Dislocation Sources Research Articles

Crack initiation mechanism of a silicide-containing high-strength Ti–5Al-7.5V alloy under low-cycle fatigue loading

In this work, the dual phase titanium alloy Ti–5Al-7.5V was subjected to low-cycle fatigue at room temperature to reveal the deformation mechanisms of fatigue and crack initiation. Transmission electron microscope analysis showed that planar dislocation slip, most of them localized at the basal and prismatic planes of α phase, is the primary deformation mode of low-cycle fatigue. Multiple slips operate concurrently in the high Schmid factor planes within a single grain. Moreover, a limited number of observed microcracks were formed along the basal slip bands. Electron back-scattered diffraction analysis evidenced that numerous microcracks were formed along basal planes. And, the microcracks were confined in primary α grains without propagation to surrounding transformed β matrix, indicating that the alloy exhibits a high tolerance to microcrack propagation. The α grain aggregate oriented for basal slip is a fatigue-critical microstructure configuration, which provides a high Schmid factor path by linking adjacent grains and potentially lead to internal crack initiation with the formation of a field of facets in the cycling process. While the silicides were observed in contact with the microcracks and slip bands, no evidence of crack initiation from silicides was detected. Given that the microcracks were formed along the pre-existing slip bands, it remains an open question whether the silicides can act as the dislocation sources for planar slips and facilitate crack nucleation from these silicides.

Micromechanism of plastic deformation enhancement in ultrafine-grained Al-Cu-Zr alloy after annealing and additional deformation

A theoretical model which describes a micromechanism of plasticity enhancement in an ultrafine-grained Al-Cu-Zr alloy after annealing and additional deformation is suggested. Within the framework of the model, it was shown that nanoprecipitates of the secondary phase Al2Cu in the grain boundaries become the effective sources of the lattice dislocations in the presence of a large number of the grain boundary dislocations near the nanoprecipitates. The theoretical dependences of the flow stress on the degree of the plastic deformation demonstrate good qualitative and quantitative agreement with the experimental data. The emission of the lattice dislocations from nanoprecipitates provides higher plasticity compared to the emission of the lattice dislocations from the triple junctions of the grain boundaries. Keywords: ultrafine-grained materials, aluminum alloys, nanoprecipitates, annealing, severe plastic deformation by high-pressure torsion, dislocations, grain boundaries.

Микромеханизм повышения пластичности в ультрамелкозернистом сплаве Al-Cu-Zr после отжига и дополнительной деформации

A theoretical model which describes a micromechanism of plasticity enhancement in an ultrafine-grained Al-Cu-Zr alloy after annealing and additional deformation is suggested. Within the framework of the model, it was shown that nanoprecipitates of the secondary phase Al2Cu in the grain boundaries become the effective sources of the lattice dislocations in the presence of a large number of the grain boundary dislocations. The theoretical dependences of the flow stress on the degree of the plastic deformation demonstrate good qualitative and quantitative agreement with the experimental data. The emission of the lattice dislocations from nanoprecipitates provides higher plasticity compared to the emission of the lattice dislocations from the triple junctions of the grain boundaries.

Enhanced plastic deformation capacity in hexagonal-close-packed medium entropy alloys via facilitating cross slip

• A novel Hf x (ZrTi) 100-x (x=0, 20, 33 and 40 at.%) MEAs with single phase HCP was developed. • Addition of Hf enhanced the strain hardening rate and tensile ductility. • Effects of Hf on stacking fault energy and dislocation slip behavior were revealed. • Facilitated cross slip and pyramidal dislocations is responsible for the outstanding mechanical properties. Alloys with a hexagonal close-packed (HCP) lattice often suffer from intrinsic brittleness due to their insufficient number of slip systems, which limits their practical uses. In this paper, nevertheless, we show that remarkably tensile ductility in HCP Hf-Zr-Ti medium entropy alloys (MEAs) was achieved, particularly in the MEAs with a higher content of Hf. Both first-principles calculation and experimental analyses reveal that addition of Hf increases basal I2 stacking fault energy and decreases prismatic stacking fault energy in these HCP MEAs, which promotes the source of pyramidal dislocations due to the facilitated cross slips of basal dislocations and eventually give rise to the observed large tensile ductility. Our current findings not only shed new insights into understanding deformation of HCP alloys, but also provide a basis for controlling alloying effects for developing novel HCP complex alloys with optimized properties.

