Mismatch check

Thermal mismatch stress for a direct joint and the number of graded steps that brings it under sigma_c. Rules R01 to R07, computed in the browser with the same functions the console used.

Pair and duty

R01 to R03

Side A, substrateSide B, deposited or builtM_H for the graded stackC-0412 uses the Paper 1 stack value of 380 GPa; both options here are placeholders until the discrete engine is portedTemperature excursion Delta T, KLPBF pulse 1 200; anneal 380; cycling 25 to 380Allowable stress sigma_c, GPadefault from the ceramic passport; 0.3 warns, 2.0 failsGraded steps nn = 50 is a direct joint

Result

R04 to R07

Delta alpha

1e-6 / K

M_film, side B

GPa

Direct joint stress

GPa, R04

Step stress, n steps

GPa, R05

R06 criterion Phi = M_H Delta alpha Delta T / ((n + 1) sigma_c)

R07 minimum steps for Phi <= 1

Bars: step stress per step count. Dashed: sigma_c.

Notes

R04 uses the biaxial modulus of the deposited side; R05 uses M_H as selected above. Both follow the registry equations in data/quantities.json.
Plastic shedding (R08, R09) and the membrane gate (R24) are applied in the stack designer, where layer thickness is known.
Every passport value in this preview is quality C. Required input for a chemistry verdict: an Ellingham or CALPHAD screen from the pycalphad connector, path Settings / Connectors.