Bcc Metals Research Articles

Exploring structural variances in monatomic metallic glasses using machine learning and molecular dynamics simulation.

BCC and FCC metals have different glass-forming abilities (GFA) and exhibit different characteristics during the glass transition. However, the structural origin of their different GFAs is still not clear. Here, we explored the structures of eight monatomic metallic glasses by combining molecular dynamics (MD) simulations and machine learning (ML). Our findings reveal that, despite their common long-range disordered atomic structure, metallic glasses can be further classified into two distinct categories indicating an underlying structural order within the disorder. Using machine learning, we found that BCC liquids can sample more diverse glass states than FCC liquids. Furthermore, glasses formed from BCC metals (GFFBs) exhibit a higher degree of disorder than glasses formed from FCC metals (GFFFs). These findings highlight the inherent differences between GFFFs and GFFBs, which help explain the different glass-forming abilities of FCC and BCC metals. Additionally, our results demonstrate the promising potential of computer vision and ML methods in exploring material structures. Classical molecular dynamics simulations were employed to generate configurations of GFFBs and GFFFs, and the simulations were performed using the LAMMPS code. Inter-atomic interactions were described using a classical embedded atom model (EAM) potential. The initial configuration of the model consists of 32,000 atoms in a three-dimensional (3D) cubic box with periodic boundary conditions applied in all three directions. For machine learning, we utilized an unsupervised machine learning method along with MobileNetV2 for classifying glass structures. Image entropy and image distances were used to measure the structural differences of the metallic glasses.

A flexible yield criterion for strength modeling from biaxial compression to biaxial tension

Accurate strength modeling from equi-biaxial tension (EBT) to equi-biaxial compression (EBC) is critical for the plastic behavior prediction covering the wide-range of stress triaxiality encountered in sheet metal forming. To date, however, few yield criteria are available that can precisely model the initial yield and hardening behavior under six typical stress states between EBC and EBT, simultaneously. Furthermore, there is still a lack of a unified yield criterion for accurate strength modeling across various stress state ranges. To address the issues, a theoretical framework for constructing yield criteria dependent on stress states is provided and a new analytically described isotropic yield criterion is presented in this study. The flexibility in terms of the yield locus and application range is thoroughly explored to make the new yield criterion general. Subsequently, the isotropic yield criterion is extended into an analytically described anisotropic-asymmetric yield criterion. Furthermore, the extended yield criterion is applied to capture the initial yield behavior of DP980, AA5754-O, and AZ31 sheets, and the strain hardening behavior of QP1180 sheets at various stress states ranging from EBC to EBT along different loading directions. The predicted results from the extended criterion agree well with the corresponding experimental findings. The applications demonstrate that the proposed anisotropic-asymmetric yield criterion can effectively model the initial yield and hardening behavior of HCP, BCC, and FCC metal sheets under EBT, EBC, uniaxial tension (UT), plane strain tension (PST), shear (SH), and uniaxial compression (UC) in an analytical way.

Chaotic discrete breathers in bcc lattice: Effect of the first- and second-neighbor interactions

Numerical simulations are performed to investigate the formation of chaotic discrete breathers (DBs) in a bcc lattice using four zone-boundary modes with frequencies exceeding the crystal’s phonon spectrum. The study analyzes the impact of the stiffness of elastic bonds between first and second neighbors and identifies a specific range where the formation of chaotic DBs due to modulational instability of four vibrational modes is possible. The time evolution of the energy localization parameter and the maximum energy of all particles were monitored to control the formation of chaotic DBs. Their spontaneous nucleation was observed in a wide range of stiffness of elastic bonds and depends on the mode’s symmetry. Considering DBs in bcc metals, the paper focuses on the scenario where first-neighbor bonds are stiffer than second-neighbor bonds, as bond stiffness typically decreases with interatomic distance. In all four zone-boundary modes, formation of chaotic DB is observed under this condition.

