Computational Materials Engineering Research Articles

Recent Advances in Near‐β Titanium Alloys: Microstructure Control, Deformation Mechanisms, and Oxidation Behavior

Near‐β titanium alloys are used as promising structural materials for aerospace, biomedical, and other advanced applications due to their excellent combination of high specific strength and superior corrosion resistance. Precise control of the microstructure and mechanical properties through thermomechanical processing and heat treatment is paramount for exploiting the full potential of these alloys. This review article provides a comprehensive and critical assessment of the state‐of‐the‐art research on the microstructure evolution, deformation mechanisms, and oxidation behavior of near‐β titanium alloys. Furthermore, the challenges and emerging opportunities in the development of near‐β titanium alloys have also been identified, ranging from alloy design and processing optimization to multiscale characterization and integrated computational materials engineering. This review article provides a timely and comprehensive roadmap for the research and development of near‐β titanium alloys, paving the way for unlocking their full potential in critical industries.

Optimizing Transformation-Induced Plasticity to Resist Microvoid Softening

Many high-performance steels that are critical for energy-efficient, lightweight designs rely on transformation-induced plasticity (TRIP) to achieve superior combinations of strength and ductility/toughness. Further development of these alloys will require greater optimization of the metastable (retained) austenite phase responsible for TRIP. Considering the complex nature of TRIP and its effects on ductile fracture, an integrated computational materials engineering (ICME) approach to materials optimization is desired. In this work, we report the results of a large series of micromechanical finite element calculations that probe the interaction of TRIP and void-mediated ductile fracture mechanisms. The simulations identify the optimal austenite stability for maximizing the benefit of TRIP across a wide range of stress states. The applied stress triaxiality significantly influences the microvoid growth rate and the computationally determined optimal stability. The simulation results are compared with existing experimental data, demonstrating good agreement.

Implementing numerical algorithms to optimize the parameters in Kampmann–Wagner Numerical (KWN) precipitation models

The Kampmann–Wagner Numerical (KWN) model of precipitation is a powerful tool to simulate the precipitation of the second phase considering the nucleation, growth, and coarsening. Some quantities such as interfacial energy and nucleation site number density are required to accomplish the simulation. Practically, those quantities are hard to measure in the experiment directly, and the derivation of those quantities through modeling can also be costly. In this work, we hereby adopt the minimization algorithm implemented in the open-source Scipy Python package to derive that important information in terms of very limited experimental data. The convergence and robustness of different algorithms are discussed. Among those algorithms, the Nelder–Mead and Powell algorithms are successfully applied to optimize multiple parameters during KWN modeling. This work will shed light on the design of experiments/processes and facilitate integrated computational materials engineering (ICME).

A Multiscale Inelastic Internal State Variable Corrosion Model.

We present a corrosion internal state variable (ISV) damage model based upon the integrated computational materials engineering (ICME) hierarchical multiscale paradigm. Structure-property experiments for magnesium alloys were used where the only inputs were the volume fractions of each element of the periodic table. This macroscale ISV corrosion model finds its basis in Horstemeyer's mechanical damage model, which includes three separate ISVs for damage nucleation, growth, and coalescence, as well as Walton's inclusion of corrosion, which introduces five new ISVs for pit nucleation, growth, and coalescence, along with general corrosion and intergranular corrosion. While Walton's corrosion ISVs are phenomenological in nature, herein we develop a multiscale physical basis for the corrosion ISVs. The parameters for the macroscale corrosion ISVs were garnered from the mesoscale Butler-Volmer equations. Pure magnesium with differing amounts of aluminum were used in corrosion tests to exemplify the different pitting, general corrosion, and intergranular corrosion rates, and the macroscale ISV model was calibrated with said data, in which the only inputs to the model are the volume percentages of the elements magnesium and aluminum. Although magnesium alloys were used to motivate and calibrate the model, the model is abstract enough to possibly capture other material systems as well.

