Motion Of Edge Dislocations Research Articles

Nanostructure and dislocation interactions in refractory complex concentrated alloy: From chemical short-range order to nanoscale B2 precipitates

Refractory complex concentrated alloys (RCCAs) have emerged as a promising class of structural materials, demonstrating exceptional mechanical performance in aggressive environments. However, the complex atomic environments, significant lattice distortion, and vast compositional space of RCCAs present challenges to understanding the mechanisms that govern structure-property relationships. In this study, we explore the dislocation mechanisms in three model quaternary RCCAs, namely Mo25Nb10Ta25W40 (at. %), Mo25Nb25Ta25W25, and Mo25Nb40Ta25W10 using large-scale atomistic simulations and machine learning based Spectral Neighbor Analysis Potential. Our atomistic simulations examine how the chemical composition and local ordering influence the mobility of both edge and screw dislocations, and how lattice distortion and diffuse anti-phase boundary energy (DAPBE) affect dislocation behaviors during nanostructural evolution. Notably, with the increase in Nb concentration in the model RCCAs, both DAPBE and lattice distortion are simultaneously enhanced as the chemical short-range order (CSRO) evolves into nanoscale B2 precipitates. This evolution results in high lattice distortion due to the lattice mismatch between B2 precipitates and the random matrix. Consequently, B2 nanoprecipitates provide a stronger pinning effect, hindering edge dislocation motion while promoting cross-slip of screw dislocations, leading to a reduced screw-to-edge ratio in slip resistance and mobility discrepancy. These findings offer valuable insights into dislocation behaviors and interactions with ordered precipitates, highlighting the importance of exploring non-equiatomic compositions and advancing beyond CSRO in RCCAs. This study has implications for optimizing alloy compositions and processing methods for superior performance in aggressive environments.

Anisotropy effect on the motion of edge dislocation in body-centered-cubic Fe

The mechanical properties of metallic materials can be dictated by nucleation, multiplication, and motion of dislocations under stress. We employed the molecular dynamics (MD) method to investigate the motion of an 1/2[111](112̄) edge dislocation in body-centered-cubic (BCC) Fe under normal stress on the 112̄ plane. Our MD results confirm that the motion of the edge dislocation can be attributed to the normal stress induced shear stress (NSISS) effect. The magnitude of this effect varies across different cubic metals. Further studies reveal that this effect is limited to the {112} planes and is associated with the disobedience of Schmid’s law in the case of twinning of BCC Fe. To summarize, the NSISS effect may be traced back to the anisotropy of cubic metals and should be considered when the twinning process in anisotropic BCC metals is studied.

Coupling strengthening mechanism of precipitate and solute atoms in edge dislocation motion of Al-Mg-Si alloy

To investigate the coupling strengthening mechanism of precipitate and Cu solute atoms in Al-Mg-Si alloy, the molecular dynamics model of edge dislocation motion interacted with precipitate and Cu solute atoms was established. The dislocation length is increased in the dislocation-precipitate interaction due to the bending and bowing of the edge dislocation around the precipitate. No coupling between precipitate and solute can be found in material strengthening in cases with lower solute concentrations. The exponential effect of the coupling effects between precipitate and solute on material strengthening is found when the solute concentration is increased above 0.3.at% at room temperature. The change of the edge dislocation caused by solute atoms around the precipitate is the key reason for the strengthening coupling effect. Furthermore, the effects of temperature variations on the coupling effect are more pronounced than the effects of shear strain rate variations. When the temperature is increased from 200K to 500K, the critical ratio of solute and precipitate strengthening is decreased from 1.5 to 0.4.

Atomistic study on effects of solute atoms on energy profile of edge dislocation mobility in FCC-Cu alloys

Solid-solution strengthening is an effective method to increase the mechanical strength of metal alloys. Revealing the solid-solution strengthening mechanism based on the energy profile of the dislocation motion is vital for the non-empirical development of high-strength metal alloys. This study provides detailed energy profiles (i.e., energy surfaces) of the edge dislocation gliding motion under the effect of solute atoms, as well as the atomic-scale origin of solute strengthening in face-centered cubic (FCC) Cu alloys. The maximum shear stress (τmax) required for the dislocation to leave the solute atoms (Ni, Co, and Mo, all with different sizes and stacking fault effects) was qualitatively evaluated by finite temperature molecular dynamics simulations. By the nudged elastic band (NEB) analysis, we determined the atomistic origin of the energy barrier for the edge dislocation motion and the maximum force required to overcome the solute pinning effect (i.e., depinning force, FNEB) in binary Cu alloys. By linking FNEB to the size misfit, a theoretical prediction model based on size effects and the volumetric strain field was used and can qualitatively explain the increment in the maximum shear stress (Δτmax) by the solute atoms. These results provide an atomistic basis for the prediction of the solute-strengthening effect correlated with the edge dislocation motion in wide FCC systems.