Neural network based rYld2004 anisotropic hardening model under non-associated flow rule for BCC and FCC metals

This paper extends the reduced Yld2004 (rYld2004) function to present the anisotropic hardening behavior for body-centered cubic and face-centered cubic metals under the proportional loading conditions based on neural network. The parameters of the rYld2004 anisotropic hardening model (AH_rYld2004) are determined by the uniaxial tensile yield stresses along 0°, 15°, 30°, 45°, 60°, 75° and 90° from the rolling direction as well as equibiaxial tension. The evolution of anisotropic parameters are described by the back propagation neural network optimized by ant colony optimization algorithm. The predicted data by AH_rYld2004 and some common anisotropic models are compared with the experimental results to verify the precision of the AH_rYld2004 in characterizing anisotropic hardening. The comparison proves that the AH_rYld2004 precisely characterize the anisotropic evolution with increasing plastic deformation for AA 3003-O and QP980. Simultaneously, the AH_rYld2004 function based on neural network is used to accurately simulate of circular cup deep drawing for AA 3003-O and uniaxial tension for QP980. The results indicate that the AH_rYld2004 model is capable to accurately represent the plastic anisotropic evolution for uniaxial tension along seven loading directions and equibiaxial tension.

On the grain level deformation of BCC metals with crystal plasticity modeling: Application to an RPV steel and the effect of irradiation

Capturing realistic deformation behavior in BCC metals at the polycrystal scale is an important aspect of predicting the material’s strength and failure. Furthermore, local deformation/strength heterogeneity also influences the lifetime and its assessments in reactor pressure vessel (RPV) steels, especially with accumulating irradiation doses during long-term operational conditions. This work utilizes a micromorphic crystal plasticity (CP) model for BCC materials with the capability to address temperature-dependent stress–strain response and irradiation effects relevant to RPV materials. The microstructure of the investigated material was characterized prior to and during testing using electron microscopy experiments, which are used for finite element model generation and simulation result validation. To analyze the validity of the model to predict strain localization under monotonic tensile loading, micro digital image correlation (DIC) was employed jointly with the CP simulations. Different modeling choices, such as the use Schmid/non-Schmid laws and gradient based CP modeling, greatly affected the capability of the model to represent similar magnitudes in strain localization and grain reorientation. The requirement for experimental measurements, including image based analyses, on a microstructural level as a validation tool for CP modeling is clearly demonstrated.

Weak strain-rate sensitivity of hardness in the VCoNi equi-atomic medium entropy alloy

In this study, high strain rate nanoindentation was utilized to elucidate the dynamic behavior and the underlying deformation mechanisms of the equi-atomic vanadium-cobalt-nickel (VCoNi) medium entropy alloy. The hardness at high strain rate (average indentation strain rate: ∼11,000 s−1) exceeded that at low strain rate (constant indentation strain rate: 0.01 s−1) by only ∼3.5 %. Planar slip was identified as the predominant deformation mechanism at both strain rates, with no evidence of deformation twinning or phase transformation. The low strain rate sensitivity of VCoNi can be attributed to its lower lattice friction relative to that of conventional BCC metals and limited dislocation-dislocation interaction compared to that in typical FCC metals. The low strain rate sensitivity observed in VCoNi may also extend to other intermediate stacking fault energy alloy systems in which planar slip is prevalent.

Solute Hardening and Softening of BCC Metals: Excerpts from an Early Life with Terry Mitchell

Solute Hardening and Softening of BCC Metals: Excerpts from an Early Life with Terry Mitchell

Atomistic Simulations of the Shock and Spall Behavior of the Refractory High-Entropy Alloy HfNbTaTiZr

AbstractUsing molecular dynamics simulation, we study the effect of a shock wave on the refractory high-entropy alloy HfNbTaTiZr. A single-crystalline sample, shocked along the [001] direction, is considered. The initial compression leads to only weak dislocation activity and a bcc $$\rightarrow$$ → hcp transformation in some regions of the sample. After the shock wave is reflected from the free back surface of the sample, hcp transforms back to bcc, and twins are formed in the bcc phase. The sample spalls under the high tensile pressures developing after wave reflection. In this stage, we observe dislocation activity from the twin boundaries and inside the nanograins generated by twinning. Under the large tensile stresses, some fcc phase appears together with disordered amorphous regions where voids nucleate and lead to spall. The fracture surfaces follow the twin boundaries set up in the compression phase. The spall strength is similar to the one found in simulations of other bcc metals at similar strain rates. Similar simulations for the equiatomic HfNbTaZr HEA show the same qualitative behavior, with twins and reduced dislocation activity, but without phase transformations.

