Motion Of Edge Dislocations Research Articles

Molecular Dynamics Simulation of Hydrogen-Edge Dislocation Interaction in BCC Iron

Hydrogen embrittlement in metals is a complex multi-causal phenomenon, which, on the atomic scale, comprises H diffusion, decohesion, cavity nucleation as well as the interaction between H and dislocations. The present atomic-level simulation uses the embedded atom method (EAM) to describe the energetics of a hydrogen atom during the interaction with a moving edge dislocation in a bcc iron crystal. Particularly, in the chosen framework it is found that an H atom taking a site in the Fe lattice can block the movement of an edge dislocation, while the stress exerted on the dislocation can reach a maximum value of 15.5 MPa. However, it is also found that an interstitial H atom does not impede the movement of the dislocation and exerts a maximum stress of 38.2 MPa at the time when the moving dislocation passes by. These quantitative findings are correlated with the macroscopically observed mechanical behavior of hydrogen charged iron, which had pointed out that hydrogen might cause an increase of the flow stress and/or a local plasticity enhancement.

Dislocation-Stacking Fault Tetrahedron Interactions in Cu

In copper and other face centered cubic metals, high-energy particle irradiation produces hardening and shear localization. Post-irradiation microstructural examination in Cu reveals that irradiation has produced a high number density of nanometer sized stacking fault tetrahedra. The resultant irradiation hardening and shear localization is commonly attributed to the interaction between stacking fault tetrahedra and mobile dislocations, although the mechanism of this interaction is unknown. In this work, we present results from a molecular dynamics simulation study to characterize the motion and velocity of edge dislocations at high strain rate and the interaction and fate of the moving edge dislocation with stacking fault tetrahedra in Cu using an EAM interatomic potential. The results show that a perfect SFT acts as a hard obstacle for dislocation motion and, although the SFT is sheared by the dislocation passage, it remains largely intact. However, our simulations show that an overlapping, truncated SFT is absorbed by the passage of an edge dislocation, resulting in dislocation climb and the formation of a pair of less mobile super-jogs on the dislocation.

Oxygen–molybdenum interaction with dislocations in Nb-Mo single crystals at elevated temperatures

A study using a transmission electron microscope was performed for the deformation microstructures of Nb-20mol%Mo single crystals containing from 0.03 to 0.65 mol% oxygen and a Nb-40mol%Mo-0.05mol%O single crystal, compressed to approximately 4% plastic strain at 298 K, 973 K and 1473 K. At 298 K, screw dislocations are predominant in all alloys. At 973 K, in Nb-20Mo-0.03O and Nb-40Mo-0.05O, the dislocation microstructure contains the same amount of edge dislocations and small edge dipoles that tend to aggregate into clusters. In Nb-20Mo-0.65O, however, the arrangement consists of long glide loops parallel to the screw direction. At 1473 K, edge dislocations are dominant in all alloys. From the results, the following conclusions are made: (1) Oxygen atoms impede screw dislocation motion at 298 K and 973 K; (2) The influence of oxygen on screw segments is significantly strong at 973 K; (3) At 1473 K, oxygen atoms impede edge dislocation motion. It is inferred that O-Mo atmosphere is formed around dislocations.

Molecular dynamics simulations of motion of edge and screw dislocations in a metal

Motions of a straight edge dislocation and a kinked screw dislocation in BCC Mo, described by the Finnis–Sinclair potential, are studied in periodic simulation cells subjected to an applied shear stress. Procedures for setting up the initial atomic configurations in each case are described, and estimate is made of the local driving force due to the image interactions. Preliminary results show that at low temperature the edge dislocation moves primarily through kink nucleation, whereas the mobility of the screw dislocation is strongly facilitated by the presence of a kink.

Discrete dislocation modeling of fatigue crack propagation

Analyses of the growth of a plane strain crack subject to remote mode I cyclic loading under small-scale yielding are carried out using discrete dislocation dynamics. Cracks along a metal–rigid substrate interface and in a single crystal are studied. The formulation is the same as that used to analyze crack growth under monotonic loading conditions, differing only in the remote stress intensity factor being a cyclic function of time. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation being incorporated through a set of constitutive rules. An irreversible relation is specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading in an oxidizing environment. The cyclic crack growth rate log(d a/d N) versus applied stress intensity factor range log(Δ K I) curve that emerges naturally from the solution of the boundary value problem shows distinct threshold and Paris law regimes. Paris law exponents in the range 4 to 8 are obtained for the parameters employed here. Furthermore, rather uniformly spaced slip bands corresponding to surface striations develop in the wakes of the propagating cracks.