Artificial intelligence enabled smart design and manufacturing of advanced materials: The endless Frontier in AI+ era

AbstractFuture‐oriented Science & Technology (S&T) Strategies trigger the innovative developments of advanced materials, providing an envision to the significant progress of leading‐/cutting‐edge science, engineering, and technologies for the next few decades. Motivated by Made in China 2025 and New Material Power Strategy by 2035, several key viewpoints about automated research workflows for accelerated discovery and smart manufacturing of advanced materials in terms of AI for Science and main respective of big data, database, standards, and ecosystems are discussed. Referring to classical toolkits at various spatial and temporal scales, AI‐based toolkits and AI‐enabled computations for material design are compared, highlighting the dominant role of the AI agent paradigm. Our recent developed ProME platform together with its functions is introduced briefly. A case study of AI agent assistant welding is presented, which is consisted of the large language model, auto‐coding via AI agent, image processing, image mosaic, and machine learning for welding defect detection. Finally, more duties are called to educate the next generation workforce with creative minds and skills. It is believed that the transformation of knowledge‐enabled data‐driven integrated computational material engineering era to AI+ era promotes the transformation of smart design and manufacturing paradigm from “designing the materials” to “designing with materials.”

LUNAR: Automated Input Generation and Analysis for Reactive LAMMPS Simulations.

Generating simulation-ready molecular models for the LAMMPS molecular dynamics (MD) simulation software package is a difficult task and impedes the more widespread and efficient use of MD in materials design and development. Fixed-bond force fields generally require manual assignment of atom types, bonded interactions, charges, and simulation domain sizes. A new LAMMPS pre- and postprocessing toolkit (LUNAR) is presented that efficiently builds molecular systems for LAMMPS. LUNAR automatically assigns atom types, generates bonded interactions, assigns charges, and provides initial configuration methods to generate large molecular systems. LUNAR can also incorporate chemical reactivity into simulations by facilitating the use of the REACTER protocol. Additionally, LUNAR provides postprocessing for free volume calculations, cure characterization calculations, and property predictions from LAMMPS thermodynamic outputs. LUNAR has been validated via building and simulation of pure epoxy and cyanate ester polymer systems with a comparison of the corresponding predicted structures and properties to benchmark values, including experimental results from the literature. LUNAR provides the tools for the computationally driven development of next-generation composite materials in the Integrated Computational Materials Engineering (ICME) and Materials Genome Initiative (MGI) frameworks. LUNAR is written in Python with the usage of NumPy and can be used via a graphical user interface, a command line interface, or an integrated design environment. LUNAR is freely available via GitHub.

Exploring large language models for microstructure evolution in materials

There is a significant potential for coding skills to transition fully to natural language in the future. In this context, large language models (LLMs) have shown impressive natural language processing abilities to generate sophisticated computer code for research tasks in various domains. We report the first study on the applicability of LLMs to perform computer experiments on microstructure pattern formation in model materials. In particular, we exploit LLM’s ability to generate code for solving various types of phase-field-based partial differential equations (PDEs) that integrate additional physics to model material microstructures. The results indicate that LLMs have a remarkable capacity to generate multi-physics code and can effectively deal with materials microstructure problems up to a certain complexity. However, for complex multi-physics coupled PDEs for which a detailed understanding of the problem is required, LLMs fail to perform the task efficiently, since much more detailed instructions with many iterations of the same query are required to generate the desired output. Nonetheless, at their current stage of development and potential future advancements, LLMs offer a promising outlook for accelerating materials education and research by supporting beginners and experts in their physics-based methodology. We hope this paper will spur further interest to leverage LLMs as a supporting tool in the integrated computational materials engineering (ICME) approach to materials modeling and design.

Design of advanced steels by integrated computational materials engineering

AbstractThe integrated computational materials engineering (ICME) has achieved great success in accelerating the rational design and deployment of new materials. It is a new route of designing new materials and processes and highlighted by Materials Genome Initiative/Engineering that stresses the high‐throughput computation in addition to high‐throughput experimentation and materials informatics. This article presents a brief review on the basic theories and multi‐scale computational tools of ICME to design advanced steel grades, including the first‐principles calculations, the CALPHAD method (i.e., computational thermodynamics) fueled by dedicated databases, diffusion and phase‐field simulations, as well as finite analysis methods and machine learning. In the ICME scheme to deal with steels, the CALPHAD method is considered as the core to readily consider multi‐component systems and integrated to link the microscopic simulations (such as diffusion and phase field method to predict microstructure evolutions in response to external conditions) and macroscopic finite analysis method to deal with mechanical properties. Two applications are also presented to address the new routes to carry out materials design, especially for advanced steels.