Interaction between basal edge/mixed dislocations and point defects in zirconium

Zirconium alloys are widely used in nuclear reactors. Due to frequent displacement cascade events under irradiation, a large number of point defects are generated in zirconium alloys. In this work, the interactions between edge/mixed dislocations and point defects (vacancies and SIAs (self-interstitial atoms)) are studied by molecular dynamics (MD) simulations. The simulation results indicate that vacancies are not absorbed by edge dislocations but by mixed dislocations. Compared with their weak pinning effect on edge dislocation motion, vacancies have an intermediate pinning effect on the motion of mixed dislocation. In contrast, SIAs are all absorbed by edge and mixed dislocations and have a strong pinning effect. Then, force equilibrium is established on point defects to explain the absorption of point defects. The attractive force between dislocations and point defects is calculated from the binding energy, and the friction force of point defects is calculated from the migration energy. We found that the friction force of vacancies on edge dislocations is larger than the attractive force, and thus the vacancies cannot be absorbed. For the other three cases, the attractive force is large enough to overcome the friction force, and the point defects are absorbed.

Atomistic simulations reveal strength reductions due to short-range order in alloys

A theory for strengthening for multicomponent non-dilute alloys possessing short-range order (SRO) has recently been developed. The theory predicts that, in addition to a well-known athermal strengthening, there is a notable effect of SRO on the solute–dislocation interactions that can decrease or increase the strength relative to a random alloy. Here, carefully designed atomistic simulations in a model binary NbW alloy are used to demonstrate that alloy strength due to solute–dislocation interactions can be increased or decreased, depending on the SRO and consistent with theoretical predictions. Specifically, SRO is introduced using fictitious solute–solute interactions in an alloy system with very small true solute–solute interactions, and the Nudged Elastic Band (NEB) method is then used to compute the energy barriers for edge dislocation motion for various levels of SRO. Energy barriers, and hence alloy strengths, can be decreased when the Warren-Cowley SRO parameters are negative (attraction of unlike solutes). The theoretical predictions for the same system are in reasonable quantitative agreement with the simulation results. These findings demonstrate the unexpected possibility of reduced strength due to SRO and also further validate the analytical theory as a tool to guide alloy design.

The Dynamic Energy-Momentum Tensor and the Logarithmic Singularity of a Generally Accelerating Edge Dislocation

Abstract The near-field logarithmic singularities in the field quantities associated with the acceleration of an arbitrarily moving edge dislocation are calculated based on a conservation law involving the dynamic energy-momentum tensor integrated over a domain enclosed by a multi-scale contour (an annulus of inner radius ϵ02 and outer radius ϵ0). The existence of the logarithmic singularities is obtained solely from the conservation law and the leading 1/r terms in the near fields of the stress and the velocity (which are those of the steady-state motion with velocity the instantaneous velocity in the accelerating motion). From the equations of motion and the symmetry in the second partial derivatives of the displacements for y≠0 we obtain that all six logarithmic terms of the near-field expansions are independent of the angle in the polar coordinates. All logarithmic terms in the near-field expansion of the strains and velocity in an arbitrarily moving edge dislocation (subsonically) are evaluated.

Effects of vacancy concentration on the edge dislocation motion in copper by atomic simulations

Nonequilibirum vacancy concentration widely appears in crystals under many extreme loading conditions, but receives relatively few attentions. In this work, we systematically explore the influence of a serial of different vacancy concentrations on the edge dislocation motion in copper using molecular dynamics (MD) simulations. Our result shows that the vacancy would hinder the dislocation motion, but the mechanism depends on the detailed dislocation motion regions. In thermally activated region, its influence is mainly reflected by modifying the dynamic and static threshold stresses required for edge dislocation initiation and continuous motion. In the linear region, the hindering mechanism is gradually transformed from phonon damping to vacancy pinning with the increasing vacancy concentration. In contrasts, the dislocation structure is almost unchanged under different vacancy concentrations in the non-linear region. Under high applied stress, high vacancy concentration will cause the dislocation velocity to jump back and forth between transonic and subsonic velocities more frequently. It has been attributed to the reactions between the dislocation and vacancies. The latter may result in dislocation local constriction and climbing. Moreover, a mobility equation suitable for describing edge dislocations at different non-equilibrium vacancy concentrations is proposed, which fits the MD results well. Finally, the roles of the nonequilibirum vacancy concentration on the edge dislocation motion is interpreted using the degrading elastic property and stacking fault energy.

