Interior Cracking of a Circular Inclusion with Imperfect Interface under Thermal Loading
Bibliographic record
Abstract
A semi-analytic solution is developed to determine the effect of an imperfect interface on the stress field inside a circular elastic inclusion containing a preexisting interior radial crack, subjected to thermal loading. The inclusion is surrounded by an infinite matrix of different elastic material with the inclusion- matrix interface assumed to be homogeneously imperfect. This is characterized by continuity of tractions and discontinuity of displacements across the interface. Using complex variable methods, we derive series representations of the corresponding stress functions both inside the circular inclusion and in the surrounding matrix. The governing boundary value problem is then formulated in such a way that these stress functions simultaneously satisfy the traction-free condition along the crack face, the imperfect interface conditions, and the prescribed asymptotic conditions. The thermal load is modeled by a prescribed volume eigenstrain which characterizes the stress-free thermal strain of the inclusion. The method is illustrated for a number of crack-inclusion geometries and shear moduli ratios (of inclusion to matrix). We present explicit values of the stress intensity factor at the crack tips. These results can be used to ascertain the direction of initial crack propagation in, for example, fiber-reinforced composites or in components subjected to thermal loading in microelectronic packaging. To demonstrate the accuracy of the results obtained in this paper, we draw comparisons with corresponding cases documented in the literature where analytical results are available.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".