Dynamic properties of edge dislocations decorated by interstitial loops in α-iron and copper

Clusters of self-interstitial atoms (SIAs) in the form of parallel crowdions are created directly in high-energy displacement cascades produced in metals by neutron irradiation. They are equivalent to small perfect dislocation loops and, in isolation in pure metals, undergo fast thermally-activated glide in the direction of their Burgers vector. Their strain field and ability to glide allows long-range interaction with other extended defects. Indeed, dislocations decorated by dislocation loops are commonly observed after neutron irradiation. Dislocations gliding under applied stress also encounter these mobile defects. These effects influence mechanical properties and require further investigation. This paper presents results from an atomic-scale study of copper and α-iron at either 0?K or 300?K. Loop drag and breakaway effects are investigated for an edge dislocation under applied stress interacting with a row of SIA loops below its glide plane. The maximum speed at which a loop is dragged is lower in copper than iron, and the applied stress at which this occurs is also lower. These differences in the dynamics of cluster-dislocation interaction are determined by the atomic structure of the defects and cannot be investigated by continuum treatment.     

Two different types of shear-deformation behaviour in Au–Cu multilayers

Localised shear deformation of a material is usually identified as a particular feature of deformation inhomogeneity. Here, we show two different types of shear deformation-behaviour that occurred in Au–Cu multilayers subjected to microindentation load, namely, a cooperative-layer-buckling-induced shear banding in a nanoscale multilayer and a direct localised shearing across a layer interface along a shear plane in a submicron-scale multilayer. Theoretical analysis indicates that the formation of the two different types of shear deformation in the multilayers depends on a competition between the dislocation-pile-up-induced stress concentration at the layer interface and the barrier strength of the layer interface for glissile dislocation transmission.     

The displacement field of a rectangular Volterra dislocation loop

The displacement field of a rectangular Volterra dislocation loop having three non-zero Burgers vector components is obtained in an analytical closed form. The solution is obtained via integrating the Burgers equation for the displacement field of any closed dislocation curve and is expressed in a relatively compact form. The current solution has utility in a number of problems including dislocation-particle interaction problems, where the boundary condition involved imposes certain restrictions on the displacements in the medium, and modelling of cracks of arbitrary shapes. The solution is also useful in benchmarking newly emerging dislocation dynamics codes which discretize a curved dislocation line in some form or another. Several verification steps of the solution correctness are made including a comparison with the displacement and stress fields of a circular Volterra dislocation loop of equal Burgers vector and comparable size.     

Homogeneous nucleation of dislocation loops under stress in perfect crystals

We present an analysis and results on the homogeneous nucleation of a dislocation loop under stress in a perfect crystal. By using a variational boundary integral method in the Peierls-Nabarro framework, we have determined the saddle-point configurations of embryonic dislocation loops and their associated activation energies under stress levels up to the ideal shear strength. The high-energy barriers under the usual levels of applied shear stresses, differing markedly from the ideal shear strength, confirm the widely held view that thermal motion should play no role in such nucleation. The result provides means for more definitive solutions of fundamental problems involving homogeneous nucleation of dislocation loops and has significant implications for models based on the mechanism of nucleation of dislocations from a perfect crystal.     

Evidence of the climb motion of a Shockley partial during glide at room temperature

A dissociated dislocation introduced by compression at room temperature in a Ag-15at.%Al alloy was studied comprehensively by the weak-beam method. In addition to the two Shockley partials of the dissociated dislocation, faint contrasts were observed near the Shockley partial with pure edge orientation. Contrast experiment was carried out on the faint contrast, and we conclude that this is evidence for the interaction between an edge-orientated Shockley partial moving under the action of an applied stress and vacancies at room temperature.     

Interaction of a dislocation with an elliptical hole in icosahedral quasicrystals

The interaction between a dislocation and an elliptical hole in icosahedral quasicrystals is considered. An explicit expression for the complex potential is derived using the extended Stroh formalism. Based on the conformal mapping method and a perturbation technique, closed-form solutions are obtained. The field intensity factors at a crack tip and the image forces on the dislocation arising from the crack are calculated. The effects of phonon–phason elastic coupling on the mechanical behavior are also observed.     

