Unstable Stacking Fault Energy Research Articles

Molecular dynamics study on the strengthening mechanisms of Cr–Fe–Co–Ni high-entropy alloys based on the generalized stacking fault energy

The correlation between the generalized stacking fault energy and the strengthening mechanisms of Cr–Fe–Co–Ni high-entropy alloys during uniaxial tensile deformation is investigated using molecular dynamics simulations. An increase in the Cr and Fe content decreases the generalized stacking fault energy, while an opposite trend is observed for the content of Co and Ni. A linear correlation is identified between the unstable stacking fault energy and the yield stress. Alloys with a lower Fe content and higher Co and Ni contents show a higher unstable stacking fault energy, and hence higher yield stress. A high density of Lomer–Cottrell locks or deformation twins leads to higher flow stress. The deformation twins play a more important role in enhancing the flow stress as compared to sessile dislocations. Additionally, high unstable stacking fault energy is required to stabilize the defects formed and contribute to increasing flow stress. For a low unstable stacking fault energy, the plastic deformation progresses at lower stress and a bidirectional defect transformation is observed. The results agree with recent experiments and serve as guidelines for how the composition can be used to enhance the yield strength and the efficiency of strengthening mechanisms in Cr–Fe–Co–Ni high-entropy alloys.

Effects of Cr/Ni ratio on physical properties of Cr-Mn-Fe-Co-Ni high-entropy alloys

Physical properties of ten single-phase FCC CrxMn20Fe20Co20Ni40-x high-entropy alloys (HEAs) were investigated for 0 ≤ x ≤ 26 at%. The lattice parameters of these alloys were nearly independent of composition while solidus temperatures increased linearly by ∼30 K as x increased from 0 to 26 at.%. For x ≥ 10 at.%, the alloys are not ferromagnetic between 100 and 673 K and the temperature dependencies of their coefficients of thermal expansion and elastic moduli are independent of composition. Magnetic transitions and associated magnetostriction were detected below ∼200 K and ∼440 K in Cr5Mn20Fe20Co20Ni35 and Mn20Fe20Co20Ni40, respectively. These composition and temperature dependencies could be qualitatively reproduced by ab initio simulations that took into account a ferrimagnetic ↔ paramagnetic transition. Transmission electron microscopy revealed that plastic deformation occurs initially by the glide of perfect dislocations dissociated into Shockley partials on {111} planes. From their separations, the stacking fault energy (SFE) was determined, which decreases linearly from 69 to 23 mJ·m−2 as x increases from 14 to 26 at.%. Ab initio simulations were performed to calculate stable and unstable SFEs and estimate the partial separation distances using the Peierls-Nabarro model. While the compositional trends were reasonably well reproduced, the calculated intrinsic SFEs were systematically lower than the experimental ones. Our ab initio simulations show that, individually, atomic relaxations, finite temperatures, and magnetism strongly increase the intrinsic SFE. If these factors can be simultaneously included in future computations, calculated SFEs will likely better match experimentally determined SFEs.

Unravelling the lamellar size-dependent fracture behavior of fully lamellar intermetallic [formula omitted]-TiAl

Strengthening of metals by incorporating nano-scale coherent twin boundaries is one of the important breakthroughs of recent years in overcoming the strength-ductility trade-off. To this effect, also twin boundaries in nano-lamellar lightweight Ti-Al alloys promise a great potential, but their contribution to the deformation and fracture behavior needs to be better understood for designing optimal microstructures. To this end, we carry out linear elastic fracture mechanics informed large-scale atomistic simulations of fully lamellar microstructures consisting of the so-called ”true twin” boundaries in γ-TiAl. We find that nano-scale lamellae are not only effective in improving the fracture toughness and crack growth resistance, but also that the lamellar size controls the crack tip mechanisms. We identify a critical lamella thickness in the region between 1.64 and 3.04 nm, above which the crack tip events are primarily dislocation-based plasticity and the critical fracture initiation toughness exhibits an increasing trend with decreasing lamella size. Below the critical thickness, a decline in fracture toughness is observed and the crack tip propagation mechanisms are quasi-brittle in nature, i.e. the cleavage of atomic bonds at the crack tip is accompanied by plasticity events, such as twin-boundary migration and dislocation nucleation. A layer-wise analysis of the unstable stacking fault energy, the energy barrier for dislocation nucleation, that the critical thickness is of a similar value as the distance from the twin boundary at which bulk properties are restored.