Interaction of Transonic Edge Dislocations with Self-interstitial Loop

The interaction of transonic edge dislocations with a sessile self-interstitial dislocation loop (SIL) in BCC tungsten is investigated using atomistic Molecular Dynamics method. The moving velocity of the transonic edge dislocations is higher than the transverse sound wave velocity. It was found that SIL has a strong pinning effect to the moving edge dislocations. The SIL was eventually annihilated through forming jogs on the moving edge dislocations. A transonic edge dislocation can be stopped by SIL at the pinning point, and then the resulting jogs could move above the sound barrier afterwards under high shear.

Effect of Rh and V Additions on Plastic Deformation Behaviour in Ni<SUB>3</SUB>Nb Single Crystals with D0<SUB>a</SUB> Structure

The effect of Rh and V additions on phase stability and plastic deformation behaviour in Ni 3 Nb single crystals with the D0 a structure was investigated, focusing on the slip behaviour of (010)[100], (010)[001] and (001)[100] systems in a wide temperature range between room temperature and 1200°C. The V addition induces no significant change in the critical resolved shear stress (CRSS) for (010)[100] slip at low temperatures, while the Rh addition is effective in increasing the CRSS at temperatures below 500°C and above 800°C, resulting in significant improvement of high-temperature strength. The increment of high-temperature strength is closely related to suppression of the climb motion of edge dislocations. The Rh addition also effectively increases the CRSS for (010)[001] and (001)[100) slip. The V addition was expected to enhance activation of the (010)[001] slip by reducing the SISF energy between the superpartials, but that was not achieved.

Compliant effect in twist-bonded systems

We describe how a buried twist-bonded interface closely set below the substrate surface alters the plastic relaxation in heteroepitaxy. For this, first—considering from an atomistic point of view, two twist-bonded semi-infinite substrates—we calculate and compare the elastic energy for several twist angles. We find that for ‘low twist angles’ (up to around 20°), the twist-bonded interface can be reconstructed without involving any dangling bonds, but for large twist angles, the twist-bonded interface becomes more unstable and involves some dangling bonds. Furthermore, for ‘low twist angles’, the strain field induced by such a twisted interface does not extend on more than several atomic layers. Second—considering a mesa made from a thin twist-bonded layer and a thick 4% compressive strained overlayer—we study the motion of edge dislocations while entering from the edge and moving towards the centre of the sample. The energy barrier at edges contravenes the introduction of a rectilinear edge dislocation at the mesa bottom interface. As far as misfit edge dislocations are concerned, it is easier to introduce it at the heterojunction between the compressive strained overlayer and the thin twist-bonded layer than at the mesa bottom twisted interface. Finally, we define a kinked edge dislocation which is able both to relax more energy than the rectilinear one and to weaken the energy barrier at the edges of a mesa, so that compliancy may become possible.

Acoustic-emission probing of line defects in silicon

The acoustic emission of donor silicon is studied. It is shown that the sound emission is due to the electric-current-stimulated motion of edge dislocations. When varying the current density flowing through a dislocated crystal, a correlation between the maximum of the acoustic-emission spectrum of the silicon and the velocity of the line-defect motion is revealed. By matching the theory with the experimental data, we estimate the diffusion constants of the atoms in the dislocation impurity atmosphere and the effective charge per atom in a dislocation line at different times (0.3–3 h) of the isothermal annealing (1273 K) of silicon samples.

The Uniformly Moving Edge Dislocation

The classical elastostatic displacement field has a biharmonic character conveniently expressed by the Papkovich-Neuber formula. This can be readily transformed into the superposition of two distinctive biharmonic components. These can be exhibited as the limits of uniformly moving wave fields, which are then coupled together to provide an acceptable resultant field. Our approach has been successfully applied to recover Easons', solution for a uniformly moving point force, and it is here applied to recover Eshelby's solution for a uniformly moving edge dislocation.

The Effect of Included Hydrogen on the Motion Parameters of Edge Dislocations in Palladium Membranes

The effect of included hydrogen on the mechanical and transport properties of palladium membranes is discussed. The dissolution of hydrogen in palladium changes the properties of the metal and can result in its hydrogen embrittlement and cracking, which depends on the motion parameters of dislocations. During the slipping motion of edge dislocations, hydrogen atoms affect the Peierls activation barrier. During the creeping motion, the included hydrogen affect the diffusivities of interstitial metal atoms. On the basis of the atomic model, the concentration dependence of the shear modulus, as well as the self-diffusivities and mass transfer coefficients of the included hydrogen and palladium atoms, is analyzed. The rates of elementary jumps of included atoms between interstitial sites are calculated according to the transition state model for imperfect reaction systems. An increase in the concentration of included hydrogen at the change in the phase state of the membrane under nonequilibrium conditions is shown to reduce the mobility of edge dislocations and promote the accumulation of internal stress.

