Edge Dislocation Dipoles Research Articles

Shock wave induced migration of an edge dislocation dipole in alpha-Fe

The mobility of a 1/2〈111〉{110} edge dipole in alpha-iron has been studied using molecular dynamics simulations. Collision cascades generated by keV recoils have been shown to induce the migration of dislocations. In order to elucidate the origin of the motion of these dislocations, and separate the production of defects from temperature or pressure effects, a stressed region of different shapes (sphere and cylinder) is simulated close to the edge dipole. We observe that the generated shock wave triggers the movement of the dislocations even when no defects are produced. The shape of the distorted region and the character of the dislocations influence the way the dislocations move, due to the change in Peach-Koehler force direction and to the fact that the shock waves arrive to the different parts of the dislocations at different times.

Diffusion and reaction behavior of palladium coating and copper matrix prepared using a halogen-free direct coating process

Herein, a palladium-coated copper wire was prepared using a halogen-free direct coating process, and the effects of the coating temperature on the morphology of the palladium coating and the mechanical properties of the wire were studied. The structural characteristics of the coating and copper matrix as well as the diffusion, reaction, and bonding characteristics of the elements at the copper–palladium interface were investigated. Results show that the deposition rate of palladium and the aggregation of palladium grains were accelerated with increasing coating temperature, promoting the formation of large palladium particles on the surface of the palladium-coated copper wire. The strength of the coated wire decreases and the elongation increases with increasing coating temperature. At 400 °C, the thickness of the coating was approximately 51 nm coating, consisting of approximately 4 nm nanocrystals. The improvement in plasticity was attributed to the distortionless recrystallized subgrain nucleus formed by the cell structure comprising dislocation tangles in the copper matrix, which reduces the matrix dislocation density. Positive and negative edge dislocations were present in the coating, and the two dislocation lines of the edge dislocation dipole offset each other. Numerous crystal defects were found in the copper–palladium bonding interface zone. Moreover, copper unidirectionally diffuses into the palladium coating, forming the intermetallic-compound CuPd in the interface bonding zone. Furthermore, the formation of twins was caused by the change in the stacking order of atoms due to the stacking fault occurring on the crystal surface, and the thickness of the diffusion zone was approximately 9 nm.

EBSD patterns simulation of dislocation structures based on electron diffraction dynamic theory

Electron backscatter diffraction (EBSD) technology is a powerful tool for materials characterization including crystal orientation mapping, phase identification, and strain analysis. However, it is still challenging for using EBSD to identify crystallographic defects due to the insufficient understanding of the diffraction patterns of different defect structures. In the present work, EBSD patterns of FCC-Fe with 1/2 < 110 > edge dislocation dipole and 1/6 < 11̅2 > screw dislocation quadrupole structures are simulated by the revised real space (RRS) method. Our results showed that the presence of dislocations deteriorates the overall quality of the diffraction pattern and have different effects on different Kikuchi bands and Kikuchi poles. The edges of the Kikuchi band corresponding to the edge dislocation glide plane are sharp and the diffraction details within the band are clear. The sharpness of the edges of the Kikuchi band corresponding to the crystal plane normal to the dislocation Burgers vector is reduced, but the intra-band diffraction details are clear. Other Kikuchi bands show obvious anisotropic blurring. The diffraction details of the Kikuchi pole corresponding to the screw dislocation Burgers vector are clear, the edges of the Kikuchi bands across this pole are sharp, and the diffraction details within the bands are clear in the segments close to this pole and blurred in the segments far away from it. Other Kikuchi bands and Kikuchi poles are blurred. Our results indicate that the EBSD pattern can be simulated based on the electron diffraction dynamic theory and the correlation between dislocation structure and EBSD pattern is revealed, which provides theoretical guidance for the resolution of dislocation structures by the EBSD technique.

