Statistical Theory of Dislocation

Groma, István

doi:10.1007/978-3-319-94186-8_3

Cited by 4 publications

(6 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The literature devoted to plastic intermittency, dislocation avalanches, and the associated criticality is steadily growing and an exhaustive review of the subject is far beyond the scope of this paper. The early work was reviewed in [52] and more recent comprehensive discussions can be found in [53][54][55][56][57][58][59][60][61]. The goal of this review is to address only the subjects in whose development some of us have played an active role.…”

Section: The Goals Of This Reviewmentioning

confidence: 99%

Fluctuations in crystalline plasticity

Weiss¹,

Zhang²,

Salman³

et al. 2021

Comptes Rendus. Physique

View full text Add to dashboard Cite

Recently acoustic signature of dislocation avalanches in HCP materials was found to be long tailed in size and energy, suggesting critical dynamics. Moreover, the intermittent plastic response was found to be generic for micro-and nano-sized systems independently of their crystallographic symmetry. These rather remarkable discoveries are reviewed in this paper in the perspective of the recent studies performed in our group. We discuss the physical origin and the scaling properties of plastic fluctuations and address the nature of their dependence on crystalline symmetry, system size, and disorder content. A particular emphasis is placed on the formation of dislocation structures, and on our ability to temper plastic fluctuations by alloying. We also discuss the "smaller is wilder" size effect that culminates in a paradoxical crack-free brittle behavior of very small, initially dislocation free crystals. We argue that the implied transition between different rheological behaviors is regulated by the ratio of length scales R = L/l , where L is the system size and l is the internal length. We link this size effect with size dependence of strength ("smaller is stronger") and the size-induced switch between different hardening mechanisms. We show that the task of taming the intermittency of plastic flow at ultra-small scales can be accomplished by generating tailored quenched disorder which allows one to control micro-and nano-forming and opens new perspectives in micro-metallurgy and structural engineering of miniature load-carrying elements. These insights were beyond the reach of conventional theoretical approaches that do not explicitly account for the stochastic nature of collective dislocation dynamics.

show abstract

Section: The Goals Of This Reviewmentioning

confidence: 99%

Fluctuations in crystalline plasticity

Weiss¹,

Zhang²,

Salman³

et al. 2021

Comptes Rendus. Physique

View full text Add to dashboard Cite

show abstract

“…This choice also explains the notations used in Eqs. (24,25): τ * and τ d are equivalent quantities with the ones obtained during the coarse graining procedure. In the following it is shown that this choice for the mobility laws is indeed compatible with Eq.…”

Section: D Dislocation Dynamicsmentioning

confidence: 99%

“…The first term P mf is the mean field elastic energy of the system, which means, that if the dislocations were distributed randomly, then P mf would exactly be the elastic energy. It reads as 23,25,29…”

Section: The Proposed Form Of the Plastic Potentialmentioning

confidence: 99%

“…where Inc is the incompatibility operator, χ is the stress potential tensor, C is the modulus tensor, and η is the incompatibility tensor related to the dislocation density tensor as 25,40…”

Section: The Proposed Form Of the Plastic Potentialmentioning

confidence: 99%

“…The consequences of the dissipative nature of dislocation motion has been thoroughly explored in strongly simplified quasi two-dimensional systems of straight parallel edge dislocations, where dislocations are treated as signed point particles moving in a plane. By a systematic coarse-graining of the evolution equations of individual dislocations [17][18][19][20][21][22][23][24][25] a continuum theory was developed during the last 20 years, that has been successfully compared to discrete dislocation dynamics (DDD) simulations 19,[26][27][28] . By now, it can be considered as a well-established theory for the 2D problem it addresses.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics of curved dislocation ensembles

2021

Self Cite

View full text Add to dashboard Cite

To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science. During the last two decades such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse-graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single slip situation. In order to reduce the complexity of the problem a "dipole" like approximation for the orientation dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the GND densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.

show abstract

Homogeneous Dislocation Nucleation in Landau Theory of Crystal Plasticity

Salman¹,

Baggio²

2019

Mechanics and Physics of Solids at Micro‐ and Nano‐Scales

View full text Add to dashboard Cite

Statistical Theory of Dislocation

Cited by 4 publications

References 48 publications

Fluctuations in crystalline plasticity

Fluctuations in crystalline plasticity

Dynamics of curved dislocation ensembles

Homogeneous Dislocation Nucleation in Landau Theory of Crystal Plasticity

Contact Info

Product

Resources

About