Discrete dislocation dynamics: an important recent break-through in the modelling of dislocation collective behaviour

Recent results obtained by 3D discrete Dislocation Dynamics (DD) simulations are reviewed. Firstly, in the case of fatigued AISI 316L stainless steel, it is shown how DD simulations can both explain the formation of persistent slip bands and give a criterion for crack initiation. The same study is performed in the case of precipitate hardened metals where the precipitate size plays a crucial role. Secondly, we show how molecular dynamics (MD) simulations can feed the DD simulations for two applications. The first concerns the modelling of BCC Fe for which the dislocation mobility is derived from MD simulations. The second considers the modelling of irradiated stainless steels (FCC), where MD is used to define the local rules of interactions between dislocations and Frank loops. To cite this article: M.C. Fivel, C. R. Physique 9 (2008).     

Nodal effects in dislocation mobility

We show that, contrary to the prevailing perception, dislocations can become more mobile by zipping together to form junctions. In a series of direct atomistic simulations, the critical stress to move a junction network in a [110] plane of bcc molybdenum is found to be always smaller ( approximately 50%) than that required to move isolated dislocations. Our data support a previously proposed hypothesis about the nature of anomalous slip in bcc transition metals, yet offer a different atomistic mechanism for conservative motion of screw dislocation networks. The same data suggest a hierarchy of motion mechanisms in which lower-dimensional crystal imperfections control the rate of sliding along the low-angle twist boundaries.     

On the dislocation image in the Bragg Case

In the Bragg case of X-ray diffraction the image of the dislocations with large screw component is examined. It is shown that the traditional white-black contrast is completed with an additional narrow black contrast. The experiments were performed by means of the double crystal spectrometer. The CuK radiation and silicon single crystals were used.     

Strongly non-local modelling of dislocation transport and pile-up

The purpose of this work is the continuum modelling of transport and pile-up of infinite discrete dislocation walls driven by non-local interaction and external loading. To this end, the underlying model for dislocation wall interaction is based on the non-singular Peierls–Nabarro (PN) model for the dislocation stress field. For simplicity, attention is restricted to walls consisting of single-sign dislocations and to continuous wall distributions on a single glide plane. In this context, the influence of strongly non-local (SNL; long-range) interaction, and its approximation as weakly non-local (WNL; short-range) are studied in the context of interaction- and external-load-driven wall pile-up at a boundary. The pile-up boundary is modelled via a spatially dependent dislocation mobility which decreases to zero at the boundary. The pile-up behaviour predicted by the current SNL-based continuous wall distribution modelling is consistent with that predicted by discrete wall distribution modelling. Both deviate substantially from the pile-up behaviour predicted by WNL-based continuous wall distribution modelling. As such, it is clearly essential to account in continuum models for the intrinsic SNL character of the interaction between same-sign dislocations ‘close’ to the boundary. Gradient-based WNL ‘approximation’ of this interaction is not justified.     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Formation of the image of an edge dislocation in an absorbing crystal

The specific features of the formation of a diffraction image of a single edge dislocation in the case where the defect region can be located at different points of the scattering triangle are investigated by computer simlation and experimentally. The dislocation images are experimentally obtained at different wavelengths and for different reflections. The diffraction geometry in which the dislocation line is perpendicular to the sample surface and the Burgers vector is parallel or perpendicular to the reciprocal lattice vector is studied. From analysis of the experimental and theoretical images, inferences are made regarding the image symmetry, as well as the angular resolution and the sensitivity of section topography to the formation of the dislocation image. Special attention is focused on the dependence of the image contrast and the image size on the radiation wavelength, the magnitude of the reciprocal lattice vector, and the interference absorption.     

Three-dimensional effects in the modelling of ICPTs

In this paper, we numerically investigate the 3-D effects of different flow operating conditions and of complete or simplified treatments of the electromagnetic field on the characteristics of Ar and Ar/N₂ discharges in inductively coupled plasma torches working at atmospheric pressure. Simulations are performed by means of the commercial code FLUENT suitably customized to solve the electromagnetic field equations in the frame of an extended grid model. Steady state continuity, momentum and energy equations are solved for optically thin plasmas under the assumption of LTE and laminar flow. Results of parameterization on the net amount of power dissipated in the discharge, frequency of the RF generator, flow rate distribution of inlet gases and swirl velocity are presented, showing the impact of these parameters on the fluid dynamic and electromagnetic behaviour of the plasma.Received: 22 May 2003, Published online: 5 August 2003PACS: 52.75.Hn Plasma torches - 52.65.-y Plasma simulation - 52.80.Pi High-frequency and RF discharges     

Surface stress mediated image force and torque on an edge dislocation

The proximity of interfaces gives prominence to image forces experienced by dislocations. The presence of surface stress alters the traction-free boundary conditions existing on free-surfaces and hence is expected to alter the magnitude of the image force. In the current work, using a combined simulation of surface stress and an edge dislocation in a semi-infinite body, we evaluate the configurational effects on the system. We demonstrate that if the extra half-plane of the edge dislocation is parallel to the surface, the image force (glide) is not altered due to surface stress; however, the dislocation experiences a torque. The surface stress breaks the ‘climb image force’ symmetry, thus leading to non-equivalence between positive and negative climb. We discover an equilibrium position for the edge dislocation in the positive ‘climb geometry’, arising due to a competition between the interaction of the dislocation stress fields with the surface stress and the image dislocation. Torque in the climb configuration is not affected by surface stress (remains zero). Surface stress is computed using a recently developed two-scale model based on Shuttleworth’s idea and image forces using a finite element model developed earlier. The effect of surface stress on the image force and torque experienced by the dislocation monopole is analysed using illustrative 3D models.     

