Body-centered Cubic Metals Research Articles

Disconnection units of twinning in body-centered-cubic metals

Twin boundary (TB) migration, facilitated by the motion of disconnections, plays a pivotal role in the deformation of body-centered cubic (BCC) crystals. Comprehending the migration rules of twinning disconnections (TDs) under shear stress is significant in elucidating the role of twin migration in BCC plasticity. Nevertheless, our understanding of the atomic structure and migration mechanics of TDs remains incomplete. In this study, we employ the theory of interfacial defects and molecular dynamics (MD) simulations to thoroughly investigate potential {112}[111] TDs in BCC tantalum (Ta). These TDs are characterized by their Burgers vectors, which were predicted through related dichromatic pattern analysis. We reveal that single-layer and double-layer TDs represent the fundamental building blocks (units) of multi-layer TDs. Their migration directions are entirely opposite under the same shear loading, and they cannot annihilate each other when they migrate “face to face”. Furthermore, these migration rules governing single-layer and double-layer TDs offer a comprehensive explanation for the complex composition and decomposition patterns observed among various multi-layer TDs. What's more, we demonstrated that TDs with zero Burgers vector can only be driven as a whole under coupled loading conditions. These findings significantly enhance our understanding of TB migrations in BCC metals.

Predicting surface-energy anisotropy of metals with geometric properties of surfaces and atoms

Surface-energy anisotropy of metals is crucial for the stability and structure, however, its determining factors and structure-property relationship are still elusive. Herein, we identify three key factors for predicting surface-energy anisotropy of pure metals and alloys: the surface-atom density, coordination numbers and atomic radius. We find that the coupling rules of surface geometric determinants, which determining surface-energy anisotropy of face-centred-cubic (FCC), hexagonal-close-packed (HCP) and body-centred-cubic (BCC) metals, are essentially controlled by the crystal structures instead of chemical bonds, alloying or electronic structures. Furthermore, BCC metals exhibit material-dependent surface-energy anisotropy depending on the atomic radius, unlike FCC and HCP metals. The underlying mechanism can be understood from the bonding properties in the framework of the tight-binding model. Our scheme provides not only a new physical picture of surface stability but also a useful tool for material design.

Anisotropy effect on the motion of edge dislocation in body-centered-cubic Fe

The mechanical properties of metallic materials can be dictated by nucleation, multiplication, and motion of dislocations under stress. We employed the molecular dynamics (MD) method to investigate the motion of an 1/2[111](112̄) edge dislocation in body-centered-cubic (BCC) Fe under normal stress on the 112̄ plane. Our MD results confirm that the motion of the edge dislocation can be attributed to the normal stress induced shear stress (NSISS) effect. The magnitude of this effect varies across different cubic metals. Further studies reveal that this effect is limited to the {112} planes and is associated with the disobedience of Schmid’s law in the case of twinning of BCC Fe. To summarize, the NSISS effect may be traced back to the anisotropy of cubic metals and should be considered when the twinning process in anisotropic BCC metals is studied.

Atomic-scale observation of nucleation- and growth-controlled deformation twinning in body-centered cubic nanocrystals

Twinning is an essential mode of plastic deformation for achieving superior strength and ductility in metallic nanostructures. It has been generally believed that twinning-induced plasticity in body-centered cubic (BCC) metals is controlled by twin nucleation, but facilitated by rapid twin growth once the nucleation energy barrier is overcome. By performing in situ atomic-scale transmission electron microscopy straining experiments and atomistic simulations, we find that deformation twinning in BCC Ta nanocrystals larger than 15 nm in diameter proceeds by reluctant twin growth, resulting from slow advancement of twinning partials along the boundaries of finite-sized twin structures. In contrast, reluctant twin growth can be obviated by reducing the nanocrystal diameter to below 15 nm. As a result, the nucleated twin structure penetrates quickly through the cross section of nanocrystals, enabling fast twin growth via facile migration of twin boundaries leading to large uniform plastic deformation. The present work reveals a size-dependent transition in the nucleation- and growth-controlled twinning mechanism in BCC metals, and provides insights for exploiting twinning-induced plasticity and breaking strength-ductility limits in nanostructured BCC metals.

