Stacking Fault Energy Research Articles

Ab-initio trained machine learning potential for MAX compound Ti2AlC: Construction, validation, and study of non linear elasticity

Abstract One of the intriguing features exhibited by the layered MAX phase compounds, is the non linear elastic behaviour. Since the experimental observation of this curious behaviour, the underlying micro-mechanism has been discussed to interpret experimental observations. However, the theoretical investigation remained a challenge due to the associated length and time scales of the phenomena. In the present work, we adopt a data driven approach to develop a machine learned interatomic potential for the MAX compound Ti$_2$AlC following the Moment Tensor Potential protocol. The constructed potential is validated in lattice constant, formation energy, elastic constant, and stacking fault energies. Finally, applying machine learned potential in classical molecular dynamics provides a faithful
representation of the experimentally observed non linear elasticity for Ti$_2$AlC. The generated atomic configurations confirm the proposal of formation of ripplocations which allow atomic layers to glide relative to each other without breaking the in-plane bonds. We find common defects, like Al vacancy, strongly influence the hysteresis properties of the stress-strain curve, paving the route to defect-engineered non linear elasticity.

Predicting stacking fault energy in austenitic stainless steels via physical metallurgy-based machine learning approaches

Predicting stacking fault energy in austenitic stainless steels via physical metallurgy-based machine learning approaches

Strong, ductile, and hierarchical hetero-lamellar-structured alloys through microstructural inheritance and refinement

The strength-ductility trade-off exists ubiquitously, especially in brittle intermetallic-containing multiple principal element alloys (MPEAs), where the intermetallic phases often induce premature failure leading to severe ductility reduction. Hierarchical heterogeneities represent a promising microstructural solution to achieve simultaneous strength-ductility enhancement. However, it remains fundamentally challenging to tailor hierarchical heterostructures using conventional methods, which often rely on costly and time-consuming processing. Here, we report a multiscale microstructural inheritance and refinement strategy to process "structural hierarchy precursors" in as-cast heterogeneous Al0.7CoCrFeNi MPEAs, which lead directly to a hierarchical hetero-lamellar structure (HLS) after simple rolling and annealing. Interestingly, it takes only 10 min of annealing time, two orders of magnitude less than that required to render the state-of-the-art properties during conventional processing of Al0.7CoCrFeNi, for us to achieve record-high strength-ductility combinations via the hierarchical HLS design that sequentially stimulates multiple unusual deformation and reinforcement mechanisms. In particular, the HLS-enabled high hetero-deformation-induced (HDI) internal stress triggers profuse <111>-type dislocations on over five independent slip systems in the supposedly brittle intermetallic phase and activates extensive stacking faults (SFs) and nanotwinning in the adjoining soft phase with a rather high SF energy. These unexpected, dynamically reinforcing hetero-deformation mechanisms across multiple length scales facilitate high sustained HDI strain hardening, along with a salient microcrack-mediated extrinsic ductilization effect, suggesting that the proposed microstructural inheritance and refinement strategy provides an efficient, fast, and low-cost approach to overcome the strength-ductility trade-off in a broad range of structural materials.

Microstructure and Tensile Behaviors of Laser-Arc Hybrid Welds Comparing to Submerged Arc Welds of High-Manganese Steel for Cryogenic Applications

The weldability and the relationship between microstructure and tensile properties at 298 and 110 K produced by laser-arc hybrid welding (LAHW) in high-Mn steel welds were thoroughly investigated. In the laser zone of LAHWs using filler wire, more Mn vaporization in the laser zone was observed than at the arc zone of LAHWs. The arc zone showed a decrease in Mn content of ~0.6 wt%, while the laser zone showed a decrease of ~0.9 wt%. The arc and laser zones of the LAHWs showed stacking fault energies (SFEs) of 17.8 and 17.3 mJ/m², respectively. The tensile deformation of LAHWs at 298 K was conducted with a deformation twins mode, while it was shifted to deformation twins + ε-martensite transformation at 110 K. The yield strength was slightly higher in the laser zone, which had a finer grain size compared to the arc zone. The formation of ε-martensite with deformation twins preceded necking during tensile testing, therefore increasing the yield strength at 110 K. In terms of performance, the LAHW process demonstrated a 25% increase in productivity compared to the conventional submerged arc welding (SAW) process, with a yield strength exceeding 400 MPa, comparable to that of SAW. These findings indicate that LAHW is a highly effective welding method for high-Mn steels, particularly in cryogenic applications.

