Continuum Dislocation Research Articles

Simultaneously enhanced strength and ductility of W-Cu bimetallic composites assisted by continuous cellular dislocation structure

W-Cu bimetallic composites are commonly employed in a wide range of critical fields due to their exceptional comprehensive performance. However, the weak interfacial bonding between two distinctive phases results in challenges such as easy deformation, poor mechanical performance, and short lifespan. In present work, by adopting thermo-mechanical processing (TMP) treatment, the W and Cu phases, connected by the nano-diffusion layer, underwent a cooperative deformation process. Meanwhile, the pre-existing nanoclusters anchored the accumulated dislocations during TMP, forming a unique continuous cellular dislocation structure (CC-D) with the nanoscale size of approximately 40 nm during the subsequent recovery annealing process. The CC-D dominated plastic deformation mechanism dynamically refined the grains by forming a multiscale network of stacking faults and deformation twins (SFs-DTs). Moreover, the slip transfer and twinning originating from the W/Cu interface were stimulated to alleviate interfacial stress accumulation. Thus, the ensuing strengthening and strain-hardening mechanisms maintained stable tensile flow, resulting in an exceptional strength-ductility combination (965 MPa, 14.8%). Moreover, the high density of twins within the Cu grains, with numerous coherent twin boundaries, reduced electron scattering and maintained a considerable electrical conductivity (30 %IACS) for the bimetallic composites.

Crack-tip cleavage/dislocation emission competition behaviors/mechanisms in magnesium: ALEFM prediction and atomic simulation

Structural properties and reliability of materials can be improved by increasing fracture toughness. At the atomic scale, the fracture is a material separation process, and the fracture toughness of materials is associated with the atomic-scale crack-tip behaviors/mechanisms. The crack-tip behaviors are relevant to the energy state of atoms in the system. Atomic thermal oscillation increases with increasing temperature, which may affect/alter the crack tip behaviors. This work is the first to investigate the temperature-dependent crack-tip cleavage/dislocation emitting competition in magnesium (Mg) using anisotropic linear elastic fracture mechanics theory, Density Functional Theory (DFT), and atomic simulation. Crack-tip behaviors are examined using a specially designed ‘K-field’ loads model. DFT calculations show that a single crystal system with lower entropy and higher Gibbs free energy implies stronger interatomic bonding that favors a higher KIc. Changes in the stress distribution initiate a brittle-ductile transition in crack-tip behavior. The ductile crack tip can be blunted by continuous crack-tip dislocations nucleation/slip, and the evolution of the ductile crack-tip geometry from sharp to semicircular structure significantly decreases the stress concentration at the crack tip. A new criterion of the crack-tip force vector is established, which reasonably explains the geometrical evolution of ductile crack tip where the angle θ between the crack plane and the slip plane is 0∘<θ<90∘ and θ=90∘. This work expands the atomic-scale brittle/ductile crack-tip behaviors/mechanisms of Mg, which provides a reference for crack-tip behavior analysis in engineering research.

Formation and strengthening mechanism of ordered interstitial complexes in multi-principle element alloys

Ordered interstitial complexes (OIC) are in the intermediate state between random interstitial solutes and chemical compounds, which can effectively improve the mechanical performance of multi-principle element alloys. Nevertheless, experimentally observing the complex atomic details of OIC formation and their interaction with dislocations remains challenging. Meanwhile, simulations of the OIC behavior faced the dilemma of lacking interatomic potentials for multi-component systems. In this work, we investigate the oxygen OICs in TiNbZr medium entropy alloys as a typical example to elucidate the strengthening and toughening mechanisms of OICs with a developed highly accurate deep learning potential. The formation mechanism, atomic packing of OICs and their interaction with dislocations, were then elucidated by molecular dynamics simulations with the developed potential. The interstitial atoms were found to aggregate energetically and increase the barrier of dislocation movement upon loading. It was found that the Nb content exerts a significant influence on the morphology and distribution of OICs. The decrease of Nb content favors the formation of larger cluster-like OICs. The existence of OICs can remarkably enhance the critical shear stress required for continuous dislocation movement. A pinning-cutting behavior was observed when an edge dislocation encounters an OIC, while a cross-slip behavior occurred when a screw dislocation encounters an OIC. The developed interatomic potential provides a valuable tool for elucidating the deformation mechanisms of TiNbZrO alloys, which highlights the significant effects of OICs on the mechanical performance of multi-principle element alloys.