Origin of thermal deformation induced crystallization and microstructure formation in additive manufactured FCC, BCC, HCP metals and its alloys

The additive manufacturing (AM) technology has received the widespread attention in the industrial application because of its unique ability to achieve the complex shape and ideal performance. Unfortunately, the impact of the material natural characteristics, such as the crystal structure and alloying, on the microstructure formation at the nanoscale has never been revealed in AM metals. Here, we use large-scale molecular-dynamics simulations to study the rapid thermal deformation processes of additively-manufactured face-centered-cubic (FCC), body-centered-cubic (BCC), hexagonal close-packed (HCP) metals and their alloys (FCC Cu, CuAl0.1, BCC Fe, FeAl0.1, and HCP Mg, MgAl0.1) in the molten pool, in an attempt to elucidate the intrinsic physical mechanisms controlling the crystal nucleation and growth under the complex thermal stress. The results show that the arcuate solid-liquid interface migrates towards the liquid phase until the complete crystallization, in good agreement with the experimental observation. The solidification rate follows a unified slow-to-fast law in the three types of metals, due to the competition between the compressive thermal stress and fast atomic motion. It is noteworthy that the critical radius of the crystal nucleus in the FCC and BCC metals is smaller than that in the HCP metal. The FCC metal exhibits the weak nucleation ability and growth rate, and yet the HCP metal shows the fast growth rate and stable columnar crystal nucleation. Especially, due to the dual regulation of the steep thermal gradient and solute redistribution on the growth driving force, the alloying increases the constitutive supercooling of the solidification front and inhibits the growth of columnar crystals. This trend is particularly prominent in FCC alloys, which is manifested by the obvious amorphous phase and discrete nucleation point in the upper part of the melt pool. The nucleation barrier free energy descends in order of FCC, BCC, and HCP pure metals, but the alloying would increase this energy in the corresponding alloys. The current work gives an insight into the atomic mechanism of the nucleation and growth in AM FCC, BCC, and HCP metals.

Lowering the ductile-to-brittle transition temperature to -36 °C via fine-grained structures in chromium

The inherent ductile-to-brittle transition (DBT) behavior of body-centered cubic (BCC) metals severely limits their applications, and leads to low-temperature brittleness. To enhance the low temperature toughness of BCC metals, we take chromium as an example and design a fine-grained structure with average grain size of 5 μm, which shows a substantial decrease of DBT temperature to -36 °C. Compared with other samples with larger average grain sizes (45–135 μm), the fine-grained chromium still exhibits excellent toughness at -20 °C, and has the highest fracture energy and the yielding load. Our results reveal that numerous grain boundaries act as dislocation sources to emit easy glide edge dislocations at low temperature and also effectively slow down crack propagation, all together toughen ambient brittle chromium.

Nanoscale ductile fracture and associated atomistic mechanisms in a body-centered cubic refractory metal

Understanding the competing modes of brittle versus ductile fracture is critical for preventing the failure of body-centered cubic (BCC) refractory metals. Despite decades of intensive investigations, the nanoscale fracture processes and associated atomistic mechanisms in BCC metals remain elusive due to insufficient atomic-scale experimental evidence. Here, we perform in situ atomic-resolution observations of nanoscale fracture in single crystals of BCC Mo. The crack growth process involves the nucleation, motion, and interaction of dislocations on multiple 1/2 < 111 > {110} slip systems at the crack tip. These dislocation activities give rise to an alternating sequence of crack-tip plastic shearing, resulting in crack blunting, and local separation normal to the crack plane, leading to crack extension and sharpening. Atomistic simulations reveal the effects of temperature and strain rate on these alternating processes of crack growth, providing insights into the dislocation-mediated mechanisms of the ductile to brittle transition in BCC refractory metals.

Interaction between cracks and dislocations in body-centered cubic crystals under mixed loads

A dislocation emission model for body-centered cubic (BCC) crystals with micro-scale grain size is described. When the critical condition of dislocation emission is reached, dislocations will be emitted from the crack tips and move along the slip planes at the crack tip. If the stress concentration at the crack tip is large enough or the distance between the crack tip and the grain boundary is small, the dislocation will move along the slip plane and accumulate at the grain boundary. Three BCC metals have been used to calculate the dislocation emission in this article. The results show the lattice friction has a significant effect on dislocation emission and distribution. Dislocations that emitted from crack tip have a shielding effect on stress concentration near the crack tip. The shielding effect of the dislocations on plane (110) is larger than that of the dislocations on plane (100), resulting in a more easy propagation of the crack in plane (100).

