The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip

Xia, Shengxu; Belak, J.; El–Azab, Anter

doi:10.1088/0965-0393/24/7/075007

Cited by 32 publications

(28 citation statements)

References 41 publications

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“…It enables the dislocation to bypass obstacles, to form new sources on adjacent planes, or to annihilate other dislocations. In FCC metals, in particular, cross-slip plays a role in, for example, dislocation structuring [1,2], and work hardening and recovery [3][4][5]. Mobile screw dislocations in FCC are dissociated into pairs of Shockley partial dislocations with mixed character, so that the partial dislocations are not able to cross-slip.…”

Section: Introductionmentioning

confidence: 99%

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Cross-slip of long dislocations in FCC solid solutions

Nöhring

Curtin

2018

Acta Materialia

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Cross-slip of screw dislocations is a dislocation process involved in dislocation structuring, work hardening, and fatigue. Cross-slip nucleation in FCC solid solution alloys has recently been shown to be strongly influenced by local fluctuations in spatial arrangement of solutes, leading to a statistical distribution of cross-slip nucleation barriers. For cross-slip to be effective macroscopically, however, small cross-slip nuclei (~40b) must expand across the entire length of typical dislocation segments (10 2-10 3 b). Here, a model is developed to compute the relevant activation energy distribution for cross-slip in a random FCC alloy over arbitrary lengths and under non-zero Escaig and Schmid stresses. The model considers cross-slip as a random walk of successive flips of adjacent1b segments, with each flip having an energy consisting of a deterministic contribution due to constriction formation and stress effects, plus a stochastic contribution. The corresponding distribution is computed analytically from solute-dislocation and solute-solute binding energies. At zero stress, the probability of high activation energies increases with dislocation length. However, at stresses of just a few MPa, these barriers are eliminated and lower barriers are dominant. For increasing segment length, the effective energy barrier decreases according to a weak-link scaling relationship and good analytic predictions can be made using only known material properties. Overall, these results show that the effective cross-slip barrier in a random alloy is significantly lower than estimates based on average elastic and stacking fault properties of the alloy.

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Section: Introductionmentioning

confidence: 99%

“…In Sec. 2, 2 A standard estimate for the average dislocation spacing L at dislocation density  is L = 1/ √  [25, p. 20]. For a cellular or mesh-like dislocation microstructure, L is also an estimate for the typical segment length.…”

Section: Introductionmentioning

confidence: 99%

Cross-slip of long dislocations in FCC solid solutions

Nöhring

Curtin

2018

Acta Materialia

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“…Other structures whose formation is thought to involve crossslip are dislocation sheets [32] and persistent slip bands [33]. Recently, the importance of cross-slip for network formation has been shown using dislocation dynamics simulations [23] and dislocation-based plasticity models [34]. Cross-slip has also been incorporated into models for macroscopic plastic behavior of FCC metals, specifically work hardening and dynamic recovery [35][36][37], creep at intermediate homologous temperatures [38][39][40][41] 1 and the copper-brass texture transition [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Dislocation cross-slip in fcc solid solution alloys

Nöhring

Curtin

2017

Acta Materialia

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Cross-slip is a fundamental process of screw dislocation motion and plays an important role in the evolution of work hardening and dislocation structuring in metals. Cross-slip has been widely studied in pure FCC metals but rarely in FCC solid solutions. Here, the cross-slip transition path in solid solutions is calculated using atomistic methods for three representative systems of Ni-Al, Cu-Ni and Al-Mg over a range of solute concentrations. Studies using both true random alloys and their corresponding average-alloy counterparts allows for the independent assessment of the roles of (i) fluctuations in the spatial solute distribution in the true random alloy randomness and (ii) average alloy properties such as stacking fault energy. The results show that the solute fluctuations dominate the activation energy barrier, i.e. there are large sample-to-sample variations around the average activation barrier. The variations in activation barrier correlate linearly with the energy difference between the initial and final states. The distribution of this energy difference can be computed analytically in terms of the solute/dislocation interaction energies. Thus, the distribution of cross-slip activation energies can be accurately determined from a parameter-free analytic model. The implications of the statistical distribution of activation energies on the rate of cross-slip in real alloys are then identified.

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“…In this paper, the vector-density based formulation of Xia et al [1,34] is considered as a starting point. In this formulation, the dislocations are represent by a set of vector fields, ()   , where…”

Section: Introductionmentioning

confidence: 99%

“…where the first term on the right-hand side shows the dislocation evolution due to dislocation transport, and the second term is dislocation collinear annihilation, and the third and fourth terms (35) must also include a cross slip rate term, see [34]. By solving equation (35), together with equations (24) (32) (33) and (34), the evolution of the dislocation system with collinear annihilation, glissile junction and sessile junction mechanisms can be studied.…”

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confidence: 99%

Implementation of annihilation and junction reactions in vector density-based continuum dislocation dynamics

Lin

El–Azab

2020

Modelling Simul. Mater. Sci. Eng.

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In a continuum dislocation dynamics formulation by Xia and El-Azab [1], dislocations are represented by a set of vector density fields, one per crystallographic slip systems. The space-time evolution of these densities is obtained by solving a set of dislocation transport equations coupled with crystal mechanics. Here, we present an approach for incorporating dislocation annihilation and junction reactions into the dislocation transport equations. These reactions consume dislocations and result in nothing as in the annihilation reactions, or produce new dislocations of different types as in the case of junction reactions. Collinear annihilation, glissile junctions, and sessile junctions are particularly emphasized here. A generalized energy-based criterion for junction reactions is established in terms of the dislocation density and Burgers vectors of the reacting species, and the reaction rate terms for junction reactions are formulated in terms of the dislocation densities. In order to illustrate how the dislocation network changes as a result of junction formation and annihilation in a continuum dislocation dynamics setting, we present some numerical examples focusing on the reactions processes themselves. The results show that our modeling approach is able to capture the respective dislocation network changes associated with dislocation reactions: dislocations of opposite line directions encountering each other on collinear slip systems annihilate to connect the dislocations on the two slip systems, glissile junctions form on new slip system behave like Frank-Read sources, and sessile junctions form and expand along the intersection of the slip planes of the reacting dislocation species. A collective-dynamics test showing the frequency of occurrence of junctions of different types relative to each other is also presented.

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The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip

Cited by 32 publications

References 41 publications

Cross-slip of long dislocations in FCC solid solutions

Cross-slip of long dislocations in FCC solid solutions

Dislocation cross-slip in fcc solid solution alloys

Implementation of annihilation and junction reactions in vector density-based continuum dislocation dynamics

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