocities.

Over low and intermediate strain rates, plasticity in face centered cubic (FCC) metals is governed by the glide of dislocations, which manifest as complex networks that evolve with strain. Considering the elastic anisotropy of FCC metals, the characteristics of dislocation motion are also anisotropic (i.e. dislocation character angle-dependent), which is expected to notably influence the overall evolution of the dislocation network, and consequently, the plastic response of these materials. The aggregate influence of the anisotropy in the Peierls stress on the mechanical response of single crystal Ni was investigated in the present work using discrete dislocation dynamics simulations. Twenty initial dislocation networks, differing in their configuration and dislocation density, were deformed under uniaxial tension up to at least 0.9% strain, and the analysis of character-dependent dynamics showed a suppression of plasticity only for segments of nearly screw character. While the increased screw component of the Peierls stress raised the initial strain hardening rate, it also resulted in longer dislocation segments overall, contrary to the reasoning that longer pinned segments exhibit a lower resistance to motion and might give a weaker response. A non-linear superposition principle is demonstrated to predict the hardening reasonably well, considering the cumulative effects of forest and Peierls stress-related strengthening. Further analysis of the network topology revealed a tendency to maintain connectivity over the course of deformation for those networks simulated using an unequal Peierls stress. The general increases in hardening rate and network connectivity contrast with the localized reduction of dislocation motion, which occurred mainly for segments of nearly screw-type character.

An interatomic potential, traditionally regarded as a mathematical function, serves to depict atomic interactions within molecules or solids by expressing potential energy concerning atom positions. These potentials are pivotal in materials science and engineering, facilitating atomic-scale simulations, predictive material behavior, accelerated discovery, and property optimization. Notably, the landscape is evolving with machine learning transcending conventional mathematical models. Various machine learning-based interatomic potentials, such as artificial neural networks, kernel-based methods, deep learning, and physics-informed models, have emerged, each wielding unique strengths and limitations. These methods decode the intricate connection between atomic configurations and potential energies, offering advantages like precision, adaptability, insights, and seamless integration. The transformative potential of machine learning-based interatomic potentials looms large in materials science and engineering. They promise tailor-made materials discovery and optimized properties for specific applications. Yet, formidable challenges persist, encompassing data quality, computational demands, transferability, interpretability, and robustness. Tackling these hurdles is imperative for nurturing accurate, efficient, and dependable machine learning-based interatomic potentials primed for widespread adoption in materials science and engineering. This roadmap offers an appraisal of the current machine learning-based interatomic potential landscape, delineates the associated challenges, and envisages how progress in this domain can empower atomic-scale modeling of the composition-processing-microstructure-property relationship, underscoring its significance in materials science and engineering.

Dislocation plasticity in bcc metals at low temperatures and stresses is well known to be controlled by screw dislocation mobility. Screw dislocations move by the nucleation of kink-pairs on the dislocation line and is a relatively well studied phenomenon. However, how screw dislocation mobility is influenced by interfaces and surfaces has not been well-studied. To provide insight into the role interfaces play in screw dislocation mobility, this study proposes an empirical model to treat a grain boundary as a dislocation source, which is then implemented into kinetic Monte Carlo simulations for body-centered-cubic (bcc) metals. This effort focuses on the roles of kink nucleation and migration processes at the interface, comparing the energetics of these events on interfaces versus those on the interior of the dislocation line. The findings reveal that interfaces can either enhance dislocation motion or not affect it at all, depending on temperature, stress, and dislocation length. This work provides insights into the mesoscale behavior of bcc metals and bridges the gap between experimental observations and computational models at small scales.

Data-driven machine learning (ML) models of atomistic interactions are often based on flexible and non-physical functions that can relate nuanced aspects of atomic arrangements to predictions of energies and forces. As a result, these potentials are only as good as the training data (usually the results of so-called ab initio simulations), and we need to ensure that we have enough information to make a model sufficiently accurate, reliable and transferable. The main challenge stems from the fact that descriptors of chemical environments are often sparse, high-dimensional objects without a well-defined continuous metric. Therefore, it is rather unlikely that any ad hoc method for selecting training examples will be indiscriminate, and it is easy to fall into the trap of confirmation bias, where the same narrow and biased sampling is used to generate training and test sets. We will show that an approach derived from classical concepts of statistical planning of experiments and optimal design can help to mitigate such problems at a relatively low computational cost. The key feature of the method we will investigate is that it allows us to assess the quality of the data without obtaining reference energies and forces—a so-called offline approach. In other words, we are focusing on an approach that is easy to implement and does not require sophisticated frameworks that involve automated access to high performance computing.

We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The fundamental thermodynamic relation between internal energy and entropy, as well as entropy production, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within an entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.