Bcc Metals Research Articles

Crystal–melt coexistence in fcc and bcc metals: a molecular-dynamics study of kinetic coefficients

As a sequel to the previous paper on the calculation of the crystal–melt interface free energy (2021 Materialia 15 100962), here we report the results on the kinetic coefficients using molecular dynamics simulations performed on six fcc metals and four bcc metals with the intention to compare the crystal structural influence. We found that the calculated kinetic coefficients are well described by the model by Broughton, Gilmer and Jackson (1982 Phys. Rev. Lett. 49 1496), and in particular, they exhibit varying degrees of anisotropy. We reveal that the anisotropies are related to the fluctuation of the crystal–melt interfaces, which causes the increase of the actual interface area in melting or solidification. The kinetic coefficients always display asymmetry between the solidification and melting process, and the difference is much more pronounced for the (111) interfaces in fcc metals which have the highest anisotropy. We found that the atomic mechanisms of the kinetic behaviors of these interfaces are closely related to the formation of twin-crystal domains during solidification, which delays the solidification process and consequently causes a decrease in the calculated kinetic coefficients.

Theoretical investigation of the 70.5[formula omitted] mixed dislocations in body-centered cubic transition metals

The low-temperature plasticity of body-centered cubic (bcc) metals is governed by 12〈111〉 screw dislocations due to their compact, non-planar core. It has been proposed that 70.5° mixed (M111) dislocations may also exhibit special core structures and comparably large Peierls stresses, but the theoretical and experimental evidence is still incomplete. In this work, we present a detailed comparative study of the M111 dislocation in five bcc transition metals on the basis of atomistic simulations. We employ density functional theory and semi-empirical interatomic potentials to investigate both the core structure and the Peierls barrier of the M111 dislocation. Our calculations demonstrate that reliable prediction of M111 properties presents not only a very stringent test for the reliability of interatomic potentials but is also challenging for first-principles calculations for which careful convergence studies are required. Our study reveals that the Peierls barrier and stress vary significantly for different bcc transition metals. Sizable barriers are found for W and Mo while for Nb, Ta and Fe the barrier is comparably small. Our predictions are consistent with internal friction measurements and provide new insights into the plasticity of bcc metals.

Understanding imprint formation, plastic instabilities and hardness evolutions in FCC, BCC and HCP metal surfaces

Nanoindentation experiments in metal surfaces are characterized by the onset of plastic instabilities along with the development of permanent nanoimprints and dense defect networks. This investigation concerns massive molecular dynamics simulations of nanoindentation experiments in FCC, BCC and HCP metals using blunted (spherical) tips of realistic size, and the detailed comparison of the results with experimental measurements. Our findings shed light on the defect processes which dictate the contact resistance to plastic deformation, the development of a transitional stage with abrupt plastic instabilities, and the evolution towards a self-similar steady-state characterized by the plateauing hardness p p at constant dislocation density ρ p . The onset of permanent nanoimprints is governed by stacking fault and nanotwin interlocking, the buildup of nanostructured regions and crystallites throughout the imprint, the cross-slip and cross-kinking of surfaced screw dislocations, and the occurrence of defect remobilization events within the plastic zone. As a result of these mechanisms, the ratio between the hardness p p and the Young's modulus E becomes higher in BCC Ta and Fe, followed by FCC Al, HCP Mg and large stacking fault width FCC Ni and Cu. Finally, when nanoimprint formation is correlated with the uniaxial response of the indented minuscule material volume, the hardness to yield strength ratio, p p / σ ys , varies from ≈ 7 to ≈ 10, which largely exceeds the continuum plasticity bound of ≈ 2.8. Our results have general implications to the understanding of indentation size-effects, where the onset of extreme nanoscale hardness values is associated with the occurrence of unique imprint-forming processes under large strain gradients.