Resonance with surface waves induces forbidden velocity bands in dislocation glide

We use molecular dynamics simulations to demonstrate a pronounced influence of free surfaces on the mobility of dislocations at near-sonic velocities. By correlating instantaneous velocities v and resolved stresses τ, we show that the mobility relations of both edge and screw characters are composed of multiple ranges of stable uniform motion separated by bands of forbidden velocity. The lower limiting velocity for uniform motion of both edge and screw dislocations is the Rayleigh wave speed, cR. When forced to propagate at an average velocity greater than cR, dislocations exhibit cyclic, intermittent jumps in instantaneous velocity between cR and higher velocity branches of the mobility relation. Bands of forbidden velocity may be calculated directly from the velocity dependence of dislocation drag functions, which contain peaks near cR and—in the edge case—one other characteristic surface wave speed, which we associate with shear-horizontal (SH) waves. We propose that peaks in the drag function are due to resonance of free surface vibrations forced by nearby moving dislocations.

Thermal dissipation induced by fast-moving edge dislocations

Microscopic mechanics of thermal dissipation induced by fast-moving edge dislocations are crucial for a deeper understanding of the nature of plastic deformation. Herein, we study the thermal dissipation induced by a fast-moving edge dislocation and discuss the effect of non-Schmid stress on the thermal dissipation using molecular dynamics simulations that can quantitatively distinguish the thermal dissipation and stored energy part of the energy emitted from a moving dislocation. We show that, of the energy emitted by the fast-moving edge dislocation, no more than 5% is used to generate elastic distortion of the local atomic structure, especially at low-stress levels, and almost all the energy emitted by the moving dislocation is converted into thermal energy and dissipated. The thermal dissipation of the moving edge dislocation depends significantly on the non-Schmid stress, specifically, temperature rise decreases almost linearly as the non-Schmid stress normal to the slip plane increases, and the possible mechanism is disclosed.

The influence of lattice misfit on screw and edge dislocation-controlled solid solution strengthening in Mo-Ti alloys

Mo-Ti alloys form solid solutions over a wide range of compositions, with lattice misfit parameters increasing significantly with titanium content. This indicates a strong increase in the critical stress for edge dislocation motion. Here, we probe the transition from screw to edge dislocation-dominated strengthening in Mo-Ti solid solutions with titanium content up to 80 at%. The alloys were scale-bridging characterized to isolate the impact of substitutional solid solution strengthening. Mechanical testing yielded no significant influence of grain boundaries or grain orientation. The results were corrected for the strengthening by unavoidable interstitial oxygen. Modelling of screw and edge dislocation-controlled solid solution strengthening was applied to the results to evaluate the contributions of both dislocation types. The analysis reveals that screw dislocation motion controls the strength in allows with less than 40 at% titanium, while edge dislocation motion provides comparable strength for 60–80 at% titanium. These results in a system of reduced chemical complexity support the recent investigations of edge dislocation-controlled strengthening found in high-entropy alloys.

Influence of kinetic effect on interaction between edge dislocation and irradiated dislocation loops in BCC Tantalum

In this paper, the interaction between an edge dislocation and irradiation <100> sessile self-interstitial atom (SIA) type dislocation loops (DLs) is studied by atomistic simulations in BCC Ta at 0 and 300 K. Both molecular dynamics (MD) and statics (MS) simulations are performed to highlight the dislocation kinetic effect (or dynamic effect) on the critical resolved shear stress (CRSS) for dislocation bypassing the DLs and on the dislocation-SIA DLs interaction mechanisms. The simulation results show that the dislocation-DLs interaction mechanisms are two-fold. When the DL size is lower than a critical value, the moving edge dislocation tends to completely absorb the DLs or fully transform the original DLs into other-type ones. However, when the DL size is higher than the critical value, the moving dislocation tends to absorb or transform the DLs partially or even marginally. Moreover, with increasing applied shear stress, the high-speed dislocation has no sufficient time to absorb SIAs from DLs, which also changes the dislocation-DLs interaction process remarkably. When the dislocation is accelerated to subsonic, an abnormal “pull forward” dislocation configuration may present upon the dislocation bypasses a small DL. More importantly, with the kinetic effect considered, the CRSS for dislocation overcoming the barriers of DLs decreases significantly for the dislocation-DLs interaction mechanisms. In order to appropriately describe the kinetic effect on the CRSS, amended dispersed barrier hardening (DBH) and Bacon-Kocks-Scattergood (BKS) hardening models for the latter dislocation-DLs interaction mechanism are proposed.