Kinetics of deformation fronts during serrated Lüders deformation in α-iron at high temperature

At room temperature, the deformation of most bcc metals, which contain a small amount of interstitial elements, is accompanied by the formation of a Lüders band and its monotonic propagation over the tensile yield area. Within the framework of the autowave concept, front of the Lüders band is a switching autowave, which realizes the transition from a metastable elastically deformable state to a stable plastically deformable state. However, in the temperature range of blue brittleness of mild steels of 423 – 510 K, when the interaction of atoms of the dissolved substance with mobile dislocations takes place, propagation of the Lüders band is accompanied by a discrete flow. The patterns of propagation of the Chernov-Lüders fronts in ARMCO iron in the temperature range from 296 to 503 K and strain rates from 6.67·10–6 to 3.7·10–2 s–1 are considered in this paper. It was established that under these conditions both monotonic and discrete kinetics of front movement can be realized. Regardless of the movement nature, the Lüders deformation and width of the front remain unchanged throughout the entire process. The local strain rate at the front depends on magnitude of the effective stress, and with monotonic kinetics it increases with stress according to an exponential law, and with discrete kinetics it increases according to a linear law. This difference is due to different autowave modes that are formed in this case. The autowave of localized plasticity switching corresponds to monotonic kinetics, and the autowave of excitation – to discrete kinetics.

Advanced modelling tool to extract the structural state boundaries from the hardness-strain experiments

High pressure torsion (HPT) is the way to form nanostructured materials with high strength properties. HPT hardening mechanisms in BCC metals, such as niobium and vanadium, are not fully understood. Here, we have demonstrated that a recently proposed piecewise model can extract from the hardness-strain experimental data the different structural states in BCC metals. The piecewise model, with overlapped stages, is based on an assumption that two separate deformation mechanisms which are responsible for the type of structure have overlapped strain region. To confirm/disprove extracted boundary values, we performed a transmission electron microscopic study of the HPT niobium and vanadium. We found that the piecewise model provides accurate extraction of the boundaries in niobium and vanadium. We proposed an explanation for the observed difference in the structure formation/transformation in niobium and vanadium upon HPT.

Deformation mechanism of metastable oriented grains in high-purity tantalum under different strain paths

High-purity tantalum is used as the sputtering target material for integrated circuits, requiring fine grains and random texture. Understanding different orientation deformation mechanisms, especially the metastable orientation (here {112} crystallographic orientations), is beneficial for controlling the structure of tantalum target materials. This paper employs EBSD and crystallographic calculations to regulate the grain deformation behavior by introducing a reverse strain at 135° clock rolling. The deformation behavior and dislocation density distribution of the metastable oriented grains under different strain paths are quantitatively analyzed. Results show that unidirectional rolling (UR) generates stress concentration, causing an uneven distribution of geometrically necessary dislocation density. The splitting behavior of {112} and {111} grains is promoted, and they have similar deformation behavior in UR process, while the deformation of {100} oriented grains is significantly suppressed. Furthermore, changing the strain path promotes the splitting of {100} grains, and makes the {112} change from the soft orientation to the hard orientation. This change makes it easier to start multi-slipping, resulting in a more uniform deformation. Additionally, crystallographic calculations show that Schmid factor is ineffective in explaining the strain localization problem in BCC metals. However, Schmid factor difference ratio makes it possible to analyze the distribution of dislocation density in local regions through the quantitative calculation of multi-slipping.

Delocalized nonlinear vibrational modes and discrete breathers in a body centered cubic lattice

Body centered cubic (bcc) lattice with nearest and next-nearest interactions described by the β-FPUT interatomic potential is considered. Exact dynamical solutions in the form of zone-boundary delocalized nonlinear vibrational modes (DNVMs) are analyzed. 31 such solutions are revealed from the analysis of only the symmetry of the bcc lattice. Frequency response of DNVMs for the case of soft- and hard-type anharmonicity is calculated. In the case of hard-type anharmonicity, four DNVMs have frequencies bifurcating from the upper edge of the phonon spectrum and growing with the amplitude. Various quasi-discrete breathers are obtained by superimposing localizing functions upon these DNVMs. Our work demonstrates a practical approach to finding quasi-discrete breathers in higher-dimensional lattices. The obtained spatially localized long-lived vibrational modes inspire the search for various discrete breathers in bcc metals.