Modeling solute drag during austenite–ferrite transformation with ab initio binding energies

The solute drag effect can have a considerable impact on the austenite to ferrite transformation. Most models describing the solute drag effect require knowledge of solute binding energies, which due to lack of accurate data typically are treated as fit parameters. In this study we use density functional theory (DFT) calculations to estimate the effective binding energies of the substitutional alloying elements in an ultra low carbon steel. For the first time these energies are used to calculate the solute drag effect considering site competition for the austenite to ferrite phase transformation. The depletion of elements in solid solution as a result from precipitation is computed and the solute drag contribution of each element is calculated. Comparison of the binding energies with the resulting solute drag effect to literature data shows reasonable agreement. The outlined approach points the way to future alloy development based on interface-controlled integrated computational materials engineering. Another field of application is given by the circular economy driven transition in the steel industry from the BF/BOF- to the EAF-based production route with increased utilization of scrap material introducing new tramp elements.

Multi-plane denoising diffusion-based dimensionality expansion for 2D-to-3D reconstruction of microstructures with harmonized sampling

Acquiring reliable microstructure datasets is a pivotal step toward the systematic design of materials with the aid of integrated computational materials engineering (ICME) approaches. However, obtaining three-dimensional (3D) microstructure datasets is often challenging due to high experimental costs or technical limitations, while acquiring two-dimensional (2D) micrographs is comparatively easier. To deal with this issue, this study proposes a novel framework called ‘Micro3Diff’ for 2D-to-3D reconstruction of microstructures using diffusion-based generative models (DGMs). Specifically, this approach solely requires pre-trained DGMs for the generation of 2D samples, and dimensionality expansion (2D-to-3D) takes place only during the generation process (i.e., reverse diffusion process). The proposed framework incorporates a concept referred to as ‘multi-plane denoising diffusion’, which transforms noisy samples (i.e., latent variables) from different planes into the data structure while maintaining spatial connectivity in 3D space. Furthermore, a harmonized sampling process is developed to address possible deviations from the reverse Markov chain of DGMs during the dimensionality expansion. Combined, we demonstrate the feasibility of Micro3Diff in reconstructing 3D samples with connected slices that maintain morphologically equivalence to the original 2D images. To validate the performance of Micro3Diff, various types of microstructures (synthetic or experimentally observed) are reconstructed, and the quality of the generated samples is assessed both qualitatively and quantitatively. The successful reconstruction outcomes inspire the potential utilization of Micro3Diff in upcoming ICME applications while achieving a breakthrough in comprehending and manipulating the latent space of DGMs.

Statistical analysis of effective crack properties by microstructure reconstruction and phase-field modeling

Understanding the relation between the microstructure and the material’s effective behavior is an important aspect in inverse computational materials engineering. Especially in the context of localized, inelastic phenomena like plasticity and crack growth, the microstructure morphology plays a crucial role. Due to the stochastic nature of heterogeneous media, a statistical analysis over multiple simulations is necessary, since even with the same material, the simulated crack paths and effective crack lengths are highly dependent on the specific locations of microstructural features. A relevant factor that limits this type of investigation is the high cost of real microstructure data. This work presents a digital workflow for exploring the fracture properties of materials. Therein, the required statistical analyses are facilitated by an algorithm that reconstructs multiple realization of a material structure given a single example. The reconstructed structures are discretized with a regular non-conforming mesh with a diffuse interface and crack representation. Crack phase-field simulations are conducted in order to analyze the effective response. An in-depth introduction to the required methods is given together with a statistical evaluation of the conducted numerical experiments. It is concluded that the statistical variation of the effective material behavior overshadows morphological trends in the presented case. This confirms the relevance and utility of complementing simulation-based workflows with microstructure reconstruction and statistical analyses.

μ2mech: A software package combining microstructure modeling and mechanical property prediction

We have developed a graphical user interface (GUI) based package μ2mech to perform phase-field simulation for predicting microstructure evolution. The package can take inputs from ab initio calculations and CALPHAD (Calculation of Phase Diagrams) tools for quantitative microstructure prediction. The package also provides a seamless connection to transfer output from the mesoscale phase field method to the microscale finite element analysis for mechanical property prediction. Such a multiscale simulation package can facilitate microstructure-property correlation, one of the cornerstones in accelerated materials development within the integrated computational materials engineering (ICME) framework.