X-ray methods for strain energy evaluation of dislocated crystals

Two X-ray methods are applied to estimate the strain energy of crystals containing dislocations, a simpler method based on the full width at half-maximum (FWHM) of the diffraction peaks, and asymptotic line profile analysis (LPA), which exploits the functional form of the Fourier transform corresponding to small Fourier parameters. It is shown analytically that, in the single-defect approximation, the modified Williamson–Hall (mWH) plot of the FWHMs is linear and the slope of the line is directly related to the strain energy of the dislocation system. Evaluation of the numerically generated peaks for randomly arranged edge dislocation dipoles shows that the method based on the mWH plot gives accurate strain energy, while asymptotic LPA overestimates it by about 50%. The accurate result given by the mWH plot is explained by the long correlation distance associated with the FWHM, which better captures the dislocation arrangement over large distances. By contrast, asymptotic LPA is related to atomic correlations over distances smaller than the mean dislocation–dislocation spacing, where the displacement gradient is mainly determined by the field of single dislocations. Therefore, asymptotic LPA leads to a very accurate dislocation density (with error less than 1%) and the result is independent of the dislocation arrangement. However, these short-range correlations overestimate the outer cut-off radius by one order of magnitude.

Interaction between the edge dislocation dipole pair and interfacial misfit dislocation network in Ni-based single crystal superalloys

Understanding the intrinsic strengthening mechanism is of great significance for microstructural design of Ni-based single crystal superalloys. In this paper, from an atomistic perspective, the interacting mechanism between edge dislocation dipole pair and interfacial misfit dislocation network has been elaborated. It is shown that a network of interfacial misfit dislocations can effectively impede the movement of matrix dislocations, accommodate and pile up the edge dislocation dipole pairs in Ni matrix. Furthermore, we have systematically elucidated the influence of loading rates on the stimulating period of edge dislocation dipole pairs and stiffness of Ni/Ni3Al substrate. These findings provide a better understanding of the interfacial strengthening mechanism of Ni-based single crystal superalloys.

Formation of Two Edge Dislocations in a Grain Due to Interface Disclination Dipoles

Abstract The formation of a dipole of edge dislocations inside one grain separated from the adjacent grains by two interfaces in which are lying disclination dipoles (one in each interface) has been theoretically investigated from an energy variation calculation. Critical grain sizes associated with the formation of the edge dislocation dipole have been determined as well as an activation energy. The effects of the inclination angle of the gliding plane of the dislocations and the characteristic parameters of the disclination dipoles have been finally analyzed.

Phase-Field Modeling of Chemoelastic Binodal/Spinodal Relations and Solute Segregation to Defects in Binary Alloys.

Microscopic phase-field chemomechanics (MPFCM) is employed in the current work to model solute segregation, dislocation-solute interaction, spinodal decomposition, and precipitate formation, at straight dislocations and configurations of these in a model binary solid alloy. In particular, (i) a single static edge dipole, (ii) arrays of static dipoles forming low-angle tilt (edge) and twist (screw) grain boundaries, as well as at (iii) a moving (gliding) edge dipole, are considered. In the first part of the work, MPFCM is formulated for such an alloy. Central here is the MPFCM model for the alloy free energy, which includes chemical, dislocation, and lattice (elastic), contributions. The solute concentration-dependence of the latter due to solute lattice misfit results in a strong elastic influence on the binodal (i.e., coexistence) and spinodal behavior of the alloy. In addition, MPFCM-based modeling of energy storage couples the thermodynamic forces driving (Cottrell and Suzuki) solute segregation, precipitate formation and dislocation glide. As implied by the simulation results for edge dislocation dipoles and their configurations, there is a competition between (i) Cottrell segregation to dislocations resulting in a uniform solute distribution along the line, and (ii) destabilization of this distribution due to low-dimensional spinodal decomposition when the segregated solute content at the line exceeds the spinodal value locally, i.e., at and along the dislocation line. Due to the completely different stress field of the screw dislocation configuration in the twist boundary, the segregated solute distribution is immediately unstable and decomposes into precipitates from the start.