Phase transformation and strengthening of the gas-atomized FeCoCrNiMo0.5Al1.3 high-entropy alloy powder during annealing

Phase evolution and strengthening of the FeNiCoCrMo0.5Al1.3 powder alloy produced via inert gas atomization and annealed in the temperature interval of 300–800 °C have been studied by X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy, and microhardness testing. It was found that annealing at 300–600 °C leads to an increase of the element segregations between the several solid solutions with a rise of the lattice misfit (ε) to 1.5 % and microhardness growth to 1070 HV. It was assumed that elastic stress caused by the element partitioning is the main strengthening mechanism: microhardness rises linearly with misfit rise with dHV/dε = 43400 MPa. Sigma arises after the maximum elastic deformation (in 1.5 %) was reached. Formation of the dispersed coherent sigma phase in the annealing interval 600–800 °C results in the microhardness rise. Oxidation that began at 800 °C in 27 h is accompanied with FCC formation due to a depletion of the B2 in Al caused by Al2O3 formation. Estimation of the activation energy of the initial stage of the solid solution decomposition gives a very low value in 0.65eV, apparently caused by the high concentration of quenched vacancies. The activation energy of sigma formation approximately coincides with the activation energy of self-diffusion in BCC metals (about 2.60 eV).

Bottom-Up Construction of Metal-Organic Framework Loricae on Metal Nanoclusters with Consecutive Single Nonmetal Atom Tuning for Tailored Catalysis.

The introduction of single or multiple heterometal atoms into metal nanoparticles is a well-known strategy for altering their structures (compositions) and properties. However, surface single nonmetal atom doping is challenging and rarely reported. For the first time, we have developed synthetic methods, realizing "surgery"-like, successive surface single nonmetal atom doping, replacement, and addition for ultrasmall metal nanoparticles (metal nanoclusters, NCs), and successfully synthesized and characterized three novel bcc metal NCs Au38I(S-Adm)19, Au38S(S-Adm)20, and Au38IS(S-Adm)19 (S-Adm: 1-adamantanethiolate). The influences of single nonmetal atom replacement and addition on the NC structure and optical properties (including absorption and photoluminescence) were carefully investigated, providing insights into the structure (composition)-property correlation. Furthermore, a bottom-up method was employed to construct a metal-organic framework (MOF) on the NC surface, which did not essentially alter the metal NC structure but led to the partial release of surface ligands and stimulated metal NC activity for catalyzing p-nitrophenol reduction. Furthermore, surface MOF construction enhanced NC stability and water solubility, providing another dimension for tunning NC catalytic activity by modifying MOF functional groups.

Critical assessment of hydrogen pipe diffusion at dislocations in metals

Hydrogen-dislocation interactions have always been a crucial problem in understanding and predicting the long-standing hydrogen embrittlement (HE) phenomenon in structural metals. Particularly with respect to hydrogen diffusion, dislocations have often been assumed with the ability to facilitate hydrogen transport via dislocation pipe diffusion (DPD). Yet the experimental and theoretical studies supporting DPD remain elusive and even controversial. In this work, hydrogen kinetics at dislocations in two representative metal systems, fcc Ni and bcc Fe, were systematically investigated combining comprehensive atomistic and kinetic activation relaxation technique simulations to reveal atomic details while enabling long-time (i.e., microsecond to second) hydrogen diffusion analysis. The dislocations were found to favor hydrogen trapping and provide regions of low migration barriers for hydrogen. However, these regions of low barriers only lead to localized fast short-circuit H diffusion, but do not translate into DPD over long time, which is attributed to fast hydrogen diffusion pathways along the dislocation line direction being periodically bound by high hydrogen migration barriers. Using the polyhedral structural units (PSUs) as an effective tool, we further quantitatively analyzed the correlation between hydrogen diffusion behaviors and local dislocation structures, illustrating the structural origin leading to local short-circuit diffusion and inhibition of DPD at dislocations. The new mechanistic insights gained not only are critical for understanding hydrogen-dislocation interaction, but also advances the general knowledge on hydrogen-microstructure interaction in structural metals.

Unifying the size effect observed in micropillar compression experiments

ABSTRACT Micropillar compression experiments show size effect, σp/μ = A(d/b)n , where σp , is the flow stress, μ is the resolved shear modulus, d is the pillar diameter and b is Burgers’ vector. With fcc metals n ≈ –0.67 and A ≈ 0.7; however, with bcc metals there is greater variation, with n closer to zero. Here we propose a different but similar empirical relation of σp/μ = σb/μ + A’(d/b)n’, where σb is a size independent resistance stress. In which case there must be a strong correlation between the original constants, A and n. This hypothesis is found to be true for the published data from a large number of bcc metals, ionic solids that possess the rock salt crystal structure, and some covalent bonded semiconductors. This correlation is shown to predict a universal power law with the exponent in the range, −1.0 < n’ < −0.5, and with A’ close to 1. These values are very similar to the empirical relation that can be used to describe the behaviour of fcc metals tested in micropillar compression with σb = 0. This universality of the empirical relation provides strong evidence for a common mechanism for the micropillar size effect across a range of materials.