Full energy range primary radiation damage model

A full energy range primary radiation damage model is presented here. It is based on the athermal recombination corrected displacements per atom (arc-dpa) model but includes a proper treatment of the near threshold conditions for metallic materials. Both ab initio (AIMD) and classical molecular dynamics (MD) simulations are used here for various metals with body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp) structures to validate the model. For bcc and hcp metals, the simulation results fit very well with the model. For fcc metals, although there are slight deviations between the model and direct simulation results, it is still a clear improvement on the arc-dpa model. The deviations are due to qualitative differences in the threshold energy surfaces of fcc metals with respect to bcc and hcp metals according to our classical MD simulations. We introduce the minimum threshold displacement energy (TDE) as a term in our damage model. We calculated minimum TDEs for various metal materials using AIMD. In general, the calculated minimum TDEs are in very good agreement with experimental results. Moreover, we noticed a discrepancy in the literature for fcc Ni and estimated the average TDE of Ni using both classical MD and AIMD. It was found that the average TDE of Ni should be \ensuremath{\sim}70 eV based on simulation and experimental data, not the commonly used literature value of 40 eV. The most significant implications of introducing this full energy range damage model will be for estimating the effect of weak particle-matter interactions, such as for \ensuremath{\gamma}- and electron-radiation-induced damage.

Rolling Textures in BCC Metals: A Biaxial Stress Texture Theory and Experiments

Rolling Textures in BCC Metals: A Biaxial Stress Texture Theory and Experiments

Melting of Tantalum at Multimegabar Pressures on the Nanosecond Timescale

Tantalum was once thought to be the canonical bcc metal, but is now predicted to transition to the Pnma phase at the high pressures and temperatures expected along the principal Hugoniot. Furthermore, there remains a significant discrepancy between a number of static diamond anvil cell experiments and gas gun experiments in the measured melt temperatures at high pressures. Our insitu x-ray diffraction experiments on shock compressed tantalum show that it does not transition to the Pnma phase or other candidate phases at high pressure. We observe incipient melting at approximately 254±15 GPa and complete melting by 317±10 GPa. These transition pressures from the nanosecond experiments presented here are consistent with what can be inferred from microsecond gas gun sound velocity measurements. Furthermore, the observation of a coexistence region on the Hugoniot implies the lack of significant kinetically controlled deviation from equilibrium behavior. Consequently, we find that kinetics of phase transitions cannot be used to explain the discrepancy between static and dynamic measurements of the tantalum melt curve. Using available high pressure thermodynamic data for tantalum and our measurements of the incipient and complete melting transition pressures, we are able to infer a melting temperature 8070_{-750}^{+1250} K at 254±15 GPa, which is consistent with ambient and a recent static high pressure melt curve measurement.

Modeling twin boundary structures in body centered cubic transition metals

The twin boundary structures in the BCC transition metals are determined by analyzing twin boundary generalized stacking fault energy curves and complete structural relaxation of the twinned crystals utilizing both interatomic potentials and density functional theory calculations. In contrast to the crystallographic description of twin elements in BCC metals, the pure reflection twin boundary structure has been found to be unstable in all seven metals considered. Instead, this work identifies three possible metastable twin boundary structures that are distorted forms of the pure reflection twin boundary structure and isosceles twin boundary structure previously proposed: a distorted reflection, distorted isosceles, and scalene structures. The DFT simulations reveal that the stability and energetic preference to form these structures differs between the Group 5 and Group 6 BCC metals despite having the same structure and general type of bonding. This work ates how these equilibrium structures and their relative stability affect the commonly reported twinning generalized stacking fault energy curves and explain why these curves (as previously computed) always have cusps.