Study on the grain development and dislocation evolution from dynamic to post-dynamic stage in IN718Plus superalloy; the role of second-phase

The introduction of hexagonal η-Ni3(Al,Ti)0.5Nb0.5 phase can refine and homogenize the microstructure of IN718Plus superalloy during hot working, but produces more complicated recrystallization behavior associated with second-phase modified structural mechanisms. Derived from this perspective, the role of η phase on recrystallization mechanisms and grain development from dynamic deformation to post-dynamic dwell was systematically investigated. The results indicated that η phase delayed the throughout recrystallization procedure and grain development. During dynamic deformation, boundary η inhibited discontinuous dynamic recrystallization via preventing the bulging of original grain boundaries, while intragranular lamellar η promoted heterogeneous strain concentration, stimulated random dislocations for continuous dynamic recrystallization and dislocation walls for banded dislocation substructures, which limited recrystallization occurrence in dynamic stage. During post-dynamic dwell, boundary η dissolution increased the nucleation sites for discontinuous static recrystallization, and η phase restricted grain boundary migration to provide abundant nucleation sites for continuous static recrystallization (CSRX). The banded dislocation substructures slowly evolved into subgrains to further form banded CSRX grains, which reduced grain size during early post-dynamic stage. After fully recrystallization, the residual η protected the small grains and impeded grain growth, meanwhile controlled the grain distribution. As a result, η phase induced sluggish dislocation evolution and recrystallization nucleation, consequently suppressed grain development and obtained the more homogeneous and fine grain configuration.

Unlocking slip-mediated bending in multilayers: Efficient modeling and solutions with high precision and simplicity

This work introduces a novel approach to understanding the bending behavior of multilayer structures with weak interfaces. Despite the existence of various theoretical models, achieving high accuracy and computational efficiency remains a challenge. To address these limitations, we propose a Non-uniform Slip Model (NSM) governed by two essential dimensionless parameters: the number of layers and the shear factor. Utilizing the Semiparametric Hybrid Variational (SHV) method, we derive theoretical solutions that require less computational effort and offer enhanced accuracy. We further simplify the NSM through homogenization to the Uniform Slip Model (USM), yielding clear and concise analytical solutions for deflection curves and effective bending stiffness with high precision. The USM is also extended to account for nonlinear slipping interfaces with continuous shearing flow, providing an analytical stiffness expression that includes the bending angle. This extension explains the experimental observation of multilayered graphene’s bending stiffness, which decreases from cubic to linear with increasing number of layers due to continuous slip and dislocation between atomic layers. Our study delivers theoretical insights for analyzing slip-mediated bending in laminated materials, paving the way for the design and optimization of such structures.

Effect of tensile and compressive strain on the gate leakage current and inverse piezoelectric effect in AlGaN/GaN HEMT devices

The influence of external strain on the gate leakage current of AlGaN/GaN high-electron-mobility transistors was studied. The magnitude of the leakage current increased by 39% under 0.1% tensile strain but decreased by 23% under −0.1% compressive strain. The leakage current obeyed the Poole–Frenkel conduction mechanism, demonstrating a decrease/increase in the barrier height for electron emission from the trap state into the continuum dislocation state. Furthermore, the magnitude of critical reverse stressing voltage for the onset of degradation induced by the inverse piezoelectric effect became lower/higher under tensile/compressive strain compared with that of the initial state, which was attributed to the modification of the total stress in the film. In addition, using the transient current method, it was established that the detrapping time constant for the traps in the AlGaN barrier increased as a result of the tensile strain, which is ascribed to movement of the dislocation level away from the conduction band.

