Analytical Modeling of Cyclic Thermal Stress and Strain in Plated-Through-Vias With Defects
Bibliographic record
Abstract
A previously published analytical model for thermal stress and strain in idealized plated-through-vias (PTVs) has been adapted to conduct elastic-plastic analyses of vias with geometric defects using elastic stress concentration factors calculated earlier. The von Mises stress amplitude, at the mid-plane of the perfect via and at the defect (Δσ0and Δσ, respectively), and the cumulative plastic von Mises strain, also at the mid-plane of a perfect via and at a defect (ε0pland εpl, respectively), compared well with results of finite element analyses (FEAs). Four types of PTV defects were evaluated: barrel thickness reduction, occasional waviness, continuous waviness, and wicking. This model provides a relatively simple alternative to FEA to calculate stresses and strains in vias with defects as well as in perfect vias subjected to multiple thermal cycles. This model provides a tool to investigate quickly the influence of possible PTV design dimensions and defects under thermal cycling conditions (i.e., which are particularly damaging in a given situation). It is much easier than FEA for parametric studies like this. It also provides a means for calculating damage metrics, such as the cumulative von Mises strain, which can then be empirically correlated with the cycles to failure data from thermal cycling tests of PTVs.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".