Nanoscale origin of the crystalline-to-amorphous phase transformation and damage tolerance of Cantor alloys at cryogenic temperatures

Based on recent experimental studies, crystalline-to-amorphous phase transformation has been proposed as a mechanism to enhance the damage tolerance of Cantor alloys at cryogenic temperatures. In this study, we provide atomistic insights, via molecular dynamics simulations, into the origin of the solid-state amorphization ahead of a crack tip, and report the deformation mechanisms contributing to cryogenic damage-tolerance. We show that the amorphization stems from the formation of multi-dislocation junctions due to the low stacking fault energy. This leads to high lattice resistance to dislocation glide and facilitates nucleation of amorphous nuclei. The deformation mechanisms in the amorphous/crystalline dual phase regions include high-density Shockley partial dislocations and multi-dislocation junctions in the crystalline region, as well as radiation-shaped shear bands and amorphous bridges in the amorphous region, which are rarely found in conventional alloys at low temperature. The amorphous bridges lead to crack shielding. Furthermore, altering the chemical composition changes the work-of-fracture and hence the damage tolerance. The Rice-criterion ductility (ratio between surface energy and unstable stacking fault energy) is an important factor affecting the degree of amorphization, which is useful for the mechanics-based design of Cantor alloys.

Deformation behaviour of Cu and Cu–Al in the dislocation starved regime: A molecular dynamics study

In general, with the addition of solutes, the yield strength of alloys is expected to increase; this phenomenon is known as solid solution strengthening. However, this model of strengthening implicitly assumes that dislocations are available and it is their motion that causes plastic deformation. On the other hand, in dislocation starved regimes, it is the nucleation of dislocations that controls the deformation behaviour. In this regime, the solute atoms can act as sites of heterogeneous nucleation for dislocations and “anomalous” softening with alloying additions are not uncommon. In this study, using Molecular Dynamics (MD) simulations, we show anomalous softening in Cu–Al alloys deformed at 300 K. We show that there are two components to this softening; in addition to the heterogeneous nucleation at solute sites, the reduction in stacking fault energy with alloying addition promotes the (homogeneous) nucleation of partial dislocation loops. In order to be consistent, we interpret the MD simulation results of deformation behaviour using parameters and energies derived from the same potentials used in the simulations. Specifically, we carry out the thermodynamic integration to evaluate the free energies in crystals with and without the stacking faults and hence calculate the SFE as a function of Al content at 300 K. Using the SFE values thus obtained, and using a continuum model of homogeneous nucleation of partial dislocation loops, we rationalise the deformation behaviour seen in pure copper. On the other hand, in Cu–Al alloys, the drop in yield strength can only be explained using a combination of the continuum model (which assumes homogeneous nucleation), and the reduction in heterogeneous nucleation barrier (which is a function of the ratio of the unstable and stable stacking fault energies). Thus, our results indicate that deformation experiments of pure copper and copper–aluminium alloys in the dislocation starved regime could be interesting and might show qualitatively and quantitatively different behaviour.

The Third-Order Elastic Constants and Mechanical Properties of 30° Partial Dislocation in Germanium: A Study from the First-Principles Calculations and the Improved Peierls–Nabarro Model

The elastic constants, core width and Peierls stress of 30° partial dislocation in germanium has been investigated based on the first-principles calculations and the improved Peierls–Nabarro model. Our results suggest that the predictions of lattice constant and elastic constants given by LDA are in better agreement with experiment results. While the lattice constant is overestimated at about 2.4% and most elastic constants are underestimated at about 20% by the GGA method. Furthermore, when the applied deformation is larger than 2%, the nonlinear elastic effects should be considered. And with the Lagrangian strains up to 8%, taking into account the third-order terms in the energy expansion is sufficient. Except the original γ—surface generally used before (given by the first-principles calculations directly), the effective γ—surface proposed by Kamimura et al. derived from the original one is also used to study the Peierls stress. The research results show that when the intrinsic−stacking−fault energy (ISFE) is very low relative to the unstable−stacking−fault energy (USFE), the difference between the original γ—surface and the effective γ—surface is inapparent and there is nearly no difference between the results of Peierls stresses calculated from these two kinds of γ—surfaces. As a result, the original γ—surface can be directly used to study the core width and Peierls stress when the ratio of ISFE to the USFE is small. Since the negligence of the discrete effect and the contribution of strain energy to the dislocation energy, the Peierls stress given by the classical Peierls–Nabarro model is about one order of magnitude larger than that given by the improved Peierls–Nabarro model. The result of Peierls stress estimated by the improved Peierls–Nabarro model agrees well with the 2~3 GPa reported in the book of Solid State Physics edited by F. Seitz and D. Turnbull.