Study of dislocation EBIC image width in GaN films and GaN based structures

The width of dislocation EBIC images in GaN films and GaN based light-emitting structures has been measured. The obtained data have been compared with the diffusion length and the depth of the space charge region boundary and a correlation between these values has been found. It has been shown that the dislocation image’s width in semiconductors with the submicron diffusion length could be used for the estimation of diffusion length values.     

Corrosion evaluation by thermal image processing and 3D modelling

Quantitative transient IR thermography has been applied to the characterization of hidden corrosion in metals. A dedicated 3D numerical model of heat transfer has been used to solve the direct thermal problem and to simulate the test. Theoretical modelling allows the verification of limits of the ID solution and the derivation of coefficients which take heat diffusion into account. An analysis of inversion accuracy was carried out. A simple algorithm based on a surface temperature time-derivative is proposed for detecting thickness variations. Then, material loss in an area of arbitrary shape is evaluated applying a modified algorithm, originally developed for a ID thermal model. The potential of dedicated image processing in enhancing a signal-to-noise ratio is explored. The feasibility of corrosion quantification by the proposed inversion algorithm is demonstrated with experimental results. Detection and evaluation of hidden material loss within a boiler section, typically used at a power plant station, has been performed. The external surface was heated with flash lamps and temperature response was analyzed both in time and space domains. The masking effect due to the noisy inspected surface (not painted and affected by a long time service) were substantially removed before evaluating corrosion. Obtained results have been compared with measurements produced by the ultrasonic method.     

Fine structure of the diffraction image of an edge dislocation in high-resolution section topography

The propagation of an x-ray wave field in an elastic field of an edge dislocation crossing a scattering triangle exactly along the bisector of the scattering angle has been considered. The scattering of the x-ray wave field by a complex elastic field of the edge dislocation has been analyzed using the methods of geometrical optics. It has been established that the fine structure of a diffraction image of defects in thick crystals is determined by the differences in scattering of the normal and anomalous modes of the x-ray wave field in the vicinity of the Bragg reflection. In the case of thick crystals, the x-ray diffraction image of defects can have a symmetry different from the symmetry of the function of local misorientations of the crystal lattice. X-ray wave scattering by local distortions of the crystal lattice can occur according to two different mechanisms depending on the gradient of space changes in the deformation field. In the crystal regions where the elastic field varies slowly with a change in the distance, the x-ray wave field has had time to adjust itself to follow the course of deviations of the crystal lattice from the exact Bragg condition. In the crystal region where the elastic field changes significantly at distances of the order of the extinction length, this region leaves the reflecting position and interference scattering occurs at the interface of the region. It is important that the form of the deformation field in this case is of no significance.     

Fatigue in precipitation hardened materials: a three-dimensional discrete dislocation dynamics modelling of the early cycles

Three-dimensional dislocation dynamics (DD) fatigue simulations in precipitation hardened metals is a major challenge in terms of numerical development. Several precipitate configurations have been investigated with an original treatment of precipitate–dislocation interactions and a parallelized DD code. In grains containing single-sized shearable particles (r _p?=?160?nm), strain is localized in clear bands where the precipitates are totally sheared-off. The fatigue behaviour involves an initial hardening followed by severe cyclic softening and significant surface slip irreversibility. In the presence of large single-sized particles (r _p?=?400?nm), the persistent slip band (PSB) structure is accompanied by highly reversible surface displacements. Slip dispersion originates from Orowan loops that have little effect on the mechanical response. The mechanical behaviour of a bimodal distribution is intermediate between the two above cases with the above microstructural features coexisting within the same grain. Unlike in the monomodal large-particle case, where all the particles retain their initial strength, some of the large particles of the bimodal distribution undergo a significant strength reduction.     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

Stochastic effects on dislocation structure development under cascade-damage irradiation

Received: 28 January 1998/Accepted: 24 March 1998     

Periodic mode hopping induced by thermo-optic effects in continuous-wave optical parametric oscillators

We show that thermal effects can lead to periodic mode hopping in cw optical parametric oscillators (OPOs). This mode hopping may occur as soon as two modes have different intensities at the point where they exchange their stability; this condition is easily fulfilled in OPOs that are triply resonant, or doubly resonant with a weakly resonant pump. We have observed such oscillations experimentally in a type II OPO in both configurations. A simple thermo-optic multimode model reproduces well the experimental regimes. We expect that multimode instabilities based on this mechanism can be observed with various aspects in many experimental setups at high pumping rate.