Mathematical Modeling on the Residual Stresses in Coatings Due to Heat Treatments
Bibliographic record
Abstract
Coatings are implemented on engineering metals and alloys to augment the surface properties such as hardness as well as resistance to wear and corrosion. Heat treatments of coated metals/alloys are performed to aid in the progress of the bonding of the coatings to the substrate. During the air cooling process, the difference in the compositions of the coating and the substrate materials causes them to cool at different rates, which leads to straining in them. The paper presents the research on the mathematical investigation to evaluate the residual stresses in coatings caused due to heat treatments and subsequent air cooling. The mathematical modelling is executed to formulate the equations to represent the residual stresses retained in the coatings due to the heat treatments and subsequent air cooling. Air cooling undergoes two stages namely the initial quenching phase and the final cooling phase. During the quenching phase, the strain was expressed by considering the elastic, plastic and thermal strain components. Poisson’s ratio, deviatoric stress differential of the modulus of plasticity, coefficient of thermal expansion and change in temperature are used to express the elastic, plastic and thermal strain components. During the final cooling phase, the strain was expressed by considering only the elastic and thermal stain components, as the plastic staining the coating material generally does not occur during the final cooling phase and occurs only during the initial quenching phase. From the strain components, the residual stresses for the coatings in the x, y and z axis were formulated. Thus, the total residual stress is the sum total of stresses caused during the initial quenching phase and the final cooling phase.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".