Slip-discreteness-corrected strain gradient crystal plasticity (SDC-SGCP) theory

Strain gradient plasticity theory addresses the plastic strain gradient induced hardening by considering the internal stress and Taylor hardening associated with the geometrically necessary dislocations (GNDs). However, the continuum description of internal stress associated with GNDs is inaccurate due to the coarsening of discrete dislocations. Corrections are thus derived as the difference between the stresses produced by the continuous configuration and the discrete configuration. We further demonstrate the capability of this correction in effectively capturing the internal stress induced strengthening effect associated with GNDs, and elucidate that its role in strengthening is to homogenize the deformation and extend the influence of grain boundaries into the interior of grains within polycrystals. This capability to capture intragranular slip distribution is validated through the simulation of a polycrystalline tensile experiment. This work explains the limitations of classical crystal plasticity theory under high strain gradients and offers a straightforward yet robust slip discreteness correction to crystal plasticity with transparent input from dislocation theory, opening a new perspective for the connections between continuum crystal plasticity theory and dislocation theory.

Combining simulation and experimental data via surrogate modelling of continuum dislocation dynamics simulations

Several computational models have been introduced in recent years to yield comprehensive insights into microstructural evolution analyses. However, the identification of the correct input parameters to a simulation that corresponds to a certain experimental result is a major challenge on this length scale. To complement simulation results with experimental data (and vice versa) is not trivial since, e.g. simulation model parameters might lack a physical understanding or uncertainties in the experimental data are neglected. Computational costs are another challenge mesoscale models always have to face, so comprehensive parameter studies can be costly. In this paper, we introduce a surrogate model to circumvent continuum dislocation dynamics simulation by a data-driven linkage between well-defined input parameters and output data and vice versa. We present meaningful results for a forward surrogate formulation that predicts simulation output based on the input parameter space, as well as for the inverse approach that derives the input parameter space based on simulation as well as experimental output quantities. This enables, e.g. a direct derivation of the input parameter space of a continuum dislocation dynamics simulation based on experimentally provided stress–strain data.

Symmetry breaking induced asymmetric dislocation-planar fault interactions in ordered intermetallic alloys

In this study, we present the first comprehensive examination of symmetry breaking in the interactions between dislocation and superlattice planar faults, including anti-phase boundary (APB), complex stacking fault (CSF), superlattice intrinsic stacking fault (SISF), to reveal the underlying asymmetric dislocation reaction mechanisms depending on the sense of applied stress, employing both large-scale atomistic simulations and continuum dislocation theory. Four ordered intermetallic alloy systems including γ−Ni/γ′−Ni3Al and γ−Ni/γ′−Ni3Fe, γ−Al/γ−TiAl, and α−Ti/α2−Ti3Al were selected as the representative model systems, with two primary symmetry breaking effects, i.e., translational and three-fold rotational symmetry breaking considered. Detailed atomic steps of asymmetrical dislocation reactions and the corresponding asymmetrical dislocation bypassing mechanisms of precipitation have been elucidated, shown to be highly dependent on the geometrical configuration of the precipitate and the relative magnitudes of APB, CSF and SISF fault energies. A continuum model framework was then developed, which, for the first time, provides accurate and quantitative predictions of the threshold conditions triggering critical asymmetrical dislocation slips, verified to be in good agreement with the simulation results. Our study also successfully reproduced the experimentally observed dislocation-induced APB-SISF transformation, with a new dislocation reaction mechanism proposed to explain the transformation process. The findings are expected to be a key enabling stepstone for future innovation in intermetallic alloys strengthened through ordered phases for advanced applications in aeronautic and automotive industries.