Phase field microelasticity theory of dislocation dynamics in a polycrystal: Model and three-dimensional simulations

A three-dimensional multidislocation system in a polycrystal under applied stress is treated as a particular case of the phase field microelasticity theory of multivariant stress-induced martensitic transformations in polycrystals. This approach reduces the problem of the evolution of a dislocation system to a solution of the nonlinear integrodifferential Ginzburg-Landau equation. In this formalism, the elastic interaction between dislocations and the elastic coupling between grains are taken into consideration through exact analytical solution of the elasticity problem. The dislocation reactions, such as multiplication and annihilation, are taken into account automatically. The dislocations are 'free' to choose the optimal evolution path. Examples of three-dimensional computer simulations are considered.     

Dislocation formation in the partially coherent interfaces of an embedded layer in a semi-infinite matrix

The formation of two misfit edge dislocations is theoretically investigated in the interfaces of a layer embedded in a semi-infinite matrix. Assuming the matrix–layer interfaces are partially coherent, the energy variation resulting from the formation of the dislocations from the lateral free surface of the structure has been determined in the shearing stress field due to the partial misfit. The mechanical stability of the structure is analysed with respect to the dislocation formation as a function of the size of the coherent region of the interface and the misfit strain.     

Irradiation-enhanced twin boundary migration in BCC Fe

The effects of irradiation on twin boundary migration in BCC Fe are studied by atomistic simulations. It is found that under the applied shear strain–stress, thermal spikes may create twinning dislocation loops (TDLs) at twin boundaries, so triggering twinning. Irradiation-generated clusters of point defect at twin boundaries may act as sources to nucleate TDLs. When a vacancy loop intersects with a twin boundary, the critical stress to activate a TDL is less than half of that required for a defect-free twin boundary.     

Continuum and discrete models of dislocation pile-ups. II. Pile-up of screw dislocations at the interface in a bimetallic solid

The methodology developed in the precursor to this paper is used to find the positions of n screw dislocations in a pile-up against an interface bonding two crystalline solids. The pile-up is caused by a constant applied stress and, as n →∞, the dislocations are located with sufficient accuracy to predict the large but finite stress distribution at the interface. Such a prediction is impossible using a conventional continuum dislocation density.     

Thermally activated plastic glide

The two main theories of thermally activated plastic glide in ductile crystals, that of Becker and that of Mott and Nabarro, differ in their predictions of the stress exponent of the activation energy. But when the Becker theory is applied to the problem of the Mott-Nabarro theory, that is the overcoming of a single localized obstacle by a short segment of dislocation line, and account is taken of the stress relaxation brought about by the movement of the segment up to the obstacle, this modified Becker theory gives the same stress exponent as the Mott- Nabarro theory. The realistic situation, however, is that of long dislocation lines making their way through a forest of obstacles. In this case the interactions between different segments of these lines considerably modify the problem. They lead to load shedding, mechanical activation and large glide avalanches. Under these conditions the original form of the Becker theory, with an unmodified stress exponent, is applicable.     

Screw dislocation in functionally graded magnetoelectroelastic solids

A screw dislocation in a functionally graded magnetoelectroelastic material is investigated. The material properties exponentially changing along both x and y directions are considered and the mechanical–electric–magnetic coupling is discussed. Closed-form expressions for the mechanical, electric and magnetic components are derived using the general stress function method. The solutions can be applied as a fundamental result and reduced into the classic and piezoelectric cases. The study puts forth a direct way for screw dislocation analysis in inhomogeneous structures with multifield coupling.     

Analytic model for the line tension of a bowing dislocation segment

The resistance of a dislocation to bowing under stress governs the strength of the gamut of metallic material systems. This resistance is commonly referred to as the dislocation line tension (Γ) and is employed ubiquitously within continuum scale models of metal plasticity. Despite its significance, a unifying model for the line tension of a bowing dislocation segment, which has been analytically derived and independently reproduces simulation results, remains lacking. Here, we report a model for Γ of a curved, semicircular bowing dislocation segment. Upon applying our model to the operative stress of a Frank–Read dislocation source, we predict a prelogarithmic scaling of the Frank–Read source strength in agreement with existing simulation results. Moreover, in the limit of infinitesimal bowout we predict a prelogarithmic line tension factor which also agrees with theoretical analyses. Our model provides insight into the evolution of an arbitrarily oriented, stressed dislocation segment without resorting to numerical methods.     