Theory of kink migration in dilute BCC alloys

Plastic deformation in elemental BCC metals and dilute alloys is controlled by the slower of the kink pair nucleation and kink migration processes along screw dislocations. In alloys nucleation is facilitated and migration inhibited, leading to a concentration- and temperature-dependent transition from nucleation dominance to migration dominance. Here, an analytical statistical model for the stress-dependent kink migration barrier in dilute BCC alloys is developed and validated. The barrier depends only on a clearly-defined solute/screw dislocation interaction parameter, the kink width, and dislocation length between jogs. The analytic model is extensively validated via fully atomistic nudged-elastic band calculations and stochastic simulations in a model Fe-Si alloy. Combined with a recent validated double-kink nucleation theory, a fully-analytic model for the temperature- and concentration-dependent flow stress is obtained that includes the transition from nucleation to migration control. The overall model is applied to Fe-Si and W-Re using independently-determined material properties and good agreement is obtained with experiments over a range of concentrations and temperatures. Overall, the two theories represent a unified, fully-statistical, parameter-free understanding of screw dislocation strength in dilute BCC alloys.

Unveiling grain size effect on shock-induced plasticity and its underlying mechanisms in nano-polycrystalline Ta

To study macroscopic mechanical response and microscopic deformation mechanism of nano-polycrystalline (NPC) Ta under shock compression, massive-scale non-equilibrium molecular dynamics (NEMD) simulations were systematically performed. The effects of grain size, shock strength on the wave structure, plasticity mechanism and flow stress were unveiled. Under the weak shock compression, as the grain size increases, a transition of plastic wave structure from single to double and then to single one was found, driven by the transition of dominant deformation mechanism from grain boundary (GB)-mediated plasticity to its coexistence with twinning and slipping and then to twinning and slipping, respectively. A transition from twinning-to slipping-preferred plastic deformation as the grain size exceeds ~30 nm was captured in the simulations and explained by a simple theoretical model proposed in this work. Under the strong and ultra-strong shock compressions, twinning-detwinning and amorphization-recrystallization were revealed as the dominant deformation mechanisms, respectively, which show weak grain size dependences. The flow stresses at the Hugoniot state were calculated, which follow the Hall-Petch relation under the weak and strong shocks but show complexity under the ultra-strong shock. These results can help understand intrinsic grain size and extrinsic shock strength effects on the mechanical and microstructural responses of Ta, as a key structural and typical BCC metal.

STUDY ON ELASTIC PROPERTY OF STAINLESS STEEL UNDER PRESSURE

The paper presents analytic expressions of the Helmholtz free energy and characteristic elastic deformation quantities such as the elastic moduli E, K, G and the elastic constants C11, C12, C44 for BCC interstitial and substitutional alloy with four components are determined by the statistical moment method. The obtained elastic quantities depend on temperature, pressure, the concentration of interstitial atoms, and the concentration of substitutional atoms. This is the elastic deformation theory of BCC interstitial and substitutional alloy with four components published for the first time. The elastic deformation theories of BCC metal, BCC binary interstitial alloy, BCC binary substitutional alloy, and BCC ternary interstitial and substitutional alloy are limit cases of the elastic deformation theory of BCC substitutional and interstitial alloy with four components. Our numerical calculations of the obtained theoretical results for metal Fe and alloy FeSi are in good agreement with other calculations and experiments. Other numerical calculations for alloys FeCr, FeNi, FeCrSi, FeNiSi, FeCrNiSi (some atoms Fe are substituted by atoms Cr and some other atoms Fe are substituted by atoms Ni) called stainless steels predict and orient experimental results in the future. Our numerical calculations for alloy FeCrNiSi are published for the first time.

Thermal activation process of plastic deformation in Fe–18Cr single-crystal micropillars with high-density dislocations