Microstructure and mechanical properties of a hypereutectic Al–Si–Cu alloy manufactured by laser powder bed fusion

A novel Al–Si–Cu alloy was designed for additive manufacturing of automotive components, such as pistons and supercharger rotors, requiring a combination of elevated temperature properties and high cycle fatigue strength. The alloy was designed with an Al–Si hypereutectic chemistry to exploit the formation of primary Si nucleants to enable an equiaxed as-printed microstructure during laser powder bed fusion (LPBF). The alloy design space was assessed using a combined integrated computational materials engineering (ICME) approach with melt-spinning experiments to select a chemistry exhibiting primary Si nucleants acting as heterogeneous grain nucleation sites. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) of the LPBF as-printed samples revealed primary Si particles with a fully equiaxed grain structure and no apparent texturing as evaluated using electron backscatter diffraction (EBSD). High-resolution scanning transmission electron microscopy (STEM) revealed sub-micron Si particles and Al2Cu θ-phase precipitates which result in enhanced room and elevated temperature mechanical strength (room temperature: UTS: 449 ± 10 MPa, YS: 336 ± 12 MPa) as compared to commercial Al10SiMg (UTS: 417 ± 3 MPa, YS: 236 ± 6 MPa).

Optimal Molecular Dynamics System Size for Increased Precision and Efficiency for Epoxy Materials.

Molecular dynamics (MD) simulation is an important tool for predicting thermo-mechanical properties of polymer resins at the nanometer length scale, which is particularly important for efficient computationally driven design of advanced composite materials and structures. Because of the statistical nature of modeling amorphous materials on the nanometer length scale, multiple MD models (replicates) are typically built and simulated for statistical sampling of predicted properties. Larger replicates generally provide higher precision in the predictions but result in higher simulation times. Unfortunately, there is insufficient information in the literature to establish guidelines between MD model size and the resulting precision in predicted thermo-mechanical properties. The objective of this study was to determine the optimal MD model size of epoxy resin to balance efficiency and precision. The results show that an MD model size of 15,000 atoms provides for the fastest simulations without sacrificing precision in the prediction of mass density, elastic properties, strength, and thermal properties of epoxy. The results of this study are important for efficient computational process modeling and integrated computational materials engineering (ICME) for the design of next-generation composite materials for demanding applications.

Understanding off-stoichiometry of Q-phase in Al-Cu-Mg-Si alloys

We perform first-principles density-functional theory (DFT) calculations to resolve the controversy of off-stoichiometry of Q-phase in Al-Cu-Mg-Si system. We compute the single and multiple defect energies (vacancy-vacancy, anti-site–vacancy, anti-site–anti-site) at 0 K and finite temperatures to understand the gap between DFT-predicted lowest energy structure and experimentally observed various stoichiometries of Q-phase. We find that i) the stoichiometry of Al4Cu2Mg8Si7 observed by Arnberg can be explained by the single anti-site defect of Al on Mg site, ii) the stoichiometry of Al5Cu2Mg8Si6 observed by Phragmen can be understood by the multiple anti-site defects of Al on Mg site and Al on Si site, iii) the physical size effect is important in determining the defect formation energetics under a similar chemistry (i.e., composition) of Q-phase. We believe that the proposed defect energetic information and mechanism will be useful to design Q-phase strengthened aluminum alloys based on Integrated Computational Materials Engineering (ICME).

Machine learning accelerated discovery of corrosion-resistant high-entropy alloys

Corrosion has a wide impact on society, causing catastrophic damage to structurally engineered components. An emerging class of corrosion-resistant materials are high-entropy alloys. However, high-entropy alloys live in high-dimensional composition and configuration space, making materials designs via experimental trial-and-error or brute-force ab initio calculations almost impossible. Here we develop a physics-informed machine-learning framework to identify corrosion-resistant high-entropy alloys. Three metrics are used to evaluate the corrosion resistance, including single-phase formability, surface energy and the compactness of oxide films formed on an alloy surface evaluated by Pilling–Bedworth ratios. We used random forest models to predict the single-phase formability, trained on an experimental dataset. Machine learning inter-atomic potentials were employed to calculate surface energies and Pilling–Bedworth ratios, which are trained on first-principles data fast sampled using embedded atom models. A combination of random forest models and high-fidelity machine learning potentials represents the first of its kind to relate chemical compositions to corrosion resistance of high-entropy alloys, paving the way for automatic design of materials with superior corrosion protection. This framework was demonstrated on AlCrFeCoNi high-entropy alloys and we identified composition regions with high corrosion resistance from a wide range of compositions. Machine learning predicted lattice constants and surface energies are consistent with values by first-principles calculations. The predicted single-phase formability and corrosion-resistant compositions of AlCrFeCoNi agree well with experiments. This framework provides a computationally efficient approach to navigate high-dimensional composition space of high-entropy alloys. It is general in its application and applicable to other complex materials, enabling high-throughput screening of material candidates and potentially accelerating the iteration of integrated computational materials engineering.

