Straight Screw Dislocations Research Articles

The gauge theory of dislocations: A nonuniformly moving screw dislocation

We investigate the nonuniform motion of a straight screw dislocation in infinite media in the framework of the translational gauge theory of dislocations. The equations of motion are derived for an arbitrarily moving screw dislocation. The fields of the elastic velocity, elastic distortion, dislocation density and dislocation current surrounding the arbitrarily moving screw dislocation are derived explicitly in the form of integral representations. We calculate the radiation fields and the fields depending on the dislocation velocities.

Kinetics of dislocations in pure Fe. Part I. In situ straining experiments at room temperature

In situ straining experiments have been carried out in pure Fe, in order to determine the geometry and the kinetics of dislocation glide at room temperature. Straight screw dislocations glide slowly in {1 1 0} elemental slip planes, at a velocity proportional to their length, whereas curved non-screw parts are highly mobile. The exact loop shape can yield the local stress as well as the difference of core energy between pure screw and near-screw orientations. The velocity–stress dependence of screws has been measured at the scale of a single dislocation source, and compared with macroscopic activation areas. The results are discussed in terms of the kink-pair mechanism.

Vibrational properties of straight dislocations in bcc and fcc metals within the harmonic approximation

We calculate the vibrational spectra of straight screw and edge dislocations in several body-centered cubic (bcc) (Mo and Fe) and face-centered cubic (fcc) (Cu and Al) metals within the harmonic approximation. We take advantage of the translational symmetry of straight dislocations to efficiently calculate their phonon eigenstates in the harmonic limit. This allows us to calculate the low-temperature contribution of straight screw and edge dislocations to the heat capacity of each respective metal, and show that the dominant temperature dependence below 5 K is linear. Comparison with heat capacity measurements of heavily cold-worked Cu reveals very good agreement with our calculations. At higher temperatures, the contribution from the non-linear terms becomes significant. As a result, maxima in the straight dislocation heat capacities are observed in the temperature range from 9% to 16% of the Debye temperature. We investigate the appearance of localized and resonance peaks in the vibrational spectra induced by dislocations, and study in detail their spatial spread around the dislocation cores by projecting vibrational eigenstates onto individual atoms. We study the deviation of these atomic-level vibrational free energies from that of the perfect crystal as a function of distance to the dislocation cores, and establish that, similar to the dislocation energy, the vibrational free energy of an isolated dislocation behaves logarithmically in the long-range limit. Finally, we obtain vibrational spectra for propagating waves along the dislocation line and find that the dispersion for these waves is consistent with the notion of kink formation and motion for screw dislocations.

Generation of c-component edge dislocations in α-zirconium during neutron irradiation – An atomistic study

The nucleation and multiplication of c-component edge dislocation segments during neutron irradiation in zirconium and its alloys is known to have important consequences to their in-reactor deformation behavior. Although there are ample experimental observations showing the close correlation between the edge-type and the screw-type of c-dislocations, the relation between them is unclear. In this paper, we performed atomistic study of the interaction between a [0 0 0 1] screw dislocation and a vacancy cluster in the form of a platelet on the basal plane. The local minimum-energy configuration was obtained using the conjugate-gradient method, with boundary relaxation achieved via a modified Green’s function method. Under stress-free conditions, the vacancy clusters maintained their cavity nature. With a [0 0 0 1] screw dislocation in the close neighborhood, vacancy clusters containing more than 23 vacancies collapse into faulted vacancy loops. Interaction at even closer range leads to the disappearance of the vacancy cluster and the development of an edge component on the originally straight screw dislocation in the form of a helical line. The implications of these findings are discussed in relation to the experimentally observed behavior of growth acceleration in zirconium and its alloys.

Evidence from numerical modelling for 3D spreading of [001] screw dislocations in Mg2SiO4 forsterite

Computer simulations have previously been used to derive the atomic scale properties of the cores of screw dislocations in Mg2SiO4 forsterite by direct calculation using parameterized potentials and via the Peierls–Nabarro model using density functional theory. We show that, for the [001] screw dislocation, the parameterized potentials reproduce key features of generalized stacking fault energies when compared to the density functional theory results, but that the predicted structure of the dislocation core differs between direct simulation and the Peierls–Nabarro model. The [001] screw dislocation is shown to exhibit a low-energy non-planar core. It is suggested that for this dislocation to move its core may need to change structure and form a high-energy planar structure similar to that derived from the Peierls–Nabarro model. This could lead to dislocation motion via an unlocking–locking mechanism and explain the common experimental observation of long straight screw dislocation segments in deformed olivine.

