3D Discrete Dislocation Dynamics Investigations of Fatigue Crack Initiation and Propagation

International audienc

Linking continuum mechanics and 3D discrete dislocation simulations

A technique is developed for linking the methods of discrete dislocation dynamics simulation and finite element to treat elasto-plasticity problems. The overall formulation views the plastically deforming crystal as an elastic crystal with continuously changing dislocation microstructure which is tracked by the numerical dynamics simulation. The FEM code needed in this regard is based on linear elasticity only. This formulation presented here is focused on a continuous updating of the outer shape of the crystal, for possible regeneration of the FEM mesh, and adjustment of the surface geometry, in particular the surface normal. The method is expected to be potentially applicable to the nano- indentation experiments, where the zone around the indenter-crystal contact undergoes significant permanent deformation, the rigorous determination of which is very important to the calculation of the indentation print area and in turn, the surface hardness. Furthermore, the technique is expected to account for the plastic history of the surface displacement under the indenter. Other potential applications are mentioned in the text

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Some Properties of the Computable Cross Norm Criterion for Separability

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte

Clear band formation simulated by dislocation dynamics

Dislocation Dynamics simulations of dislocations gliding across a random populations of Frank loops are presented. Specific local rules are developed to reproduce elementary interaction mechanisms obtained in Molecular Dynamics simulations. It is shown that absorption of Frank loops as helical turns on screw dislocations governs the process of clear band formation, because: (1) it transforms the loops into jogs on dislocations, (2) when the dislocations unpin, the jogs are transported along the dislocation lines, leading to a progressive clearing of the band and (3) the dislocations are re-emitted in a glide plane different from the initial one, allowing for a broadening of the band. It is also shown that a pile-up of dislocations is needed to form a clear band of finite thickness.У термінах дислокаційної динаміки представлено моделювання дислокацій, що перетинають розташовану випадковим чином сукупність петель Франка. Розроблені локальні правила для відтворення елементарних механізмів взаємодії, що отримані при моделюванні методом молекулярної динаміки. Показано, що поглинання петель Франка у вигляді гелікоїдальних витків на гвинтових дислокаціях визначає процес утворення вільних зон, оскільки: 1) воно перетворює петлі у східці на дислокаціях, 2) у випадку відкріплення дислокації східці переносяться вздовж ліній дислокацій і 3) дислокації знову надходять у площину ковзання, яка відрізняється від вихідної, забезпечуючи тим самим розширення вільної зони. Крім того, показано, що скупчення дислокацій необхідне для утворення вільної зони з кінцевою товщиною.В терминах дислокационной динамики представлено моделирование дислокаций, пересекающих расположенную случайным образом совокупность петель Франка. Разработаны локальные правила для воспроизведения элементарных механизмов взаимодействия, полученных при моделировании методом молекулярной динамики. Показано, что поглощение петель Франка в виде геликоидальных витков на винтовых дислокациях определяет процесс образования свободных зон, поскольку: 1) оно преобразует петли в ступеньки на дислокациях, 2) в случае открепления дислокации ступеньки переносятся вдоль линий дислокаций и 3) дислокации вновь поступают в плоскость скольжения, отличающуюся от исходной, обеспечивая тем самым расширение свободной зоны. Кроме того, показано, что скопление дислокаций необходимо для образования свободной зоны с конечной толщиной

q- Deformed Boson Expansions

A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between the exact result, our q- deformed boson expansion and the usual non - deformed expansion.Comment: 8 pages plus 2 figures (available upon request

Separability and Fourier representations of density matrices

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d)$ is a basis for $d\times d$ matrices. If $N=d_{1}\times d_{2}\times...\times d_{b}$ and H^{[ N]}=\bigotimes H^{% [ d_{k}]}, we give a sufficient condition for separability of a density matrix $\rho$ relative to the $H^{[ d_{k}]}$ in terms of the $L_{1}$ norm of the spin coefficients of $\rho >.$ Since the spin representation depends on the form of the tensor product, the theory applies to both full and partial separability on a given space $H^{[ N]}$% . It follows from this result that for a prescribed form of separability, there is always a neighborhood of the normalized identity in which every density matrix is separable. We also show that for every prime $p$ and $n>1$ the generalized Werner density matrix $W^{[ p^{n}]}(s)$ is fully separable if and only if $s\leq (1+p^{n-1}) ^{-1}$

Probabilistic implementation of universal quantum processors

We present a probabilistic quantum processor for qudits. The processor itself is represented by a fixed array of gates. The input of the processor consists of two registers. In the program register the set of instructions (program) is encoded. This program is applied to the data register. The processor can perform any operation on a single qudit of the dimension N with a certain probability. If the operation is unitary, the probability is in general 1/N^2, but for more restricted sets of operators the probability can be higher. In fact, this probability can be independent of the dimension of the qudit Hilbert space of the qudit under some conditions.Comment: 7 revtex pages, 1 eps figur

Mécanique des matériaux à topologie autobloquante

Les matériaux à topologie autobloquante sont un nouvel exemple de "matériaux hybrides", intermédiaires entre les matériaux et les structures, tout comme les composites, les mousses structurales, les matériaux enchevêtrés, les structures sandwich. Ils sont constitués de blocs élémentaires ajustés périodiquement et maintenus en contact par des conditions aux limites de compression. Nous avons étudié expérimentalement l'influence du coefficient de frottement et des conditions limites sur le comportement en indentation d'assemblages de blocs ostéomorphes réalisés en glace. Nous avons modélisé par éléments finis le contact avec frottement entre deux blocs ostéomorphes élastiques, en fonction du confinement par les autres blocs et du coefficient de frottement. Nous implémentons actuellement un code C++ basé sur la méthode des éléments discrets qui utilisera les lois locales déterminées par éléments finis pour simuler le comportement élastique et l'endommagement de grandes structures autobloquantes

Homogenization of dislocation dynamics

In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study two cases: i) the particular case of parallel straight dislocations and ii) the general case of curved dislocations. In each case, we perform rigorously the homogenization of the dynamics and predict the corresponding effective macroscopic elasto-visco-plastic flow rule