Displacement field due to glide and climb of rectilinear dislocations in gradient elasticity
Bibliographic record
Abstract
The aim of this article is to provide the displacement field of a straight dislocation in gradient elasticity that can be implemented in dislocation dynamics simulations. The displacement and plastic strain fields of a dislocation depend on the history of the dislocation motion. The cut surface (or the branch cut) represents this history. When an edge dislocation glides, the branch cut must be parallel to the Burgers vector, and when a dislocation moves by a combination of glide and climb, extra terms need to be added to the displacement field to capture the correct discontinuity in the displacement field. The existing formulas for the dislocation displacement in gradient elasticity lack such considerations, which make them unsuitable for simulations. In addition, the previous formulas both in classical and gradient elasticity have contained some inaccuracies and miscalculations. In this paper, the displacement field of a dislocation and the corresponding plastic strain are derived in detail and a distinction between the dislocation due to glide and that due to climb has been made. Moreover, we discuss the shortcomings of Mura's [Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff Publishers, 1987.] and Lazar and Maugin's [Dislocations in gradient elasticity revisited, Proc. R. Soc. Math. Phys. Engin. Sci. 462(2075) (2006), pp. 3465–3480.] calculations. We illustrate that Orowan's law is a direct result of the correct displacement and plastic strain fields.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".