Atomistic study of ordinary screw dislocations in single-phase and lamellar γ-TiAl

Computer simulation of the core structure and glide of ordinary screw dislocations in single-phase L10 TiAl and in two lamellae forming a twin γ/γ-interface has been performed using recently constructed Bond-Order Potentials (BOPs). BOPs represent a semi-empirical, numerically efficient scheme that works within the orthogonal tight-binding approximation and is able to capture the directionality of bonding. We have studied dislocation glide in perfect L10 TiAl and along a twin interface, transmission of an ordinary screw dislocation between lamellae, and the core structure, mobility and detachment of an interfacial screw dislocation from a twin boundary under applied shear stresses in directions parallel and perpendicular to a (111) plane. Our results show that the glide of ordinary straight screw dislocations under applied stresses in L10 TiAl is characterized by zigzag movement on two conjugated {111} planes. The non-planar core of the screw dislocation is distorted asymmetrically when the elastic centre of the dislocation is close to a twin γ/γ-interface and the dislocation moves on one of the (111) planes, depending on the magnitude of the corresponding Schmid factor. Ordinary dislocations become ordinary interfacial dislocations when they reach the interface. With increasing applied stress they can glide into the adjacent lamella, leaving no remnant interfacial dislocation.

Work hardening in Fe–Al alloys

Work hardening in polycrystalline Fe–Al alloys has been examined for alloys containing from nearly no Al up to about 40 at.% Al. A sharp maximum in work hardening is seen for alloys containing 26–30% Al. Examination of dislocation structures with increasing Al content over the region of the maximum shows that the most important change, apart from the formation of superdislocation dipoles instead of single dislocation dipoles, is the predominance of straight screw dislocations and the formation of sessile dislocation segments by reactions of mobile dislocations. The peak in work hardening rate coincides with increased elastic anisotropy, but this is believed to reflect the importance of core/Peierls effects rather than to be a direct cause of high work hardening.

Transmission of a screw dislocation across a coherent, slipping interface

A Peierls model is used to study the role of interfacial sliding during dislocation transmission. A straight screw dislocation parallel to a bimaterial interface is considered, with incoming and outgoing slip planes that are continuous and coplanar. Interfacial sliding is predicted to increase the critical applied shear γ crit of interfaces for transmission. A simple explanation is that sliding delocalizes the dislocation core within the interface, thereby creating a larger, more abrupt fluctuation in dislocation line energy during transmission. Interfacial sliding and dislocation trapping are promoted by weak interfacial bonding, which is characterized primarily by small interfacial unstable stacking fault energy. The results are consistent with atomistic documenting showing dislocation trapping at interfaces.

Molecular dynamics study of solute strengthening in Al/Mg alloys

The strengthening of Al by Mg solute atoms is investigated using molecular dynamics (MD) studies of single dislocations moving through a field of randomly placed solutes. The MD method permits explicit treatment of “core” effects, dislocation pinning and deceleration, and dislocation unpinning by thermal activation, all under an applied load. Choice of an appropriate MD simulation cell size is assessed using analytic concepts developed by Labusch. The interaction energy of a single Mg atom with straight edge and screw dislocations is computed and compared with continuum models. Using the single Mg energies, a one-dimensional energy landscape for the motion of a straight edge dislocation through a random field of Mg solutes is computed. The minima in this landscape match well with those found in the MD simulations at zero temperature. The stress to unpin a straight edge dislocation trapped in a local energy minimum generated by the solutes is then predicted semi-analytically using the energy landscape, and good agreement is obtained with the MD results. At temperatures of 300 and 500 K, the thermally activated rate of unpinning vs. stress and temperature is calculated semi-analytically, and agreement with the full MD results is again obtained with the fitting of a single attempt frequency in a transition state model. The agreement of the semi-analytical models provides a basis for calculating yield stress vs. strain rate and temperature, resulting from statistical pinning, for the case of non-interacting dislocations on a single slip system, and for extending the analysis to study dynamic strain aging effects resulting from diffusion of Mg atoms around a pinned dislocation.

