Identification of the Plane Strain Yield Strength of Anisotropic Sheet Metals Using Inverse Analysis of Notch Tests
Bibliographic record
Abstract
Plane strain tension is the critical stress state for sheet metal forming because it represents the extremum of the yield function and minima of the forming limit curve and fracture locus. Despite its important role, the stress response in plane strain deformation is routinely overlooked in the calibration of anisotropic plasticity models due to challenges and uncertainty in its characterization. Plane strain tension test specimens used for constitutive characterization typically employ large gage width-to-thickness ratios to promote a homogeneous plane strain stress state. Unfortunately, the specimens are limited to small strain levels due to fracture initiating at the edges in uniaxial tension. In contrast, notched plane strain tension coupons designed for fracture characterization have become common in the automotive industry to calibrate stress-state dependent fracture models. These coupons have significant stress and strain gradients across the gage width to avoid edge fracture. A single notch test can thus provide both constitutive and fracture information. However, an overlooked complication of using notch tensile tests is that non-trivial shear stresses develop within the gage region. Tensile loading occurs over a range of material directions, rendering the inverse analysis non-unique if additional constraints are not imposed. The present study proposes a simple inverse methodology to exploit the stress gradients in notch tension tests to calibrate the local arc of the anisotropic yield surface from uniaxial-to-plane strain tension. The influence of the shear stress is investigated with a two-step calibration procedure proposed to ensure agreement with the local strain path at the notch center and the global engineering stress response. Only the uniaxial tensile stress response to the uniform elongation and R-value are required as input data. The plane strain yield strengths for a variety of automotive metals were characterized including 5xxx and 6xxx-series aluminum, 3rd Gen advanced high strength steels, mild and stainless steel. The notch data was then compared with plane strain cruciform test data in the literature. Simple correlations to estimate the plane strain yield strength based upon the tensile R-value are then developed for use in yield surface calibration when notch or cruciform data is unavailable.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.001 | 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".