Design of High Entropy Superalloy FeNiCrCoAl Using Molecular Dynamics, Computational Thermodynamics, and Machine Learning

The development of High Entropy Superalloys (HESAs) represents a significant advancement in alloy design, offering superior mechanical properties and cost-effectiveness compared to traditional superalloys. However, the complex and time-consuming nature of HESA development, often requiring costly experimentation, poses a challenge. This study introduces a novel approach to the compositional design of HESA FeNiCrCoAl, utilizing Molecular Dynamics (MD) simulations to analyze lattice parameters, stacking fault energy (SFE), and compression strength. By integrating machine learning with computational thermodynamics, we enhance the efficiency of SFE prediction through extensive data analysis. Our findings clearly show that increasing Ni, Cr, and Co concentrations decrease lattice parameters, while higher Al concentrations increase them, validating our MD simulations. The non-equiatomic HESA FeNiCrCoAl exhibits outstanding tensile and compression strength compared to its equiatomic, with microstructural and dislocation analyses providing key insights into its deformation behavior. SFE calculations reveal that non-equiatomic HESA FeNiAlCrCo has a higher SFE than the equiatomic variant, with consistent trends observed across MD and thermodynamic analyses. Increasing concentrations of Cr and Co decreases SFE, while increasing Ni and Al concentrations increases SFE. Our machine learning models, notably the random forest algorithm, effectively predict SFE, underscoring the critical roles of Co and Cr in alloy design. The optimized HESA FeNiCrCoAl, designed for low to medium SFE, offers exceptional strength, hardness, and improved ductility, making it ideal for high-temperature applications. We propose an optimal design guide for achieving desired SFE: Ni (17-25 at.%), Cr (24-30 at.%), Al (5-15 at.%), Co (20-35 at.%), and Fe (20-35 at.%). This research provides valuable insights into the mechanical behavior of HESAs, particularly in improving creep resistance, and represents a significant step toward a deeper understanding of HESA properties and behavior.

Effect of precipitates on martensite formation and shape memory effect of FeMnSi-based shape memory alloys fabricated by laser powder bed fusion

The initial and evolving microstructure during the tensile test of two Fe-17Mn-5Si-10Cr-4Ni shape memory alloys, with and without V, C and fabricated by laser powder bed fusion are investigated and compared via electron backscattered diffraction, transmission electron microscopy and in-situ neutron diffraction. Tensile samples are fabricated from the two alloys in order to analyze their thermo-mechanical properties. The addition of V and C leads to the formation of a high area density of fine precipitates, mainly carbides, after heat treatment. The chemistry modifications caused by carbide precipitation cause a decrease in the stacking fault energy (SFE), promoting the formation of wider stacking faults and higher volume fractions of martensite phase under loading, which affect the pseudo-elastic properties and deformation behavior of the material. The carbide-containing alloy shows higher strength, work-hardening capability and pseudo-elasticity compared to the carbide-free alloy. However, the shape memory effect is reduced in the former. The present work sheds light on the crucial role of alloy composition, precipitation and SFE in shaping the mechanical and shape memory properties of Fe-based shape memory alloys. The findings hold potential implications for the design and optimization of materials for specific engineering applications, where either enhanced pseudoelasticity or shape memory effect is desired.

Stability of high energy superlattice faults in Ni-based superalloys from atomistic simulations

High energy stacking faults generated by lattice dislocations entering the strengthening precipitates of Ni-based superalloys are responsible for the unique mechanical properties of these structural materials. However, the question about stability of these faults has not received the attention it deserves. Using atomistic simulations, we show that the anti-phase boundary (APB) can spontaneously transform into super intrinsic stacking fault (SISF) and the complex stacking fault (CSF) can spontaneously transform into L12 lattice structure. The former transformation explains the experimentally observed presence of isolated SISFs and super extrinsic stacking faults (SESFs) in the precipitates. Finally, multiple studies were focused on finding alloying additions which increase the APB and CSF energies. We demonstrate therefore that alloying additions which increase stacking fault energies may conversely decrease their stabilities.