Machine-learning potentials enable predictive and tractable high-throughput screening of random alloys

We present an automated procedure for computing stacking fault energies in random alloys from large-scale simulations using moment tensor potentials (MTPs) with the accuracy of density functional theory (DFT). To that end, we develop an algorithm for training MTPs on random alloys. In the first step, our algorithm constructs a set of $\ensuremath{\sim}10$ 000 or more training candidate configurations with 50--100 atoms that are representative for the atomic neighborhoods occurring in the large-scale simulation. In the second step, we use active learning to reduce this set to $\ensuremath{\sim}100$ most distinct configurations---for which DFT energies and forces are computed and on which the potential is ultimately trained. We validate our algorithm for the MoNbTa medium-entropy alloy by showing that the MTP reproduces the DFT $\frac{1}{4}[111]$ unstable stacking fault energy over the entire compositional space up to a few percent. Contrary to state-of-the-art methods, e.g., the coherent potential approximation (CPA) or special quasi-random structures (SQSs), our algorithm naturally accounts for relaxation, is not limited by DFT cell sizes, and opens opportunities to efficiently investigate follow-up problems, such as chemical ordering. In a broader sense, our algorithm can be easily modified to compute related properties of random alloys, for instance, misfit volumes, or grain boundary energies. Moreover, it forms the basis for an efficient construction of MTPs to be used in large-scale simulations of multicomponent systems.

Atomistic studies of ductile fracture of a single crystalline cantor alloy containing a crack at cryogenic temperatures

In this paper, atomistic studies show that Cantor alloys containing a pre-existing crack under tension are ductile at cryogenic temperatures. Specifically, the effects of crack length on the mechanical properties of single-crystalline Cantor alloys under mode I loading at the temperature of 0.1 K are investigated via molecular dynamics (MD) simulations. For different initial crack lengths ranging from 25 to 45 nm, the J-integral is calculated at the critical point of dislocation emission, and the work-of-fracture is calculated at the fracture strain. The results show that the Young’s modulus and yield stress decrease with the increased crack length. The J-integral is not significantly affected by the crack length, due to the fact it is governed by the length-independent unstable stacking fault energy. However, the work-of-fracture increases with increased crack length. Nucleation and growth of nanosized cavities in front of the crack tip are observed and the crack propagates through coalescence of cavities, which agrees well with previous experimental findings. As the tensile strain increases, there is a transition from cavitation to shear faulting, after which the stress-strain responses are independent of the crack length. The cavitation and shear faulting dissipate a large amount of energy needed for crack propagation, leading to ductile fracture of Cantor alloys at cryogenic temperatures.

Alloying effects on phase stability, mechanical properties, and deformation behavior of CoCrNi-based medium-entropy alloys at low temperatures

Alloying plays an important role in determining the phase stability and mechanical behavior of medium/high-entropy alloys (M/HEAs). In this work, the effects of Al, Ti, Mo, and W additions on the phase stability, strengthening behavior, and stacking fault energies of CoCrNi alloys are quantitatively investigated by using first-principles calculations. Our results reveal that the Al, Ti, and W additions enhance the structural stability of metastable face-centered cubic structures, whereas Mo is in favor of the formation of hexagonal close-packed structures at low temperatures. Through analyzing the elastic moduli and lattice mismatch based on a Labusch-type model, we show that the solute strengthening effect decreases in the order W > Mo > Ti > Al. The compositional dependence of intrinsic stacking fault energy (ISFE) and unstable stacking fault energy (USFE) of CoCrNi MEAs was calculated, and the results indicate that the Al, Ti, Mo and W additions significantly reduce the USFE, leading to a reduction in the energy barriers of dislocation slips. The alloying effects on the deformation behaviors of CoCrNi MEAs are discussed in terms of the ratio of ISFE to the energy barrier of dislocation slips. The present study not only sheds light on the fundamental understanding of phase stability and deformation mechanisms of M/HEAs but also provides useful guidelines for the alloy design of advanced M/HEAs with superior mechanical properties.

