P92 published-figure screen: design and evidence¶
Decision before implementation¶
Keep this scientific screen outside the constitutive catalogue. The existing published-parameter ODE reference can now be checked against independently read plot coordinates, not just another integrator using the same equations. Use the version-2 PDF of Zhang et al., Metals 10 (2020) 307, already pinned by SHA-256 in the equation reference.
Two different targets must remain separate:
- First-cycle model dashes in Figure 11(b): a transcription/implementation comparison against the authors' plotted calculation.
- First-cycle experimental hollow squares in Figures 11(b), 11(d) and 14(b): a sparse held-out-condition screen at 600 C / 60 s, 600 C / 600 s and 650 C / 600 s. Section 5 states that the authors fitted the 0.8% range, 180 s dwell tests; this screen does not refit those parameters.
Retain original embedded-image size/hash, tick calibration and selected symbol centres. Use clearly identifiable, uncluttered symbols; exclude legends, overlapping ambiguous marks and points outside the dwell. Declare a combined four-pixel coordinate-reading bound. It is a digitization sensitivity bound, not experimental repeatability or material uncertainty. Keep the original strain-rate/startup assumption visible. Images/PDFs need not enter the repo.
The implementation must report signed errors, absolute relative errors and coordinate-reading sensitivity separately. This sparse nonuniform sample is not the article's one-second-grid MRE and must not be presented as such. Do not select/reject samples by model agreement or fit parameters after viewing the errors. Numerical checks test axis calibration, integration agreement and immutable source/parameter identities; experimental disagreement is retained, not converted into a green engineering capability claim.
This screen does not certify multiaxial behavior, full cyclic history, fatigue life, structural discretization or another P92 batch/temperature. It narrows the next gate: distinguish implementation error from the published model's remaining discrepancy before creating a general structural material provider.
Reproduction and visual audit¶
evidence/creep/p92-published-figure-points.json contains the observations and
calibrations. The PDF's first embedded image on printed page 12 is Figure 11
(3036 x 2178); the first on page 13 is Figure 14 (3091 x 2178). These are not
the page-render dimensions. With pypdf, inspect reader.pages[11].images[0]
and reader.pages[12].images[0], respectively. The record includes the PNG
hashes produced by saving those decoded images through Pillow. The PDF hash,
pixel dimensions and source coordinates are the primary provenance, since
different PNG encoders can produce different byte hashes for identical pixels.
Selected centres were overlaid on the extracted source images and visually checked: 24 experimental hollow squares, six separate black model dashes, no legend entries or adjacent-cycle symbols. The four-pixel reading bound corresponds to about 1.3 MPa, with time sensitivity about 0.2 s for the 60 s panel and 2 s for the 600 s panels. Model changes over those time intervals are included; experimental scatter is not invented from that reading bound.
Run python tools/p92_dwell_figure_screen.py --output <new-json-path>;
repeat with --method BDF and a different new path. Existing evidence is never
overwritten. The complete source-figure record can be reviewed without running
FEM or downloading a dataset during normal software installation.
Executed first-cycle screen¶
Published Table 4 parameters remained unchanged. The source-model dash comparison has maximum absolute difference 1.32 MPa; all six differences are inside the declared coordinate-reading sensitivity intervals. This provides a separate plot-transcription check, unlike two integrators sharing one rate law.
| Held-out condition | Selected experimental time coverage | Mean absolute relative error | Maximum absolute error |
|---|---|---|---|
| 600 C, 60 s dwell | 5.86-56.70 s | 5.80% | 32.61 MPa |
| 600 C, 600 s dwell | 35.46-571.98 s | 4.99% | 20.19 MPa |
| 650 C, 600 s dwell | 25.08-569.82 s | 6.10% | 18.38 MPa |
These are eight identifiable markers per panel, not uniformly sampled complete curves. They do not reproduce the paper's reported MRE or define an acceptance tolerance for engineering. Some experimental differences exceed digitization uncertainty; retaining that discrepancy is part of the result. No fitting, initial-state tuning or transfer to the different BAM 620 C material occurs.
Radau/BDF predictions agree within 0.001 MPa at all selected samples. The equation, analytical-discriminator, figure-screen and CI-routing group passes 98 tests; Ruff passes. The numerical/source checks do not assert that the experimental discrepancy is acceptable. Full cyclic curve comparison and a verified multiaxial structural provider remain separate gates.
Follow-up cyclic-state audit¶
The local implicit corrector is also checked after twenty complete 600-second dwell cycles at both published temperatures. A further hold, unloading and reloading each compare the fixed-old-state axial tangent with independent strain differences, verify nondecreasing accumulated inelastic strain, and preserve the supplied old state. This strengthens numerical integration coverage; a correct tangent is not experimental cyclic validation.
Colored later-cycle markers in Figure 14(b) were inspected separately. Many symbols overlap one another or the plotted model line. Automated connected components can then identify an enclosed gap instead of a complete symbol. No such ambiguous detections were promoted to observations, and no later-cycle experimental error is claimed from them. Future curve digitization needs individually audited symbols or author-supplied data, with its own reading uncertainty; the first-cycle screen remains unchanged.
Fixed-partition substeps: numerical preparation, not core admission¶
MOOSE's radial-return documentation distinguishes material-local substeps from reducing the system-wide increment. This motivates a small reference experiment, not a claim to reproduce MOOSE's implementation or its runtime. No new package dependency is introduced.
For N equal local steps, h=dt/N, the backward-Euler state Jacobian is
J_k = I - h * df/dy. The derivative of the complete state with respect to the
total strain increment obeys
B_k = solve(J_k, B_(k-1) + [E/N, 0, 0, 0, 0]), starting at zero. The first
component of the last B is the complete axial algorithmic tangent. The old
state is fixed, but intermediate histories are not frozen. Substep count is
fixed during differentiation; adaptive partition selection requires its own
policy and verification.
substepped_update remains in the independent local reference tool. At 600 C,
after the initial 0.004 tensile ramp, a 60 s hold gives maximum stress-like
state errors against Radau of 23.0603, 6.5644, 3.4565, 1.8099 and 0.9396 MPa
for 1, 4, 8, 16 and 32 substeps. These are local integration errors, not
experimental errors. For a further strain increment 0.001 over 60 s, eight
substeps give a complete tangent of 14635.93 MPa, while the last substep alone
gives 59292.42 MPa. Using that last tangent in a global Newton solve would not
differentiate the actual update.
Checks cover full-chain strain differences after twenty long dwell cycles at both temperatures, unchanged single-step behavior, hold refinement, invalid partitions and failure without mutation of the caller's old state. There is no structural acceleration claim; local work increases and only a measured global comparison can establish whether avoided cutbacks compensate for it.