Strengthening and toughening mechanisms of γ-TiAl dominated by shear induced “catching bonds”

TiAl alloys, especially polysynthetically twinned (PST) TiAl, have great potential to be an advanced lightweight engineering materials for key aero-engines components like turbine blades due to their high service temperature. Most researches focus on improving the strength and ductility of TiAl, but the origin of strengthening and toughening mechanisms remain unexplored so far. This work aims at understanding the chemical bond related intrinsic mechanical behavior in essence and revealing the origin of excellent mechanical properties of TiAl alloy. We found that the excellent ductility of γ-TiAl origins from the metallic catching bonds (Ti-Ti and Al-Al) and the high strength is due to high strength Ti-Al covalent catching bond. The (111)/[112̅] system is most likely to be activated under pressure. The pure shearing along (111)/[112̅] leads to the interlayer slip of 1/6 [112̅] Burger vector with the breakage and reformation of Ti-Ti, Al-Al metallic bonds (“catching bonds”). The deformation mechanisms are attributed to the metallic catching bonds induced twin boundary (TB) formation, TB migration, superlattice intrinsic stacking fault (SISF) formation (detwinning) and SISF annihilation. These processes can continuously dissipate the strain energy, resulting in the excellent ductility of γ-TiAl. The structure becomes a hard slip system of (111)/ [1̅1̅2], and the ideal shear strength is 16.5GPa, which is about three times higher than that along (111)/ [112̅], on account of the high strength covalent catching bonds (Ti-Al) dominate the deformation mechanism of 1/2[1̅1̅2] full dislocation. The generalized stacking fault energy (GSFE) shows the true atomic slip path along 1/2[1̅1̅2] perfect dislocation (provide a degree of ductility) is: 1/2[1̅1̅2] → 1/6[12̅1] + 1/6[1̅1̅2] + 1/6[2̅11] + 1/6[1̅1̅2], which agrees well with the previous experimental results.

Plastic deformation mechanism of γ-phase U–Mo alloy studied by molecular dynamics simulations

Abstract Uranium–molybdenum (U–Mo) alloys are critical for nuclear power generation and propulsion because of their superior thermal conductivity, irradiation stability, and anti-swelling properties. This study explores the plastic deformation mechanisms of γ-phase U–Mo alloys using molecular dynamics (MD) simulations. In the slip model, the generalized stacking fault energy (GSFE) and the modified Peierls–Nabarro (P–N) model are used to determine the competitive relationships among different slip systems. In the twinning model, the generalized plane fault energy (GPFE) is assessed to evaluate the competition between slip and twinning. The findings reveal that among the three slip systems, the {110}〈111〉 slip system is preferentially activated, while in the {112}〈111〉 system, twinning is favored over slip, as confirmed by MD tensile simulations conducted in various directions. Additionally, the impact of Mo content on deformation behavior is emphasized. Insights are provided for optimizing process conditions to avoid γ → α″ transitions, thereby maintaining a higher proportion of γ-phase U–Mo alloys for practical applications.

Synergistic impact of Mg and Ge co-doping on stacking fault energy and underlying mechanisms in Al

Abstract This study utilizes first-principles calculations to explore the impact of element additions of Mg and Ge on the stacking fault energy (SFE) of aluminum alloys, with a particular emphasis on elucidating the electronic structure modifications underlying these effects. The findings indicate that both Mg and Ge additions, either alone or in combination, substantially diminish the SFE of the Al alloys, with Ge additions exhibiting a more marked influence. The introduction of Mg and Ge elements alters the electronic structure of the Al-based alloy, largely due to adjustments in the interplanar spacing. Specifically, Ge additions lead to a more uniform electron cloud distribution, while Mg additions cause a redistribution of charge density. Building upon the computed SFE results, this study further analyzes their implications on plastic deformation. The mechanisms behind the SFE reduction differ: Al alloys with Mg additions achieve this through increased interlayer spacing and weakened bonding strength, whereas those with Ge additions exhibit a combination of larger interlayer spacing and a homogeneous region of low Electron Localization Function. By linking electronic structure analysis with the SFE and its effects on plastic deformation, this study offers profound insights into the underlying reasons for the observed changes in SFE. Ultimately, it provides a theoretical foundation for designing novel Al alloys with tailored mechanical properties through precise control of element additions of Mg and Ge.