Prediction of the configuration of a ‘Bardeen–Herring’ dislocation climb source under dynamic conditions

Abstract

The sequence of events during the operation of a ‘Bardeen-Herring’ climb source is predicted by using a numerical method in which the dislocation is modelled as a set of finite straight elements. The configuration is determined as a function of the applied stress and an approximate analytical treatment is presented which describes the time dependence of the source operation.     

Atomistic calculation of the interaction between an edge dislocation and a free surface

By using molecular statics, we compute the variation in the excess energy associated with the gradual approach of an edge dislocation towards the free surface of a crystal. The calculations rely on a phenomenological potential adapted to aluminium and an appropriate constraint procedure that allows investigations of both the extended and the perfect configurations of the dislocation core. Thereby, an estimation of the energy required for the introduction of a dislocation in a thin film is obtained.     

The orientation and temperature dependences of dislocation velocity in Ni 3 Al single crystals

The average velocities of screw dislocations in Ni 3 Al single crystals have been directly measured as a function of resolved shear stress (RSS) and orientation in the temperature domain of the flow stress anomaly using the etch-pit technique. The velocity was found to be extremely sensitive to the RSS in all cases. In contrast with ordinary metals, the screw dislocation velocities in Ni 3 Al show anomalous behaviour; under a constant RSS, the velocities decrease dramatically with increasing temperature. Furthermore, the velocities and the tension-compression asymmetry of the velocities depend on the orientation of applied stress.     

Modelling of irradiation-induced hardening in metals using dislocation dynamics

A new simulation technique (three-dimensional dislocation dynamics) enabling the capture of a hardening effect in metals due to irradiation is reported. When bombarded with high-energy particles, metals accrue internal damage. In irradiated Pd, for example, damage takes the form of interstitial loops. Such loops are nano-sized and typically have a high number density. The stress field of a loop is given from dislocation theory. It is shown here the hardening is due to the elastic interaction of gliding dislocations with a high number of spatially dispersed interstitial loops. Results are found to correlate well with experiments.     

A microscopic theory of Andrade creep

A microscopic theory is developed which gives the exact expression for Andrade creep when work hardening is small, as observed in practice. The microscopic model is that of the forest theory of work hardening and in which glide dislocation lines require supplementation of the applied stress, in order to cut their way through the forest obstacles. The loads shed on neighbours when individual obstacles give way play a major role in this, and thermal activation releases blocked avalanches of yielding to enable them to continue to grow.     

Creep behaviour of ice single crystals loaded in torsion explained by dislocation cross-slip

Torsion creep experiments are carried out in order to understand the physics of ice plasticity. A dislocation spreading mechanism based on double cross-slip of basal dislocations is proposed to explain the strong plastic anisotropy and the power law relationship between stress and strain rates. The scenario is tested using three-dimensional dislocation dynamics simulations. Numerical investigations give a stress exponent n?=?2.3 in agreement with experimental measurements. This dislocation spreading mechanism sheds a new light on the interpretation of former experimental observations.     

Derivation of the antiphase-boundary energy of L1 2 long-range-ordered precipitates from measurements of the minimum size of stable dislocation loops

In an alloy that is strengthened by long-range-ordered particles, a matrix dislocation generates an antiphase boundary (APB) when it cuts through such a particle. The specific energy n APB of this APB has been measured for two fcc alloys with spherical coherent L12 ordered particles: an Al-7.5at.%Li-alloy and the commercial Ni-base superalloy Nimonic PE16. Peak-aged specimens have been deformed and Orowan loops searched for using transmission electron microscopy. n APB has been derived from the radii of the smallest dislocation loops which have been left behind around particles. Such an approach had been used previously, for example, by Raynor and Silcock and by Nembach et al . Here an improved evaluation method has been applied; it is based on the results of computer simulations of the equilibrium configurations of dislocation loops.