Steady state problem of a piezoelectric half-plane containing a curvecrack under thermal loading
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Bibliographic record
Abstract
Abstract: In this study, the fracture problem of a piezoelectric half-plane with a curve crack subjected to in-plane thermal loading is analyzed. The crack is modeled as distributed thermo-mechanical dislocations, and the Fourier heat conduction equation is solved using thermal dislocation. The governing equation of the piezoelectric material is also solved by applying the electromechanical dislocation and boundary conditions, resulting in obtaining stress, electric displacement, and heat flux. These solutions are used to formulate singular integral equations for the piezoelectric half-plane with a crack under general thermal loading, which are then numerically solved to determine dislocation density functions on the crack surface. These functions are utilized to calculate field intensity factors for the crack tips. Additionally, the study investigates the impact of various factors, such as the boundary, the crack length, and the radius of the crack, under different loading conditions. The results of this investigation can help identify critical conditions for crack propagation and inform the design of piezoelectric materials for applications where fracture is a concern.
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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 | 0.000 |
| 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 it