# Reading a tensile measurement

All material and noise parameters are hypothetical. This is a synthetic calculation, not a test of a specimen. Engineering stress is force divided by original cross-sectional area; engineering strain is gauge extension divided by original gauge length. “Noiseless imposed stress” must not be called true stress: true stress has a different mechanical definition involving instantaneous area.

The specimen starts with5mm width,0.50mm thickness and25mm gauge length. An assigned engineering curve has initial slope1200MPa, an arbitrary transition at2.5% strain and post-transition slope40MPa through10% strain. Its chosen endpoint is33MPa, requiring82.5N under the original-area convention. No failure, necking, unloading or permanent-strain law is defined;33MPa is not a measured ultimate strength and the kink is not a measured yield point.

Seed20260924 generates101load readings with Gaussian0.05N standard deviation. The same random stream then generates10000independent width/thickness errors, each Gaussian with2% relative standard deviation. Those errors alter inferred stress even with a fixed force. The central95% simulated error range is-5.3084% to+5.9570%, with median-0.02488%. This interval describes the assigned uncertainty model, not a confidence interval for any material. CSV exports contain every trace point and every geometry draw; the generator states the empirical quantile rule.

Independent checks convert N/mm² to SI pascals and back to MPa, reconstruct strain from extension, check continuity at the imposed transition, and confirm inverse-area error for every draw. First-order uncertainty propagation gives sqrt(0.02²+0.02²)=2.8284% relative SD, compared with2.8650% in the seeded nonlinear propagation. These checks support implementation consistency only. A Gaussian dimension model can in principle generate a nonphysical negative value; the generator explicitly checks that all sampled dimensions are positive.

Changing geometry is not changing the material. A broader lesson can show DeltaL=F*L0/(E*A0) in a separately bounded small-strain elastic widget. Doubling section area halves extension at fixed force, whereas doubling gauge length doubles extension. The full bilinear curve here must not be treated as globally Hookean, and it does not measure flexural properties.

Run `python generate.py` with Python3 and matplotlib. Outputs: engineering-curve.csv, geometry-uncertainty.csv, study.json and the original PNG/SVG/PDF figure. NIST primary method references in study.json contextualize tensile measurement and its limitations; none supplies the assigned material properties. No standard compliance, design allowable, product readiness or improved material performance is claimed.