Beyond Fundamental Building Blocks: Plasticity in Structurally Complex Crystals.

Intermetallics, which encompass a wide range of compounds, often exhibit similar or closely related crystal structures, resulting in various intermetallic systems with structurally derivative phases. This study examines the hypothesis that deformation behavior can be transferred from fundamental building blocks to structurally related phases using the binary samarium-cobalt system. SmCo2 and SmCo5 are investigated as fundamental building blocks and compared them to the structurally related SmCo3 and Sm2Co17 phases. Nanoindentation and micropillar compression tests are performed to characterize the primary slip systems, complemented by generalized stacking fault energy (GSFE) calculations via atomic-scale modeling. The results show that while elastic properties of the structurally complex phases follow a rule of mixtures, their plastic deformation mechanisms are more intricate, influenced by the stacking and bonding nature within the crystal's building blocks. These findings underscore the importance of local bonding environments in predicting the mechanical behavior of structurally related intermetallics, providing crucial insights for the development of high-performance intermetallicmaterials.

Study on the Effect of Co Microalloying on the High‐Temperature Tensile Behavior of 4Cr5Mo2V Hot Work Die Steel

The hot work die steel 4Cr5Mo2V has insufficient high‐temperature strength, making it difficult to meet advanced manufacturing requirements. Herein, a novel modified 4Cr5Mo2V‐Co steel with 0.5% Co addition is designed and subjected to tensile tests at room and high temperature, and the precipitation formation and microstructure evolution are characterized by optical microscopy, scanning electron microscopy, electron backscatter diffraction, X‐ray diffractometer, and high‐resolution transmission electron microscopy. The results show that Co microalloying increases the strength of 4Cr5Mo2V steel while slightly decreasing its plasticity with temperatures ranging from 25 to 700 °C. The increased high‐temperature strength of 4Cr5Mo2V‐Co steel is mainly attributed to dislocation and precipitation strengthening. This can be attributed to the addition of Co lowering the stacking fault energy of bcc grains, preventing dislocation climb and cross slip, thus increasing the dislocation density. In turn, the dislocations provide more nucleation sites for M2C phase precipitation, promoting more dispersed nanoscale M2C phase formation. During high‐temperature tensile deformation, the recrystallization softening phenomenon of 4Cr5Mo2V steel is more pronounced due to the presence of continuous dynamic recrystallization.

Influence of non-rare earth elements on basal stacking fault energy of Mg binary alloys in solid solution

Using first principle alloy theory, we calculate the basal stacking fault energies as a function of chemical composition for a series of Mg binary alloys by accounting for the chemical disorder in solid solution. We show that while the basal stacking fault energies significantly increase with the addition of Co, Ni, Ag, and Li, they obviously decline upon alloying with Sn, Y, Ca, and Al. In contrast, Zn and Ti exhibit negligible influence on the basal stacking fault energy of I1 and I2 fault. The varied influence of alloying species on basal stacking fault energies are demonstrated to predominately determined by the volume- and composition-dependent relative phase stability between face-centered cubic and hexagonal close-packed structure. The influence of alloy species predicted in solid solution are obviously different from those computed for segregated ones, underlining the significance of chemical disorder to the intrinsic energy barriers of Mg solid solutions.