Stacking fault energy and ductility in a new zirconium alloys: A combined experimental and first-principles study

A combined experimental and first-principles study was performed on a new zirconium alloy. Experimental results showed that alloy elements, such as Cu, Nb, etc., mainly dissolve into the matrix of zirconium alloy where a larger number of slip traces are detected except for dislocation after deformation. First-principles calculation showed that Nb significantly reduces unstable stacking fault energy (γus), leading to the increment of {101-0}〈112-0〉 slip systems activity, and the stable and unstable stacking fault energies are both dramatically decreased with the addition of Cu, which is beneficial to the activation of the {0001} <101-0> and {101-1} <112-3> slip systems. It is suggested that basal or pyramidal plane becoming the second primary slip system givesriseto excellent forming properties, especially ductility. A new zirconium alloy containing Nb, Fe, and Cu elements was tested through uniaxial tension tests with digital image correlation (DIC) equipment. Both experimental and theoretical results showed that adding Nb, Fe, and Cu can enhance the ductility of zirconium alloys. Electronic properties of various stacking faults were also analyzed to explore the origin of excellent forming properties. Added element and its matching amount can be considered from the aspects of electronegativity and concentration effect for the preparation of zirconium alloys with excellent forming properties.

Effect of alloying elements on stacking fault energy and ductility of iron

First principles calculation has been directed to calculate the surface energy, stacking fault energy, and ductility parameter of the {110}<111> and {112‾}<111> slip systems of BCC Fe and Fe47X (X = Cr, Mo, Pb, and Bi). It is found that Cr and Mo should have a negligible effect on surface energy, unstable stacking fault energy, and ductility parameter of the two slip systems of BCC Fe. Calculation also reveals that both Pb and Bi could considerably reduce the ductility, surface energy, and unstable stacking fault energy of BCC Fe, and that such a decrease of the {110}<111> slip system is much greater than that of the {112‾}<111> slip system. In addition, the decrease of the surface energy of both slip systems of Fe47Pb and Fe47Bi is much more remarkable than that of the unstable stacking fault energy, i.e., the easier cleavage because of the weaker cohesion with a lower surface energy intrinsically brings about the brittleness of Fe47Pb and Fe47Bi. The obtained results are in nice agreement with experimental and theoretical evidence in the literature, and could offer a deep understanding of the intrinsic mechanism of liquid metal embrittlement of the T91 steel.

The effects of second-alloying-element on the formability of Mg-Sn alloys in respect of the stacking fault energies of slip systems

Generalized stacking fault (GSF) energies of the basal 0001112̅0，prismatic 101̅0112̅0 and pyramidal 112̅2112̅3 slip systems in the primary phase of Mg-Sn based-alloys have been studied using first-principles calculations in this work, where twenty-one third elements (X) have been taken in to consideration for their solution in primary (Mg, Sn) phase. The relative positions of Sn and X in Mg142Sn1X1 supercell have been determined by searching the minimum formation energies points. It is shown that, with alloying-elements of Sn and X, the unstable stacking fault energy (γus) of the basal and prismatic slip systems are decreased compared with that of Mg144. For the pyramidal slip system, only certain second-alloying-elements, namely Ag, Al, Cd, Ga, In, Li and Zn, soluted into the Mg-Sn alloys, make the γus lower than that of pure Mg. The atomic radius of element X has a significant impact on the γus value of Mg142Sn1X1, and also indirectly affects the γus by affecting the relative substitution positions of Sn and X atoms in the structure. Accordingly, the plastic formability parameters χ have been analyzed based on the calculated stacking fault energy (SFE) values. The effects of second-alloying-elements on GSF energies and χ provide a guidance for the design of high-performance multi-elements-alloying Mg alloys.