Collision cascade effects near an edge dislocation dipole in alpha-Fe: Induced dislocation mobility and enhanced defect clustering

Collision cascades near a 1/2⟨111⟩{110} edge dipole in alpha-iron have been studied using molecular dynamics simulations for a recoil energy of 20 keV and two temperatures, 20 K and 300 K. These simulations show that the collision cascade induces the migration of the dislocations through glide along its slip plane. The motion of the dislocations starts at the peak of the collision cascade and expands a time scale much longer than the cascade duration, until restoring the equilibrium distance of the dipole, regardless of the damage produced by the cascade. At the initial stages, kinks are formed at the dislocation that enhance glide. When defects reach the dislocations, jogs are produced. We show that the initial dislocation motion is triggered by the shock wave of the collision cascade. The cascade morphology is also strongly influenced by the presence of the dislocations, having an elongated form at the peak of the displacement, which demonstrates the strong interaction of the dislocations with the cascade even at the early stages. Finally, we show that larger vacancy clusters are formed in the presence of dislocations compared to isolated cascades and that these clusters are larger for 300 K compared to 20 K.

Direct observations of collinear dislocation interaction in a Fe-17.4 Mn-1.50 Al-0.29 C (wt.%) austenitic steel under cyclic loading by in-situ electron channelling contrast imaging and cross-correlation electron backscatter diffraction

In this study we present an integrated experimental approach combing in-situ electron channelling contrast imaging under controlled diffraction conditions (cECCI) and cross-correlation based electron backscatter diffraction (CC-EBSD) to explore the dislocation pattern evolution in a high-Mn austenitic steel under low-cycle fatigue. We experimentally observed that the interactions between dislocations of same Burgers vectors gliding on intersecting slip systems led to the annihilation of the screw parts and the formation of edge dislocation dipoles. This collinear dislocation interaction facilitated the construction of edge dislocation walls in the studied material deforming in planar slip mode.

An improved method to model dislocation self-climb

Dislocations can provide short circuit diffusion paths for atoms resulting in a dislocation climb motion referred to as self-climb. A variational principle is presented for the analysis of problems in which fast dislocation core diffusion is the dominant mechanism for material redistribution. The linear element based self-climb model, developed in our previous work [1] Liu, Cocks and Tarleton (2020 J. Mech. Phys. Solids 135 103783), is significantly accelerated here, by employing a new finite element discretisation method. The speed-up in computation enables us to use the self-climb model as an effective numerical technique to simulate emergent dislocation behaviour involving both self-climb and glide. The formation of prismatic loops from the break-up of different types of edge dislocation dipoles are investigated based on this new method. We demonstrate that edge dipoles sequentially pinch-off prismatic loops, rather than spontaneously breaking-up into a string of loops, to rapidly decrease the total dislocation energy.

Molecular Statics Analyses of Thermodynamics and Kinetics of Hydrogen Cottrell Atmosphere Formation Around Edge Dislocations in Aluminum

Aluminum alloys are being explored as lightweight structural materials for use in hydrogen-containing environments. To understand hydrogen effects on deformation, we perform molecular statics studies of the hydrogen Cottrell atmosphere around edge dislocations in aluminum. First, we calculate the hydrogen binding energies at all interstitial sites in a periodic aluminum crystal containing an edge dislocation dipole. This allows us to use the Boltzmann equation to quantify the hydrogen Cottrell atmosphere. Based on these binding energies, we then construct a continuum model to study the kinetics of the hydrogen Cottrell atmosphere formation. Finally, we compare our results with existing theories and discuss the effects of hydrogen on deformation of aluminum-based alloys.

