Self-organization approach to cyclic microplasticity: A model of a persistent slip band

Gregor, V.; Kratochvı́l, Jan

doi:10.1016/s0749-6419(97)00046-6

Cited by 18 publications

(12 citation statements)

References 27 publications

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“…In this case, the dislocation current which gives rise to the gradient terms in Eq. (1) also contains a contribution resulting from the interaction between gliding dislocations and loops (Gregor & Kratochvil, 1998). As shown there, these terms account for a sweeping mechanism which may be responsible for the early stages of dislocation patterning.…”

Section: Dislocation Patterningmentioning

confidence: 99%

On certain problems of deformation-induced material instabilities

Walgraef

Aifantis

2012

International Journal of Engineering Science

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Section: Dislocation Patterningmentioning

confidence: 99%

On certain problems of deformation-induced material instabilities

Walgraef

Aifantis

2012

International Journal of Engineering Science

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“…(12) also contains a contribution resulting from the interaction between gliding dislocations and loops, as discussed in 725, 35,367. The first one corresponds to materials with low forest density, at the beginning of the deformation process.…”

Section: Stability Analysis and Bifurcationsmentioning

confidence: 99%

On Dislocation Patterning: Revisiting the W-A Model Part I: The Role of Gradient Terms in Dislocation Dynamics

Walgraef¹,

Aifantis²

2009

Journal of the Mechanical Behavior of Materials

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The Walgraef-Aifantis reaction-diffusion framework (W-A model) for dislocation patterning, proposed a quarter of a century ago, is revisited in view of new advances made in the field, including stochastic aspects.In the course of plastic deformation induced by dislocation glide, dislocation distributions, which are rather uniform at the beginning, quickly become unstable as deformation proceeds and undergo successive transitions towards various types of spatial patterns such as walls, cells, slip bands, labyrinth structures, etc.In the initial W-A model it was shown how the coupled nonlinear evolution of forest and gliding dislocation densities can generate spatially periodic dislocation patterns during cyclic deformation, commonly known as ladder structures of persistent slip bands. This model is updated here (Part I), to take care properly of the gradient terms of the mobile dislocation dynamics. It is shown that these terms generate space-dependent, nonlinear, self-and cross-diffusion terms, but also space-dependent advection terms which affect pattern formation and stability. Furthermore, it is argued that persistent slip bands nucleate preferentially through front propagation from stress inhomogeneities. The highly anisotropic character of the propagation velocity accounts for fast propagation in the slip direction, and very slow propagation in the climb direction. Next (Part II), the model is updated by incorporating the basics of the recently advanced stochastic/statistical approach of Groma-Zaiser and co-workers. It is shown that the resulting framework can conveniently describe self-assembly and self-organization phenomena as the external stress is increased. 49

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“…It could help to resolve the problem of the pathological zero wave length patterning modes encountered in the phenomenological patterning models. 42 The computer simulations in Ref. 17 have shown the importance of the dipolar loop interaction.…”

Section: ͑81͒mentioning

confidence: 99%

Statistical foundation of continuum dislocation plasticity

Kratochvı́l

Sedláček

2008

Phys. Rev. B

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A continuum model of mesoscale plasticity intended to cover dislocation pattering and size effects is proposed. The statistical approach to dislocation dynamics put forward by Groma et al. ͓Acta Mater. 51, 1271 ͑2003͔͒ is applied to curved glide dislocations and dipolar dislocation loops appearing in a crystal deformed by single slip. Due to the very different size and mobile properties of the glide dislocations and the loops, the two entities are differently treated. The statistics of Groma et al. is directly applicable to the loops, which behave as rigid objects of restricted mobility. The glide dislocations are divided into groups, which in the averaging process lead to so-called single-valued dislocation fields. The averaged continuous distribution of the glide dislocations is treated as a superposition of these fields. The system of equations of the continuum model consists of ͑i͒ equations for the flow of glide dislocations of each single-valued field and the balance equation for the density of dipolar loops ͑these equations are derived from the discrete equations of motion and contain constitutive functionals representing short range interactions͒, ͑ii͒ the conservation of Burgers vector in the single-valued fields, ͑iii͒ the equations of continuum crystal plasticity, and ͑iv͒ the Orowan law for the shear strain rate caused by the glide dislocations. The possibilities for specification and evaluation of the constitutive functionals, namely, the short range correlations among dislocations ͑both the glide dislocations and the loops͒, are indicated.

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Self-organization approach to cyclic microplasticity: A model of a persistent slip band

Cited by 18 publications

References 27 publications

On certain problems of deformation-induced material instabilities

On certain problems of deformation-induced material instabilities

On Dislocation Patterning: Revisiting the W-A Model Part I: The Role of Gradient Terms in Dislocation Dynamics

Statistical foundation of continuum dislocation plasticity

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