An approach towards a self-consistent EAM model for bcc metals Lithium and Vanadium

Recently, a four-parameter embedding function that is sufficiently rich to handle both positive and negative Cauchy discrepancy has been produced by modifying the embedding function of Yuan et al. (2003)1, a modification to MEAM92, which failed to produce a reasonable surface energy when applied to bcc Vanadium V. We compute the three low-index surface energies of Li and V using the novel model Generalized Embedding Atom method (GEAM) (Oni-Ojo et al, 2007) parameters (iterated values), and the results fall within the experimental average.

Activation entropy and enthalpy of creep in pure metals

Previously published results on the power law creep of a selection of fcc, bcc and hcp pure metals are discussed using a modified Stokes – Einstein equation originally describing Newtonian viscosity of spherical particles in a fluid. Activation energy is modified to include terms representing activation enthalpy, activation entropy and the effect of strain rate. It is similar to the Dorn equation for power law creep but with strain rate rather than stress as the independent variable. Curves of activation energy vs shear rate are linear rather than having a discontinuity as have those with stress as independent variable. All metals have linear curves of activation energy at zero rate vs temperature, the slope of which reflects the activation entropy and is similar for all metals. Intercepts which represent activation enthalpy are dependent on lattice structure.

Evolution of Microstructure and Crystallographic Texture in Deformed and Annealed BCC Metals and Alloys: A Review

Dislocation slips, twinning, shear banding (SBs), strain localization, and martensite formation are a few deformation modes that are activated in BCC metals and alloys. Strain, strain rate, and deformation temperature are other parameters that determine the activation of deformation modes in BCC alloys. This review focuses on several BCC alloys, such as beta-titanium (β-Ti), tantalum (Ta), and ferritic stainless steels (FSSs), all of which exhibit differences in deformation behavior. These alloys often undergo thermo-mechanical processing (TMP) to enhance their mechanical properties. TMP leads to the evolution of deformation-induced products, such as SBs, strain-induced martensite (SIM), strain localizations, and mechanical/deformation twins (DTs) during plastic deformation, while also influencing crystallographic texture. The deformation modes in β-Ti depend upon the stability of the β-phase (i.e., β-stabilizers); low-stability alloys show the formation of SIM along with slips and twins, whereas in highly stable β-Ti alloys, only slip+twin modes are observed as the primary deformation mechanisms. In the case of Ta, slip activity predominantly occurs on {110} planes, but it can also occur on planes with the highest resolved shear stress. The breakdown of Schmid’s law or non-Schmid behavior for Ta and Ta-W alloys has been discussed in detail. The cold rolling (CR) of FSSs results in the formation of ridges, which is an undesirable phenomenon leading to very low formability. The microstructures of the rolled sheets consist of elongated ferrite grains with in-grain SBs, which are preferentially formed in the γ-fiber-oriented grains. The formation of finer grains after recrystallization improves both the mechanical properties and ridging resistance in FSS. Therefore, this review comprehensively reports on the impact of TMP on the microstructural and crystallographic texture evolution during the plastic deformation and annealing treatment of β-Ti, Ta alloys, and FSSs in BCC materials, using results obtained from electron microscopy and X-ray diffraction.

A new analytical surface energy model for arbitrary (h k l) planes in BCC and FCC metals

A new analytical surface energy model (Eq. 9) that is free of adjustable parameters has been developed to accurately predict the surface energies of arbitrary (h k l) planes in both BCC and FCC ground-state pure metals at 0 K, using only (100), (110) and (111) surface energies as input. The formulation is established by expanding the original broken-bond model up to the 3rd nearest neighbor shell and considering the surface relaxation effect. In addition, this model consists of only one single formula per crystal structure, overcoming the geometric complexities in previous models in which multiple equations are needed for different surface groups. The analytical model has been validated through the comparison with 4357 independent surface energies. These data include the energies of 517 unique surfaces per metal in Fe, Cr, W, Cu, Ni, and Al (a total of 3102 surface energies) that are calculated through our molecular dynamics simulations, and excellent agreement is obtained. The validation data also include 1255 independent surface energies in literature or online database for up to 46 BCC and FCC metals that were calculated by either empirical potentials or density functional theory. The agreement is still very good for most of the data, demonstrating the robustness of our new model.