Compositional effect on pressure-induced polymorphism in high-entropy alloys

Recently, pressure-induced polymorphic phase transitions were discovered in several fragmented high-entropy alloys (HEAs), offering a valuable opportunity to deepen our understanding of these materials. However, the chemical and physical factors that govern these transitions are still unclear. Here, we combined in situ high-pressure synchrotron X-ray diffraction, X-ray emission spectroscopy (XES), and high-resolution transmission electron microscopy (HRTEM) to systematically study the evolution of the atomic and electronic structures in the Cantor alloy and its face-centered-cubic (fcc) subset alloys (CoCrFeMnNi, CoCrFeNi, CoCrMnNi, CoFeMnNi, CoCrNi, CoFeNi, CoMnNi, CrFeNi, and FeMnNi). Surprisingly, diverse behavior was observed among these closely related alloys during compression and decompression, which includes irreversible, reversible fcc to hexagonal close-packed (hcp) phase transitions, or even no detectable phase transitions up to ∼40 GPa. HRTEM measurements confirmed that the fcc and hcp phases abided by the classic Shoji-Nishiyama orientation relationship during the transitions. XES data indicated that high-pressure suppresses the local magnetic moments in all the studied alloys, suggesting that magnetic states do not significantly influence the polymorphic transitions. By comparing the effects of the atomic size difference, entropy, valence electron concentration, and stacking fault energy across all the compositions studied, only the stacking fault energy shows a strong correlation with the phase transitions, indicating it plays a key role in inducing polymorphism in HEAs.

Twinning mediated cryogenic toughness in an additively manufactured high Mn steel by manipulating stacking fault energy

The insufficient cryogenic toughness of wire-arc additively manufacturing (WAAM) component hinders their application in cryogenic fields. We report that tungsten is effective in enhancing the impact toughness of WAAM components, increasing it from 42 to 106J at 77K. The outstanding cryogenic toughness depends on the interaction between dislocations and twins, where the thickness of twins plays a pivotal role in determining whether they hinder or facilitate dislocation movement. Twins below 6.1nm hinder dislocations, impeding deformation, while those exceeding 21.7nm coordinate with the matrix orientation, aiding dislocation movement and forming microbands. The W element reduces the critical twinning stress from 112.3 to 83.5MPa by manipulating the stacking fault energy and grain size, thereby altering the twinning structure. However, excessive W content forms large-sized precipitates, serving as crack initiation sites and reducing crack initiation energy.

The role of temperature and strain on the deformation behaviour and microstructural evolution of FCC (CrFeNi)99Si1 medium-entropy alloy

A detailed experimental investigation was conducted to develop a mechanistic understanding of the evolution of the microstructure, texture, and mechanical properties of a low stacking fault energy (CrFeNi)99Si1 medium entropy alloy during rolling, The rolling process involved symmetric rolling to 90% reduction in thickness at 77 K and 300 K as well as asymmetric rolling to 80% reduction in thickness at 300 K. Symmetric rolling at 300 K showed a transition from planar slip-dominated plastic deformation to twinning with increasing strain while cryorolling at 77 K exhibited shear band-assisted transformation of FCC γ-austenite to HCP ε-martensite for 60% reduction in thickness. In contrast, asymmetric rolling at 300 K revealed planar dislocation slip, leading to grain refinement with a heterogeneous microstructure. The crystallographic texture evolution of the FCC γ-austenite phase in all the processed samples reveals an increase in the Brass and S texture components similar to any low SFE FCC materials. The 90% cryorolled sample exhibited a significantly higher yield strength (1.03 ± 0.012 GPa) and back transformation from ε-HCP to ϒ- FCC phase was observed during tensile testing which was further validated using synchrotron. The microstructural heterogeneity achieved in asymmetric rolling contributes to better strength-ductility synergy than that achieved in symmetric rolling at both temperatures.

Effect of ultrasonic surface rolling extrusion on microstructural evolution and wear resistance of laser-clad CoCrFeMnNi high-entropy alloy with low stacking fault energy

Ultrasonic surface rolling extrusion (USRE) was employed to strengthen face-centered cubic (FCC) phase CoCrFeMnNi high-entropy alloy (HEA) coatings prepared by laser cladding. The influence of USRE's static load on the microstructure, mechanical properties, and wear resistance of the coatings was examined to elucidate the grain refinement mechanism. The findings indicate that USRE preserves the phase composition of the CoCrFeMnNi HEA coatings. After USRE at loads of 100 N, 200 N, and 300 N, the measured thicknesses of the severe plastic deformation layers are 2.51 μm, 3.03 μm, and 3.45 μm, respectively. The process triggers dislocation multiplication, which accumulates at the boundaries of Mn-rich regions, forming dislocation cells and evolving into subgrains, thereby refining the grain structure under severe plastic deformation. Statistical analysis reveals that the dislocation density within the grains is 7 × 1014 m−2, while at the grain boundaries, the dislocation density is 4 × 1015 m−2. The average grain size has been refined from 97.7 μm to 34.7 μm. Both microhardness and wear resistance escalate with increased static load, with the maximum microhardness of 347 HV and the minimum wear rate of 2.6 × 10−5 mm3·N−1·m−1 achieved at a 300 N static load. This hardness enhancement is due to the combined effects of grain refinement, dislocation strengthening, and sub-grain formation. The wear mechanisms for the USRE-treated CoCrFeMnNi HEA coatings include adhesive wear, abrasive wear, and oxidative wear. While adhesion and abrasion diminish with higher static pressures, oxidative wear intensifies.

