Why the stress-strain curve appears to drop after the ultimate tensile strength — even though the material never stops getting stronger.
Every stress-strain curve you've ever plotted from a tensile test relies on one quiet assumption: that the cross-sectional area carrying the load is the area you measured before the test started. That assumption is engineering stress — load divided by the original area, A₀, a fixed number that never changes for the rest of the calculation. It's simple, it's standard, and it's what every published stress-strain curve and design allowable is built on. But it isn't what's physically happening inside the specimen. True stress divides the same load by the actual, instantaneouscross-sectional area — the area the material actually has at that exact moment, which shrinks continuously in tension. Early in a test the two numbers are nearly identical. Near necking, they diverge sharply — and the direction of that divergence is exactly what produces one of the most persistently misread features of the tensile test: the apparent post-peak "weakening" that isn't weakening at all.