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).     

Graphite dislocations induced by collision of neutral mercury droplets

High speed neutral clusters and mercury droplets from a gas jet impactor are allowed to collide with graphite surfaces. These collisions produce a variety of dislocations. One of the dislocations is a narrow dislocation band with atomic resolution. This band has two partial dislocations on the sides of a central region of abc structure.     

Defect reduction in sublimation grown SiC bulk crystals

For several years the major focus of material issues in SiC substrates was laid on the reduction of macroscopic defects like polytype inclusions, low angle grain boundaries and micropipes. Although significant improvements have been achieved, there are still shortcomings in material quality that have to be overcome. Since it is clear that dislocations are the main reason for degradation in power devices the prevailing attention has shifted to that field of material research. The aim of our work was to investigate the mechanisms that affect the generation of macroscopic and microscopic defects during sublimation growth. Intense studies were utilized on dislocation and stacking fault formation. For this reason we systematically varied parameters of the growth process and applied several methods for the characterization to evaluate material properties most precisely, e.g. KOH-defect-etching, X-ray-diffraction, electron microscopy and optical microscopy. The investigations were accompanied by failure analysis of devices of the Schottky type. We found out that for the improvement of substrate quality emphasis has to be laid on the reduction of thermoelastic stress in the growing crystal. From results of numerical calculations we were able to derive moderate growth conditions with reduced temperature gradients prevailing during the growth process. As a consequence we succeeded in decreasing the defect concentration. The best value so far achieved for the sum of both BPD and TED was 7×10³ cm⁻².     

Mechanical Properties of Machined Nanostructures

"Three-dimensional molecular dynamics simulations have been carried out to predict the mechanical properties of a single crystalline copper with different scratching depths and no defects by embedded-atom method potential respectively. The mechanical properties for nanostructure with no defects and machined groove are investigated by various strain rates, scratched depths and scratching directions. Through the visualization technique of atomic coordination number, the onset and movement of defects in workpiece such as dislocations are analyzed under tensile loads. Work-harden formation, recrystallization behavior and the properties of rupturing process of nanostructure are exhibited at the atomic view. The relation between stress and the onset and evolvement of defects in specimen is analyzed for fundamental understanding the mechanical properties of nanostructure."     

A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales

Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.     

The use of channeling-effect techniques to locate interstitial foreign atoms in silicon

When the channeling-effect technique is used to determine the lattice location of an impurity which is not completely substitutional, quantitative interpretation of the results requires knowledge of the interaction yield between a channeled beam and an interstitial atom. We have investigated this problem for Yb implanted into silicon. Along the <110> direction, a peak of almost a factor of two is observed in backscattering yield from the Yb atoms, using a 1-MeV He beam. The height and angular width of the peak is satisfactorily interpreted in terms of flux-peaking of the channeled beam in the central region of the <110> channels.

The existence of such a large flux-peaking effect seriously complicates quantitative determination of the location of non-substitutional impurities. However, it is still possible to establish rather accurately the lattice position of the impurity, provided the measured minimum yields and angular widths of the <111> and <100> dips are taken into account.     

New insight on acoustoplasticity - Ultrasonic irradiation enhances subgrain formation during deformation

Many industrial applications make use of ultrasonic vibration to soften metals. The existing understanding of such an acoustoplastic effect is one in which the ultrasonic irradiation either imposes additional stress waves to augment the quasi-static applied load, or causes heating of the metal, whereas the metal’s intrinsic deformation resistance or mechanism is assumed to be unaltered by the ultrasound. In this study, indentation experiments performed on aluminum samples simultaneously excited by ultrasound reveal that the latter intrinsically alters the deformation characteristics of the metal. The deformation microstructures underneath the indents were investigated by a combination of cross-sectional microscopic techniques involving focused-ion-beam milling, transmission electron microscopy and crystal orientation mapping by electron backscattered diffraction. The softening effect of the ultrasound is found to constitute recovery associated with extensive enhancement of subgrain formation during deformation. By comparing the microstructures of samples deformed with and without simultaneous application of ultrasound, and those subsequently excited by ultrasound after deformation, the enhanced subgrain formation is proved to be one due to the combined application of the quasi-static loading and the ultrasound, but not a simple addition of the two. Similarly, by comparing with samples deformed while being simultaneously or subsequently heated up, the enhanced subgrain formation by the ultrasound is proved to be a lot greater than that due to the heat that it generates within the metal. Such effects of the ultrasound are interpreted by its ability to enhance dipole annihilation. The superimposed ultrasound causes dislocations to travel longer distances in a jerky manner, so that they can continuously explore until dipole annihilation.     