Investigation of the size effect on flow stress and deformation mechanism in Cu-Zn thin sheets

Understanding and regulating flow stress is crucial for producing high-performance metal thin sheets. Uniaxial tensile tests on Cu-Zn thin sheet metal reveal that the grain size at the inflection point of the size effect on flow stress (SEFS) increases with higher Zn content. This study investigates the intrinsic mechanisms affecting the SEFS, with a focus on how Zn content, grain size, and free surface influence deformation mechanism transitions in face-centered cubic metal thin sheets. Increasing Zn content reduces stacking fault energy, promotes the transition from dislocation wavy slip to planar slip and deformation twinning, increases geometrically necessary dislocation density, and mitigates SEFS. The relationship between the critical stress and strain for the onset of planar slip and deformation twinning and the square root of the grain size deviates from linearity, highlighting the size effect on the deformation mechanisms transition in metal thin sheets. This study identifies the size effects on deformation mechanisms and elucidates their underlying mechanisms. It provides new insights into controlling SEFS in metal thin sheets and lays a foundation for the design of high-performance metal thin sheets.

Comparing Machine Learning Models for Strength and Ductility in High-Entropy Alloys

AbstractWe compare several machine learning (ML) models that predict the yield strength and plasticity of high-entropy alloys (HEAs) for achieving high-accuracy with notably low root mean square errors (RMSE). Our models, developed using a comprehensive database of single-phase body-centered cubic (BCC) HEAs and BCC + B2 HEAs (where B2 is ordered BCC), integrate advanced feature engineering reflecting the current understanding of electronic factors, atomic ordering informed by mixing enthalpy, and the D parameter associated with stacking fault energy in HEAs. This approach enables systematic comparisons of different ML models, providing deep insights into the mechanical properties of BCC and related alloys. By leveraging genetic algorithms for feature selection and meticulous hyperparameter optimization, our ML framework excels in both predictive power and interpretability. The rigorous validation process includes repeated k-fold cross-validation and leave-one-out cross-validation (LOOCV), ensuring robust generalization. Moreover, our use of Shapley Additive Explanations (SHAP) revealed critical predictors such as the testing temperature-to-melting temperature ratio $$\left(\frac{{T}_{test}}{{T}_{melt}}\right)$$ T test T melt , the mixing enthalpy $$\left(\Delta {\text{H}}_{\text{mix}}\right)$$ Δ H mix and the D parameter, which play key roles in determining plasticity and yield strength. Our work represents an advancement in designing high-performance HEAs with optimized strength and ductility, offering a powerful tool for predicting mechanical properties and exploring new candidate alloys with exceptional mechanical behavior.

Deformation pseudo-twinning of the L21-ordered intermetallic superlattice

Ordered intermetallic materials are promising candidates for applications in extreme environments due to the strong localized bonding schemes that stabilize the structures against degradation. Here, we investigate the propensity for deformation twinning modes in the L21-ordered MnCu2Al intermetallic by inducing a state of severe plastic deformation. Post-mortem microstructural analysis reveals the presence of meso-scale deformation twins accompanied by a high degree of nano-scale crystalline heterogeneity. The orientation relationship between the parent and twin structures is consistent with activation of the 〈111〉{112} deformation twinning mode. Ab initio generalized stacking fault energy curve calculations corresponding to 〈111〉{112} twinning shear suggest that the magnitude of the twinning partial is 14〈111〉{112} and results in the local formation of a metastable orthorhombic phase within the pseudo-twin. This work highlights the discrepancy between the deformation modes of ordered/disordered structures and promotes an increased awareness for the role that long-range chemical order plays in determining deformation modes.