Electronic effects of light impurities on edge dislocation motion in iron at T=0 K

The first principles discrete variational method is employed to study the effect of some light impurities, such as B, C, N and O, on the edge dislocation motion in bcc iron at T=0 K. The results of the simulation to the dislocation motion show that a dislocation line, when crossing an atom on the slip plane, must surmount an energy barrier, and that the impurity atoms trapped in the dislocation core can raise this energy barrier. This indicates the resistance of the lattice and light impurities to dislocation motion. According to the degree by which the energy barrier is raised, C has the strongest, O the weakest and B and N a medium resisting effect, which may explain the solid solute hardening of B, C and N in iron. B, C and N also have strong site-competition abilities against O in the dislocation core as they do in the grain boundary. The interactions between the impurities and their first nearest neighbor Fe atoms play an important role in the above effect, while the 2p–3d hybridization is the major part of the bonding.

Electrically stimulated movement of edge dislocations in silicon in the temperature range 300–450 K

The movement of edge dislocations and the related acoustic emission of Si (111) carrying a direct current of density 0.5−5×105 A/m2 in the [110] direction are studied in the temperature range T=300–450 K. It is shown that the basic mechanism of dislocation movement is the electric wind determining the magnitude of the effective charge (per atom of the dislocation line) Zeff=0.06 (n-Si) and −0.01 (p-Si). Matching theory with experimental data has made it possible to determine the main contribution of edge dislocations to the acoustic-emission response of the silicon samples under investigation. The characteristic transition frequencies of dislocations in n-and p-Si from one metastable state into another are found to be fmax=0.1–0.5 Hz. The numerical values of the diffusion coefficient for atoms in the dislocation impurity atmosphere are estimated as 3.2×10−18 m2/s (n-Si) and 1.5×10−18 m2/s (p-Si).

Atomic scale modelling of edge dislocation movement in the -Fe-Cu system

The aim of the present work is to investigate by molecular dynamics (MD) calculations the interaction between a moving edge dislocation in an -Fe crystal and a copper precipitate. In the absence of external stresses, two edge dislocations with the same slip plane and opposite Burgers vectors within a perfect -Fe crystal lattice are investigated. In agreement with Frank's rule, the movement of the dislocations under mutual attraction is found and attention is focused on the interaction between one of the dislocations and the Cu precipitate. The critical resolved shear stress of the Fe was calculated and the influence of different sizes of Cu precipitates on the dislocation mobility was studied. The pinning of the dislocation line at the Cu inclusion as derived from the atomistic modelling agrees with previously published continuum theoretical behaviour of pinned dislocations. Therefore, nanosimulation as a way to model precipitation hardening could be established as a useful scientific tool.

Radio-frequency paramagnetic resonance spectra, detected from dislocation displacement in NaCl single crystals

Results are reported here of a study of the resonance effect of a constant magnetic field and a variable magnetic field crossed with it on the rate of macroplastic deformation and motion of edge dislocations in NaCl crystals. The frequencies of the variable magnetic field at which the maximum variations in the plasticity of the crystals are observed correspond to the resonant frequencies for transitions between the Zeeman sublevels in paramagnetic complexes of point defects and complexes consisting of a point defect and a dislocation. Analysis of the radio-frequency spectra obtained enabled us to establish the role of intercrystal reactions in the formation of the mechanical properties of the crystals.

Kinematics of edge dislocations. I. Involutive distributions of local slip planes

The geometry of continuous distributions of dislocations and secondary point defects created by these distributions is considered. Particularly, the dependence of a distribution of dislocations on the existence of secondary point defects is modeled by treating dislocations as those located in a time-dependent Riemannian material space describing, in a continuous limit, the influence of these point defects on metric properties of a crystal structure. The notions of local glide systems and involutive distributions of local slip planes are introduced in order to describe, in terms of differential geometry, some aspects of the kinematics of the motion of edge dislocations. The analysis leads, among others, to the definition of a class of distributions of dislocations with a distinguished involutive distribution of local slip planes and such that a formula of mesoscale character describing the influence of edge dislocations on the mean curvature of glide surfaces is valid.