A novel continuum dislocation density field-based crystal plasticity theory

In this work, a novel dislocation density field-based crystal plasticity formulation, that incorporates up-scaled continuum dislocation density fields to represent all possible characters of the dislocation density, is presented. The continuum dislocation field theory, formulated assuming large strain kinematics, is based on an all-dislocation concept, whereby individual dislocation density types are described as vector fields. The evolutionary behaviour of the dislocation density fields is defined in terms of a glide component derived from the classical general conservation law for dislocation density fields proposed originally by Kroner and Acharya, a rotation one given by the curl of the dislocation velocity vector as proposed originally by Ngan and co-workers, and a statistically stored dislocation source/sink component.The proposed formulation has been numerically implemented within the finite element method using a modified up-wind stabilisation approach, which results on eight extra independent nodal degrees of freedom per slip system, associated with the upscaled dislocation densities of pure edge and screw character. Furthermore, the required boundary conditions are simple: initial total dislocation density and dislocation flux or velocity, without the need for higher order boundary conditions. Full details of the numerical implementation of the crystal plasticity theory are given.The theory is then used to investigate classical boundary value problems involving 1D and 2D dislocation pile-ups, and the development of boundary layers in a deforming single crystal strip under constrained conditions. The main general understanding that emerges from the case studies is that, as either the dislocation pile-ups or the boundary layers develop with deformation, geometrically necessary dislocations are generated and lead to an overall behaviour that is size-dependent. Furthermore, it is shown that, in the absence of sources or sinks, which are statistically stored in nature, that total number of dislocations in the pile-up problems is preserved. The numerical predictions of the 1D pile-up and strip simple shear problems are in good agreement with published solutions.

Role of interfaces on the mechanical response of accumulative roll bonded nanometallic laminates investigated via dislocation dynamics simulations

Unraveling the effects of continuous dislocation interactions with interfaces, particularly at the nanometer length scales, is key to a broader understanding of plasticity, to material design and to material certification. To this end, this work proposes a novel discrete dislocation dynamics-based model for dislocation interface interactions tracking the fate of residual dislocation on interfaces. This new approach is used to predict the impact of dislocation/interface reactions on the overall mechanical behavior of accumulative roll bonded nanometallic laminates. The framework considers the dynamic evolution of the interface concurrent with a large network of dislocations, thus, accounting for the local short and long range effects of the dislocations under the external boundary conditions. Specifically, this study focuses on two-phase Fe/Cu nanometallic laminates, and investigates the role of the underlying elastic and plastic contrast of the Fe and the Cu layers on the composite response of the material. Moreover, the role of initial microstructures, resulting from processing is also investigated. Subsequently, the model is used to examine the effect of layer thickness and interface orientation relationship on the residual stresses of the relaxed microstructure. The associated mechanical response of these laminates are compared when loaded under normal direction compression, as well as shear compression. Finally, this work predicts a dominant effect of the layer thickness, as compared to the interface orientation relationship, on the macroscopic response and on the residual stresses of these nanolaminates, while the local dislocation transmission propensity through the interface is significantly influenced by the corresponding orientation relationship.

Application of rigorous interface boundary conditions in mesoscale plasticity simulations

The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical properties of materials. However, the traditional approaches used to simulate grain boundaries lack physical fidelity and are often incompatible across different simulation methods. We review a new mesoscale interface boundary condition based on Burgers vector conservation and kinetic dislocation reaction processes. The main focus of the paper is to demonstrate how to unify this boundary condition with different plasticity simulation approaches such as the crystal plasticity finite element (CPFEM), continuum dislocation dynamics (CDD), and discrete dislocation dynamics (DDD) methods. In DDD and CDD, plasticity is simulated based on dislocation activity; in the former, dislocations are described as discrete lines while in the latter in terms of dislocation density. CPFEM simulates plasticity in terms of slip on each slip system, without explicit treatment of dislocations; it is suitable for larger scale simulations. To validate our interface boundary condition, we implemented simulations using both the CPFEM method and a two-dimensional CDD model. Our results show that our compact and physically realistic interface boundary condition can be easily integrated into multiscale simulation methods and yield novel results consistent with experimental observations.