Characterization and modelling of evolving plasticity behaviour up to fracture for FCC and BCC metals

Yield surfaces evolve depending on loading directions (anisotropic hardening) and stress states (differential hardening) during plastic deformation of sheet metals. A new analytical yield function is proposed by coupling an enhanced pDrucker function and SY2009 anisotropic hardening functions to model both the differential and anisotropic hardening behavior. All the parameters are solved analytically for the proposed function so that the proposed function can model the differential hardening from uniaxial compression to equibiaxial tension and anisotropic hardening of uniaxial tension with three different loading directions. Its convexity during evolution is analysed from plasticity onset to ultimate fracture by a geometry-inspired numerical convex analysis approach. Several tests were conducted for an aluminium alloy 2A12-O and a high-strength steel QP1180 including uniaxial tension/compression, simple shear, notched tension and bulge tests. The proposed yield function is applied to describe the plastic behaviour of AA2A12-O and QP1180 steel under the non-associated flow rule. Parameter calibration is conducted at pre-necking and post-necking stages for modelling yield surface evolution more accurately under large deformation especially at shear and equibiaxial tension states. The applications to the two metals show that the proposed function is more suitable for pressure-sensitive face-centered cubic (FCC) and body-centered cubic (BCC) metals compared to the pressure-coupled Yld2000–2d and CQN models since both the anisotropic and differential hardening behaviours are precisely modelled by the proposed yield function. The proposed function could also be utilized as a stress-based fracture criterion to model four stress states fracture from uniaxial compression to equibiaxial tension.

Scanning Three-Dimensional X-ray Diffraction Microscopy with a Spiral Slit

Recently, nondestructive evaluation of the stresses localized in grains was achieved for plastically deformed low-carbon steel using scanning three-dimensional X-ray diffraction (S3DXRD) microscopy with a conical slit. However, applicable metals and alloys were restricted to a single phase and evaluated stress was underestimated due to the fixed Bragg angles of the conical slit optimized to αFe. We herein propose S3DXRD with a rotating spiral slit adaptable to various metals and alloys and accurate stress evaluation with sweeping Bragg angles. Validation experiments with a 50-keV X-ray microbeam were conducted for low-carbon steel as a body-centered cubic (BCC) phase and pure Cu as a face-centered cubic (FCC) phase. As a result of orientation mapping, polygonal grain shapes and clear grain boundaries were observed for both BCC and FCC metals. Thus, it was demonstrated that S3DXRD with a rotating spiral slit will be applicable to various metals and alloys, multiphase alloys, and accurate stress evaluation using a X-ray microbeam with a higher photon energy within an energy range determined by X-ray focusing optics. In principle, this implies that S3DXRD becomes applicable to larger and thicker metal and alloy samples instead of current miniature test or wire-shaped samples if a higher-energy X-ray microbeam is available.

A unified model for ductile-to-brittle transition in body-centered cubic metals

Ductile-to-brittle transition (DBT) is a well-known phenomenon in body-centered-cubic (BCC) metals, intermetallics and semiconductor materials. A quantitative prediction of the DBT temperature, however, has so far remained intractable. Here, we propose a unified model based on the efficacy of dislocation multiplication as the controlling factor for DBT, with the dislocation source efficiency governed by the relative mobility of screw versus edge dislocations. The model successfully predicts the DBT temperature of iron, molybdenum and tungsten, and also covers the influence of grain size, initial dislocation density, and the multiplicity of dislocation sources. A comparison with experiments indicates that the model captures the key DBT features, providing new insight into the toughness of BCC metals.

Unstable stacking fault energy and peierls stress for evaluating slip system competition in body-centered cubic metals

Determining the competition between the {110}⟨111⟩, {112}⟨111⟩ and {123}⟨111⟩ slip systems in body-centered cubic (BCC) metals is important to understand their mechanical properties. In this paper, the unstable stacking fault energy (γus) and Peierls stress (σp) of the three slip systems of a series of BCC metals are calculated in order to evaluate the competition among them. We find that γus of BCC metals is proportional to (B+G)/a2/3, where B, G and a are the bulk modulus, shear modulus and lattice constant, respectively. The calculations of γuss predict that the {110}⟨111⟩ dislocation slip is prior to the {112}⟨111⟩ and {123}⟨111⟩ slips, however, γus may not be used to identify the priorities of the latter two slips because γuss of these two slip systems are too close to each other. According to σps, the mobility of dislocations decreases in the sequence of {110}⟨111⟩, {112}⟨111⟩, {123}⟨111⟩ for all the metals considered except for K. Noticeably, it is shown that γus and σp are not monotonically related to each other.

