Trace through elastic, yield, plastic, and fracture regions while watching a tensile specimen deform in real time.
Pull a bar in a testing machine and plot the stress (force/area) against the strain (elongation/length). The resulting curve tells you everything: how stiff the material is (slope), when it starts to deform permanently (yield point), how much abuse it can take (ductility), and when it finally breaks (fracture). Every material property used in structural design is read directly from this curve.
In the elastic region, removing the load returns the material to its original length — like a spring. The slope of this line is Young's Modulus E. Once stress exceeds the yield strength Fy, the atomic planes slip permanently. Unloading from the plastic region follows a line parallel to the original elastic slope, leaving behind a permanent set — the bar is longer than it started.
Steel's curve has a long plateau and gradual hardening — it warns you before it breaks by deforming visibly. Concrete's curve peaks sharply and drops — it crushes without warning. This is why structural codes require concrete to always be reinforced with steel: the steel provides the ductility that concrete lacks. The area under the curve represents the total energy the material can absorb before failure — steel absorbs far more than concrete.