Stepless space-regulation of topological acoustic controller with high fault tolerance

In this paper, the stepless space-regulation of topological acoustic transmission channels with high fault tolerance is proposed through introducing structural defect dislocations into a topological acoustic controller. Due to the stability of topological order against local disturbance, the acoustic wave transmission is immune to dislocation boundaries with strong stability, and thus the topological acoustic controller has high fault tolerance. By continuous changing the dislocation, the position relationship between the outgoing and incident acoustic signals no longer limited to the integer multiple distance related to the lattice size, and can realize the efficient acoustic energy transmission without energy loss at the fractional multiple distance, that is, the topological controller can realize lossless acoustic energy transmission and reception in arbitrary position relationship. Furthermore, the coupling relationship between the defect dislocation and the topological acoustic channel is explored, which can realize the stepless space-regulation of the lossless channel in the wide band range. In addition, by further introducing multi-layer continuous dislocations, this high-fault-tolerant topological acoustic controller still has strong stability, and multiple error factors do not affect the transmission results, which greatly reduces the difficulty of manufacturing. Finally, the stepless space-regulation of topological acoustic channels and the high-fault-tolerant topological acoustic controller that are easy to manufacture are verified by our experiments. This research paves the way for the engineering applications of acoustic micro-control, micro-nano fabrication, remote acoustic energy transmission manipulation, acoustic measurement, weak signal processing, acoustic flexible control and other micro-shape and multi-functional acoustic devices, and will bring more inspiration to other classical wave communication fields such as light wave, electromagnetic wave and so on.

Activating continuous dislocation pinning enhanced toughness of nanocomposite coating through specially oriented semicoherent heterointerface lattice distortion

Ionic crystal ceramics are known to be susceptible to brittle cracks along the intergranular due to the strong ionic bond forces. Accordingly, an outstanding toughened coating consisting of yttria-stabilized tetragonal zirconia (YSTZ) and MgO, with a reinforced heterointerface, has been successfully achieved through the plasma electrolytic oxidation process. The results demonstrate that the enhanced Zr/Y–O bond strength improves the interfacial strength of the ionic crystal, while the lattice distortion activates continuous dislocation pinning at the (101) YSTZ//(111) MgO semicoherent heterointerface effectively hinders crack propagation of the coating. With the YSTZ content approaching 65 %, the toughness (KIC) value surpasses that of PEO coating by 42 %. These findings not only elucidate the scientific foundation for the improved toughness of the YSTZ/MgO nanocoating but also provide valuable insights into design strategies for improving ceramic toughness.

Tailored nanocrystalline Niobium coatings on steel substrates for superior resistance to micro-crack initiation

Fracture of metallic thin films during deformation hampers extensive applications of coated engineering components. In this study, the resistance to micro-crack initiation of Niobium (Nb) coatings deposited on stainless steel substrates is improved remarkably by tuning the substrate bias voltages during unbalanced magnetron sputtering. With the tailored nanocrystalline microstructure, the failure strain for coating fracture is increased to 30 %, which is far greater than that of previous metallic coatings (below 10 %). Microstructure characterizations reveal that intergranular nano-pinholes and amorphous phases can be eliminated effectively with a moderate ions bombardment effect to avoid brittle film fracture. At the same time, compact and homogenous nanocrystalline grains with appropriate intragranular defects are obtained via enhanced atom diffusivity during deposition. Therefore, large plastic deformation can be accommodated through both stress-driven grain coarsening and continuous dislocation plasticity, avoiding fracture of the Nb coatings.

Atomistic and continuum study of interactions between super-screw dislocations and coherent twin boundaries in [formula omitted]-structured [formula omitted

Informed by previous experimental observations, this study employed a combination of molecular dynamics simulations and dislocation continuum theory to investigate the interplay of super-screw dislocations and coherent twin boundary (CTB) in Ni3Al. The results reveal multiple interaction mechanisms depending on both the applied stress and the pathway for dislocation gliding. A continuum model framework has been developed to quantitatively evaluate the critical shear stress necessary for the CTB to accommodate dislocations along different pathway with the effects of anti-phase boundary (APB) and Complex Stacking fault (CSF) considered. The critical shear stress exhibits a significant inverse dependence on the quantity of dislocations, rendering it unsuitable as a measure of twin boundary strength. Instead, the resistant force of the CTB against all gliding dislocations is suggested as a more appropriate metric for quantifying its strength. This enables a direct comparison of the twin boundary strength between Ni and Ni3Al containing different amounts of Shockley dislocations, thereby extending its applicability to a wider range of materials. Our work offers new mechanistic insights critical for understanding and quantitative analysis of the interplay of super-dislocations and micro twining in nickel-based superalloys.