Brownian Motion of Dislocations in Thin Films

The motion of edge dislocations in a single monolayer film of Cu on Ru(0001) was studied by time-resolved scanning tunneling microscopy. The dislocations were observed to make rapid 1D random walks in the film. This dislocation motion is attributed to the equilibrium thermal exchange of atoms between the solid film and the adatom gas covering the film. These results highlight a fundamental difference between the dynamics of dislocations in thin films and the bulk, which is in principle important in understanding the mechanical properties of thin films. {copyright} {ital 1997} {ital The American Physical Society}

Shielding effects and residual stresses at cleavage due to pre-existing dislocations

The motion of pre-existing edge dislocations in an infinite linear elastic body is studied at initiation of crack growth and at quasi-static steady-state crack growth. Dislocation nucleation is assumed not to occur. Thus, the study concerns only dislocations that are present in the virgin material. A dislocation is assumed to glide if its driving force exceeds a critical value. Changes in dislocation density, crack tip shielding and residual stresses are obtained. The shielding of a stationary crack tip is found to be small compared with the shielding of a growing crack tip. At steady-state the residual stresses far behind the crack tip are tensile near the crack, decreasing to zero at a certain distance from the crack plane. It is shown that the shielding due to pre-existing dislocations, e.g., for cleavage in α-iron crystals may be considerable.

Slip systems and dislocation emission from crack tips in single crystal TiC at low temperatures

Low temperature (20–900°C) plastic deformation in TiC 0.91 single crystals has been studied using microindentations on (111), (001) and (110) surfaces, the dislocation structures around microindents being characterized by transmission electron microscopy (TEM). Deformation occurs primarily by {111}〈11̄0〉 and {110}〈11̄0〉 slip, with the favored slip system determined by crystal orientation. Indentations below 300°C produced distinct dislocation half loops-hexagonal loops arising from {111} slip and elongated loops from {110} slip. At 500°C, much more extensive plastic deformation occurred, accomplished mainly by the motion of edge dislocations from these same systems. The dislocation configurations suggest a relatively high mobility of edge segments and a large Peierls stress for screw dislocations. Thermal activation apparently increases the mobility of screw segments, and results in dislocation structures containing mixed dislocations with no preferred orientation; this signals the onset of the brittle-ductile transition between 700 and 900°C. Cleavage cracks around indents on {111} and {110} surfaces introduced below 500°C, but not those on {001}, arrested with dislocation emission at the crack tips. The emitted dislocations were coplanar dislocation half loops, arising from {001}〈110〉 slip, and resulted from mode II or mode III loading of the cleavage crack. The local mode II and mode III stress intensity factors must have been sufficiently high to activate {001} slip, even through this slip system has not, to date, been reported in macroscopic tests.

Mechanical behavior of aluminum deformed under hot-working conditions

The stress-strain behavior of aluminum 3–9 purity deformed at elevated temperatures has been analyzed on a rational basis. Emphasis has been given to the analysis of the curves corresponding to typical deformation conditions of interest for hot rolling of commercial aluminum alloys. The strainhardening behavior has been modeled assuming the validity of the typical saturation exponential equation earlier proposed by Voce. The temperature and strain dependence of the flow stress parameters involved in such an equation has been introduced by means of a model based on the power law relationship, where the stress-sensitivity exponent of the strain rate is considered to be temperature dependent. The strong temperature dependence of this parameter precluded the use of the exponential relationship expressed in terms of the Zener-Hollomon parameter. Therefore, a different temperature-compensated strain rate parameter similar to the MacGregor-Fisher parameter has been employed following the earlier developments put forward by Kocks. Thus, a satisfactory correlation of the flow stress parameters with the deformation conditions has been obtained. The final constitutive equation derived provides a satisfactory reproduction of the experimental values of the flow stress and follows quite closely the strain-hardening behavior. The mean activation energy determined by the different models confirmed the predominance of both climb of edge dislocation segments and motion of jogged screw dislocations as the rate-controlling mechanisms during deformation of this material under hot-working conditions. The use of a constitutive equation which expresses the flow stress of the material in terms of the applied strain, rate of straining, and deformation temperature to calculate the power dissipation efficiency of the material(η) deformed under hot-rolling conditions has shown that it could be strongly strain dependent, particularly toward the end of the rolling schedule. Hence, it has been concluded that the calculation of both the power co-content as defined in dynamic material modeling (DMM) and its maximum value, taking into consideration the constitutive equation previously developed, represents a more plausible and soundly based approach toward the determination of η.