On energy balance and the structure of radiated waves in kinetics of crystalline defects

Traveling waves, with well-known closed form expressions, in the context of the defects kinetics in crystals are excavated further with respect to their inherent structure of oscillatory components. These are associated with, so called, Frenkel–Kontorova model with a piecewise quadratic substrate potential, corresponding to the symmetric as well as asymmetric energy wells of the substrate, displacive phase transitions in bistable chains, and brittle fracture in triangular lattice strips under mode III conditions. The paper demonstrates that the power expended theorem holds so that the sum of rate of working and the rate of total energy flux into a control strip moving steadily with the defect equals the rate of energy sinking into the defect, in the sense of N.F. Mott. In the conservative case of the Frenkel–Kontorova model with asymmetric energy wells, this leads to an alternative expression for the mobility in terms of the energy flux through radiated lattice waves. An application of the same to the case of martensitic phase boundary and a crack, propagating uniformly in bistable chains and triangular lattice strips, respectively, is also provided and the energy release is expressed in terms of the radiated energy flux directly. The equivalence between the well-known expressions and their alternative is established via an elementary identity, which is stated and proved in the paper as the zero lemma. An intimate connection between the three distinct types of defects is, thus, revealed in the framework of energy balance, via a structural similarity between the corresponding variants of the ‘zero’ lemma containing the information about radiated energy flux. An extension to the dissipative models, in the presence of linear viscous damping, is detailed and analog of the zero lemma is proved. The analysis is relevant to the dynamics of dislocations, brittle cracks, and martensitic phase boundaries, besides possible applications to analogous physical contexts which are marked by macroscopic energy release through emission of waves and possibly linear viscous damping.     

Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation

Mechanics of nano- and meso-scale contacts of rough surfaces is of fundamental importance in understanding deformation and failure mechanisms of a solid surface, and in engineering fabrication and reliability of small surface structures. We present a micro-mechanical dislocation model of contact-induced deformation of a surface step or ledge, as a unit process model to construct a meso-scale model of plastic deformations near and at a rough surface. This paper (Part I) considers onset of contact-induced surface yielding controlled by single-dislocation nucleation from a surface step. The Stroh formalism of anisotropic elasticity and conservation integrals are used to evaluate the driving force on the dislocation. The driving force together with a dislocation nucleation criterion is used to construct a contact-strength map of a surface step in terms of contact pressure, step height, surface adhesion and lattice resistance. Atomistic simulations of atomic surface-step indentation on a gold (1 0 0) surface have been also carried out with the embedded atom method. As predicted by the continuum dislocation model, the atomistic simulations also indicate that surface adhesion plays a significant role in dislocation nucleation processes. Instabilities due to adhesion and dislocation nucleation are evident. The atomistic simulation is used to calibrate the continuum dislocation nucleation criterion, while the continuum dislocation modeling captures the dislocation energetics in the inhomogeneous stress field of the surface-step under contact loading. Results show that dislocations in certain slip planes can be easily nucleated but will stay in equilibrium positions very close to the surface step, while dislocations in some other slip planes easily move away from the surface into the bulk. This phenomenon is called contact-induced near-surface dislocation segregation. As a consequence, we predict the existence of a thin tensile-stress sub-layer adjacent to the surface within the boundary layer of near-surface plastic deformation. In the companion paper (Part II), we analyze the surface hardening behavior caused by multiple dislocations.     

Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.