Prediction of shear strength of cluster-strengthened aluminum with multi-scale approach describing transition from cutting to bypass of precipitates by dislocations

We investigate the deformation of aluminum alloy containing copper in the form of fine Al-Cu clusters 1–4 nm in diameter with multiscale approach. A part of these precipitates (clusters of 1–2 nm in diameter) reproduce that were experimentally obtained by (Sun et al., 2019) by cyclic dynamic loading of aluminum alloy. At the first stage, molecular dynamics (MD) reveals that main mechanism of interaction of dislocation with the copper-containing cluster are cutting of precipitate for 1 nm cluster and bypass by Orowan mechanism for clusters with diameters above 1.4 nm. Single events of climb are observed in MD, frequency of which increases with a temperature raise. The stresses level realized for the climb mechanism practically do not differ from that of the basic mechanism for the considered inclusion diameters. Also, the results of MD simulations show that the strength of the cluster depends on the presence of enough number of copper atoms on the slip plane of dislocation and does not directly depend on the concentration of copper when it varies in the range of 20–100% inside the precipitate. Reduction of copper concentration below 20% decreases the precipitate resistance, and the system behavior converges to the case of pure aluminum at 0%. These results are supported by MD calculations of generalized stacking fault energy, which demonstrate a weak dependence of unstable stacking fault energy on copper concentration in the range of 30–70%. A continuum model of dislocation motion in aluminum containing the copper-containing cluster is proposed, which considers the kinetics of dislocation-precipitate interaction and accounts for the transition from cutting to bypass. Parameters of the model are fitted to MD data with Bayesian algorithm. Model of dislocation motion and dislocation-precipitate interaction is implemented into 2D discrete-dislocation dynamics (DDD). Flow stress of alloy predicted with DDD demonstrates reasonable agreement with the experimental data. Calculations show that the cluster-strengthened alloy demonstrates much less inhomogeneity of plastic deformation in comparison with the alloy with a comparable flow stress and volume fraction of typical phases precipitated during classical aging, which is also in line with the experiment.

Investigation of aluminum concentration on stacking fault energies of hexagonal close-packed high-entropy alloys Hf0.25Ti0.25Zr0.25Sc0.25−xAlx (x < 15%)

The stacking fault energy (SFE) is fundamental to understand the mechanical behavior of materials, and is also closely related to the structural phase transition. In present work, the generalized stacking fault energies of basal plane for novel hexagonal close-packed high-entropy alloys Hf0.25Ti0.25Zr0.25Sc0.25−xAlx (x < 15%) are studied using density functional theory and special quasi-random structure for modeling the chemical disorder, and the effect of aluminum is emphasized. With increase of Al content, the lattice constant a decreases, while c/a increases. Especially, the addition of Al is favorable to reduce the unstable and stable stacking fault energies of the studied alloys. The lower SFE further improves the ductility, creep resistance and yield strength of materials. Moreover, with replacement of Sc by Al, lower γISF/γUSF ratio of stable intrinsic SFE (γISF) to unstable intrinsic SFE (γUSF) and higher γUSF/γUTF ratio of unstable intrinsic SFE to unstable twin-like SFE (γUTF) suggest that although both the dislocation decomposition and twinning are favored, the dislocation decomposition is still predominant due to stronger decrease of γISF/γUSF. Furthermore, the much larger unstable twin-like SFE γUTF than the unstable intrinsic SFE γUSF also indicates that the main deformation mechanism in Hf0.25Ti0.25Zr0.25Sc0.25−xAlx (x < 15%) may be dislocation-mediated slip. The further calculated electronic structure shows that replacement of Sc by Al enhances the covalent bonding of high-entropy alloys Hf0.25Ti0.25Zr0.25Sc0.25−xAlx (x < 15%), and reduces the energy difference during the sliding process, thus lower the stacking fault energy. The present investigation is very valuable and helpful for understanding and developing of high performance of novel hexagonal close-packed high-entropy alloys.