Short-range ordering alters the dislocation nucleation and propagation in refractory high-entropy alloys

The role of short-range ordering (SRO) in the dislocation kinetics in refractory high-entropy alloys (RHEAs) remains controversial. On one hand, it was shown by simulations that the mobility of edge dislocations was enhanced while that of screw dislocations was reduced, leading to the conclusion that screw dislocations should be dominant. On the other hand, experiments exclusively showed the dominance of edge dislocations. Here, we investigate the impact of SRO in the grain interior and grain boundary on dislocation nucleation and propagation in a BCC MoTaTiWZr RHEA, using a combination of the density-functional theory calculations, Monte Carlo method, and molecular dynamic simulation. Our results show that this RHEA is energetically favorable to undergo SRO, thus forming a pseudo-composite microstructure. This microstructure consists of three categories of clusters: high energy clusters (HECs), medium energy clusters (MECs), and low energy clusters (LECs), with the HECs in grain boundaries acting as weak fillers to induce dislocation nucleation while the MECs/LECs serving as a strong matrix to stabilize the weak HECs. Importantly, SRO is found to enhance the energy barriers for both edge and screw dislocation motion and make the mobility of edge dislocations comparable to or even lower than screw dislocations, contributing to the dominance of edge dislocations in the BCC RHEA. Our work highlights the importance of SRO in influencing the dislocation activity of RHEAs and presents a fascinating route for designing RHEAs to achieve superior mechanical properties.

Coupled effect of Cr and Al on interactions between a prismatic interstitial dislocation loop and an edge dislocation line in Fe-Cr-Al alloy

Segregation of alloying elements to a prismatic dislocation loop under irradiation is an important phenomenon in understanding the role of loops in radiation effects in alloys. In this work, various segregation sequences of Cr and Al atoms to a 〈100〉 and a 1/2〈111〉prismatic dislocation loop in a Fe-Cr-Al alloy are explored using molecular dynamics method and ab initio energy calculation. The results reveal that Cr can readily segregate to the loops while Al atoms cannot by themselves, but the segregated Cr atoms are able to promote Al segregation at the loops, defined as a coupled segregation of Cr and Al. After interacting with Cr and Al, a previously mobile 1/2〈111〉 loop becomes sessile. Al segregation through the coupled segregation process can further affect the pinning behavior of a dislocation loop to an edge dislocation motion. By varying the Al fraction in the segregated solutes, a nonlinear dependence of the pinning effect on dislocation motion is determined. At lower fractions, the pinning strength increases with the increasing Al fraction until Al fraction reaches a critical value of about 19%, above which the pinning strength decreases with further increase of Al fraction. All these results suggest that, in addition to the effect of Al on the surface resistance to oxidation, Al effect on the dislocation loop behavior is important to optimize the composition of Fe-Cr-Al alloys for their applications in accident tolerant fuel concepts.

Analytic formulation of elastic field around edge dislocation adjacent to slanted free surface.

Explicit and tractable formulation of the internal stress field around edge dislocations is indispensable for considering the mechanics of fine crystalline solids, because the motion of edge dislocations in a slanted direction with respect to the free surface often plays a vital role in the plastic deformation of the solids under loading. In this study, we formulated an analytical solution for the stress distribution that occurs around edge dislocations embedded in a semi-infinite elastic medium. This formulation is based on the image force method and the Airy stress function method; it describes the variation in the stress distribution with changes in the slanted angle between the traction-free flat surface of the medium and the Burgers vector of the edge dislocation. Furthermore, our analytical solution shows that the attractive force acting on the edge dislocation due to the presence of the free surface is always perpendicular to the surface, regardless of the relative angle of the Burgers vector with the surface.

Glide Mobility of a-Type Edge Dislocations in Aluminum Nitride by Molecular Dynamics Simulation.

Classical molecular dynamics simulations are performed to investigate the motion of a-type edge dislocations in wurtzite aluminum nitride (AlN). The nucleation and propagation of kinks are observed via the dislocation extraction algorithm. Our simulation results show that the nucleation energy of the kink pair in AlN is 1.2 eV and that the migration energy is 2.8 eV. The Peierls stress of the 1/3⟨112̅0⟩{101̅0} edge dislocation at 0 K is 15.9 GPa. The viscous motion of dislocations occurs when τ > τp, and the dislocation velocity is inversely proportional to the temperature and directly proportional to the applied stress. Below room temperature, the value of the critical resolved shear stress (CRSS) on the prismatic plane is the lowest, which suggests that the dislocation mobility on the prismatic plane is the easiest. The CRSS on the pyramidal plane is always the highest at all temperatures, which suggests that pyramidal slip is the hardest among these three slip systems.