The effect of chemical vapor infiltration process parameters on flexural strength of porous α$\alpha$‐SiC: a numerical model

AbstractThe flexural strength variability of ‐ based ceramics at elevated temperatures creates the need for an Integrated Computational Materials Engineering (ICME) framework that relates the strength of a specimen directly to its manufacturing process. To create this ICME framework, a model must first be developed which establishes a relationship between the chemical vapor infiltration (CVI) process and parameters, the resulting mesoscale pores, and the overall macroscale flexural strength. Here, a nonlinear single‐pore model of CVI is developed used in conjunction with a four‐way coupled thermo‐mechanical damage model. The individual components of the model are tested and a sample system under a four‐point bending test is explored. Results indicate that specimens with an initial porosity greater than 30% require temperatures below 1273 K to maintain structural integrity, while those with initial porosities less than 30% are temperature‐independent, allowing for optimization of the CVI processing time without compromising strength.

Microstructural Evolution in a 6060 Extrudable Al-Alloy: Integrated Modeling and Experimental Validation.

Desirable properties including strength, ductility and extrudability of 6060 Al-alloys are highly dependent on processing to control the development of microstructural features. In this study, the process chain of an extrudable 6060 Al-alloy was modeled in an Integrated Computational Materials Engineering framework and validated experimentally via quantitative SEM-EDX and TEM. All critical processing stages were considered including casting, homogenization heating and holding, extrusion cooling and two-stage aging. Segregation and intermetallics formation were accurately predicted and experimentally verified in the as-cast condition. Diffusion simulations predicted the dissolution of intermetallics and completion of β-AlFeSi to α-AlFeSi transformation during homogenization, in excellent agreement with quantitative SEM-EDX characterization. Precipitation simulations predicted the development of a β″ strengthening dispersion during extrusion cooling and aging. Needle-shaped β″ precipitates were observed and analyzed with quantitative high-resolution TEM, validating predictions. Ensuing precipitation strengthening was modeled in terms of aging time, presenting good agreement with yield strength measurements. Precipitate-Free Zones and coarse, metastable β-type particles on dispersoids and grain boundaries were investigated. The proposed integrated modeling and characterization approach considers all critical processing stages and could be used to optimize processing of extrudable 6xxx Al-alloys, providing insight to mechanisms controlling microstructural evolution and resulting properties.

Computational high entropy alloy design

Materials scientists are developing new materials to meet increasing demands by employing a systematic approach linking material performance to composition, processing, and microstructure. Computational techniques, such as Calculation of Phase Diagrams and Integrated Computational Materials Engineering, play a crucial role in this process, enabling fast and efficient material design. This study focuses on developing a high damage-tolerant high entropy alloy for hydrogen service, using the two computational techniques to identify optimal composition, predict mechanical properties, and elucidate strengthening mechanisms.

Calibration of constitutive models using genetic algorithms

Constitutive models, describing material response to load, are an essential part of computational materials engineering. Semi-empirical constitutive laws including the Johnson–Cook and Zerilli–Armstrong models are widely used in finite element simulation for easy computability and rapid run time. The reliability of these models depends on accurate and reproducible fitting of parameters. This work presents a genetic algorithm (GA) based tool to fit parameters in constitutive models. The GA approach is capable of finding the global optimum parameter set in a robust, repeatable, and computationally efficient manner. It has been demonstrated that the obtained fits are better than those using traditional term-wise optimisation. Allowed to fit freely, the GA method will be likely to produce non-physical parameter values. However, by constraining the fit, the GA method can produce parameters that are physically reasonable and minimise the error when extrapolating to unseen data. Finally, the GA method may be used to choose between a variety of possible constitutive models based on a transparent best fit approach. The model has been demonstrated by using datasets from the literature for DH–36 steel and Ti-6Al-4V. This includes data from different studies, in which there are both random and systematic variations. The framework developed here is made freely available and modifiable, and may be extended to include other constitutive models as required.