Dislocations in second strain gradient elasticity

A second strain gradient elasticity theory is proposed based on first and second gradients of the strain tensor. Such a theory is an extension of first strain gradient elasticity with double stresses. In particular, the strain energy depends on the strain tensor and on the first and second gradient terms of it. Using a simplified but straightforward version of this gradient theory, we can connect it with a static version of Eringen’s nonlocal elasticity. For the first time, it is used to study a screw dislocation and an edge dislocation in second strain gradient elasticity. By means of this second gradient theory it is possible to eliminate both strain and stress singularities. Another important result is that we obtain nonsingular expressions for the force stresses, double stresses and triple stresses produced by a straight screw dislocation and a straight edge dislocation. The components of the force stresses and of the triple stresses have maximum values near the dislocation line and are zero there. On the other hand, the double stresses have maximum values at the dislocation line. The main feature is that it is possible to eliminate all unphysical singularities of physical fields, e.g., dislocation density tensor and elastic bend-twist tensor which are still singular in the first strain gradient elasticity.

Dislocation Structure for Ambient Temperature Creep in Titanium Metal

The primary creep behavior at ambient temperature of typical h.c.p., b.c.c. and f.c.c. metals and alloys of annealed state was surveyed and the deformation mechanism of CP-Ti was discussed through transmission electron microscopy. Only h.c.p. metals and alloys demonstrated significant creep at ambient temperature. Arrays of straight screw dislocations of b=1/2<2110> and <2110> direction were observed in the crept CP-Ti.

Mode III Interfacial Edge Crack in a Magnetoelectroelastic Bimaterial

This paper deals with a Mode III interfacial edge crack in a magnetoelectroelastic bimaterial subjected to line singularities such as an out-of-plane line force, a line electric charge, a line magnetic charge and a straight screw dislocation. The surfaces (including crack surfaces) of the bimateral are assumed to be electrically open and magnetically closed. The closed-form analytical solution to the problem is obtained by employing the complex variable approach in conjunction with the conformal mapping technique. The intensity factors of stress, electric displacement and magnetic induction are given explicitly. The obtained results can be used as the Green's function to solve more complicated problems.

Screw dislocation in two dissimilar piezoelectric layers

AbstractThe elastic and electrical fields produced by a straight screw dislocation in two dissimilar piezoelectric layers are derived through the use of conformal mapping technique, where the solution for a semi‐infinite piezoelectric bimaterial is used as a base. The expression for the image force acting on the dislocation is given explicitly. The equilibrium position of the dislocation is further determined by letting the image force be equal to zero. In the case where one of the two layers is pure elastic, the numerical results for the image force are provided to illustrate the influence of piezoelectric effect on the behavior of the dislocation. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Incorporation of γ-surface to phase field model of dislocations: simulating dislocation dissociation in fcc crystals

Phase field method has become an attractive alternative to study dislocations of arbitrary configurations. Recently the model has been generalized for dislocation nodal reactions and network formation. Within the same framework, we study dissociation of various dislocation configurations into Shockley partials by incorporating directly γ-surface data from ab initio calculations into the crystalline energy of the phase field model. The model is first validated against the generalized P–N model for dissociation of straight edge and screw dislocations in Al and Pd using the same sets of γ-surface data and elastic constants. Then dissociation of dislocation nodes and a bent dislocation gliding on two intersecting {1 1 1} planes are investigated. The former leads to either an extended or a contracted node, depending on the directions of the sense vectors of the unit dislocations that join the node, while the latter leads to a stair-rod dislocation at the intersection of the two planes. With reliable ab initio γ-surface data being calculated routinely by first principles, the extended phase field model could provide a flexible and realistic treatment of dissociation of dislocations of arbitrary configuration, interactions among extended dislocations, and creation and annihilation of various planar faults.

A nonplanar Peierls–Nabarro model and its application to dislocation cross-slip

A novel semidiscrete Peierls–Nabarro model is introduced which can be used to study dislocation spreading at more than one slip plane, such as dislocation cross-slip and junctions. Within this essentially continuum model, the nonlinearity which arises from the atomic interaction across the slip plane is dealt with atomistic and/or ab initio calculations. As an example, we study the dislocation cross-slip and the constriction process in two contrasting fcc metals, Al and Ag. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with the screw dislocation in Ag, which splits into two partials, and thus cannot cross-slip without first being constricted. The response of the dislocations to an external stress is examined in detail. The dislocation constriction energy and the critical stress for cross-slip are determined, and, from the latter, we estimate the cross-slip energy barrier for the straight screw dislocations.

