Plastic Deformation Instabilities: Lambert Solutions of Mecking-Lücke Equation with Delay

The aim of this paper is the study of instabilities during plastic deformation at constant cross‐head velocity. The deformation is supposed to be controlled by the emission of dislocation loops. Under some hypothesis analogous to the Mecking‐Lücke relation, we derive a linear delay differential‐difference equation. The “retarded” time term appears as the phase shift between the time of loop nucleation and the time at which the mean strain is recorded. We show the existence of the solution of strain equation. We give an analytic approach of solution using Lambert functions. The stability is also investigated close to the stable solution using a linearization of the number of nucleated loops functions

Buckling-induced dislocation emission in thin films on substrates

AbstractAtomistic simulations of the evolution of a strained thin film on a substrate has been reported and the formation of dislocations has been observed in the film/substrate interface after the film has buckled. In the framework of the linear elasticity theory, an analytical model has been developed to explain the buckle effect on the formation of the dislocations. A stability diagram with respect to the buckling and dislocation emission phenomena is finally presented for the film as a function of the uniaxial strain and the Burgers vector

A pile-up of edge dislocations to relax Misfit strain

It is shown that very large stresses may be present in the thin films that comprise integrated circuits and magnetic disks and that these stresses can cause deformation and fracture of the material. For a crystalline film on a non-deformable substrate, a key problem involves the movement of dislocations in the thin film. An analysis of this problem provides insight into both the formation of misfit dislocations in epitaxial thin films and the high strengths of thin metal films on substrates. We develop in this paper, theoretical calculations for dislocation nucleation phenomena in nanomaterials obtained by hetero-epitaxial growth of thin films on substrates having lattice mismatch defects. Atomic force microscopy observations showed the nucleation of dislocations from free lateral surfaces to relax the "misfit" strain, here we explain the principle of nucleating edge dislocations from these surfaces by the theoretical calculation, using the method of image stress and energy study. We begin, by treating the case of a single dislocation and then generalize the work at a pile-up of n interface dislocations.

Energetics and atomic mechanisms of dislocation nucleation in strained epitaxial layers

We study numerically the energetics and atomic mechanisms of misfit dislocation nucleation and stress relaxation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Relaxation processes from coherent to incoherent states for different transition paths are studied using interatomic potentials of Lennard-Jones type and a systematic saddle point and transition path search method. The method is based on a combination of repulsive potential minimization and the Nudged Elastic Band method. For a final state with a single misfit dislocation, the minimum energy path and the corresponding activation barrier are obtained for different misfits and interatomic potentials. We find that the energy barrier decreases strongly with misfit. In contrast to continuous elastic theory, a strong tensile-compressive asymmetry is observed. This asymmetry can be understood as manifestation of asymmetry between repulsive and attractive branches of pair potential and it is found to depend sensitively on the form of the potential.Comment: 11 pages, 9 figures, to appear in Phys. Rev.

Instabilities in crystal growth by atomic or molecular beams

The planar front of a growing a crystal is often destroyed by instabilities. In the case of growth from a condensed phase, the most frequent ones are diffusion instabilities, which will be but briefly discussed in simple terms in chapter II. The present review is mainly devoted to instabilities which arise in ballistic growth, especially Molecular Beam Epitaxy (MBE). The reasons of the instabilities can be geometric (shadowing effect), but they are mostly kinetic or thermodynamic. The kinetic instabilities which will be studied in detail in chapters IV and V result from the fact that adatoms diffusing on a surface do not easily cross steps (Ehrlich-Schwoebel or ES effect). When the growth front is a high symmetry surface, the ES effect produces mounds which often coarsen in time according to power laws. When the growth front is a stepped surface, the ES effect initially produces a meandering of the steps, which eventually may also give rise to mounds. Kinetic instabilities can usually be avoided by raising the temperature, but this favours thermodynamic instabilities. Concerning these ones, the attention will be focussed on the instabilities resulting from slightly different lattice constants of the substrate and the adsorbate. They can take the following forms. i) Formation of misfit dislocations (chapter VIII). ii) Formation of isolated epitaxial clusters which, at least in their earliest form, are `coherent' with the substrate, i.e. dislocation-free (chapter X). iii) Wavy deformation of the surface, which is presumably the incipient stage of (ii) (chapter IX). The theories and the experiments are critically reviewed and their comparison is qualitatively satisfactory although some important questions have not yet received a complete answer.Comment: 90 pages in revtex, 45 figures mainly in gif format. Review paper to be published in Physics Reports. Postscript versions for all the figures can be found at http://www.theo-phys.uni-essen.de/tp/u/politi

FORMES D'ÉQUILIBRE DES DISLOCATIONS HÉLICOÏDALES

Le calcul de l'énergie des dislocations hélicoïdales permet de déterminer leur pas d'équilibre quand la dislocation peut glisser sur son cylindre. Quand les forces exercées aux extrémités sont nulles le rapport du pas sur le diamètre doit être égal à 1,5. Quand des forces sont appliquées aux extrémités l'hélice se comporte comme un ressort de coefficient élastique égal à µb2. Les résultats sont appliqués dans le cas où les forces sont dues aux dislocations prolongeant l'hélice.The computation of the energy of a helicoïdal dislocation allows its equilibrium pitch for glide motion to be determined. When the forces applied to its ends are zero, its pitch divided by its diameter must be equal to 1.5. When forces are applied to its ends, the helix behaves like a spring whose elastic coefficient is µb2. The results are discussed when the forces are originated by dislocations extending the helix

Fracture of Solids, par D. C. Drucker et J. J. Gilman, 1963

Grilhé Jean. Fracture of Solids, par D. C. Drucker et J. J. Gilman, 1963. In: Bulletin de la Société française de Minéralogie et de Cristallographie, volume 86, 4, 1963. p. 443