Effect of strain on generalized stacking fault energies and plastic deformation modes in fcc-hcp polymorphic high-entropy alloys: A first-principles investigation

The generalized stacking fault energy (GSFE) is a material property that can provide invaluable insights into describing nanoscale plasticity phenomena in crystalline materials. Lattice strains have been suggested to influence such phenomena. Here, the GSFE curves for sequential faulting pathways in dual phase [face-centered cubic (fcc) and hexagonal close-packed (hcp)] ${\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{20}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{20}, {\mathrm{Cr}}_{25}{\mathrm{Fe}}_{25}{\mathrm{Co}}_{25}{\mathrm{Ni}}_{25}, {\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{34}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{6}, {\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{30}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{10}$, and ${\mathrm{Cr}}_{10}{\mathrm{Mn}}_{30}{\mathrm{Fe}}_{50}{\mathrm{Co}}_{10}$ high-entropy alloys are investigated on ${{111}}_{\text{fcc}}$ and ${(0002)}_{\text{hcp}}$ close-packed planes using density-functional calculations. The dependence of GSFEs on imposed volumetric and longitudinal lattice strains is studied in detail for ${\mathrm{Cr}}_{20}{\mathrm{Mn}}_{20}{\mathrm{Fe}}_{20}{\mathrm{Co}}_{20}{\mathrm{Ni}}_{20}$ and ${\mathrm{Cr}}_{10}{\mathrm{Mn}}_{30}{\mathrm{Fe}}_{50}{\mathrm{Co}}_{10}$. The competition between various plastic deformation modes is discussed for both phases based on effective energy barriers determined from the calculated GSFEs and compared with experimentally observed deformation mechanisms. The intrinsic stacking fault energy, unstable stacking fault energy, and unstable twinning fault energy are found to be closely related in how they are affected by applied strain. The ratio of two of these planar fault energies can thus serve as characteristic material property. An inverse relationship between the intrinsic stacking fault energy in the hcp phase and the axial ratio ${(c/a)}_{\text{hcp}}$ is revealed and explained via band theory.

Mechanical properties and deformation mechanisms in CoCrFeMnNi high entropy alloys: A molecular dynamics study

We used molecular dynamics simulations to investigate the relationship between mechanical properties and deformation mechanisms in CoCrFeMnNi alloys having different compositions. According to deformation twinning activity, the deformation mechanisms in the different CoCrFeMnNi compositions under tensile loading can be classified into three major categories: easy-shear (ES), inter-locks (IL) and bulk hexagonal closed packed (hcp) transformation (BH). We found that the compositions with ES were more likely to rupture early because of the short and fragmented twins. The compositions following the IL pattern promoted the movement of interlocking stacking faults in the twin boundaries that could prolong tensile deformation. Moreover, BH could further increase ductility because the hcp transformation could absorb and dissipate the stacking faults. Experimental observations of immobile stacking-fault networks that impede dislocation motion and further provide preferred sites for the formation of the hcp phase were commonly found in the ES, IL and BH patterns. The calculated intrinsic stacking fault energies of CoCrFeMnNi and CoCrFeNi were consistent with the experimental measurements. The combination of high unstable stacking fault energy with the formation of the IL pattern results in high strength and high ductility in the CoCrFeMnNi HEA system.

Effect of Fe on the Hall-Petch relationship of (CoCrMnNi)100-x Fex medium-and high-entropy alloys

In the present study, a systematic investigation on the effect of Fe content on the Hall-Petch coefficient of (CoCrMnNi)100-x Fex (x = 20, 40, 50, and 60) medium- and high-entropy alloys (M/HEAs) was carried out. The cold-rolled alloys were annealed at 900 °C and 1000 °C between 3 min and 10 h for recrystallization. Scanning electron microscope with a backscattered detector was used to obtain micrographs of recrystallized specimens for grain size calculation. Tensile testing was used to evaluate the mechanical properties of the alloys. The microstructure showed that regardless of the alloy composition, the grain size was approximately similar when subjected to the same heat treatment condition. Moreover, all the alloys obeyed the classical Hall-Petch relationship. Friction stress (solid solution, SS strengthening) decreased with an increase of Fe content, which was attributed to weak lattice distortion caused by the reduction of the atomic size misfit. The Hall-Petch coefficient, which represents grain boundary (GB) strengthening, also decreases as the Fe content increases. A linear relationship between intrinsic stacking fault energy and Hall-Petch coefficient was found not to exist. However, it is proposed that the monotonic decrease of the Hall-Petch coefficient is directly related to the unstable stacking fault energy (γUSFE). As a result, an increase of Fe content in (CoCrMnNi)100-x Fex alloy system leads to an increase of γUSFE, which in turn weakens GB strengthening (Hall-Petch coefficient). Moreover, HEAs and MEAs with higher Fe content tend to have low yield strength due to weak contributions from both SS and GB strengthening. Therefore, to design superior MEAs and HEAs with enhanced strength, the choice of principal elements and their respective contents is imperative for an optimized contribution from both SS and GB strengthening mechanisms.