Shear stress relaxation through the motion of edge dislocations in Cu and Cu–Ni solid solution: A molecular dynamics and discrete dislocation study

Shear stress relaxation through the motion of multiple edge dislocations in a periodic cell is studied by molecular dynamics and discrete dislocation methods. In both methods, we consider systems with an initial edge dislocation on the parallel slip planes. The initial shear strain is applied to the system along the Burgers vector of the dislocations. The velocity profile for a single edge dislocation fitted from a molecular dynamics (Bryukhanov, 2020) is used as the input to discrete dislocation dynamics. The dependence of shear stress, plastic strain, and plastic strain rate on time are analyzed. We show that when dislocations are sufficiently far from each other, relaxation occurs due to dislocation motion, and dislocation velocity can exceed the anisotropic speed of sound. If the dislocations are closer together, relaxation is due to the growth of stacking faults. We find that the stress at which the stress relaxation mechanism changes decreases with increasing dislocation density. Stress relaxation in a Cu–Ni solid solution occurs faster than in pure Cu due to a higher dislocation velocity in the high-velocity regime. However, the shear stress at which nickel atoms increase the plastic strain rate increases with an increase in dislocation density. The dependence of the relaxation time on the dislocation density obtained in discrete dislocation simulations is approximated using the power law. The elastic interaction between dislocations reduces the exponent of the power law from 1/ρ to approximately 1/ρ0.8 for both pure Cu and Cu–Ni solid solutions.

High energy barriers for edge dislocation motion in body-centered cubic high entropy alloys

Recent theory proposes that edge dislocations in random body-centered cubic (BCC) high entropy alloys have high barriers for motion, conveying high strengths up to high temperatures. Here, the energy barriers for edge motion are computed for two model alloys, NbTaV and MoNbTaW as represented by interatomic potentials, using the Nudged Elastic Band method and compared to theoretical predictions. The average magnitude of the barriers and the average spacing of the barriers along the glide direction agree well with the analytical theory, with no adjustable parameters. The evolution of the barriers versus applied stress is modeled, and the mean strength is in reasonable agreement with the predicted zero-temperature strength. These findings validate the analytic theory. A reduced analytic model based on solute misfit volumes is then applied to Hf-Mo-Nb-Ta-Ti-Zr and Mo-Nb-Ta-Ti-V-W alloys, rationalizing the observed significant strength increases at room temperature and 1000 ∘C upon addition of solutes with large misfit into a base alloy. The analytic theory for edge motion is thus a powerful validated tool for guiding alloy selection.

Atomic-scale mechanisms of void strengthening in tungsten

Neutron and heavy-ion irradiation of tungsten produces nanometer-size vacancy voids, gas-filled bubbles and dislocation loops. These defect features can affect mechanical properties and the impact can be quite significant because of their high density. Understanding the basic mechanisms of mechanical properties degradation is necessary for predicting radiation effects. Predictions can be made using discrete dislocation dynamics or/and finite element approaches which, however, need local interaction mechanisms as inputs. Such knowledge can be provided only by atomic-scale modeling. This paper reports the results of an extensive atomic-scale modeling study of the interactions between moving edge dislocations and voids in tungsten. The main focus is on the effects of the void size and ambient temperature. Critical resolved shear stress was calculated for voids up to 9 nm in diameter. Atomistic results are compared with the theoretical approach and with those obtained earlier for voids in body centered cubic (bcc) iron. An important role of the void surface has been revealed.

Effect of shape geometry on electromagnetic radiation under quasi-static compression in sintered aluminium preforms

This paper presents the effect of shape geometry on electromagnetic radiation (EMR) emissions from sintered aluminium preforms during deformation under unrestricted quasi-static compression. The EMR emissions under compression show shape anisotropy. The end surface conditions of the compressing platens, i.e. lubrication, also influence the EMR emission characteristics. The first EMR emission invariably occurs near the yield. The dead metal zones formed on the top and bottom portions of the specimens during axial compression, possibly generate a climbing motion of edge dislocations in the radially outward mid-regions. These edge dislocations form accelerated electric line dipoles and emit electromagnetic radiation during the climbing motion. These results appear significant in understanding the mechanism of plastic deformation in metal powder preforms at the microscopic level and are expected to give a deeper insight into the metal forming processes.