Study of Crack-Propagation Mechanism of Al0.1CoCrFeNi High-Entropy Alloy by Molecular Dynamics Method

The crack propagation mechanism of Al0.1CoCrFeNi high-entropy alloy (HEA) was investigated with the molecular dynamics method. The pre-crack propagation and stretching processes of single-crystal Al0.1CoCrFeNi HEA and Al0.1CoCrFeNi HEA with grain boundaries were simulated. The effects of strain rates and different crystal structures on the crack propagation of the alloy therein at room temperature were studied. They both exhibited plastic deformation and ductile fracturing, and the crack tip involved dislocations at 45° and 135° under the tensile stress. The dislocations formed in the intrinsic-stacking fault and stacking fault based on hexagonal closely packed structures spread and then accumulated near the grain boundary. At the position where hexagonal closely packed structures were accumulated, the dent was obviously serious at the 1/3 position of the alloy where the fracturing finally occurred. The yield strength for Al0.1CoCrFeNi HEA with grain boundaries was lower than that of the single-crystal Al0.1CoCrFeNi HEA. However, Young’s moduli for Al0.1CoCrFeNi HEA with grain boundaries were higher than those of the single-crystal Al0.1CoCrFeNi HEA. The grain boundaries can be used as the emission source of dislocations, and it is easier to form dislocations in the-single crystal Al0.1CoCrFeNi HEA, but the existence of grain boundaries hinders the slippage of dislocations.

γ′′ Phase transformation, precipitation hardening, hetero-deformation induced hardening and deformation mechanisms in a Nb-alloyed medium-entropy alloy

In present work, a novel γ′′-strengthened Nb-alloyed medium-entropy alloy (MEA) was successfully fabricated and systematically investigated. Our results evidence that the γ′′ phase brings out significant precipitation hardening effect (∼10.2 %volume fraction contributes ∼ 685 MPa strength enhancement). The metastable γ′′ phase could abnormally transform to ε phase, and the morphology and distribution of ε phase shows great impacts on mechanical properties. A hetero-lamellae grain coupling with dual-precipitation (HLG + dual-P) structure was successfully constructed in this Nb-alloyed MEA, which could effectively combine precipitation hardening and hetero-deformation induced (HDI) hardening effects. Deformation characters investigations reveals that the absence of mechanical twinning in γ′′-strengthened MEA originates from the improved critical twinning stress related to the fine dislocation source size and the difficulty of high-energy complex SFs reordering. The combination of massive stacking-faults, Lomer-Cottrell locks and dynamically reinforced HDI hardening contribute to the excellent ductility and work-hardening capacity at high-level strength in the HLG + dual-P structural alloy. Our work provides a useful insight and helpful guidance for developing high-performance precipitation-hardened multi-principal element alloys.

Size effect in nanoindentation: Taylor hardening or dislocation source-limited effect?

In the present work, a 3D discrete dislocation dynamics (DDD) method was used to explore the indentation size effect (ISE) in the nanoindentation of single crystals. The distribution of geometrically necessary dislocation (GND) underneath the indent obtained from the DDD simulations was compared with that in experiments. The results show that the GND density increases as the indentation depth increases, which is inconsistent with the Nix-Gao model that is usually used to interpret the ISE phenomenon. The spatial-temporal evolution of dislocation structures indicates that the available dislocation sources are limited at smaller indentation depths, thus requiring higher stress to accommodate the plastic deformation. The authors do not have permission to share data. • The indentation size effect was investigated by 3D discrete dislocation dynamics. • The patterns of GNDs are correlated with the dislocation motions on slip planes. • The GND density increases as the indentation depth increases. • The indentation size effect is caused by the limitation of dislocation sources.

An end-to-end 3d seismic simulation of underground structures due to point dislocation source by using an FK-FEM hybrid approach

An end-to-end 3d seismic simulation of underground structures due to point dislocation source by using an FK-FEM hybrid approach

Additional dislocation slip determined excess yield stress in titanium

The excess yield stress induced slip system variations at the early stage of plastic deformation in Ti was in-depth studied. As a common sense, both the normal grain refinement according to the Hall-Petch relationship and the suppressed dislocation source activation in refined-grain can extensively increase the yield stress. In this study, combined calculations of Schmid factor and critical resolved shear stress suggest that small-grain samples with much higher yield stress could incorporate both <a>-prismatic slip and <c+a>-pyramidal slip, while only <a>-prismatic slip can be activated in the large-grain counterparts. This slip system transition can explain the abnormal fine-grain strengthening effect, which the experimental yield stress of small-grain sample deviates from the value that predicted by using Hall-Petch relationship, as well as the stress drop right after yielding in Ti. These findings could also provide a new strategy for designing high-strength metallic materials.