Micropillar compression testing was performed on bcc solid-solution single-crystal micropillars with two diameter (d) ranges (2–3 and 5–6 μm) prepared on the surfaces of fully annealed and subsequently 10% cold-rolled 18Cr ferritic steel specimens. This was done to investigate the effect of initial dislocations on the plastic deformation of micron-sized crystals. The 10% cold rolling process significantly increased the stress level (provided by an activated single slip system) required to initiate slip in the annealed micropillars with different diameter ranges. In the case of the annealed micropillars, the strain-rate sensitivity (m) of the yield stress becomes lower for larger specimens (the m value decreased from 0.12 to 0.04). However, the 10% cold-rolled micropillars exhibited a much lower strain-rate sensitivity regardless of the specimen size. The activation volume (v*) of the annealed micropillars showed a significant specimen size dependency (v*∝d1.47), consistent with published data on the micropillar compression experiments of single-crystals of the bcc metals and alloys. For the 10% cold-rolled micropillars, the high v* values (88b3 and 112b3) showed a slight dependency on the specimen size (v*∝d0.33). The v* values appeared somewhat higher but were equivalent to those of bulk-size specimens, suggesting that the initial high-density dislocations would provide sufficient sources for dislocation multiplication in the micron-sized specimens under compression. The observed high v* values might be associated with the strong dislocation interactions in the α-(Fe, Cr) solid-solution matrix.

Noble gas bubbles in bcc metals: Ab initio-based theory and kinetic Monte Carlo modeling

Understanding the interactions of noble gases with metals is of fundamental importance for the design of radiation-resistant structural materials for fission and fusion nuclear reactors. Here we present a unified theory for describing the energetics of He, Ne, Ar, and Kr bubbles in bcc metals in group 5B (V, Nb, Ta), 6B (Cr, Mo, W) and 8B (Fe). Our predictive analytical model is based on the effective-medium and isotropic elasticity theories, and is parameterized using density functional theory (DFT) calculations of small gas-vacancy clusters. By performing kinetic Monte Carlo (KMC) simulations driven by our analytical model, we have predicted the lifetimes of noble gas bubbles and their coarsening by Ostwald ripening. Our most notable finding is the exceptionally higher thermal stability of Ne, Ar and Kr bubbles than He bubbles in bcc metals, conferring them outstanding resistance to Ostwald ripening. The physical origin of the unexpected stability of bubbles formed by large noble gas atoms has been further elucidated. Our theoretical finding is consistent with the experimental observation of He gas bubble superlattice (GBS) coarsening under thermal annealing, and provides new insights on the exceptional stability of fission GBS in bcc U-Mo up to a high homologous temperature of 0.78. The present calculated results also compare favorably with the existing thermal helium desorption spectrometry experiments in the literature.

Breakdown of the Hall-Petch relationship in extremely fine nanograined body-centered cubic Mo alloys

Mechanical properties and deformation behavior have been studied in face-centered cubic (fcc) metals with extremely fine grain sizes, even below about 20 nm, but this range is rarely studied in the body-centered cubic (bcc) metals. Here, we study the hardness and deformation behavior of bcc Mo(O) alloys with grain sizes from 120 to 4 nm, covering the range of classical Hall-Petch behavior as well as the regime where that scaling law breaks down, between about 11 and 4 nm. A hardness as high as 17.3 GPa was achieved at the strongest grain size of 11 nm, and the breakdown at smaller grain sizes is associated with a number of changes in behavior: an inflection in activation volume (associated with a change in rate dependence of deformation) and increasing shear localization. At coarser grain sizes this is associated with shear offsets at grain boundaries, pointing to an increasing prevalence of intergranular deformation (by sliding or grain rotation). At finer grain sizes localization is associated with the formation of large shear bands at scales far greater than the grain size. These behaviors are suggestive of a crossover from crystal-like to glass-like deformation behaviors at the finest grain sizes, consistent with the increasing fraction of disordered regions in the structure.

On the migration of {3 3 2} 〈1 1 0〉 tilt grain boundary in bcc metals and further nucleation of {1 1 2} twin

{3 3 2} 〈1 1 0〉 tilt grain boundaries (GB) move conservatively under a shear stress by the creation and glide of disconnections. When crystal dislocations interact with the GB they are absorbed and transformed into GB dislocations (GBD). The behaviour of GBDs under shear stress depends on the orientation of the Burgers vector and sense of shear stress. There are two possible scenarios: a) the GBD moves together with the GB in a compensated climb, then plastic deformation is accommodated by shear-coupled GB migration; b) the GBD is sessile because it cannot undergo a compensated climb when interacting with the disconnections. If so, the sessile GBD is the nucleus of a {1 1 2} twin. The nucleation of the twin is produced by the pileup of disconnections at both sides of the GBD. Then, plastic deformation is accommodated by the combination of the motion of the {3 3 2} GB and the growth of {1 1 2} twins inside the grain.