The influence of hydrogen on cyclic plasticity of oriented nickel single crystal. Part II: Stability of edge dislocation dipoles

A competition between hardening and softening hydrogen effects on the cyclic behaviour of <001> oriented nickel single crystal has been observed and discussed in terms of effective and back stresses partitioning. Moreover, the consequences of hydrogen have been studied in terms of composite model which illustrates the interaction between hydrogen and dislocation organisation. The hydrogen hardening associated with dislocation wall phase is a key feature which has been discussed and elucidated at edge dislocation dipoles scale using atomic calculations in nickel single crystal. The aim of our study was to evaluate the stability of this dislocation organisation in the presence of hydrogen, vacancies and vacancy clusters. As the main result, we noted that hydrogen in Cottrell's atmosphere hardens dipole configurations following solid solution strengthening and vacancies induced by hydrogen incorporation and cyclic loading attenuate this result. Moreover, the consequences of vacancies are more important when they are regrouped as clusters than when they are homogeneously distributed in the Cottrell's atmosphere. Such results can explain the complex behaviour of the wall phase and the consequence on long-range internal stresses observed in the first part of this study.

The influence of hydrogen on cyclic plasticity of oriented nickel single crystal. Part I: Dislocation organisations and internal stresses

The present paper discussed the impact of hydrogen on the mechanical response of cyclically strained nickel single crystal oriented for multi-slips at different length scales. At macroscale, hydrogen seems to induce competition between softening and hardening of the metal as a function of the plastic strain amplitude. Then, by separating internal stresses induced by long-range and short-range interactions between dislocations (represented by back and effective stresses, respectively), we noted that hydrogen reduces the effective stress but has a more complex behaviour with the back stress. Therefore, observations with transmission electron microscope and nano-indentation tests have been performed on cyclically pre-strained nickel single crystal with and without hydrogen. The dislocation organisation induced by the cyclic tests is similar for nickel with and without hydrogen. In both cases, the dislocation arrangement can be affiliated to a composite structure with a wall phase containing mainly edge dislocation dipoles and a channel phase where the mobility and cross-slip events of screw dislocations occurred. From both approaches, we observed that hydrogen hardens the wall phase while it softens the channel phase. These results are discussed on the base of plasticity mechanisms.

Estimation of diffusional effects on solution hardening at high temperatures in single phase compositionally complex body centered cubic alloys

Solution hardening in body centered cubic alloys as a function of temperature can be well described by the Suzuki model. This model includes significant strengthening from the dragging of edge dislocation dipoles produced by kink collisions along the screw dislocations. However, the model does not consider diffusion-controlled processes. Here we estimate a critical temperature Tcr above which diffusional effects become important, resulting in the collapse of edge dipoles. Loss of edge dipoles leads to a significant decrease in yield strength above Tcr and marks the temperature limit for structural applications of these single phase body centered cubic alloys.

Characteristics of atomic elastic stiffness at GSF energy surface, edge and screw dislocation cores in fcc, bcc and hcp metals

Basic characteristics of 6 × 6 matrix of atomic elastic stiffness (AES), Bija=Δσia/Δεj, or the deformation resistance at each atom point, are discussed first in static analyses of generalized stacking fault (GSF) energy surface for 8 fcc, 4 bcc and 4 hcp metals with Zhou’s EAM potential. For hcp metals, the stress–strain peak along the GSF path exactly coincides with the point where the AES loses the resistance showing negative 1st eigenvalue ηa(1), or the solution of BijaΔεj=ηaΔεi=Δσia; however, all fcc and 2 bcc (Mo and W) never have negative ηa(1) along the GSF path. Fe and Ta transiently show ηa(1) &amp;lt; 0 while they also have positive ηa(1) at the GSF energy peak. Then we performed MD simulations of edge and screw dislocation dipoles in a periodic slab cell of typical elements of fcc, bcc and hcp; and discussed the eigenvalue and the corresponding eigenvector {Δεxx, Δεyy, Δεzz, Δγyz, Δγzx, Δγxy} of the dislocation cores. As expected from the results of the GSF analyses, dislocation cores in fcc Ni have no ηa(1) &amp;lt; 0 atoms, even in their glide process under external shear loading. Bcc Fe and hcp Co definitely have ηa(1) &amp;lt; 0 atoms in the dislocation cores and their migration direction can be visualized by the maximum shear direction of the strain tensor of the corresponding eigenvector.

