A gradient theory of grain boundary that accounts for surface gradient of the Burgers tensor
Bibliographic record
Abstract
This paper presents an extension of Gurtin’s theory of grain boundaries, which accounts for grain misorientation and grain-boundary orientation, by introducing the surface gradient of the grain boundary Burgers tensor. This new framework elucidates the behavior of grain boundaries within polycrystalline materials at the micron scale, enabling the characterization of jump discontinuities in the plastic distortion tensor and slip fields. These jumps, quantified by the grain boundary Burgers tensor, are expressed through orientation tensors tailored for each slip system within intersecting grains. By leveraging the principle of virtual power, we formulate both macroscopic and microscopic force balances, seamlessly augmenting them with pertinent constitutive relations compatible with the free-energy imbalance. It is shown that dislocation densities at grain boundaries become tractable through the surface gradient of the grain boundary Burgers tensor, particularly when slip plane normals are parallel to the grain boundary normal. Moreover, the incorporation of a surface gradient in our framework permits the presentation of the flow rule as a system of second-order partial differential equations in slips, navigating through appropriate boundary conditions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".