On stress assisted dislocation constriction and cross-slip

A novel semidiscrete Peierls–Nabarro model is introduced which can be used to study dislocation spreading at more than one slip plane, such as dislocation cross-slip and junctions. The strength of the model, when combined with an atomistic simulation for dislocation core properties, is without suffering from the uncertainties associated with empirical potentials. Therefore, this method is particularly useful in providing insight into alloy design when empirical potentials are not available or not reliable for such multi-element systems. The model is applied to study the external stress assisted dislocation cross-slip and constriction process in two fcc metals, Al and Ag, exhibiting different deformation properties. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, where the screw dislocation splits into two partials that cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. The dislocation constriction energy and the critical stress for cross-slip are determined, and from the latter, we estimate the cross-slip energy barrier for straight screw dislocations.

Deformation behaviour of duplex stainless steel during industrial hot rolling

Industrially processed duplex stainless steel sheet was investigated after the reheating, the roughing mill and the finishing rolling. Light optical microscopy revealed that the cast structure that existed before rolling was removed and changed into a banded microstructure. During the process, the ferrite-austenite volume fraction ratio changed from 72 %a + 28 %y to 48 %a + 52 %y. The microhardness was measured for both phases after each process step. Texture measurements were executed by means of the electron backscattering diffraction technique (EBSD). These measurements revealed that extensive static recrystallisation of the austenite occurred during the roughing but that recrystallisation was inhibited during the finishing. Transmission electron microscopy (TEM) on the finish rolled material indicated that the ferrite softened efficiently by extended dynamic recovery. The dislocations in ferrite grains with rotated cube orientation were often found to be straight screw dislocations which were inclined 55° to the surface of the sheet. The importance of the partitioning of the alloying elements and the strain partitioning on the deformation behaviour is highlighted.

Dislocation constriction and cross-slip: Anab initiostudy

A novel model based on the Peierls framework of dislocations is developed. The new theory can deal with a dislocation spreading at more than one slip planes. As an example, we study dislocation cross-slip and constriction process of two fcc metals, Al and Ag. The energetic parameters entering the model are determined from ab initio calculations. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, which splits into partials and cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. We determine dislocation constriction energy and critical stress for cross-slip, and from the latter, we estimate the cross-slip energy barrier for the straight screw dislocations.

Elastic Interaction of Micropipes in Crystals

The stress field, strain energy and interaction force are calculated for an isolated pair of straight parallel screw dislocations, one or both of which is (are) associated with (a) micropipe(s). The effect of the attraction of two dislocated micropipes (or a dislocated micropipe and a full-core screw dislocation) with Burgers vectors of the same sign is examined in detail. An analytical expression for the critical distance below which a dislocated micropipe attracts a full-core screw dislocation is found. It is shown that two parallel dislocated micropipes with the same signs of the Burgers vectors may attract each other if the distance between the micropipes is small enough and the ratios of the micropipe radii and the Burgers vector magnitudes are sufficiently different. The stress field and strain energy of a dislocated micropipe near a planar free surface and the force of the interaction between the micropipe and the free surface are also found.

A TEM investigation on indentation plastic zones in Ni 3Al(Cr,B) single crystals

Nanoindentation has been carried out on (111) single crystals of Ni 3Al with the maximum applied load ranging from 800 to 8000 μN. The indentation plasticity fields are found to consist of two regions, namely, a core with a very high dislocation density and a surrounding region where the dislocation density is much lower. In the zone with lower dislocation density, individual dislocations were discernible, and three sets of dislocations, with Burgers vector of the 1 1 ̄ 0 type and parallel to the sample surface, were identified in all specimens. The dislocation segments were curvy at small loads but long and straight screw dislocations appeared at large loads. Measurements of the radii of the plasticity zones from TEM images indicate that the core and the surrounding low dislocation density zone did not evolve in a self-similar manner with increasing load. From the dislocation structure observed just after the pop-in in the load–displacement curve, the strain rate in the indent core during pop-in is estimated to be about 170 s −1. The nominal hardness calculated using the Oliver–Pharr scheme exhibits a sharp and negative dependence with respect to load, with the hardness dropping from ~12 GPa at 800 μN to about 6 GPa at 8000 μN. The value of P/ πc 2, where P is the load and c the radius of the surrounding dislocation zone, is however fairly constant with respect to load, with a variation of only about 10% in the same load range. The yield stress Y calculated from the equation Y=1.5 P/ πc 2 is about 356±32 MPa. These results suggest that, while nanohardness can still be expected to depend critically on the yield stress, there is an additional functional relationship that causes the hardness to vary with the indent size in the submicron regime.