Elastic <i>T</i>-Stress Solutions of Embedded Elliptical Cracks Subjected to Uniaxial and Biaxial Loadings
Bibliographic record
Abstract
Abstract The elastic T-stress has been found to be an important parameter in characterizing the near crack tip elastic-plastic stress states of 2-D and 3-D crack problems. In addition to the J-integral, the T-stress provides an effective two-parameter characterization of 2-D and 3-D elastic-plastic crack tip fields in a variety of crack configurations under small scale yielding conditions. Embedded elliptical crack in an infinite solid subjected to uniaxial or biaxial tension conditions represents an excellent model for many engineering components with embedded cracks. Although extensive analyses are available for stress intensity factors (SIFs) for embedded elliptical cracks, to date no analytical T-stress solutions are available. This paper presents the exact close form solutions for elastic T-stress of an embedded elliptical crack in an infinite body under remote uniaxial or biaxial tension. The foundation of the derivation is based on the potential method for three-dimensional elasticity. Solutions of stress components parallel to and perpendicular to the cracked plane are derived first. T-stress is then obtained from the asymptotic stress field near the crack front. Complete solutions of T-stress along the crack front are established. Further, three-dimensional finite element analyses are conducted to verify the derived solutions; excellent agreements are achieved. When combined with the corresponding K or J solutions, these T-stress solutions are suitable for the analysis of constraint effects for embedded elliptical shaped cracks in engineering components.
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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 | 0.000 |
| 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 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".