Growth of a vortex polycrystal in type II superconductors

We discuss the formation of a vortex polycrystal in type II superconductors from the competition between pinning and elastic forces. We compute the elastic energy of a deformed grain boundary, that is strongly non-local, and obtain the depinning stress for weak and strong pinning. Our estimates for the grain size dependence on the magnetic field strength are in good agreement with previous experiments on NbMo. Finally, we discuss the effect of thermal noise on grain growth.Comment: 4 pages, 2 figure

Depinning transition of dislocation assemblies: pileup and low-angle grain boundary

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in non-active slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long range interactions between dislocations. In light of this result, we revise statistical depinning theories and find novel results for Zener pinning in grain growth. Finally, we discuss the scaling properties of the dynamics of dislocation assemblies and compare theoretical results with numerical simulations.Comment: 13 pages, 8 figure

Depinning transition of dislocation assemblies: pileup and low-angle grain boundary

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in non-active slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long range interactions between dislocations. In light of this result, we revise statistical depinning theories and find novel results for Zener pinning in grain growth. Finally, we discuss the scaling properties of the dynamics of dislocation assemblies and compare theoretical results with numerical simulations.Comment: 13 pages, 8 figure

Superplasticity and anelasticity in fine-grained Sn-Pb alloys

Mechanisms which may play a role in superplastic deformation (grain strain mechanisms, grain boundary sliding (GBS) mechanisms) are reviewed. Two well-known lattice dislocation mechanisms are re-evaluated for grain boundary dislocations (GBDs). The manner in which the deformation mechanisms interact, or are inhibited or obscured, is discussed. Mechanisms of anelastic deformation are outlined, with particular reference to fine-grained materials. Expressions for anelastic recovery caused either by grain boundary (GB) tension or by the relaxation of GBD pile-ups are derived. The plastic properties of Sn-38.1w/o Pb and Sn-2w/o Pb are measured. They are similar in both alloys. No threshold stress for plastic deformation is detected, for stresses and strain rates as low as 0.IMPa and 10-10s-1 respectively. The presence of GB diffusion creep (Coble creep) is established experimentally in Sn-2w/o Pb with grain sizes ≥ 50μm. Coble creep is inhibited for small grain sizes (~10μm). The inhibition is explained by GBS caused by GBDs. In disagreement with the measurements, high threshold stresses are predicted for Sn-38.1w/o Pb. This implies that GBD line tensions are lower than those of lattice dislocations. The anelastic properties of Sn-2w/o Pb and Sn-38.1w/o Pb are determined from the elastic after-effect (anelastic recovery after unloading). They are remarkable: anelastic contractions larger than 0.2% and relaxation strengths (= ratio of anelastically recovered to elastically recovered strain) in excess of 100 are found. The anelastic strains are approximately proportional to the stress and the inverse grain size. A wide range of relaxation times (~ 6 decades) is observed. A mechanism based on the relaxation of GBD pile-ups is in qualitative agreement with the measured anelasticity. The high measured relaxation strengths, however, imply that the interaction between GBDs is much weaker (~ 2 orders of magnitude) than that between lattice dislocations. This could be due to a relatively low self-energy of GBDs and would be in qualitative agreement with the low GBD line tensions suggested above. The influence of anelasticity on transients (e.g. stress relaxation, dip test) is investigated using a rheological model with three Voigt elements (anelasticity) and a nonlinear dashpot (plasticity). Using independently determined plastic and anelastic parameters the 4-th order differential equa tion corresponding to the model is solved numerically for several examples. Measured transients are much more accurately predicted with the present model than with models neglecting anelasticity.</p

DISLOCATION MULTIPOLES

Examen théorique détaillé de la formation et des configurations d'équilibre des multipôles de dislocation sur deux plans de glissement. Les dispositions prévues, qui supposent un mécanisme de formation par prégeage, sont en bon accord avec celles observées dans les alliages de Cu à 10 % at. d'Al, déformés durant le 1er stade de la courbe de durcissement. Les calculs montrent que, si deux sources de Frank-Read, sur des plans de glissement parallèles, émettent des boucles de dislocation, les dislocations formeront un dipôle spontanément, en l'absence de contrainte. Si les deux sources, situées sur des plans de glissement distants de γ, sont séparées par une distance L, le nombre de dislocations que chacune peut émettre varie entre 2 L/7 γ (si la droite joignant les sources est perpendiculaire au vecteur de Burgers b) et L/6 γ (si cette droite est parallèle à b). On trouve que la contrainte nécessaire pour décomposer un multipôle, une fois formé, est presque indépendante de n, nombre de dipôles du multipôle, et donnée avec une bonne approximation par τp = Gb/2 πkγ, où k = 2 ou 4(1 - v), suivant que les dislocations sont vis ou coin. Une théorie de la relation travail-durcissement fondée sur les calculs précédents fournit une relation entre la tension τn - τF et la déformation ε, de la forme ε = q[(τa - τF)/G]3, ou q dépend de la densité et de la répartition des sources de Frank-Read. Si on suppose la distance moyenne des sources, projetée sur un plan normal au plan de glissement, de l'ordre de 10µ, on obtient un bon accord entre la théorie et les courbes expérimentales tension-déformation obtenues pour le magnésium par Hirsch et Lally (1965).The formation and the equilibrium configurations of dislocation multipoles on two slip planes are considered theoretically in detail. It is found that the predicted arrays, assuming a trapping formation mechanism, are in fair agreement with those observed in Cu 10 % at. Al alloys deformed into stage I of the work-hardening curve. The calculations show that if two Frank-Read sources on parallel slip planes emit dislocation loops, the dislocations will form a multipole spontaneously in the absence of any effective applied stress. If the two sources lie a distance l apart on slip planes separated by y, the maximum number of dislocations which each source can emit varies between 2 l/7 y (when the line joining the sources is perpendicular to the Burgers vector, b) and 116 y (when the line is parallel to b). The stress required to decompose a multipole, once formed, is found to be almost independent of n, the number of dipoles in the multipole, and is given to a good approximation by : τp = Gb/2 πkγ where k = 2 and 4(1 - v) for screw and edge dislocations respectively. A theory of stage I work-hardening based on the above calculations yields a relationship between stress (τa - τF) and strain (ε) of the form : ε = q [(τa- τF)/G]3 where q depends on the density and distribution of active Frank-Read sources. If a random distribution of sources, whose average separation projected into a plane normal to the slip plane is ∼ 10µ is assumed, good agreement is obtained between theory and the experimental stress-strain curve of magnesium measured by Hirsch and Lally (1965)