Influence of Cold Rolling on the Recrystallization Texture and Ridging of AISI 430 Type Ferritic Stainless Steel

The effect of cold rolling on the recrystallization texture and ridging of AISI 430 type ferritic stainless steel is investigated. For comparison, the steel was cold-rolled under different reductions, two-stage rolled, and cross-rolled, respectively, and the recrystallization texture was determined by EBSD and microstructure was characterized by SEM, and the uniaxial deformation was conducted on MTS electronic universal material testing machine. The results show that in the one-stage cold rolling and annealing process, γ-fiber texture component increases with the rolling reduction, and the maximum orientation density of which appears at {334} orientation with a slight deviation from {111} . The intensity of {100} texture decreases and the other main texture components remain unchangeable. After two-stage cold rolling, the recrystallization texture returns to the γ-fiber texture that is of the feature of the ordinary bcc metals, while cross-rolling results in a recrystallization texture of mainly {100} and {111} components. It is indicated that intermediate annealing obviously improves the deviation of orientation from γ-fiber texture, which is beneficial for the steel obtaining the typical texture of bcc metals. By one-stage cold rolling and annealing process, AISI 430 type ferritic stainless steel possesses a microstructure with the texture components of {100} , {211} , {111} and {111} , with clusters of {111} , {hkl} and {hkl} grains, which deteriorates the ridging resistance, while in the two-stage rolling and annealing process, the microstructure of dispersed oriented grains shows a much better surface ridging resistance.

Accurate prediction of vacancy cluster structures and energetics in bcc transition metals

Knowledge on structures and energetics of vacancy clusters is fundamental to understand defect evolution in metals. Yet there remain no reliable methods able to determine essential structural details or to provide accurate assessment of energetics for general vacancy clusters. Here, we performed systematic first-principles investigations to examine stable structures and energetics of vacancy clusters in bcc metals, explicitly demonstrated the stable structures can be precisely determined by minimizing their Wigner-Seitz area, and revealed a linear relationship between formation energy and Wigner-Seitz area of vacancy clusters. We further developed a new physics-based model to accurately predict stable structures and energetics for arbitrary-sized vacancy clusters. This model was well validated by first-principles calculations and recent vacancy cluster annealing experiments, and showed distinct advantages over the widely used spherical approximation. The present work offers mechanistic insights that crucial for understanding vacancy cluster formation and evolution, provides crucial benchmarks for assessing empirical interatomic potentials, and enables a critical step towards predictive control and prevention of vacancy cluster related damage processes in structural metals.

Experimental determination of the Hosford yield function exponential parameter for metal plates

The Hosford yield function can be used to describe both the plastic yield and plastic deformation of metal plates very well when the value of its exponential parameter $$\eta$$ is known. The values of $$\eta$$ for BCC and FCC metals have been determined to be 6 and 8, respectively, based on the Taylor crystal plasticity model. However, an effective experimental method has not been developed to determine the value of $$\eta$$ for metal plates. This work addresses the above issue by developing an experimental method for determining the value of $$\eta$$ for metal plates based on a theoretical model. Deep drawing experiments are conducted with 0.8 mm thick 5052 aluminum alloy plates, and the experimental value of $$\eta$$ is determined according to the theoretical model based on the experimentally measured thickness anisotropy coefficient, the known drawing coefficient, and the radial elongation ratio of the drawing cup obtained during the deep drawing experiments. The experiments yield an $$\eta$$ value of 8.02 for the aluminum alloy plates. The experimental value is verified by applying it within deep drawing simulations using Dynaform software based on the finite element method. The simulated cup height is in good agreement with the experimentally derived cup height. The value of $$\eta$$ can be determined for metal plates through deep drawing experiments based on the proposed methodology.

