Journal ArticleDOI
On the dynamical origin of dislocation patterns
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TLDR
In this article, the formation and stability of dislocation patterns are interpreted on the basis of instabilities occurring in partial differential equations modelling the dynamics of dislocations species under certain circumstances, these equations are shown to be a coupled system of the diffusion reaction type for the densities of immobile and mobile dislocation populations.About:
This article is published in Materials Science and Engineering.The article was published on 1986-08-01. It has received 109 citations till now. The article focuses on the topics: Dislocation.read more
Citations
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The physics of plastic deformation
TL;DR: In this article, a simplified physical picture is extracted from the many complicated processes occuring during plastic deformation, based upon a set of continuously distributed straight edge dislocations, the carriers of plastic deformations, moving along their slip plane, interacting with each other and the lattice, multiplying and annihilating.
Journal ArticleDOI
Discrete dislocation plasticity: a simple planar model
TL;DR: In this article, a method for solving small-strain plasticity problems with plastic flow represented by the collective motion of a large number of discrete dislocations is presented, modelled as line defects in a linear elastic medium.
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On plastic deformation and the dynamics of 3D dislocations
TL;DR: In this article, a 3D mesoscopic model to simulate the collective dynamic behavior of a large number of curved dislocations of finite lengths has been developed for the purpose of analyzing deformation patterns and instabilities, including the formation of dislocation cell structures.
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Gradient Deformation Models at Nano, Micro, and Macro Scales
TL;DR: In this article, various deformation models incorporating higher-order gradients are discussed and their implications are considered in a variety of problems ranging from the determination of the size of dislocation cores or elastic dislocation interactions, to the determined of wavelengths of dislocations patterns or heterogeneous dislocation distributions and the determined the structure of solid interfaces and of localized strain zones during adiabatic shear deformation.
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Link between the microscopic and mesoscopic length-scale description of the collective behavior of dislocations
TL;DR: In this paper, a hierarchy of equations for the one-, two-, three-, etc., particle distribution functions is derived for the dislocation pattern formation, which is similar to the derivation of the so called BBGKY hierarchy which is frequently used in plasma physics.
References
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Journal ArticleDOI
Dislocation Cell Formation in Metals
TL;DR: In this article, it is shown that an array of dislocations, modelled by parallel screw dislocation, of uniform density, is unstable, and that the instability grows ultimately into a dislocation cell structure and the cell size is given by the dominant wavelength of the density modulation.
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Dislocation patterning in fatigued metals as a result of dynamical instabilities
TL;DR: In this article, the nucleation of persistent slip bands in stressed materials is described as a cooperative phenomenon for dislocation populations, and it is the competition between their mobility and their nonlinear interactions (creation, annihilation, and pinning) which causes the instability of uniform dislocation distributions versus inhomogeneous ones and leads to the formation and persistence of dislocation patterns.
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Theory of dislocation cell sizes in deformed metals
TL;DR: In this article, it was shown that the experimentally observed cell sizes and link lengths represent the minimum total strain energy for a fixed dislocation content, whereas the reverse is true when at constant dislocations content the cell size increases.
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On the formation and stability of dislocation patterns—III: Three-dimensional considerations
TL;DR: In this article, a set of partial differential equations of the diffusion-reaction type for the evolution of dislocation species was derived by distinguishing among mobile and immobile dislocations and operating within the framework of continuum mechanics.