Phase field dislocation dynamics (PFDD) modeling of non-Schmid behavior in BCC metals informed by atomistic simulations

Body-Centered Cubic (BCC) metals exhibit anomalous mechanical properties such as twinning/anti-twinning and tension/compression asymmetry, which are attributed to asymmetric behavior of screw dislocations. Unlike Face-Centered Cubic (FCC) metals, the Critical Resolved Shear Stress (CRSS) of BCC metals deviates from the Schmid law. We use a mesoscale modeling approach called Phase Field Dislocation Dynamics (PFDD) to understand the critical factors that control this non-Schmid behavior and reproduce atomistic predictions of the CRSS (Peierls stress). All inputs to the PFDD model are obtained from Molecular Statics (MS) simulations. Multiple pathways for modeling the non-Schmid behavior are investigated by incorporating the representative dislocation properties into different energy terms in the PFDD model. One way to understand non-Schmid behavior is to incorporate stress components projected on inclined planes into the external energy term within PFDD. Alternatively, we propose that non-Schmid behavior can also be accounted for by considering the variation of the {110} unstable stacking fault energy and the dislocation core width as a function of the applied tensorial stress field. The CRSS predicted using PFDD modeling is in excellent agreement with MS predictions.

Screening of generalized stacking fault energies, surface energies and intrinsic ductile potency of refractory multicomponent alloys

Body-centered cubic (bcc) refractory multicomponent alloys are of great interest due to their remarkable strength at high temperatures. Optimizing the chemical compositions of these alloys to achieve a combination of high strength and room-temperature ductility remains challenging. Systematic predictions of these correlated properties across a vast compositional space would speed the alloy discover process. In the present work, we performed first-principles calculations with the special quasi-random structure (SQS) method to predict the unstable stacking fault energy (γusf) of the (11¯0)[111] slip system and the (11¯0)-plane surface energy (γsurf) for 106 individual binary, ternary and quaternary bcc solid-solution alloys with constituent elements among Ti, Zr, Hf, V, Nb, Ta, Mo, W, Re and Ru. Moreover, with the first-principles data and a set of physics-informed descriptors, we developed surrogate models based on statistical regression to accurately and efficiently predict γusf and γsurf for refractory multicomponent alloys in the 10-element compositional space. Building upon binary and ternary data, the surrogate models show outstanding predictive capability in the high-order multicomponent systems. The ratio between γsurf and γusf can be used to populate a model of intrinsic ductility based on the Rice model of crack-tip deformation. Therefore, using the surrogate models, we performed a systematic screening of γusf, γsurf and their ratio over 112,378 alloy compositions to search for alloy candidates that may have enhanced strength-ductility synergies. Search results were also validated by additional first-principles calculations.

Cooperative roles of stacking fault energies on dislocation nucleation at bimetal interface through tunable potentials

By tuning consistent potentials for bimetal system, the cooperative roles of stacking fault energies (SFEs) such as intrinsic SFE (ISFE) and unstable SFE (USFE) on the dislocation nucleation are comprehensively explored. It reveals that the dislocation nucleation at semi-coherent interface is determined by the misfit dislocations, but the critical yield stress depends strongly on the values of ISFE and USFE that are function of external loadings. To account for such relationship, a modified analytical model is proposed based on the nucleation and propagation of double kinks at the interface, showing good agreement with the simulation results. These results not only resolve the previous inconsistency in the role of stacking faults on plastic deformation but shed light on evaluating the atomistic mechanism according to the synergistic effect between stacking faults and loading schemes.