Inherent and multiple strain hardening imparting synergistic ultrahigh strength and ductility in a low stacking faulted heterogeneous high-entropy alloy

Alloys with high yield strength and ductility are attractive for application because of their potential to offer mass reduction, energy savings, and enhanced structural reliability. However, increasing strength usually comes at the expense of ductility, which is commonly known as the strength-ductility trade-off for metal alloys. In this work, we explored a strategy of using a heterogeneous grain size structure and a reduced stacking fault energy in a CoCrFeNiMn FCC high entropy alloy to overcome the limitations of this trade-off. By this approach, the alloy achieved a yield strength of 980 MPa, a tensile strength of 1385 MPa, and tensile elongation to failure of 48% benefiting from cooperative strain hardening via multiple mechanisms, such as hetero-deformation induced (HDI) hardening, deformation twinning, Frank-Read dislocation sources and Lomer–Cottrell dislocation locks instigated by such structures. These micromechanisms of deformation help to harden the alloy via in situ refinement of the mean free paths for dislocations.

Unveiling the grain boundary-related effects on the incipient plasticity and dislocation behavior in nanocrystalline CrCoNi medium-entropy alloy

• The incipient plasticity and dislocation behavior in nanocrystalline (NC) CrCoNi alloy were systematically investigated and compared with its coarse-grained (CG) counterpart and NC Ni. • Multiple pop-ins appear in the P-h curves of NC and CG CrCoNi alloys but disappear in the curves of NC Ni. • The incipient plasticity is mediated by dislocation nucleation in NC CrCoNi alloy but by GBs in NC Ni. • Chemically complex GBs in NC CrCoNi alloy facilitate dislocation nucleation but impede dislocation propagation. • Spatial restrictions from GBs in NC CrCoNi alloy induce size-dependent pop-in behaviors. The incipient plasticity and dislocation behavior in a nanocrystalline (NC) CrCoNi medium-entropy alloy were systematically investigated in terms of pop-in events during instrumental nano-indentation tests. Quantitative statistical analysis and molecular dynamic simulations were performed to reveal the effects of grain boundaries (GBs) on initial stages of plastic deformation . Multiple pop-in events appeared during loading on the NC CrCoNi. The first pop-in that represents the initial yielding was identified to be controlled by dislocation nucleation, which is in sharp contrast to the continuous elastic-plastic transition mediated by GB mechanisms in NC pure metals. This can be attributed to the sluggish kinetics of the chemically complex GBs (CCGBs) in the NC CrCoNi that hinders diffusive GB activities but facilitates dislocation nucleation. Subsequent pop-ins were also found to be closely related to the extra dragging effects imposed by the CCGBs on dislocation propagation in the NC alloy . Moreover, the extremely small grain sizes and the consequent high-volume fraction of GBs in the NC alloy severely restrict the lengths of dislocation source and the radii of dislocation loop, giving rise to a higher critical stress, smaller activation volume and lower pop-in width as compared with its coarse-grained counterpart. These results provide new insights into the onset of nano-plasticity in concentrated multi-principal element alloys.

Transient Green's functions of dislocations in transversely isotropic and layered poroelastic half-spaces

We derive, for the first time, the transient response (or Green's function, GF) induced by a general point dislocation in a transversely isotropic and layered poroelastic half-space where the contributions from the fluid dislocation and fluid-phase coupling effect are considered. The GF is expressed in terms of the powerful Fourier-Bessel series system of vector functions recently introduced (with the expansion coefficients being the novel dislocation Love numbers). The corresponding source functions, i.e. discontinuities across the source level, are derived, which show that 1) the fluid-phase creates a new type of source functions called fluid dislocation, and 2) it further contributes directly to the traditional solid horizontal tensile dislocation (or tensile-fracture) via the Biot effective stress coefficient. While the dual-variable and position (DVP) method is applied to take care of multilayers, the Talbot's method is employed to carry out the inverse Laplace transform, both showing excellent numerical stability, efficiency, and accuracy. Key features of these GFs are analyzed numerically. It is shown that 1) the poroelastic process is featured by some transient statuses, including drained and undrained limits; 2) while these two limits are sharply different when the dislocation source is a vertical strike-slip or horizontal tensile-fracture, they are the same when a vertical dip-slip or vertical tensile-fracture is in a homogeneous half-space; 3) in all the cases, there are temporal poroelastic deformations which are significantly different from these two limits; and 4) the fluid dislocation alone could significantly contribute to the poroelastic deformation at the earlier time history. These GFs provide the kernel functions in the corresponding boundary element formulation and the method of fundamental solutions, with potential applications in geomechanics and biomedical engineering.