Dislocation density-based modeling of the yield drop phenomenon in nickel-based single crystal superalloy

The phenomenon of yield drop, characterized by a decrease in flow stress after initial yield, has been observed in various nickel-based superalloys. Despite numerous proposed physical mechanisms, there is still a lack of a meso-mechanism-based constitutive model to explain this phenomenon. In this study, the tensile behavior of a nickel-based single crystal superalloy (DDX), was investigated at different strain rates and a temperature of 900 °C. It was observed that the yield drop phenomenon in DDX became more pronounced with increasing strain rate. To predict the yield drop phenomenon during tensile processing, an improved strength law based on continuum dislocation density theory was considered in the crystal plasticity framework. The proposed constitutive model was implemented using nonlinear iteration and incorporated into a finite element analysis software. The simulation results exhibited a good agreement between the experimental data and the stress–strain curve in the vicinity of the yield drop region, affirming the predictive aptitude of the proposed model in elucidating the yield drop phenomenon at various strain rates.

Enhancing corrosion resistance of AZ91D alloy through yttria-stabilized tetragonal zirconia (YSTZ)/MgO repaired ceramic coating with improved embrittlement cracking

The oxide ceramic coating for improving the corrosion of magnesium alloy remains challenging especially generated embrittlement cracking of the coating. A remarkable ameliorating embrittlement cracking behavior has been observed in this contribution on our developed yttria-stabilized tetragonal zirconia (YSTZ)/MgO repaired ceramic coating. It is related to stabilized specially oriented YSTZ grains affected by the (101) t-ZrO2 // (101) Y2O3 coherent interface and (101) YSTZ // (111) MgO semi-coherent interface continuous dislocation pinning. The high-quality repaired ceramic coating has few cracks after 48 h of immersion, which is expected to be beneficial to providing a suitable long-term protection to magnesium alloy.

Interfacial Fracture Caused by Electromigration at Copper Interconnects

Abstract The present investigation delves into the failure model of cracking at the Cu/dielectric interface, specifically at the anode end of a copper interconnect that is triggered by electromigration. The study employs the continuous dislocation model to determine the stress field caused by interfacial mass diffusion that exists within and outside of the copper line. Apart from the anticipated tensile or compressive stress on the cathode or anode side, an anomalous stress singularity is identified at the interface between the dielectric layer and the anode end of the copper line. This singular stress distribution leads to cracking in the compressive portion of the dielectric layer at the anode end under the influence of electromigration. The theoretical predictions are in good agreement with experimental data, and a novel failure criterion akin to the stress intensity factor in fracture mechanics is formulated.

A continuum model for dislocation climb

Dislocation climb plays an important role in understanding plastic deformation of metallic materials at high temperature. In this paper, we present a continuum formulation for dislocation climb velocity based on densities of dislocations. The obtained continuum formulation is an accurate approximation of the Green’s function-based discrete dislocation dynamics method (Gu et al., 2015). The continuum dislocation climb formulation has the advantage of accounting for both the long-range effect of vacancy bulk diffusion and that of the Peach–Koehler climb force, and the two long-range effects are canceled into a short-range effect (integral with fast-decaying kernel) and in some special cases, a completely local effect. This significantly simplifies the calculation in the Green’s function-based discrete dislocation dynamics method, in which a linear system has to be solved over the entire system for the long-range effect of vacancy diffusion and the long-range Peach–Koehler climb force has to be calculated. This obtained continuum dislocation climb velocity can be applied in any available continuum dislocation dynamics frameworks. We also present numerical validations for this continuum climb velocity and simulation examples for implementation in continuum dislocation dynamics frameworks.