Twinning and antitwinning in body-centered cubic metals

Deformation twinning in body-centered cubic (BCC) metals occurs by shearing the crystal along {112} planes parallel to 〈111〉 directions. One of these directions (twinning shear) produces a twin, but it is often argued that the opposite sense of shearing (antitwinning shear) does not lead to twin formation. However, recent slip trace and orientational mapping analyses made on many BCC metals after low-temperature plastic deformation show clear evidence of fine misoriented lamellae along the traces of {112} planes sheared in the antitwinning sense. To resolve this controversy, we have utilized molecular statics simulations to determine the energy barriers for uniformly shearing all transition and alkali BCC metals in the twinning and antitwinning sense. The results of these simulations show that twins in transition BCC metals of the 5th and 6th groups can be produced on both types of {112} planes, irrespective of whether the shear is applied in the twinning or the antitwinning sense. However, this is not the case for α-Fe and the BCC structures of the alkali metals Li, Na, and K, where twins are likely to occur only on {112} planes sheared in the twinning sense. Furthermore, we have used TEM diffraction pattern analyses to investigate the characters of misoriented deformation lamellae in Nb and Cr compressed at 77 K, which were found along {112} planes sheared in the antitwinning sense. We demonstrate that these regions constitute regular twins. Similar studies on α-Fe compressed at 77 K prove that twinning in this material takes place exclusively on {112} planes sheared in the twinning sense.

Effect of twin boundaries on the strength of body-centered cubic tungsten nanowires

Twin boundaries (TBs) are assumed to be obstacles to dislocation motion and increase the strength of metals. Here, we report the abnormal phenomenon that TBs reduce the strength of body-centered cubic (BCC) tungsten (W). [1–11]-oriented W nanowires with (121) twin planes and free of dislocations were fabricated by chemical vapor deposition. In situ tensile tests within the transmission electron microscope were performed on single-crystal and twinned W nanowires. The fracture strength of the twinned W nanowire was 13.7 GPa, 16% lower than that of the single-crystal W nanowire (16.3 GPa). The weakening mechanism of the TB was revealed by a combination of atomic-resolution characterizations and atomistic simulations. Twinned W nanowires failed by the early nucleation of a crack at the intersection of the TB with the surface. The standard strengthening mechanism by dislocation/TB interaction was not operative in W because the high Peierls barrier and stacking fault energy in W hinder dislocation nucleation and glide. These findings provide a new insight into the influence of TBs on the mechanical properties of BCC metals.

Shock-induced α" martensitic transformation in Nb single crystals

The structural and mechanical response of pure body-centered cubic (BCC) Nb under shock loading were systematically studied. Shock-induced orthorhombic (α") martensitic transformations were observed in single crystals Nb with different orientations, in which dense lenticular α" martensite variants distribute uniformly along different directions by forming a hierarchical structure. Neighbouring martensite variants share a {111}<110>α" twinning relationship between each other, and high-density dislocations are found distributing along the α"/BCC(β) interface. The formation of α" martensite was dominated by a mechanism of collinear shuffling of alternating {110}β planes along with <1 1¯ 0>β direction by a displacement δ. The collision between martensite variants along different direction induce abundant microcracks, with BCC-to-ω and BCC-to-FCC phase transformations occurring at the crack tips. These findings not only provide the experimental evidence of shock-induced α" martensitic transformation in pure BCC metals, but also link the microstructure interaction of materials to their macroscopic shock failure directly, which may have a broad impact on the study of shock deformation in different materials.

Discrete twinning dynamics and size-dependent dislocation-to twin transition in body-centred cubic tungsten

• We present a direct visualization of twinning dynamics in BCC W nanowires, with a discrete behaviour at atomic level. • Quantitative experimental studies directly demonstrate that deformation twins in W nanowires have a minimum size of six-layers and grow in increments of approximately three-layers, in contrast to the layer-by-layer growth of deformation twins in FCC. • These discrete twinning dynamics are generally applicable to different BCC metals across different length scales, which can help interpret the major twinning characteristics observed in previous and current studies of bulk BCC metals. • These findings not only advance the understanding of size-dependent dislocation-twinning competition in BCC nanocrystals, but also stimulate the investigation of plasticity in a broad class of small-volume BCC metals and alloys. Body-centred cubic (BCC) metals are known to have unstable intrinsic stacking faults and high resistance to deformation twinning, which can strongly influence their twinning behaviour. Though twinning mechanisms of BCC metals have been investigated for more than 60 years, the atomistic level dynamics of twinning remains under debate, especially regarding its impact on competition between twinning and slip. Here, we investigate the atomistic level dynamics of twinning in BCC tungsten (W) nanowires using in situ nanomechanical testing. Quantitative experimental studies directly visualize that deformation twins in W nanowires have a minimum size of six-layers and grow in increments of approximately three-layers at a time, in contrast to the layer-by-layer growth of deformation twins in face-centred cubic metals. These unique twinning dynamics induces a strong competition with ordinary dislocation slip, as exhibited by a size-dependent dislocation-to-twin transition in W nanowires, with a transition size of ∼40 nm. Our work provides physical insight into the dynamics of twinning at the atomic level, as well as a size-dependent dislocation-twinning competition, which have important implications for the plastic deformation in a broad class of BCC metals and alloys.