A Fault-Based Crustal Deformation Model with Deep Driven Dislocation Sources for the 2023 Update to the U.S. National Seismic Hazard Model

Abstract A fault-based crustal deformation model with deep driven dislocation sources is applied to estimate long-term on-fault slip rates and off-fault moment rate distribution in the western United States (WUS) for the 2023 update to the National Seismic Hazard Model (NSHM). This model uses the method of Zeng and Shen (2017) to invert for slip rate and strain-rate parameters based on inputs from Global Positioning System (GPS) velocities and geologic slip-rate constraints. The model connects adjacent major fault segments in California and the Cascadia subduction zone to form blocks that extend to the boundaries of the study area. Faults within the blocks are obtained from the NSHM geologic fault section database. The model slip rates are determined using a least-squares inversion with a normalized chi-square of 6.6. I also apply a time-dependent correction called “ghost transient” effect to account for the viscoelastic responses from large historic earthquakes along the San Andreas fault and Cascadia subduction zone. Major discrepancies between model slip rates and geologic slip rates along the San Andreas fault, for example, from the Cholame to the Mojave and San Bernardino segments of the San Andreas, are well reduced after the ghost transient correction is applied to GPS velocities. The off-fault moment rate distribution is consistent with regional tectonics and seismicity patterns with a total rate of 1.6×1019 N·m/yr for the WUS.

Multiscale and dual-structured reinforcing particulates enhance the strength of aluminum matrix composites at no ductility loss

To conquer the poor ductility of particulate-reinforced metal matrix composites, multiscale and dual-structured (M&D) reinforcing particulates, which consist of nano-/submicro-particulates with monolithic structure (<2 μm) and micro-particulates with core-shell structure (>2 μm), are synthesized in the model material of pure aluminum matrix composites. During plastic deformation, dislocations should be firstly emitted from nano-particulates at grain boundaries and then their motion is blocked by those in grain interior. Subsequently, submicro-particulates should start to act as dislocation sources to accommodate the increase in tensile stress. Finally, microscale spheroidal core-shell structured particulates further delay crack formation and propagation by fracturing successively from hard intermetallic shell to soft titanium core. As a result, the M&D reinforcing particulates exhibit a comparatively good toughening effect among pure aluminum matrix composites, achieving a high strength and enhanced ductility comparable to pure aluminum simultanously.

Dislocation exhaustion and ultra-hardening of nanograined metals by phase transformation at grain boundaries

The development of high-strength metals has driven the endeavor of pushing the limit of grain size (d) reduction according to the Hall-Petch law. But the continuous grain refinement is particularly challenging, raising also the problem of inverse Hall-Petch effect. Here, we show that the nanograined metals (NMs) with d of tens of nanometers could be strengthened to the level comparable to or even beyond that of the extremely-fine NMs (d ~ 5 nm) attributing to the dislocation exhaustion. We design the Fe-Ni NM with intergranular Ni enrichment. The results show triggering of structural transformation at grain boundaries (GBs) at low temperature, which consumes lattice dislocations significantly. Therefore, the plasticity in the dislocation-exhausted NMs is suggested to be dominated by the activation of GB dislocation sources, leading to the ultra-hardening effect. This approach demonstrates a new pathway to explore NMs with desired properties by tailoring phase transformations via GB physico-chemical engineering.

Microseismic wavefield propagation in a fracture‐induced anisotropic medium based on a general dislocation source model

The propagation of microseismicity in subsurface media is complex. We developed an anisotropic petrophysical model based on an empirical formula, linear slip theory and the bond transform method considering real underground conditions. Using Biot's equations, the seismic response to a general dislocation source in fracture-induced anisotropic two-phased media was solved using a staggered grid high-order finite-difference algorithm. To understand the relationship between the microseismic wave and fracture parameters, we then designed several different models to calculate the wavefield snapshots and analyse the effect of the fracture volume ratio and orientation. The modelling results indicate that the shear faulting source generates three types of waves in two-phase media. Fractures can render homogeneous media anisotropic, and anisotropy becomes more noticeable with an increase in the fracture volume ratio. This decreases the velocity of the fast longitudinal and transverse waves in the vertical direction and increases the velocity of the slow longitudinal wave in a certain range. The fracture orientation mainly influences the moment tensor and then affects the wavefronts. These simulations lay the foundation for further studies on microseismic wave propagation in fracture-induced anisotropic media.