Fatigue behavior, microstructural evolution, and fatigue life model based on dislocation annihilation of an Fe-Ni-Cr alloy at 700 °C

Dislocation annihilation behavior of Sanicro 25 alloy was investigated based on various total strain amplitudes (Δεt/2). The slopes of cyclic stress response curves during stage ΙΙ were compared and showed that obvious stable cyclic behavior occurred at Δεt/2=0.3%. Microstructure analysis reveals that the number of slip plane increased with increasing Δεt/2. When Δεt/2=0.3%, dislocations can slip on the slip plane (111¯). When Δεt/2 increased to 0.4%, the slip planes included (1¯11) and (111¯). The fraction of substructured grains under Δεt/2=0.3% was obviously larger than that under Δεt/2=0.4%, which was attributed to the obvious dislocation annihilation. The deformed grains were dominant at Δεt/2=0.4%. The annihilation mechanisms of dislocations were analyzed during tensile and compressive loading based on the cyclic stress-time curves. The results showed that when Δεt/2=0.3%, during stage ΙΙ, dislocation annihilation mainly occurred during compressive loading. Dislocation annihilation included annihilation caused by cross-slip of screw dislocations and annihilation of adjacent edge dislocation dipoles. Furthermore, considering the critical annihilation distance between two adjacent edge dislocation dipoles, a modified dislocation annihilation model was presented. The dislocation annihilation model was verified based on the actual annihilation rate of dislocations. Further, the relationship of microstructure and fatigue properties was discussed. Based on the dislocation annihilation mechanisms, the fatigue life model considering dislocation annihilation was established. When the ratio of ρ¯− to ρ¯ increased, the fatigue life increased. Therefore, for cyclic hardening materials, obvious dislocation annihilation can increase fatigue life.

Characterizing the interactions of edge dislocation dipole in hexagonal close packed Ti-Al alloys

The aim of the present work is to elucidate the interaction between dislocation dipoles decorated by trace addition of solute atoms in the model material of as-annealed coarse-grained Ti-3Al (weight percent, wt%) alloys. The morphology, activity, structure, strain field, and interaction of dislocation cores were systematically characterized. Theoretical predictions of equilibrium distribution of edge dislocation dipoles presenting an angle of 45° relative to each other were experimentally demonstrated. More importantly, we observed for the first time the 45°-rotating of strain fields around the dislocation core along a clockwise direction for stress equilibrium which is driven by the dislocation-dislocation interactions.

Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model.

A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.

Cyclic softening in annealed Zircaloy-2: Role of edge dislocation dipoles and vacancies

The mechanism of cyclic softening in annealed Zircaloy-2 at low strain amplitudes under strain controlled fatigue at room temperature is rationalized. The unusual softening due to continuous decrease in the phenomenological friction stress is found to be associated with decrease in the resistance against movement of dislocations because of the formation and easy glide of pure edge dislocation dipoles and consequent decrease in friction stress from reduction in the shear modulus. Positron annihilation spectroscopy data strongly support the increase in edge dislocation density containing jogs, from increased positron trapping and increase in annihilation lifetime.

Hydrogen-induced strain localisation in oxygen-free copper in the initial stage of plastic deformation

Single crystals of oxygen-free copper oriented to easy glide of dislocations were tensile tested in order to study the hydrogen effects on the strain localisation in the form of slip bands appearing on the polished specimen surface under tensile straining. It was found that hydrogen increases the plastic flow stress in Stage I of deformation. The dislocation slip localisation in the form of slip bands was observed and analysed using an online optical monitoring system and atomic force microscopy. The fine structure of the slip bands observed with AFM shows that they consist of a number of dislocation slip offsets which spacing in the presence of hydrogen is markedly reduced as compared to that in the hydrogen-free specimens. The tensile tests and AFM observations were accompanied with positron annihilation lifetime measurements showing that straining of pure copper in the presence of hydrogen results in free volume generation in the form of vacancy complexes. Hydrogen-enhanced free-volume generation is discussed in terms of hydrogen interactions with edge dislocation dipoles forming in double cross-slip of screw dislocations in the initial stage of plastic deformation of pure copper.