Development of a physically-informed neural network interatomic potential for tantalum

Large-scale atomistic simulations of materials heavily rely on interatomic potentials, which predict the system energy and atomic forces. One of the recent developments in the field is constructing interatomic potentials by machine-learning (ML) methods. ML potentials predict the energy and forces by numerical interpolation using a large reference database generated by quantum-mechanical calculations. While high accuracy of interpolation can be achieved, extrapolation to unknown atomic environments is unpredictable. The recently proposed physically-informed neural network (PINN) model improves the transferability by combining a neural network regression with a physics-based bond-order interatomic potential. Here, we demonstrate that general-purpose PINN potentials can be developed for body-centered cubic (BCC) metals. The proposed PINN potential for tantalum reproduces the reference energies within 2.8 meV/atom. It accurately predicts a broad spectrum of physical properties of Ta, including (but not limited to) lattice dynamics, thermal expansion, energies of point and extended defects, the dislocation core structure and the Peierls barrier, the melting temperature, the structure of liquid Ta, and the liquid surface tension. The potential enables large-scale simulations of physical and mechanical behavior of Ta with nearly first-principles accuracy while being orders of magnitude faster. This approach can be readily extended to other BCC metals.

Screw dislocations in BCC transition metals: from ab initio modeling to yield criterion

We show here how density functional theory calculations can be used to predict the temperatureand orientation-dependence of the yield stress of body-centered cubic (BCC) metals in the thermallyactivated regime where plasticity is governed by the glide of screw dislocations with a 1/2 Burgers vector. Our numerical model incorporates non-Schmid effects, both the twinning/antitwinning asymmetry and non-glide effects, characterized through ab initio calculations on straight dislocations. The model uses the stress-dependence of the kink-pair nucleation enthalpy predicted by a line tension model also fully parameterized on ab initio calculations. The methodology is illustrated here on BCC tungsten but is applicable to all BCC metals. Comparison with experimental data allows to highlight both the successes and remaining limitations of our modeling approach.

User-friendly anisotropic hardening function with non-associated flow rule under the proportional loadings for BCC and FCC metals

This paper presents a user-friendly function under non-associate flow rule to capture anisotropic hardening (or evolution of yield surface) and the curvature of yield loci for body-centred cubic (BCC) and face-centred cubic (FCC) under the proportional loading conditions. The calibrated model for BCC and FCC metals is applied to illustrate the hardening behavior of uniaxial tension along different loading directions and of the equibiaxial tension for several steels and aluminum alloys (718AT, QP980, AA5182-O and AA 6xxx-T81) to evaluate its accuracy. The prediction is compared with the experimental results and modeling results of several popular plasticity models. The comparison demonstrates that the proposed model is pressure-insensitive, relatively simple for numerical implementation, capable of illustrating the different yielding behaviors between BCC and FCC metals and, capable of accurate modeling of flow curves under directional loading directions and equibiaxial tension both under the plane stress and triaxiality loading conditions. The proposed model is also flexible on adjusting the curvature of the yield surface between uniaxial tension and equibiaxial tension. Accordingly, the proposed anisotropic hardening model is useful to illustrate anisotropic hardening behaviors under uniaxial and equibiaxial tension.

Nanoindentation of single crystalline Mo: Atomistic defect nucleation and thermomechanical stability

The mechanical responses of single crystalline Body-Centered Cubic (BCC) metals, such as molybdenum (Mo), outperform other metals at high temperatures, so much so that they are considered as excellent candidates for applications under extreme conditions, such as the divertor of fusion reactors. The excellent thermomechanical stability of molybdenum at high temperatures (400–1000 oC) has also been detected through nanoindentation, pointing toward connections to emergent local dislocation mechanisms related to defect nucleation. In this work, we carry out a computational study of the effects of high temperature on the mechanical deformation properties of single crystalline Mo under nanoindentation. Molecular dynamics (MD) simulations of spherical nanoindentation are performed at two indenter tip diameters and crystalline sample orientations [100], [110], and [111], for the temperature range of 10–1000 K. We investigate how the increase of temperature influences the nanoindentation process, modifying dislocation densities, mechanisms, atomic displacements and also, hardness, in agreement with reported experimental measurements. Our results suggest that the characteristic formation and high-temperature stability of [001] dislocation junctions in Mo during nanoindentation, in contrast to other BCC metals, may be the cause of the persistent thermomechanical stability of Mo.