Dislocation dynamics in heterogeneous nanostructured materials

Crystalline materials can be strengthened by introducing dissimilar phases that impede dislocation glide. At the same time, the changes in microstructure and chemistry usually make the materials less ductile. One way to circumvent the strength–ductility dilemma is to take advantage of heterogeneous nanophases which simultaneously serve as dislocation barriers and sources. Owing to their superior mechanical properties, heterogeneous nanostructured materials (HNMs) have attracted a lot of attention worldwide. Nevertheless, it has been difficult to characterize dislocation dynamics in HNMs using classical continuum models, mainly due to the challenges in describing the elastic and plastic heterogeneity among the phases. In this work, we advance a phase-field dislocation dynamics (PFDD) model to treat multi-phase materials, consisting of phases differing in composition, structural order, and size in the same system. We then apply the advanced PFDD model to exploring two important but divergent materials design problems in HNMs: dislocation/obstacle interactions and dislocation/interface interactions. Results show that the interactions between a dislocation and distribution of obstacles varying in structure and composition cannot be understood by simply interpolating from their individual interactions with a dislocation. It is also found that materials containing interfaces with nanoscale thicknesses and compositional gradients have a much higher dislocation bypass stress than those with sharp interfaces, providing an explanation for the simultaneous high strength and toughness of thick interface-containing nanolaminates as observed in recent experiments.

Strengthening effect of high-entropy alloys endowed by monolayer graphene

The graphene (Gr) can effectively confine the dislocation propagation, allowing for the pronounced strengthening effect. However, due to the technical limitations of atomic resolution, an in-depth understanding regarding the potential strengthening mechanisms at atomic level is still insufficiently comprehended. In this paper, molecular dynamics (MD) simulations were performed to investigate dislocation-Gr interactions and strengthening mechanisms in FeNiCrCoCu high-entropy alloy (HEA)/Gr nanopillars. The hindrance of Gr sheet to mobile dislocations was demonstrated to promote the onset of massive immobile dislocations, especially the Stair-rod dislocation which gave rise to the remarkable strengthening effect. The immobile Hirth, 1/3<110> and 1/6<301> dislocations exerted the subsidiary effect on strengthening the composite pillars. Meanwhile, the diminished dislocation length induced by dislocation reactions and the absorption effect to mobile dislocations was verified to endow a more appreciable dislocation starvation for composite pillars which was conducive to forming more Stair-rod dislocations. In addition, the results also confirmed that the reduction in Gr diameters would directly weaken the pillars attributing to the fact that the Gr edges acted as a dislocation source. These findings may contribute to the design of HEA/Gr composites toward better mechanical properties.

Revealing the effects of concomitant grain coarsening and refinement on the internal variable evolution and mechanical properties of gradient nanostructured nickel

The outstanding mechanical properties of gradient nanostructured (GNS) metals and alloys such as a superior combination of strength and ductility can be attributed to two important deformation mechanisms: hetero-deformation induced (HDI) strengthening and strain hardening, as well as grain growth. Recent experimental evidence indicates that GNS Ni specimens undergo concomitant grain coarsening and refinement during tensile deformation. Nevertheless, how such grain growth behaviors affect the evolution and distribution of their internal variables such as dislocation density and HDI hardening, and how such effects are manifested in their mechanical properties, are still unknown. Therefore, this work strives to answer these questions by incorporating a modified strain gradient plasticity formulation taking into account the saturation of geometrically necessary dislocations (GND) accumulation due to the dynamic equilibrium between dislocation source formation and deactivation into a crystal plasticity finite element framework, in conjunction with two other models accounting for the evolution of statistically stored dislocations (SSD) and HDI stress, respectively, to explore the effects of grain coarsening and refinement on the internal variable evolution and mechanical properties of GNS Ni specimens with different grain size gradients under deformation. It is revealed that SSD density increases throughout the samples as a result of reduced dynamic recovery in the fine grains induced by grain coarsening as well as enhanced dislocation storage in the coarse grains due to their refinement. In contrast, grain coarsening and refinement leads to a decrease in GND density and HDI stress in the fine grains and an increase in the coarse grains as a result of the corresponding changes in strain gradient intensity. Last but not least, the overall effect of grain growth on the mechanical behaviors of GNS Ni is the outcome of the synergy and competition between its individual effects on the Hall-Petch strengthening, forest dislocation hardening and HDI hardening, respectively, and the different grain size gradients of the GNS Ni specimens give rise to the opposite variations in their mechanical behaviors with respect to grain growth.

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.