Repulsive coupled screw dislocation pairs cause work hardening in bcc metals

Repulsive coupled screw dislocation pairs cause work hardening in bcc metals

Micro-mechanical response of ultrafine grain and nanocrystalline tantalum

In order to investigate the effect of grain boundaries on the mechanical response in the micrometer and submicrometer levels, complementary experiments and molecular dynamics simulations were conducted on a model bcc metal, tantalum. Microscale pillar experiments (diameters of 1 and 2 μm) with a grain size of ~100–200 nm revealed a mechanical response characterized by a yield stress of ~1500 MPa. The hardening of the structure is reflected in the increase in the flow stress to 1700 MPa at a strain of ~0.35. Molecular dynamics simulations were conducted for nanocrystalline tantalum with grain sizes in the range of 20–50 nm and pillar diameters in the same range. The yield stress was approximately 6000 MPa for all specimens and the maximum of the stress–strain curves occurred at a strain of 0.07. Beyond that strain, the material softened because of its inability to store dislocations. The experimental results did not show a significant size dependence of yield stress on pillar diameter (equal to 1 and 2 um), which is attributed to the high ratio between pillar diameter and grain size (~10–20). This behavior is quite different from that in monocrystalline specimens where dislocation ‘starvation’ leads to a significant size dependence of strength. The ultrafine grains exhibit clear ‘pancaking’ upon being plastically deformed, with an increase in dislocation density. The plastic deformation is much more localized for the single crystals than for the nanocrystalline specimens, an observation made in both modeling and experiments. In the molecular dynamics simulations, the ratio of pillar diameter (20–50 nm) to grain size was in the range 0.2–2, and a much greater dependence of yield stress to pillar diameter was observed. A critical result from this work is the demonstration that the important parameter in establishing the overall deformation is the ratio between the grain size and pillar diameter; it governs the deformation mode, as well as surface sources and sinks, which are only important when the grain size is of the same order as the pillar diameter.

Low-temperature tensile properties of Cu-Fe laminated sheets with various number of layers

The Cu-Fe laminated sheets with various number of layers were produced by the accumulative roll bonding process, and the effects of the number of layers on the microstructure and low-temperature tensile properties of the sheets were elucidated. Then the reason for the excellent low-temperature tensile properties in dual-phase materials of Cu and Fe was discussed. The tensile properties of the pure Cu and Fe sheets used for fabricating the Cu-Fe laminated sheets exhibited the typical temperature dependence seen in the case of face-centered cubic (fcc) and body-centered cubic (bcc) metals. The layered structure of the laminated sheets was maintained till the number of layers was 100 but broke in the case of the 1000-layer sheet, which showed a network-like structure. The electrical conductivity of the sheets was independent of the number of layers and significantly higher than that of a Cu-Fe alloy, indicating that Fe had neither dissolved nor precipitated in the Cu layers of the laminated sheets. In the case of the 50-, 100- and 1000-layer sheet, the strength increased with lowering the temperature, while its elongation remained constant. A facet fracture surface was observed until the number of layers was 7, while in the case of the sheets consisting of more than 50-layers, fine dimples were observed on the fracture surfaces of both layers, indicating that ductile fracturing occurred. The strain in the Cu layers around the strain concentration sites of the Fe layers was high in the 50-layer laminated sheet when it was subjected to tensile deformation at 77 K. The strain concentration in the Fe layers might be accommodated by the surrounding soft Cu layers, resulting in the suppression of the nucleation of cleavage cracks in the Fe layers. This should be one of the reasons that the Cu-Fe layered sheets exhibited excellent elongation at low temperatures. Thus, the Cu-Fe layered structure take an important role for the excellent low-temperature tensile properties in the fcc and bcc dual-phase materials.